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國立臺灣科技大學
工業管理系
碩士學位論文
學號： M10701849
用於發電量預測的短期太陽輻照度實用
預測之研究
Pragmatic Short -Term Solar
Irradiance Prediction for Power
Generation Prediction
研 究 生：Siti Bariroh Maulidyawati
指導教授： Shuo -Yan Chou 郭伯勳 博
士中華民國一一零年一月
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3
4
ABSTRACT
Owing to its essential contribution to the production of environmentally sustainable
energy sources, the issue of renewables has captured the world's attention. Solar energy is one
of the sources used to produce renewable energy.
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Solar irradiation estimation is a critical
component for renewable energy systems such as photovoltaic (PV) systems to be built. It may
also help reduce energy costs and provide high energy quality in distributed solar photovoltaic
generation electricity grids. Thus, this study aims to forecast one -step and multi -step solar irradiation ahead. The
effect of weather conditions plays a significant role in helping to predict solar irradiation. Besides, much of the analysis focuses on minimizing the Mean Absolute Percentage Error. Yet,
depending on the prediction model's reliability based on the error calculation and a closer look
deep down into the data, there was still a weakness. This research's results are suggested scenarios to find a system based on the short -term
horizon for forecasting solar irradiance. As the error target is below 8 percent, the error for
solar irradianc e prediction is generally correct. The granularity of the prediction data affects
the probability of error values being obtained by prediction. The classification used was based
on the month in this report. The average of each month's prediction MAPE was 5 .8%. Proposing a pragmatic way in doing error analysis by comparing several error
approaches and data volatility to deepen the analysis. Moving average proven could improve
prediction accuracy because it may help capture the dramatic change of the data. In future
research, more factors should be considered to capture hidden behaviour . Keywords : Solar Irradiance, Prediction, Short -term, Pragmatic Error Analysis
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ACKNOWLEDGMENT
Firstly, I would like to extend my sincerest gratitude to my advisor, Prof. Shuo -Yan Chou who has
supported and guided me throughout my research and thesis.
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His ideas, kindness, advice, and
passion always inspire and motivate me to further enhance my work and achieve a great outcome. I would also like to acknowledge Prof. Po -Hsun Kuo and Prof. Tiffany Yu as my thesis defense
committee for their encouragement, insightful comments, evaluation and suggestions for my
research. I would also li ke to thank all my lab mates in Information Technology Application and Integration
(ITAI) laboratory for their friendliness and support every single day during this past two years. Besides, I would also like to give tons of thanks to my dearest classmates, roommates, and friends
that have been with me through my journey in NTUST. Furthermore, I must express my very profound gratitude to my family for providing me with
unfailing support and continuous encouragement throughout my years of study and through the
process of researching and writing this thesis. This accomplishment would not have been possible
without them. Thank you. Last but not least, my deepest appreciation and praise goes out to Allah SWT, for letting me achieve
another of my life accompli shments. Taipei, 26 January 2021
Siti Bariroh Maulidyawati
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CONTENTS
ABSTRACT ................................ ................................
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.................... 14
2.4. Research on Solar Irradiance Prediction ................................ .............................. 15
3 CHAPTER 3 METHODOLOGY ................................ ................................ ................. 17
3.1 Pre-analysis Method ................................ ................................ ................................ 17
3.1.1. Data Visualization ................................ ................................
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...................... 11
Figure 3.1 Research Framework ................................ ................................ .............................. 17
Figure 3.2 Framework Analysis Procedure ................................ ................................
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................... 22
Figure 4.2 One -Minute Feature Correlation ................................ ................................ ............ 23
Figure 4.3 Feature Correlation 10 -minutes Granularity ................................ .......................... 24
Figure 4.4 Correlation Between Variable ................................ ................................
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.................... 26
Figure 4.8 Auto -Correlation Solar Irradiance ................................ ................................ .......... 27
Figure 4.9 ANOVA Test Monthly Irradiance ................................ ................................ .......... 28
Figure 4.10 Monthly Irradiance Boxplot ................................ ................................ ................. 29
Figure 4.11 ANOVA Seasonal Irradiance ................................ ................................ ............... 29
Figure 4.12 Seasonal Irradiance Boxplot ................................ ................................
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............................... 33
Figure 4.15 Percentage Error and Actual Irradiance Relationship ................................ .......... 34
Figure 4.16 Relationship between Absolute Error and Percentage Error ................................ 35
Figure 4.17 Pragmatic Error for Month of May ................................ ................................ ...... 37
Figure 4.18 A Closer Look into May’s Data ................................ ................................ ........... 38
Figure 4.19 Captured Moving Average ................................ ................................
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....................... 36
Table 4.6 Improvement Model Average Results ................................ ................................ ..... 39
Table 4.7 Moving Average Improvement in the Chance of Getting Error .............................. 39
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1 CHAPTER 1
INTRODUCTION
1.1 Background
According to the International Energy Agency (IEA), global renewable electricity capacity is
projected to rise by over 1 TW, a 50% (1 220 GW) percent increase from 2018 to 202 4 [1]. Over half of this expansion is accounted for by s olar PV and dominates the production of
renewable capacity . By 2025, Taiwan will use renewable energy to produce 20 percent of its
electricity, a target endorsed by the Four -year Wind Power Promotion Plan and the Two -year
Solar PV Promotion Plan. Within fi ve years, renewable energy capacity is projected to hit 26.9
gigawatts (GW) following these ventures [2]. In a global economy shaken deeply by COVID -19, short -term demand declines for
fossil fuels, while renewables are estimated to grow slightly. The International Energy Agency
(IEA) estimates that primary energy demand in 2020 could decline for oil ( –9%), coal (–8%),
natural gas ( –5%), and nuclear ( –2%), while renewables would grow by 1% [3]. Solar PV plays
the highest annual growth for Renewable Energy, it was also proven by the gradual increase
between the year’s capacity. In 2019 it reached 627 gigawatts of world total [4]. Given the current solar PV growth scenario, the modern grid faces the above
uncertainties in power generation. To compensate for the intermittent generation of PV,
solutions exist to overcome this issue, such as energy storage [5]. Besides, knowing how much
PV power would be produced could dramatically decrease the operating costs of power plants
[6]. For the efficient integration of solar energy into the grid, accurate PV energy forecasting
for different timescales (weekly, day -ahead, next hour, and intra -hour) is essential [7, 8] . [9]
Solar PV produces energy that converts solar irradiance in to energy from sunlight —
weather parameters such as temperature influence PV systems' efficiency [10]. Therefore, PV
power relies on solar irradiance and meteorological conditions, contributing to PV generation
instability and uncertainty. This study aims to propose a real -time prediction model for the day ahead of the next
hour and hour. The machine learning algorithms studied are long -short -term memory networks. The ana lysis uses historical weather data from a sensor located in Tainan, Taiwan, from the
Central Weather Bureau. The period of the forecast focuses mainly on short -term forecasts. For
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applications relevant to system operations, such as real -time dispatch, mark et clearing, and load
following, short -term weather forecasting contributes beneficial. Besides, precise weather forecasts can also provide short -term energy trading and
system balancing advantages. This contributes to increased grid stability and encourag es
renewable energy resources to be used effectively. Moreover, reliable weather forecasts will
allow renewable power generators to estimate production better and bid on day -to-day markets,
reducing the penalties levied for discrepancies between real and s cheduled power generation. 1.2 Research Purpose
The purposes of this research are:
1. Conducting one -step ahead and multistep -ahead solar irradiance prediction
2. Provide prediction error analysis in a pragmatic way
3. Suggest future expansion for solar irradiance prediction for solar power generation
prediction
1.3 Research Limitations
According to the background and research purpose above, here are the limitations of this
research:
1. This research only focuses on solar irradiance prediction. 2. The prediction horizon focused on very short -term and short -term period. 3. The details of weather sensor’s type and specification used are not analyzed . 1.4 Organisation of Thesis
The framework of this research is explained in the following chapters. Chapter 1 is the
background, obje ctives, limitations, and organization of the research. Chapter 2 presents the
previous researches on renewable energy issues, solar energy issues , and solar irradiance
prediction issues. Chapter 3 illustrates this research methodology and the particular me thod
used for pre -processing method , prediction method , and research framework. Chapter 4
presents the result of the pre -analysis and data description, solar irradiance prediction, and error
analysi s. Chapter 5 would wrap up the conclusion from all chapter s and also future research. Figure 1.1 below illustrates the organization of this thesis.
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Figure 1.1 Organization of the Thesis
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2 CHAPTER 2
LITERATURE REVIEW
2.1. Renewables Issues
Recently, renewable energy has been the most resilient energy source to the Covid -19
lockdown measures. Renewable electricity has been mostly unaffected, while demand for other
uses of renewable energy has declined. Global use of renewable energy in all sectors incr eased
by about 1.5 percent in Q1 2020 compared with Q1 2019. Renewable electricity generation has
increased by almost 3%, mainly due to the completion of new wind and solar PV projects over
the past year and the fact that renewables are generally shipped b efore other electricity sources. In addition to the depressed demand for electricity, the power grids managed to increase
wind and solar PV share. The use of renewable energy in biofuels decreased in Q1 2020 as the
consumption of mixed fuels for road trans port decreased. Researchers estimate that the total
global use of renewable energy increased by about 1% in 2020. Despite supply chain
disruptions that have slowed or delayed activity in some key regions, the expansion of solar,
wind, and hydropower is exp ected to help generate renewable electricity by almost 5% in 2020. However, this growth is smaller than expected before the Covid -19 crisis. Faster recovery
would have a minimal impact on renewable energy production, although it would allow newer
renewable -based projects to be completed. If the recovery is slower, renewable energy will
continue to increase, making renewables the most resilient energy source to the current Covid -
19 crisis [3]. 2.2. Solar Energy Issues
The use and production of renewable energy sources (RES) have been promoted by global
warming and the critical depletion of fossil fuels in recent decades [6]. Not only have renewable
energy sources such as solar, wind, hydropower, and geothermal energy been recognized as
innovative solutions to the problems mentioned earlier, but they also represent the future of
energy advancement [11]. Solar energy has emerged as the most common technique in
replacing traditional sources and i s applied to many nations worldwide. The most promising
source of power generation for residential, commercial, and industrial applications is solar
energy [12]. Solar photovoltaic (PV) systems use PV cells that transform solar radiation into
electric al energy [9]. Solar PV is used to su pply electricity for home appliances, lighting, and
commercial and industrial equipment in stand -alone and grid -connected systems [13]. 13
The number and size of solar PV plants have increased worldwide due to their essential
role in generating electricity [14]. In collaboration with the International Energy Agency (IEA),
several nations are supposed to generate 196GW (in most grid -connected plants) by the end of
2015. An additional 40 nations excluded from the IEA Photovoltaic Power System Program
(IEA PVPS) produced about 31GW of solar power. Solar PV installation for both IEA PVPS
and other countries has increa sed dramatically from 2007 to 2015. About 70% of the solar PV
installation came from IEA PVPS countries [15]. In early 2016, 120 solar PV plants with a
capacity of more than 50MW operated in at least 23 countri es, i.e., the Philippines, Uruguay,
Pakistan, Kazakhstan, Honduras, Guatemala, Denmark, and Australia [14]. The complicated existence of Renewable Energy Sources (RES) relies heavily on
geographical locations and weather condi tions. It is becoming a significant challenge to
incorporate large -scale RES into existing energy systems. Among other RES [16] tools, solar
energy is a renewable fuel. Because of its electrical power capacity, solar PV plants'
incorpora tion into power grids have gained a lot of attention. In smart grids, solar plants are
used extensively. Implementation of large -scale grid -connected solar photovoltaic plants has
shown major problems for power grids, such as system stability, reliability, energy balance,
compensation of reactive power, and frequency response [9]. Forecasting solar photovoltaic
power output has emerged as a great way of solving these problems. A primary factor that is efficient and cost -effective for large -scale integration of the
traditional electricity grid is photovoltaic power forecasting [17]. Besides, photovoltaic (PV)
power forecasting is essential for the restructuring and constructing large PV generating
stations, stabilizing po wer systems, the green energy sector, and the alert of power disruption
to self -governing power systems [18]. The prediction of power is also crucial for monitoring
the power system's utilization, which helps to min imize the use of generating station reserve
capacity by making the right unit commitment decisions [19]. It thus plays an essential role in
reducing the cost of generating electricity and is useful for the grid's efficiency. A PV output power prediction error may harm the economic benefit of PV storage systems. At the same time, other influential vari ables affect the precision of prediction in prediction
modelling. Solar radiance was one of the most critical variables [20, 21] . Accurate solar
irradiance forecasting and, thus, the generation of PV power will reduce the effect of PV
generation instability, boost the control algorithms of battery storage charge controllers, and
offer significant economic benefits to PV storage systems [22]. 14
2.3. Solar Irradiance Prediction
To reduce energy costs and provide high power quality for distributed solar photovoltaic
generations in electricity grids, the prediction of solar i rradiance is essential [22]. For the design
and evaluation of solar energy systems, c limate studies, water supplies control, estimating crop
productivity, etc., solar irradiation is essential. In making the solar radiation prediction,
accurate models can, therefore, be developed [21]. The stability of solar irradiation and its
application is limited because of seasons, atmosphere, cloud density, and other climatic factors. The intrinsic characteristics of variability and ambiguity are solar radiance. Therefore, to
overcome these uncertainties, resource planners must adjust during preparati on, which is of
great importance for designing and managing solar power systems. Thus, forecasts of solar
irradiance in the short term are highly critical [23]. 15
2.4. Research on Solar Irradiance Prediction
Solar irradiance value is more challenging to impute, depen ding on whether time of
days it was captured and the weather condition combination . The missing value is inevitable
when collecting data from the sensor. Some imputation method has been tried to fill the missing
value. However, the result of the graph also does not satisfy the accuracy of the prediction. As
a result, LSTM Masking is use d in this research to no longer need missing -value imputation. Keras' masking layer is used to let the algorithm understand that time steps need to be ignored
or skipped during the learning process. Ignoring it is safer than imputing it with the wrong
beliefs. It is quite a challenge to predict solar irradiance with only a year's results. In essence,
according to the prior clarification. Predicting solar irradiance can consist of many scenarios
to see the highest precision for the forecast outcome . Four gra nularities have been used in this research method to recognize solar irradiance
trends over time better. Comparison and analysis will also be discussed throughout these four
granularities. The granularities are data of a minute, three minutes, five minutes , and ten
minutes. The monthly forecasting scenario results in the best outcome, as the best scenario is
selected from the scenarios explored . Moreover , the monthly irradiance forecasting scenarios
will be conducted under scenario illustrated in Chapter 3. Table 2.1 Solar Irradiance Prediction Literature Review
Title Granularity Features Method Dataset
Improving time
series prediction of
solar irradiance after
sunrise: Comparison
among three methods
for time series
prediction [24] Measured 10
secondly,
aggregated
into hourly Solar irradiance,
Delay
information Kwasniok &
Smith,
barycentric
coordinates,
InDDeCs Chubu Electric
Power Company
(61 sites at the
central region of
Japan)
Hourly day -ahead
solar irradiance
prediction using
weather forecasts
by LSTM [22] Hourly Temperature,
dew point,
humidity,
visibility, wind Persistence,
Linear
Regression,
BPNN, LSTM Solar
power plant in
island of
Santiago, Cape
Verde. 16
Title Granularity Features Method Dataset
speed, weather
type
Deep solar
radiation
forecasting with
convolutional
neural network and
long
short -term memory
network algorithms
[25] 30 minutes Solar Irradiance CLSTM,
LSTM, GRU,
RNN, DNN,
MLP, DT Global Solar
Radiation
dataset
A Proposed Model to
Forecast Hourly
Global Solar
Irradiation
Based on Satellite
Derived Data, Deep
Learning and
Machine
Learning Approaches
[26]
Hourly
Global Hourly
Irradiance
LSTM
Sensor data from
Al-Hoceima city,
Morocco
Solar radiation
prediction using
recurrent neural
network and
artificial neural
network: A case
study with
comparisons [27] 10 minutes,
30 minutes,
hourly Solar irradiance,
air-dry bulb
temperature,
relative humi dity,
dew point
temperature, wind
speed, wind
direction Artificial Neural
Network (ANN),
Recurrent Neural
Network (RNN) Local weather
station in
Alabama
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3 CHAPTER 3
METHODOLOGY
Figure 3.1 Research Framework
The research aims to build scenarios of multistage solar irradiance prediction. Since most of
the research has mentioned that solar irradiance has lin ear relationship with the solar power
generation. Thus, it is important to predict the irradiance value so that it may help to improve
the prediction accuracy. 3.1 Pre-analysis Method
The pre -processing approach was carried out to gain insight that could be useful for further
research or feedback for the prediction model. Visualization, ANOVA Test, Post -Hoc Test,
and Correlation matrix consist of pre -analysis. Visualization is the traditional process but an
efficient method to extract and explain the pattern of data. ANOVA, post -hoc test, statistical
information, and Correlation matrix is vita l to see the correlation between features. Besides,
the auto -correlation test also essential to get to know the sequence of the data. Irradiance has a
complicated relationship with the weather situation, as mentioned in Chapter 2. Therefore,
analysing the complicated relationship between each variable is crucial. The detail explanation of each pre -processing stages will be explained below. 18
3.1.1. Data Visualization
The visualization is divided into two key components: the correlation of the individual
characteristics and the correlation between them. The individual feature correlation of the
weather variable and irradiance was performed to extract the time -series pat tern. Besides, it
also will be used for prediction model consideration. Moreover, the extraction of interaction
between features will be captured from the correlation visualization. Thus, the visualization,
and the insight derived will be presented in Chap ter 4.1. to describe the data.
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3.1.2. Auto -Correlation Test
Auto -correlation tests are often carried out in the process of handling time -series data. Auto -
correlation test performed to see the correlation of data in time (t) with its past -data (denoted
as time lags x (t -1), x (t -2) and so on), a time window could be calculated. The magnitude of
the correlation will be statistically calculated by the 95% confidence interval. The partial -
autocorrelation also determining the correlation data 𝑥𝑡 with its past data . The difference lies
in the way partial -autocorrelation deleting the interference of the data. For example, when
determining its correlation with 𝑥𝑡−2 in the partial auto -correlation model, the model will try
to delete the influence of the 𝑥𝑡−1 and wh en determining the correlation with the 𝑥𝑡−3, the
model will try to delete the influence of the 𝑥𝑡−2 and 𝑥𝑡−1. In time -series data, the auto -correlation determination could help the next step decision. The autocorrelation result might help determine parameters in the prediction model. In this
research, the auto -correlation would influence the decision in determining batch -size, tensor -
data transformation shape, and output size. 1.1.3 ANOVA Test
ANOVA test conducted to measure the significance of the influ encing factor statistically. ANOVA test described by Ronald A. Fisher [28]. In the experiment data, it is subjective to
decide how far the difference so that a variable could be said as an influencing factor. ANOVA
test designed to test the significance statistically. In the ANOVA test , the null hypothesis which
states that the me ans between two groups of data or more is the same. The threshold used to
determine the hypothesis is correct or not called p -Value or known as a statistical probability
value. When p -Value is below the particular predefined alpha value , the null hypothesi s
rejected [29]. 19
In conclusion , the means between two groups of data o r more is different significantly. In other words, the factor is influencing the response variable. In the experiment , the controlled
variable stated as the factor , and the experiment result considered as the response variable. In
this research , the confid ence interval used is 95% , then the alpha value would be 0.05. The
response variable is the energy consumption , and the other variable identified to see its
influence respect to energy consumption. In this research, the ANOVA test conducted in
Minitab . 3.2 Prediction Method
The prediction method is chosen to capture the time -series pattern of weather data, especially
the irradiance feature. Building a robust and accurate prediction model always helps in terms
of data -driven planning. Irradiance is always chall enging due to the high uncertainty in the
pattern of weather combinations during the day. Hence, masking LSTM models will be tried
to be utilized and will be tested in several scenarios to build prediction. At the end of this
chapter, the moving average wa s used as an additional feature to improve the prediction's
destructive results. 3.2.1. Masking Long -Short Term Memory (LSTM)
Combining masking and LSTM is the algorithm used to forecast the prediction of wind speed. Weather data characteristics, especially irradiance, are highly uncertain.
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The weather data
collected by the sensor is inevitable, so the missing value . Since the irradiance data consists of
a few missing values, filling out the missing value of the prediction is another problem since it
will pro duce bias in the prediction results. Masking informs sequence -processing layers that
there are missing those timesteps in the input and should therefore be skipped when processing
the information. In general, with neural networks, it is safe to input missing values as 0, with the condition
that 0 is not already a meaningful value. The network will learn from exposure to the data that
the value 0 means missing data and will start ignoring the value. Meanwhile, if in the study
expecting mi ssing values in the test data, but the network was trained on data without any
missing values, the network won’t have learned to ignore missing values . In this situation, the
researcher should artificially generate training samples with missing entries: co py some
training samples several times, and drop some of the features that you expect are likely to be
missing in the test data . 20
Thus, assigning zero to NaN elements will also considering that zero is not used in the data. The data can be normalized to a range, say [1,2], and then assign zero to NaN elements. Besides,
alternatively, all the values also can be normalized to be in the range [0,1] and then use -1
instead of zero to replace NaN elements [30]. The second statement will be examined in this
study . Combining the masking theory and LSTM is a suitable algorithm for the data, consisting
of several missing values. Minimizing bias from missing values could be tackled by masking
algorithm and LSTM to build predictions for irradiance with uncertainty and vo latile data. 3.3 Detailed Analysis Procedure
As a means to create a systematic analysis, the prediction result analysis will be divided into
several steps. Further details of each analysis stage will be examined in the Figure 3.2 below. Figure 3.2 Framework Analysis Procedure
Here is the detail process from the framework analysis procedure above:
• Irradiance prediction for each month and calculate the error
In order to measure the prediction error, Mean Absolute Percentage Error (MAPE) and
Mean Absolute Error (MAE) were utilized in this study. • Error visualization
Scatter plot was used to pointed ou t the error visualization. The comparison between MAPE
and MAE, also MAPE with actual data were aiming to find out why the error might happen
in the data. 21
• Individual chance of getting error
Average error of each month could not be only the representative o f the error in the specific
month. Since the high actual data will be resulted in high value of absolute error, meanwhile,
small actual value resulted in a higher percentage error. Thus, as the basic target in
Taipower policy in energy prediction, further error exploration was done by calculating the
chance of getting error below eight percent for each data points. • Pattern analysis
Intending to get to know what lead the error caused in each data points, in this study, the
plot relationship between true and predicted value of irradiance was examined. • Error toleration
A pragmatic error analysis was examined to measure how far the erro r at each data points
could be accommodated. • Model improvement
Put the worst prediction as an example for doing model improvement, moving average was
added as a feature of the prediction. • Multistep -ahead prediction
Multistep -ahead prediction wa s conducted to get to know how well the model could work. 22
4. CHAPTER 4
RESULT AND DISCUSSION
4.1 Data Description
The data used to analyze is weather data located at one of the weather stations from Central
Weather Bureau of Taiwan located in Tainan City . Figure 4.1 The location of Data Source
The variables gathered to support the analysis are presented in Table 4.1 below:
Table 4.1 Data Collect ion
Variable Name Source Explanation Unit of
Measurement
Taipei Minutely Weather
Data Central Weather Bureau
Taiwan Irradiance, Temperature,
Relative Humidity, and
Pressure 𝑊
𝑚2,℃,%,
𝑎𝑛𝑑 ℎ𝑃𝑎
Each variable was analyzed in month, season, and its relationship with each variable also will
be analyzed for feature extraction before entering the model prediction . Due to the solar
irradiance coming from the solar energy and it will only be appeared during the days, thus, in
this study th e data for night time will be neglected. 23
4.1.1.
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Feature Correlation
One of the mechanisms for seeing the characteristics of the data is feature correlation. Input
from the prediction method would be based on the predictor variable, which correlates
positively with the expected value. The way to find the correlation between two or more
variables may be done through many methods. Accessible data for all variables consists of one -minute granularity. In Tainan, Taiwan,
the location of the weather sensor is. The tec hnical details of the sensor are not specified in the
restrictions on the data. The correlation of the data to other variables is defined in the Figure
4.2 below. Figure 4.2 One-Minute Feature Correlation
According to the graph above, the graphs showed that correlation is not shown clearly in the
graph between irradiance and the weather condition (temperature, humidity, pressure) . It was
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because in the minutely data, the variance of the data was small since the gap was so short. The
pattern in the Figure 4.2 could not represents the pattern of the relationship between variable. Hence, in this study, the data will be aggregated into three minutes, five minutes and ten
minutes. However, for the feature correlation will be visualized in ten minutely granularity can
be seen in the Figure 4.3 below. Figure 4.3 Feature Correlation 10 -minutes Granularity
According to the figure above it can be seen that the shape of relationship between variable
was improved. Nonetheless, though the pattern already improved, the contact among the
feature still could not see clearly. Thus, another approach needed to be examined to capture t he
relationship. 25
The correlation of each variable to solar irradiance described in Figure 4.4 below. Figure 4.4 Correlation Between Variable
Pearson correlation was used because the data value of each variable was continuous. Based
on the correlation matrix above, it can be seen that the positive correlation to the solar
irradiance only hold by the temperature. Besi des, humidity and pressure also have correlation
to solar irradiance, but the relationship was negative. It was because they were not directly
affecting the irradiance value. Figure 4.5 Factors Affecting Solar Irradiance
The figure above depicted that the most affected factor of solar irradiance value was the
clearness index of the sky condition [31]. In addition, the clearness index was affected by the
temperature a nd cloud amounts at the specific time of day. As described in the figure, pressure
and humidity [32] wasn’t as close as temperature in affecting the irradiance value. 26
Figure 4.6 ANOVA Test between Variables
Figure 4.6 depicted the correlation between each prediction variables. It showed that all o f the
variable has p -value 0.000 which is below 0.05 and it means that all of them significantly
affecting the solar irradiance value. In addition, according to the description of the data
correlation and ANOVA test, further statistical approaches were con ducted to convince the
relationship of irradiance with other prediction variable using regression equation. The result
will be shown in the figure below. Figure 4.7 Regression Equation Result
Figure 4.7 showed the similar relationship with what been mentioned in Figure 4.4 and Figure
4.5. It can be seen that at both results performed, the positive influenced of temperature and
pressure. However, humidity showed the negative influence of irra diation. Since the regression
will only capture the linear correlation, thus, the pressure showed a positive value. However,
theoretically pressure has the negative correlation with the irradiance. It was because pressure
does not directly affect irradianc e. It has an opposing relationship with temperature which has
the direct relation with the solar irradiance.
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4.1.2. Autocorrelation
Auto -correlation is a way to find the required time -lag configuration in the prediction model's
parameter settings. To find out th e explicit dependency, time series analysis requires auto -
correlation analysis. The effects of auto -correlation have been used to extend independent
27
variables to predict the generation of electricity. Furthermore, the extraction of time series
dependencies assists in further steps of data processing. Besides, results from auto -correlation
may be used to work out the tuning parameter. Here is the auto -correlation result from four
variables. Figure 4.8 Auto -Correlation Solar Irradiance
According to the figure above, the ACF analysis shows that the data's auto -correlation with
previous data points is strongly correlated even it is already reached the 60th data points with
confident interval of 95 percent. Thus, previous data points correlate closely with the next data
points based on the auto -correlation analysis. In short, to predict the upcoming data points, the
time minus specific previous data points are considered as a new variable. The further
explanation will be showed in the Table 4.2 below. Table 4.2 Time -Lag Configuration
According to the Figure 4.5 from the CWB database that has been collected, there were
four variables can be used for predicting the irradiance value. Th en, from the mentioned
variable, further exploration needs to be done in order to define the time lag of prediction. Since
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Figure 4.8, the data still ha s a relationship to each other until 60th data, the individual variable
was examined how often the data change between the time. The data observation found several
changes and will be considered for creating the scenario. Table 4.2 showed several time lag
scenarios. From fifth scenarios, the third scenario with combination t -10 irradiance, t -6&t
temperature, t -3&t humidity, and t -10&t pressure outperformed the other scenario within
chance of getting MAPE below 8 percent 88.57 percen t. 4.2 Prediction Results
4.2.1. Grouping Analysis
The data used in this forecast is a year with minute granularity data from September 2019 to
September 2020. Besides, depending on environmental conditions and time of day, the
irradiance value is high. Meanwhile, t here are distinct weather characteristics in various regions,
periods, and seasons. In terms of averages and range, the figure below shows how was the
monthly influences for irradiance values . Figure 4.9 ANOVA Test Monthly Irradiance
The monthly solar irradiance varies significantly based on a p -value < 0.05, according to the
statistical analysis of the variance analysis for the monthly irradiance results. The ANOVA test
was carried out to emphasize that the grouping method's effects based on the month differ
significantly, hence, that pattern and data characteristics vary every month. As each month's
data characteristics are substantially different, the prediction model will be evaluated for each
month. 29
The figure below shows the interval plot for a year data . Figure 4.10 Monthly Irradiance Boxplot
The grouping based on the average irradiance within a year will help predict irradiance
by the model capability. On the other hand, looking at the average irradiance in a year, the
seasonal grouping influenced examined in the Figure 4.11 below. Figure 4.11 ANOVA Seasonal Irradiance
The above figure clarified that the ANOVA test results were substantially d ifferent based on
time-slicing classification, which corresponds to a p -value of less than 0.05. In the boxplot
below the speediness of the data will be discussed further . 30
Figure 4.12 Seasonal Irradiance Boxplot
In the Figure 4.12 above, it can be seen that there was inconsistency in the data representative. Though the ANOVA result showed p -value < 0.05 which means there is a difference between
the monthly data characteristic, however the boxplot showing us otherwise. The Autumn and
Spring plot showed similar boxplot pattern. To sum up , the grouping may help to improve the accuracy of prediction performa nce. Basically , to explain the data pattern, homogeneous data may become a simpler model. Characteristics of irradiance value grouping data for each month are already evaluated to see
each month's similarity . In addition, monthly grouping showed better performance. Thus, in
this research monthly grouping will be examined for batching the prediction. 4.2.2. Solar Irradiance Prediction
Before entering the prediction explanation, in this study, there are four -time granularity that
will be considered; minutely, three minutely, five minutely, and ten minutely. According to the
Figure 4.2, one minutely data could not capture the data pattern wisely. It was because the
31
variance of the data was small and may resulting in a bigger prediction error. The figure below
will show four different gran ularity’s data patterns. Figure 4.13 Data Pattern for Different Granularity
According to the Figure 4.13, three minutely data still could not capture the data pattern
enough. Moreover, due to the data used in this study was coming from CWB of Taiwan, thus
some of Taiwan energy policy will be cons idered . Based on the Taipower energy policy for
energy dispatching, it was important in knowing the supply demand change between five
minutes until fifteen minutes. Thus, five minutely and ten minutely granularity will be
considered in this study. Fifteen minutely will not be included because the data become further
than two previous granularities. Meanwhile, three minutely was considered to capture smaller
granularity because there was still limited information how’s smaller granularity works in solar
irradiance prediction. 32
Here is the data separation for predicting solar irradiance showed in the Table 4.3 below. Training set was the data input for the m odelling, due to the default parameter usage, in this
study, the training data already cover the validation data. Moreover, the testing data will be
used to test the prediction model that already built during the training phase. Table 4.3 Parameter Setting
Training Set Testing Set
1st – 26th day of each month 27th and the rest of each month
The Table 4.4 showed the summary result of the prediction for different time horizon. Table 4.4 MAPE Result Summary
According to the prediction result above, it can be seen that the best result in term of
MAPE was belong to the ten minutely granularity. However, this could not be the only
parameter of measuring how good or how bad a prediction was. Thus, in the figure Figure 4.15
and Figure 4.16 will examine a further error analysis by capturing the visualization between
percentage error (PE), absolute error (AE), and actual value of solar irradiance data. In the
scatterplot, the blue colour represents the PE value above eight percent, and the pink colour
represents the PE value below 8 percent. 33
According to the Figure 4.14 above, it can be seen that there was a bias of the prediction error. Though the data already got the small absolute error, the percentage error was high, and vice
versa. In addition, the small actual data has a big potential in resulting higher value of
percentage error. Besides, the big actual irradiance value has more chance in getting higher
value of absolute error. Figure 4.14 Bias Error Analysis
PE = 116.3%
AE = 3.23
Irr = 2.8
PE = 9.4%
AE = 10.44
Irr = 111.11
Percentage Error
Absolute Error
34
Figure 4.15 Percentage Error and Actual Irradiance Relationship
The Figure 4.15 showed overall months of rel ationship between PE and actual value of
solar irradiance. It can be seen that for all the months, the smaller value of solar irradiance
resulted in higher percentage error. In addition, here is another visualization in the Figure 4.16
below will examine the relationship between absolute error and percentage error. It also
showed that the data which having the high percentage error might showing a small absolute
error an d vice versa. 35
Figure 4.16 Relationship between Absolute Error and Percentage Error
The fact of percentage error and absolute error above showed that there was a bias of
error. Thus, both error measuremen t could not capture the overall error. In this case, a further
error analysis will be examined to get to know the deepen analysis of the data. 36
On the other hand, Table 4.5 Chance of Error Summary below shows the summary of each
month prediction result for minutely, three, five, and ten minutely granularity. Table 4.5 Chance of Error Summary
Table 4.5 depicted that compared to the other granularity, ten minutely granularity showed the
best chance in getting prediction error below 8 percent; both for average and for each month of
the year. Besides, there is a decrement percentage in chance of getting MAPE below eight
percent from one minute to three minutes data. However, from three minutes to five minutes
and five minutes to ten minutes there were an increment. The possibility of getting error for each data was really affected by the data pattern and
variance of the data. Thus, due to ten minutes already outperformed the other month, in this
study ten minutely granularity will be used for further analysis. In addition, according to the Table 4.4 Table 4.5, the worst chance of error performance
belon gs to May. Hence, the further analysis will be more focused in the month of May to get
to find a proposed approach in improving the prediction model. 37
The Figure 4.17 below shows the pragmatic way of error toleration in the month of May. Figure 4.17 Pragmatic Error for Month of May
In the figure above, the average percentage error of less than eight percent is 2.02
percent, and the absolute error of 2.02 percent is 2.45 absolute error. Also, the value of the
position of 2.45 absolute error for solar irradiance is 80 W/m2. Thus, in the ignorer's rectangle,
the error boundary, which represents the bias calculation, shows. The percentage error appears to get significant values because the true value of solar
irradiance was small; however, it is suggested that the data might ignore the points in that
region —another boundary analysis of the greater irradia nce as an actual value, which is over
80 W/m2. The maximum power generation location is 160 W/m2 under 8 percent error still
acknowledged, other than another value might find another point as a boundary in the 16
percent error for smaller value. Overall, t he chance of getting error in the month of May was
2.205 percent. Thus , the points are still under control under the line boundary. 38
In the Figure 4.18 below shows the pattern of actual irradiance value, prediction value, and
the percentage error. Figure 4.18 A Closer Look into May’s Data
After looking at the figure above, it can be seen in the upper graph that when there is a dramatic
change on the actual data, it will be affecting the percentage error of the prediction. In addition,
during the month of May, the data was quite dramatic in change between each data point. Thus,
the cyclic of data patter n in the month of May will captured by the moving average analysis. Some of centred moving average time series was examined within Minitab software. However, the most suitable pattern was drawn by the centred moving average three with error
rate of MAPE 6 .58 percent. The Figure 4.19 will describe the mentioned pattern. Figure 4.19 Captured Moving Average
39
From the figure above, it can be seen that the pattern of the centred moving average three could
capture the pattern of the data points. Thus, the improvement for prediction model will
considering the moving average result as a predicted variable. The Table 4.6 below will show the average result for each time granularity MAPE
improvement. Table 4.6 Improvement Model Average Results
According to the table above, it can be seen that in all granularity the model could improve the
MAPE result. It means that the addition centred moving average as a feature has significant
influenced in the MAPE improvement. Moreover, in this following table the chance of each
data poi nt in getting error below eight percent will be examined. Table 4.7 Moving Average Improvement in the Chance of Getting Error
Based on the Table 4.7 above showed that there is an essential improvement after adding
centred moving average as a predictor variable. It can be seen that at all of the granularity
increased the percentage of the chance in getting error from less than one percent until less th an
eight percent. Furthermore, for five- and ten -minutes granularity can reach 100 percent starting
from chance of getting error below five percent. It means that the MAPE for all data point in
the month of May in five and ten minutely data were less than five percent percentage error. 40
4.2.3. Multistep -Ahead Prediction
The prediction model used in this study will be tested to see the capability in predicting the
multistep -ahead data for each month. The granularity used in this data was ten minutely due to
the re ason that already mentioned in the previous analysis. In the Figure 4.20 below the result
of multistep -ahead prediction was shown for further analysis. Figure 4.20 Multistep -Ahead Prediction Result
According to the figure above, it can be seen that the prediction model can work on the
multistep -ahead prediction. It showed on the Figure 4.20 that some of the error still below eight
percent for some timesteps in some month. However, if looking at detailed orientation of the
result , it depicted that the multistep -ahead prediction could not perform well in the month of
May, November, and December. It described in the graph that at all of the timesteps the
prediction result was exceeded the eight percent of MAPE. Besides, for the othe r month, the
model still can perform well at least until the third timestep. Even in March it might performed
well in all of the timesteps. In order to the result for the multistep -ahead prediction, the future result may consider
additional feature in cap turing the data such as moving average or another time series approach
analysis. In addition, the configuration of the prediction model could be explored more. Adding
some promising feature as mentioned in the Figure 4.5 can be considerate. 41
5 CHAPTER 5
CONCLUSION AND FUTURE RESEARCH
Comparing four different granularities (one, three, five, and ten minutely), the ten minutes
shows better accuracy both for average and the chance of getting an error below eight percent . In minutely granularity, the variation of irradiance data was small, yet the other variable is not. Thus, aggregating the data improves the prediction model in capturing the data. On the other
hand, a month with more significant irradiance ranges, as validated by the standard deviation,
is more difficult to predict. The dramatic change between each data points also leads to a more
significant percentage error of prediction. To sum up, each month's solar irradiance prediction depicted that the error is relatively
small, with an average of 5.8%. However, the error of 5.8% comes from MAPE computation,
which produced biased caused the actual value of the data is minimal. The most e xcellent
accuracy was performed in October, with the chance of getting an error below 8 percent to
exceed 99 percent. Meanwhile, the worst one was shown in May with only cover about 68
percent. Dramatic change between data points have a huge influence on t he prediction accuracy. Thus, moving average addition in the variable prediction was applied in May data. The result
shows that it could accommodate all of the data to get an error below 8 percent. In order t o see the reliability of the prediction model, a nother error study is also
recommended. The entire state of the findings c ould not be captured by MAPE. Proposing a
closer look review of errors may assist the stakeholder from other points of view to see detailed
errors. This study looks at the absolute e rror (AE) and the gap between data points. AE and the
distance between data points are investigated in this research. Multistep -ahead prediction also conducted in this study to check the prediction model
performance. The result convinced that it may work w ell at least until thirty minutes ahead
prediction . Furthermore, model improvement is needed to accommodate the multistep -ahead
prediction
Due to the limited variables in the database of this study. For future research, it would
be better weather predictio n data could be provided from the trusted sources. Thus, it could be
considered to capture data more deepen for prediction. Moreover, another variable such as sky
condition, sky images, cloud motion, and meteorological forecast might help capture another
hidden behavior. The detailed proposed will be described in the Figure 5.1 below. 42
Figure 5.1 Future Research Proposed Framework
To sum up, the contribution of this research would like to emphasize more the
evaluation of MAPE performance in term of prediction result measurement and the time lag
configuration . In addition, this study also proposed a pragmatic way of error analysis. 43
REFERENCES
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investment." Taiwan News. https://www.taiwannews.com.tw/en/news/3880997
(accessed December 1, 2020). [3] "Global Energy Outlook: ," in "Energy Transition or Energy Addition?," Resources for
the Future, 2020. [Online]. Available: www.eef.org/geo
[4] "Renewables 2020 Global Status Report," REN 21, 2020. [Online].
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khahh, João P.S. Catalãoi, "A minutely solar irradiance forecasting method based on
real-time sky image -irradiance mapping model," Energy Conversion and Management,
vol. 220, 2020.
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Path-to-Renewable -Powered -Future (accessed December 15, 2020). [12] "Solar is now the most popular form of new el ectricity generation worldwide." The
Conversation. https://theconversation.com/solar -is-now-the-most -popular -form -of-
new-electricit y-generation -worldwide -81678 (accessed December 15, 2020). [13] R.
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"Energy yield estimation of thin -film photovoltaic plants by using physical approach
and artificial neural networks," Solar Energy, vol. 130, pp.
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國立臺灣科技大學
工業管理系
碩士學位論文
學號：M10801866
再生能源預測不確定性於出價市場中之
儲能容量補償測定
Battery capacity determination for the
compensation of renewable energy
forecast uncertainty in a bidding -based
power market
研 究 生：David Wacker
指導教授：周碩彥
中華民國一一零年七月
摘要
可再生能源被認為是應對全球暖化 及其後果的最重要能源之一。無論它
們的潛力如何，在它們完全取代傳統的發電方式包括煤炭、天然氣和核電廠之
前，它們都伴隨著一系列的挑戰。其中一個問題是，太陽能和風能都不是按需
求提供的，而是取決於當下的天氣，但是為了確保電網穩定，需求和供應總是
必須匹配，這就要求電網運營商提前知道可用的電量。這項研究提出了一個實
用的解決方案，它可以利用電池儲能提前確定發電量，而且在當前的技術和市
場機制方面也適用。研究表明，將多個太陽能發電系統視為一個單一的組成，
可以提高預測的平均精度、誤差分佈並減少預測中的異常值。這反過來又導致
了對誤差所需的補償需求減少。利用這種構成，此研究提出了一種基於模擬決
定電池容量的方法。該方法考慮了緩衝區、轉換損失、循環壽命、最大放電深
度和自放電。其結果是對所需電池容量的估計以完全補償任何預測錯誤，包括
優化電池操作的電池管理政策。
關鍵詞。電池存儲系統，容量規劃，預測，間歇性補償，可再生Abstract
Renewable Energy is regarded as one of the most important ways to combat
global warming and its conse quences. No matter their potential they come with a series
of challenges that need to be address ed before they are ready to fully replace the
traditional means of power production, which nowadays mainly consists of coal , gas
and nuclear power plants.
|
One o f these issues is that both solar and wind energy are not
available on demand but rather depend on the current weathe r. But to ensure grid
stability demand and supply always must be matched , which requires the grid operator
to known the available amount of power ahead of time. This research propose s a
practical solution, which allows to reliably determine power production ahead of time
utilizing battery storage and that is also applicable under current circumstances in
regards to technology and market mecha nisms . The research shows how considering
multiple solar power systems as a single composition can improve a forecast’s average
accuracy, error distribution and reduce the occurrence of outliers in the prediction. This
in turn leads to a reduced need for c apacity to compensate for made errors.
|
Using the
composition, a simulation -based approach on determining storage capacity is
presented. The approach considers buffers, conversion losses, cycle life, maximum
depth of discharge and self -discharge. The result is an estimate for required battery
capacity to fully compensate any forecast errors made including a battery management
policy for optimized battery operation. Keywords: Battery Storage Systems, Capacity Planning, Forecasting, Intermittency
Compensation, Renewable EnergyAcknowledgement
First and foremost, I would like to express my gratitude to my advisor Prof. Shou -Yan Chou for his continuous support and guidance.
|
Without a doubt this sharing of wisdom is the most significant
source of motivation for me . Further I w ould like to thank the other committee member of my Thesis: Prof. Po-Hsun Kuo, and Prof. Loke Kar Seng, for their insightful comments and questions
that elevate the contents of my writing. Also, I thank my fellow labmates at the Information Technology Application
and Integration (ITAI) laboratory and fellow students at the National Taiwan University
of Science and Technology (NTUST). The y provided insightful discussion and even
more important a comfortable and joyful stay for me so far from home. Lastly, I am thankful and consider myself of utmost luck to have the parents I
do, that always assist me in reaching my dreams and provide me with the opportunity
to study in Taiwan so far from home . The experience o f a country so different in culture
from my own, made me reflect on life and taught me to see everything from more than
one perspective. David Wacker
Taipei , July 20 21
Table of Contents
List of Tables ................................
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65
Appendix 1. Forecast Composition – MAPE Distributions ................................ ......... 68
Appendix 2. Forecast Composition – Maxim um PE Distribution ............................... 70
Appendix 3. Forecast Composition – Share PE over 5% ................................ ............
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.. 54
Table 4: Forecast Composition – MAPE Distributions ................................ ............... 68
Table 5: Forecast Composition – Maximum PE Distributions ................................ .... 70
Table 6: Forecast Compos ition – Distribution of PE over 5% ................................ .... 72
List of Figures
Figure 1: Worldwide Power Generation [(EIA) 2019] ................................ ................ 13
Figure 2: Worldwide Power Generation from Renewable Sources [(EIA) 2019] ....... 14
Figure 3: Energy Storage Technologies [Das, Bass et al. 2018] ................................
|
.. 42
Figure 9: Cumulative Error over Time (Adjusted data) ................................ ............... 43
Figure 10: Forecast Composition – Percentage Error Progression .............................. 44
Figure 11: Forecast Composition – Maximum Percentage Error Progression ............ 46
Figure 12: Forecast Composition - PE Distribution Progression ................................ . 47
Figure 13: Forecast Composition - PE Distribution Progression (11 onwards) .......... 47
Figure 14: Simulated Battery Load (Tesla Powerwall 2) ................................ ............ 52
Figure 15: Simulated Battery Load (sonnen eco) ................................ ........................ 53
Figure 16: Power Forecast of Station 1 - Inverter 7 ................................ ...................... 56
Figure 17: Power Forecast Composition ................................ ................................
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...... 56
Nomenclature
𝐸𝑡 Energy stored in BESS at time 𝑡
𝐵𝐸𝑆𝑆 𝑐𝑎𝑝 Storage Capacity
𝛿𝐷𝑜𝐷 Maximum depth of discharge (%)
𝑃𝑐𝑡 Power charged at time 𝑡
𝑃𝑑𝑡 Power discharged at time 𝑡
𝜂𝑐 Charging efficiency
𝜂𝑑 Discharging efficiency
𝐴𝑡 Actual Power at time 𝑡
𝐹𝑡 Forecasted Power at time 𝑡
𝜏𝑆𝐷 Self-Discharge factor of BESS
𝐶𝐿 Desired Cycle Life
𝐿𝑖𝑚 𝑢𝑝 Upper Limit of BESS
𝐿𝑖𝑚 𝑙𝑜𝑤 Lower Limit of BESS
𝛽 Buffer size (%)
𝛼 Adjustment factor Introduction
12
1. Introduction
Due to the rising g lobal temperature s and the potential severity of problems
connected with it, in 2006 the Paris Agreement was signed with the aim of holding the
increase of global average temperatures below 2°C.
|
One of the measurements to be
taken is the significant reduction or even complete elimination of greenhouse gases . As
production of electricity with fossil fuels is one of the main contributors to CO 2-
emission [Boden, Marland et al. 2009] , production from renew able energy sources have
come into focus . Most countries set a specific target for their renewable energy
production, many of them even 100% electricity generation from renewable sources by
2050 or even earlier [Parliament 2018] . As seen in Figure 1, power generation is continually rising in response to global
development. While the absolute amount of both power from fossil and renewables has
increased, the relative share of renewable energy is continuously increasing, from 20%
in 2000 to 27% in 2018. Note that share of fossil fuels has remained more or less
constant in that time and it is instead nuclear power which relative share has been
decreased. Introduction
13
Figure 1: Worldwide Power Gene ration [(EIA) 2019]
This substantial increase in power from renewable ene rgy sources is
predominately carried by wind and solar as seen Figure 2 below. Hydroelectricity is
still the major source of renewable energy but it’s relative share has decreased from
91% in 2000 to just 62% in 2018. Power generat ion from solar and wind has increased
from about 1% for both to 9% and 19%, respectively within the same time. This does lead to new challenges in ensur ing power grid stability and consumer s
on-demand access to power , as all pow er demand must be met with the equal amount
of supply. Beyond that also the opposite is true, all supply must be met with demand,
or in other words produced electricity must be consumed. This is because power
transmission lines are not able to store power , any power inserted must also be
retrieved. 050001000015000200002500030000
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018Power Generation Worldwide
Nuclear (billion kWh) Fossil fuels (billion kWh) Renewables (billion kWh)Introduction
14
Figure 2: Worldwide Power Generation from Renewable Sources [(EIA) 2019]
One option to achieve this balance is building up storage systems that allow to
store power when supply exceeds demand and provide this excess when demand
surpass supply . Another option are systems like smart gr ids, virtual power plants or
auto-DR programs, which all fill a similar role. The idea is to utilize a plethora of sensor
and meters to automatically control power generation sources and demand devices to
keep up the equilibrium [Shabanzadeh and Moghaddam 2013] . These cases are
especially interesting in a grid that operates solely on renewable energy (RE). Currently though most grids in the world still have a mix of power production. To ease the integration, power supply from renewable energy sources (RES) can be
made p lannable when used in conjunction with storage system. 010002000300040005000600070008000
2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 2016 2017 2018Power Generation from Renewable Sources
Hydroelectricity (billion kWh) Geothermal (billion kWh)
Tide and wave (billion kWh) Solar (billion kWh)
Wind (billion kWh) Biomass and waste (billion kWh)Introduction
15 1.1. Research Goal
The central goal of this research is to provide a practical solution that reduces
the difficulties associated with the integration of RE into power grid under current
circumstances in re gards to technology and market mechanisms. More clearly the
benefits should affect and ease the grid operator’s task of balancing the power grid , by
reducing or even eliminating the uncertainty of RE production, which in turn reduces
the need for power res erve as well as cost . As a result, this hopefully leads to sooner
large -scale adoption of RE . Not just because associated cost is reduced but primarily
because the existing power reserve in some gird might not be sufficient to add
significant shares of RES into the grid. The provided solution is an approach to
determine minimum battery capacity in such a way that any forecast error can be
compensat ed trough the battery, making the forecast indirectly fully reliable. In practice
suppliers of RE can utilize t his approach to plan small scale BESS capacity. The
premise is that power committed to the grid operator ahead of times can be always
delivered at any point in time with minimum capacity of the battery and therefore
minimizing investment cost. Followingly the individual relevant parts of the goal are
addressed to specify target and scope of this research , as well as to elaborate the relevant
background in detail . 1.1.1. Power Bidding Market & Grid Balancing
Understanding how power is balanced within a grid and the dynamics of the
electricity market is essential to understand why renewable energy is so difficult to
integrate into currently existing grid and why even a supposedly small percentage has
a substantial effect on the rest of the market. While in detail thi s far more complex then Introduction
16 followingly explained, the fundamental mechanisms are essential to the underlying idea
of the research. In a privatized power bidding market, the grid operator buys power off
independent suppliers . The grid operator estimates the p ower consumption ahead of
time. Subsequently the suppliers offer set amount units of power for a certain time
contingent to a fixed price , also ahead of time . The offers are ranked based on price,
which s imply ensures that sources with the lowest marginal cost will be tapped first and
the one with the highest at last . This is known as the “Merit Order Effect” and allows
to grid operator to reliably match most of the demand with minimum cost [Sensfuß,
Ragwitz et al. 2008] .
|
But as exac t demand is uncertain, the operator must still be able
to adjust power supply within short time (less than 30 seconds). To do so operating
reserve is necessary, which are basically forms of power production that can be started
or shut down almost immediate ly. As aforementioned, renewable energy sources do not
allow for controlled production of power and the production can vary tremendously
within minutes . This not only does make it difficult to know supply from RES ahead of
time but also makes them unfittin g to function as operating reserve. Therefore, new
methods and technology is required to perform successful balancing in a grid with high
penetration of renew ables [Hirth and Ziegenhagen 2015] . Assuming a current market
with a power mix, operating reserve is not an issue as it can be covered through
traditional means. Therefore, this researc h focuses on making RE supply plannable and
reliable in the scope of a power bidding market.Introduction
17 1.1.2. Battery Energy Storage Systems
Battery Energy Storage Systems (BESS) emerge as a potential solution to not
just to solve the mismatch of PV output and demand profi les, but also the intermittency
and inherent unpredictability of RE . There a many different Energy Storage Systems
(ESS) , of which an overview is presented in Figure 3. Opposed to other ESS, BESS and
especially Li -ion batteries have a number of benefits including: High Energy Density –
Modularity – Scalability – Failure -safety – Replaceability – High Roundtrip Efficiency
[Diouf and Pode 2015] . Nevertheless, battery solution s are expensive and suffer from
relatively short lifetime. Therefore, a method for optimal sizing is necessary to prevent
over-dimensioning. Figure 3: Energy Storage Technologies [Das, Bass et al. 2018]
Introduction
18 1.1.3. Multi system consideration
Further it will be demonstrated how combining forecasts from multiple systems
into a composition will results in overall reduced percentage error and why this
approach is to be preferred over the more common single system analysis. The issue
lies within that in the electricity grid a single system is not isolated but instead all
systems are feeding into the same network. Therefore, the forecast of a system should
also not be viewed in isolation but rather in conjunction with other systems. The effect
of this that the relative error will decrease as the natural result of th e fact that whil e
some forecast will overestimate others will underestimate the true power production . The reduction of this error will also lead for a smaller capacity of BESS, as opposed to
planning the capacity based on individual forecasts. 1.1.4. Error Analysis
When evaluat ing the quality or performance of a forecast this is often done
through a unidimensional metric, like MSE, RMSE, MAPE. While this often helps to
have a general assessment of the forecast, it does not convey the unique characteristics
of each model. Varianc e between errors, forecast tendencies, weaknesses , strengths and
many other characteristics of the forecast are not able to be assessed solely by those
metrics. This information is of critical value though when employing any forecast in a
practical scenari o. Only by understanding in under which circumstances a forecast
performs well and when it does not, allows that the appropriate amount of trust can be
given and the forecast becomes valuable for practical application . So, we should view
forecasting more l ike it was expressed by Paul Saffo: “The goal of forecasting is not to
predict the future but to tell you what you need to know to take meaningful action in
the present.”, because no forecast is always 100% correct. For the capacity planning of Introduction
19 a BESS that is relevant as even only one large error that is an outlier from the rest could
cause issues with the capacity of the BESS . Either it can’t cover up for the error or the
battery capacity must be large enough to cover, but making it generally oversized
considering all other errors. Therefore, reliability of the errors is more important than
average accuracy for this case.
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The
first reason that the model architectures are and have been extensively explored and
summarized in other research [Lai, Chang et al. 2020] . The second reason is that
according to “No free lunch theorem” there is no single model which will perform best
for every problem. The theorem states : “that all optimization algorithms perform
equally well when their performance is averaged across all possible problems ”. In short
there is not one best forecast model for any domain. The authors also highlight the
importance of applying problem -specific knowledge when creating an algorithm. Therefore, the expectation can never be th at one model will perform equally on two
different sets of data of different origin [Wolpert and Macready 1997] . While this
theory does not originate in machine learning it has been proven to be true for it as well
[Kuhn and Johnson 2013] .Introduction
20 1.2. Existing Research
To solve the issue intermittency and unpredictability various solu tion
have been proposed. Besides BESS common discussed topics are super grids and smart
grids. Since the stated goal is providing a solution that can be applied immediately
under current circumstances, these two solutions are not alternate option as shown
followingly [Anees 2012] . Further a short summary o f the existing battery related
studies is given.
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1.2.1. Super grid
One solution the European Union is currently investing in a so called “Super
grid”, which links European countries and surrounding countries through an additional
high-voltage power grid that sits on top of the existing grids [Cole, Vrana et al. 2011] .The idea is that by covering a wider area the irregularity of sources like solar and
wind can be reduced and therefore serve baseload, which it is currently unable to do. Simply put when covering a larger area a perce ntage of all wind capacity will become
reliably utilizable [Archer and Jacobson 2007] . But isolated locations like islands do
not have physical access to such a power grid nor most countries are in the political
situation to realize such a s ystem, which requires transnational cooperation and
stability, as such a system is prone to geo -political risk [Czisch and Schmid] . Beyond
that there are also many tec hnical challenges present, such as different utility frequency
between grids, which requires expensive conversion to interconnect them. Further
expansion of power lines is necessary to cope for the geographical mismatch between
production and consumption i s a super grid [Aghahosseini, Bogdanov et al. 2020] .Introduction
21 1.2.2. Smart Grids
One commonly proposed system to make renewabl e energy a viable solution
are smart grids. Instead of only providing the one -way process of delivering power from
its generation source to the consumer, s mart grids can be described as the integration
of power generation sources, storage systems and consu mers into a network, which
allows bi -directional energy flow and exchange of information. This technology, that
enables communication, and therefore automated control of the all its systems to
achieve grid balance and stability, is what gives the grid its smart prefix . The supposed benefits are improved efficiency and reliability, also allowing for
large -scale integration of renewable energy source and their unstable power production
patterns. This achieved not only just by powering devices on and off depe nding on the
available energy but also using sensor to accommodate for upcoming changes in power
production. An example for this would be a wind turbine, which operations relies on
numerous sensor which in turn can also feed various information to the grid about
climate and environment [Hu and Lanzon 2019] . But to transform currently existing grids into smart grids, extensive amount of
work is required . The transition is not only costly but also requires time for installation
and tuning of the network. The Electric Power Research Institute estimated a cost of
$338 billion to $476 billion to implement a fully functional smart grind in the USA
[EPRI 2011] . Introduction
22 1.2.3.
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Battery Storage Systems
Due to drawbacks in regards of cost but also considering the aspect of time that
is required to realize super and smart grids, do not deliver an immediate solution for
solving intermittency issues of renewable energy. Electrical Storage Systems (ESS)
instead can be integrated into existing grid and are already available. The application
of ESS is widely researched . It can be summarized into a f ew categories, based on scope
and goals. For the scope, there are three different applications: Off-Grid – Micro -Grid
– Large Power -Grid ( e.g., national grid). The goals can be summed up as: Cost -
Optimization – Intermittency Negation – Curtailment Reductio n. This research falls
within the scope of a large power -grid with the goal of negating intermittency.
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Therefore, the followingly describe d research, also mainly evolves around this topic as
well. The effectiveness of a battery system in national grids ha s been demonstrated
through the Hornsdale Power Reserve in Australia, a 150 MW battery built by Tesla. As
presented by the “Aurecon Hornsdale Power Reserve Impact Study” since the
introduction of the power reserve it allowed for savings of nearly AUD 40 mil lion in
regulation costs [aurecon 2018] . Keck et. Al. present in reference to the Hornsdale
Power Reserve a simulation -based approach on estimating the required ESS capacity
for all of Australia [Keck, Lenzen et al. 2019] .
|
Al. consider battery sizing for
the behind the meter application, with the goal of reducing electricity cost of
commercial and industrial customers with high consumption in markets where
electricity rates changes depending on time of use [Wu, Kintner -Meyer et al. 2017] .
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Al. provides a comprehensive comparison of a pproaches for storage sizing
in hybrid power systems, where solar, wind and a battery are coupled to satisfy demand Introduction
23 requirements. These approaches optimize cost while having a set constraint on demand
mismatch [Hatata, Osman et al.
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Arnold and Andersson present a research closest
to the idea of this thesis, which is using BESS to counter forecast errors. They use a
Monte -Carlo simulatio n to simulate errors and determine required battery capacity to
counter these errors. The approach is optimized around a cost metric, meaning it allows
to that large errors are not compensated if beneficial to overall cost model [Arnold and
Andersson 2011] . In the presented studies the solution was optimized around a cost metric. But
solely considering co st does might lead to suboptimal solution in regards to solving the
issue of intermittency . In other words what might be beneficial from an economic
perspective of different parties, does not have to be optimal for ensuring a stable supply
of power . Furthe r the studies rely solely on simulated or probabilistic data for
determining the battery size, which always carries the risk of not being transferable to
real-world case. This research instead provides a new approach where the goal is the
compensation of e rrors with minimal capacity for the BESS at any given point in time ,
based on real forecast data . While this approach might not lead to the most cost -optimal
solution in short -term, it provides a solution that is feasible long -term. The assumption
is that while it can be short -term optimal to allow not being able to fully compensate
errors for some of the parties in the market, long -term full compensation must be
ensured for grid stability and therefore market mechanisms, li ke fees for not being able
to del iver power, will eventually make anything but full -compensation of errors
suboptimal, also in terms of cost.Research design and methodology
2. Research design and methodology
Before determining the battery capacity, all data required for the simulation first
must be created. Therefore, after obtaining the solar power data, the first step is the
creation of forecasts for all datasets are produced via an automated process. This is
followed by post -processing, including adjustment of the error to a mean of zero. Afterwards all dataset is combi ned into a single composition covering all forecasts. An
evaluation of the error characteristics of the composite forecasts is shown, as well as a
demonstration of the improvement provided over using individual forecast in
insolation. The acquired composit ion is subsequently is utilized through a simulation -
based approach to establish the capacity necessary, to compensate for the forecast error . In other words, the capacity needed , so that the power retrieved from or stored to the
battery in addition to the actual produced power is always equal to the forecasted power
value at any given point in time . Besides this main condition, further requirements in
regards maximum depth of discharge (DoD) and Cycle Life can be defined and battery
capacity adjusted based on those requirements. For validation purposes all variables are
established and tested on two different sets of data.Research design and methodology
2.1.
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Data Origin
The data used within this research all stems from a single provider. In total 3 6
datasets were considered (one dataset per i nverter) , stemming from three different
locations. All datasets range from the 13th of December 2019 to the 30th of June 2020,
a total of 2 01 days with one datapoint every ten minutes . The dataset s in their original
form all include the same six columns – Datetime , Irradiance , Inverter Temperature
and Power Output . Pre-processing of the data was minimal, since there were no missing
values , a minimal number of outliers were present, and only few implausible irradiance
values during the night time were replac ed with 0 (since there can’t be solar power
generation when there is no sunshine) . To further enhance the data, feature engineering
is employed, which allows to add additional features to data, which can improve model
performance [Cassano 2018] :
1. Deriving the current time of the day in minutes
2. Deriving if an observation occurred at night or during sunshine hours as
True or False, which were obtained from https://sunrise.maplogs.com/ . This
helps the model to better learn when irradiance and therefore power
production starts. It is also valuable in post -processing, as any faulty
predictions can be corrected, by setting any prediction value to zero if it does
occur at a time known to be before sunrise or after sunset. 3. Various statistical distribution of inverter temperature, irradiance and
power . In detail, the mean, median, maximum value and standard deviation
over the last hour is computed.
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Research design and methodology
2.2. Forecast Modelling
As mentioned earlier the intention of this paper is not to explore and explain
forecasting models and their performance. Therefore, also few explanations or
justification for the choices made during the modelling process is given , as it would
divert from the focus of the research. Not only are the re already many papers existing
on this topic , but also, any model is fitted specific to one da taset or in other words, one
system [Lai, Chang et al. 2020] . Transferability of a model with same results from one
system to another is usually not the case . This is d ue to the many different variables
that influence any forecast model, which tend to strongly differ between systems. Nevertheless, the approach of obtaining the forecast results will be explained as
it is essential for correctly positioning the results an d for the purpose of reproducibility . Figure 4 below gives an overview of the model training process. Figure 4: Forecast modelling process
Research design and methodology
27 The forecasts target is to predict the power pr oduced for 10 minutes ahead,
which is equal to one step ahead for the used datasets. The LSTM model used is a
simple one -layer model, it consists of one LSTM layer with number of nodes equal to
the current combination in the grid search (refer to Table 1), this is followed by one
Dense layer with the same number of nodes as the LSTM layer and a final Dense layer
of size one.
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The layer has no additional configuration,
all settings are d efault. The reason for this choice, is previous research on the data that
adding layers, regulations or dropout does not significantly improve performance or
even does worsen it. Again, the chosen architecture and configuration might not be the
most optimi zed but model accuracy is not a target of this research, the simplicity helps
reducing the time for training the models, as there are 36 individual datasets for which
a model must be trained. Also d ue to the large number of datasets to be processed
handcra fting and tuning a model for each of those would be too time -consuming,
instead a fixed automated pipe is developed utilizing a grid search to generate various
models with varying parameters for each dataset . The input to the training is the datasets
after being processed as described in the previous chapter. The 201 days of data are
split into 139 days for training and another 62 days for testing. The training is fed to a
grid search , where a model for each possible combination for a set of parameters is
traine d. The set of parameters are displayed in Table 1. For each combination five
LSTM models are trained. This repetition is necessary, weight initialization of the
model training part is stochastic, which causes e ach new repetition to create models
with different final weights, which in turn affects a model’s performance. Finally, the
best model/configuration for each dataset is chosen based on the lowest average mean
absolute error for this configuration. Research design and methodology
28 Table 1: Grid search parameters
Parameter Values
Nodes 16, 32, 64, 128
Epochs 25, 50, 75
Lookback Period 3, 6, 9
This approach should lead to better results than using just one fixed
configuration for each dataset, while still allows the whole process to be automated,
shorting development time, as compared to manual hyperparameter optimization. Additionally, as will be shown later on, high accuracy for all datasets in the composition
is not important for the research conducted but shou ld be reasonable to ensure real -
world applicability of the results.
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After the modelling process, post -processing is
applied the forecast in results in following ways:
1. All forecasts that predict power generation during known night are set to
zero. 2. The pow er value of the original dataset has the property of only occurring
in a fixed interval size of 0.06. Since the original value is non -continuous,
while our forecast is continuous, the error might be unfairly high. Instead,
the forecasted is rounded to next closest multiple of 0.06. 3. The true singed error of each forecast is adjusted to have a mean of zero. The exact approach is explained in the following chapter, due to the
importance of this step to the effect of the forecast composition.Research design and methodology
2.3. Forecast Composit ion
The majority of papers related to renewable energy forecasts does focus only a
single or few systems /datasets but most often on each of them independently . Basically,
a set of model s is evaluated through multiple datasets. While this make sense for off -
grid cases, the problem with this common approach is that systems (in case of solar
usually on an inverter basis) are being viewed in isolation although in reality those
systems are not isolated at all. A solar farm consists of many panels and inverters , all
with the same operator and all feeding into the same grid. Same does hold true for wind
power, where there is usually more than wind turbine owned by an operator. A
composite view can utilize the effect that while forecast for some systems will produce
errors of overestimation, others will produce errors of underestimati on. Therefore,
when combining those forecast these oppositely singed errors will naturally equal each
other out to some extent. The approach is similar to that of a forecast ensemble, wh ere
multiple forecasts are created for one dataset and the average of these forecasts is used
to make a prediction. In this case, one forecast per dataset/system is present. Instead of
taking the average of the predictions for each timestep , the prediction s are simply just
summed up and the same is done for actual values, as the total amount of power
produced and fed into grid is relevant, but necessarily how much each individual system
produces. Therefore, also the relevant error is the difference between the actuals and
forecasts of all systems. 𝐴𝑡𝑐𝑜𝑚=∑ 𝐴𝑡𝑖𝑚
𝑖=1 ; 𝐹𝑡𝑐𝑜𝑚=∑ 𝐹𝑡𝑖𝑚
𝑖=1 (1)
𝐸𝑟𝑟𝑜𝑟 𝑡𝑐𝑜𝑚= 𝐴𝑡𝑐𝑜𝑚−𝐹𝑡𝑐𝑜𝑚 (2)
Research design and methodology
30 With the assumption that some of the forecasts have positive error , while others
have negative errors t his should decrease all common relative error metrics, but
especially the MAPE metric is influenced by that. Also, the MAPE error of multiple
combined forecasts can never be greater than the maximum error of its individ ual
components, as better performing forecasts will compensate for worse performing once. The mathematical notation are as follows
𝑀𝐴𝑃𝐸 = 1
𝑛∑|𝐴𝑡−𝐹𝑡
𝐴𝑡|𝑛
𝑡=1 (3)
𝑀𝐴𝑃𝐸 𝑐𝑜𝑚 = 1
𝑛∑|∑ 𝐴𝑡𝑖𝑚
𝑖=1 − ∑ 𝐹𝑡𝑖𝑚
𝑖=1
∑ 𝐴𝑡𝑖𝑚
𝑖=1|𝑛
𝑡=1 (4)
𝑀𝐴𝑃𝐸 𝑐𝑜𝑚 ≤max ({𝑀𝐴𝑃𝐸 1,…,𝑀𝐴𝑃𝐸 𝑖}) (5)
Where 𝐴𝑡 is the actual value and 𝐹𝑡 is the forecasted value of period 𝑡, 𝑛 is the
number of total observations, and 𝑚 is total number of forecasts . The Hypothesis
therefore is that with inc reasing number of forecasts combined, the overall combined
MAPE also continues to decrease. To validate this hypothesis, sets of combinations of forecasts are created and
the respective percentage error of each of the combinations is calculated. Each set
includes only combinations of a certain size, the first set would be all the individual
forecasts, the second set would be combinations of two forecasts and so on, until the
last set, which represents all forecasts combined. The number of sets is therefore equal
to the number of individual forecasts. Successively the error of each combination is
calculated and the range of errors within each set is obtained. The progression of
average, maximum and minimum error throughout these sets will be visualized and
should deliver a robust basis to judge effectiveness of forecast composition. Particular Research design and methodology
31 attention is to be brought on whether the changes in error with each additional
increment of set size is linearly or exponentially increasing or decreasing. Optimally ea ch set includes all possible combinations, but the number of
possible combinations the largest set will have increases exponentially with the number
of individual forecasts (n), as depending on set size (r) their number is equal to
𝑛! 𝑟!(𝑛−𝑟)! (6)
This might be feasible when only a small pool of forecasts is present. In this
case 36 individual forecasts are used for validation, the largest set where 18 forecasts
are to be combined would thereby have 9,075,135,300 possible combinations. Creating
all combinations therefore is not feasibly in terms of computational time . Instead,
forecasts are randomly chosen to be combined, so that per set the number of
combinations is equal to number of individual forecasts ( , meaning each s et has 36
combinations), with the exception being the last set which includes the combination of
all forecasts, where there is only one possib le combination, therefore it includes only a
single combination. Additionally, t o utilize this effect to its fulle st the condition must be that forecast
are balanced in regards to over - and underestimation, meaning neither the forecast have
predominantly positive or negative errors. The mean of all real integer errors must be
zero or at least close to zero . In the cas e the present data does not inherently have this
property, it must be adjusted towards a zero -mean error . One method to undertake this
adjustment is presented followingly. Using the forecast o f each training data, the singed
integer error is calculated. Afterwards the average of this error per hour of the day is
computed . This information is then translated to the forecast on the unseen test data, by
adjusting a forecast value by the mean error of is respective time group established on Research design and methodology
32 the training data. As a result, the average error is closer zero than it was before the
adjustment , as it is now tendency of over - and underestimation is accounted for. This
method is simple and is not able to account for seasonality or changes in the mean error
over time. B ut due to the short time period of the data these factors cannot be accounted
for.
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Nevertheless, an improvement should be present. Lastly it should be addressed why the data is not combine first and only a
singular forecast is created. T he reason why there is not only singular forecast for all
these systems together is that each system has their own unique characteristics that
influence their power production (efficiency coefficients, installation angles etc.). Producing only one forecast would not be able to cover all these. Therefore, influential
unique information is lost and likely a worse performance would be achieved
[Korotcov, Tkachenko et al. 2017] .
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2.4. Derivin g Storage Cap acity
The goal is to calculate the minimal required battery size that can compensate
all forecasting error of the composition at any given point in time 𝑡. Besides an initial
charge the battery can only be charged by the system s considered in the composition.
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Multiple factors impact the required battery capacity, which will be laid out
followingly. From these factors a set of conditions is derived. These conditions are
applied to a simulation of the battery charge over time from which the battery capacity
is derived as a result.Research design and methodology
2.4.1. Relevant Factors
The following discussed factors are viewed in relation to Li -Ion batteries . While
partly also applying to other batteries like Redox -Flow battery, not all of them do and
might not in the same way. Due to the c haracteristics of Li-Ion batteries explained in
Chapter 1 and under the goal of provid ing a solution that is applicable now, a solitary
view on just Li -ion batteries is justified and reasonable from the author’s point of view. 2.4.1.1. Depth of Discharge
The Depth of Discharge (D oD) or more precisely the maximum DoD determines
how much power can ex tracted from or charge to a battery within a given time . Exceeding this limit can cause significant permanent damage to the battery and
therefore reduce its lifetime or even cause outright failure. The effect of DoD on the
cycle life of the battery is show n below in Figure 5. Therefore, the battery capacity must
consider the resulting DoD to prevent short -lived battery systems [Qadrdan, Jenkins et
al. 2018] . Figure 5: DoD impact on cycle life [Qadrdan, Jenkins et al. 2018]
Research design and methodology
2.4.1.2. Conversion Losses
Whenever a battery is charged or discharged some of the energy is lo st as hea t,
a conversion loss occurs, usually termed efficiency in the context of BESS. While the
charging and discharging efficiency might differ, often a single parameter, the roundtrip
efficiency, is provided by the manufacturer. For the simulation that means that
whenever power is charged or discharged these efficiencies must be conside red
[Toman, Cipin et al. 2016] .
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2.4.1.3. Permanent Capacity Loss
Permanent ca pacity loss, refers due losses in capacity that are not recoverable
through charging. The permanent capacity loss is mainly affected by the number of full
charge and discharge cycles, battery load/voltage and temperature. This capacity loss
is unavoidable but can be reduced through proper battery management. For once partial
charges and discharges instead of full ones, improve the lifetime of the battery. Further
avoiding times where the battery is in fully charged condition also benefits lifetime. This is due to chemical reaction that occur within a Li -ion battery which are fastened
by high voltage and temperatures [Broussely, Biensan et al.
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While these factors and their influence actual capacity loss are not be evaluated
in numerical terms , they are still be considered within the model. Ensuring partial
charging and discharging, is inherently covered as the power will only be charged or
discharged to equal out forecast error. Therefore, unless a continuous series of positiv e
or negative errors occurs, no full charging or discharging will occur. To prevent the
battery from being fully charged a buffer will be defined. This means if the current
charge of the BESS in the model exceeds a certain limit, the following forecast wil l be
adjusted upwards, such that a discharge will occur, reducing the battery’s charge level. Research design and methodology
35 2.4.1.4. Self-Discharge
Batteries self -discharge over time regardless of if they are connected to a grid
or not. The rate of which a battery discharges differs depending o n model, state -of-
charge ( SoC), temperature and age. For current Li -ion batteries the rate of self -
discharge is estimated to be around 1.5 -3% per month. While this effect is neglectable
in the very short term, it can accumulate to large amount over time an d must be factored
in when determining storage size. [Zimmerman 2004] . As this research presents
theoretical work, a fixed s elf-discharge rate (𝜏𝑠𝑑) is assumed, as the influencing factors,
like temperature cannot be accurately modeled. 2.4.2.
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Constraints
Based on the set goal and relevant factors explained before, a set of constraints
can be derived. Some of these constraints are necessary to be ful filled while other are
only optional, which will be outlined clearly in their respective description. The final
required capacity of the BESS is equal to the smallest value satisfying all constraints. The major constraint which represents the essence of ou r goal, is represented
through Equation (7), that at any given point in time 𝑡 the actual amount of produced
power in addition with either charging and discharging power must be equal to
forecasted amount of power. 𝐹𝑡=𝐴𝑡−𝑃𝑐𝑡+𝑃𝑑𝑡 (7)
This true when the energy stored in BESS ( 𝐸𝑡) never drops below zero and also
never exceeds its capacity, while 𝐸𝑡 is equal to the energy stored at the previous
timestep factoring in self -discharge plus either the energy that has been charged to it or
minus the energy that has been discharged to it. Research design and methodology
36 𝐵𝐸𝑆𝑆 𝑐𝑎𝑝≥𝐸𝑡≥0 (8)
𝐸𝑡=𝐸𝑡−1∗(1−𝜏𝑠𝑑)+(η𝑐 ∗𝑃𝑐𝑡−𝑃𝑑𝑡
η𝑑) (9)
Since the battery in this model is solely either charged or discharged, at any
given point in time either 𝑃𝑐𝑡 or 𝑃𝑑𝑡 is zero while the other is difference between
forecasted power and actual power. (𝐴𝑡>𝐹𝑡) →𝑃𝑐𝑡=𝐴𝑡 −𝐹𝑡 ; 𝑃𝑑𝑡=0
(𝐴𝑡<𝐹𝑡) →𝑃𝑑𝑡=𝐹𝑡 −𝐴𝑡 ; 𝑃𝑐𝑡=0 (10)
Further the maximum depth of discharge must be considered . The amount of
power that can be charged to or discharged from the battery in one timestep , cannot
exceed the maximum depth of discharge in W which depends on the capacity of the
battery. ∆ (𝐸𝑡−𝐸𝑡−1) ≤ 𝛿𝑑𝑜𝑑∗𝐵𝐸𝑆𝑆 𝑐𝑎𝑝 (11)
In connection to the preceding equation, the buffer size ( β) of the battery must
be considered. The buffer size in percent can be freely determined, but must at least
cover the maximum value of 𝑃𝑐𝑡 and 𝑃𝑑𝑡. The buffer function as a soft buffer, meaning
it can be temporary crossed. Here the reliability of the model is extremely important
and fundamental knowledge of the occurrence of large errors.
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If Equation (7) must be
fulfilled without any exception than it must consider the highest possible error, even if
it is a single outlier. ∆(𝐵𝐸𝑆𝑆 𝑐𝑎𝑝− 𝐿𝑖𝑚 𝑢𝑝)>𝑚𝑎𝑥 (𝑃𝑐) (12)
∆(0 − 𝐿𝑖𝑚 𝑙𝑜𝑤)>𝑚𝑎𝑥 (𝑃𝑑) (13) Research design and methodology
37
Lastly as an optional constraint the desired cycle life ( 𝐶𝐿) of the battery can be
considered. As described previously a batter y’s life time is usually determined by a
number a fixed n umber of cycles and the remaining capacity afterwards . A desired
cycle life ( 𝐶𝐿) can be defined as a number of cycles over a period of time. The
accumulated amount of charged and discharged power for a given time period divided
by the desired cycle life for the same time period, is equal to the required battery
capacity to reach desired cycle life. While partial charges and discharges are not causing
capacity loss to the same degree as full ones, it is common to consider them as such [de
Vries, Nguyen et al. 2015] .
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𝐵𝐸𝑆𝑆 𝑐𝑎𝑝 = ∑𝑃𝑐𝑡𝑡 + ∑𝑃𝑑𝑡𝑡
𝐶𝐿(𝑡) (14)
2.4.3. Simu lation Method
To determine the required capacity for a set of systems in a composition a
simulation -based approach will be employed. This method is inspired by dam capacity
planning, where demand (the required water flow out) and the water flow into a
reservoir over time is simulated to decide on its capacity [Jain 2017] . The process of
the simulation consists of the following steps:
1. Split data into two sets, one for establis hing capacity the other one for
validation . Meaning the following steps will only consider the first set for
establishing the initial capacity. All conditions are then tested through the
simulation for both sets . 2. Define an initial capacity. This is achieve d by making use of the DoD
condition expressed in Equation (11). This limits the maximum Resear ch design and methodology
38 charge/discharge in relation to the battery capacity that can occur for one
timestep. The maximum charge/discharge (ignoring efficiencies) is equal to
the highest absolute error made by the forecast. The initial capacity for the
BESS therefore can be defined as:
𝐵𝐸𝑆𝑆 𝑐𝑎𝑝𝑖𝑛𝑖𝑡= ⌈max (𝑃𝑐,𝑃𝑑)
𝛿𝑑𝑜𝑑⌉ (15)
3. Determine the initial battery charg e (𝐸0). This serves the purpose of not
going below zero charge level of the BESS , in case early in the simulation
discharges are necessary. 𝐸0 is set to half of 𝐵𝐸𝑆𝑆 𝑐𝑎𝑝𝑖𝑛𝑖𝑡, basically saying the
battery initial charge level is half o f its capacity. 4.
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Determine the values for 𝐿𝑖𝑚 𝑢𝑝 and 𝐿𝑖𝑚 𝑙𝑜𝑤. This simply depend on the
buffer size (𝛽), which can be freely determined. 𝐿𝑖𝑚 𝑢𝑝𝑝𝑒𝑟 = 𝐵𝐸𝑆𝑆 𝑐𝑎𝑝 ∗(1 −β)
𝐿𝑖𝑚 𝑙𝑜𝑤𝑒𝑟 = 𝐵𝐸𝑆𝑆 𝑐𝑎𝑝 ∗𝛽 (16)
5. Define a battery management policy. To keep the size at a minimum , an
active component can be added to the method . Whenever 𝐸𝑡 does exceed
𝐿𝑖𝑚 𝑢𝑝 or falls below 𝐿𝑖𝑚 𝑙𝑜𝑤 the next forecast can be simply adjusted by a
small amount to bring the battery charge back within the boundaries. For
example, if the upper boundary is exceeded and the forecast value is
purposefully increased, then as a result it is likely that power needs to be
discharged, as almost certainly the forecast is now higher than the actual
amount of power produced. This in turn lowers the charge of the battery. Besides keeping this value relatively small there is no obvious guidelines to Research design and methodology
39 decide on the exact value . To keep the correction in line with oth er charging
and discharging values, it is set to the half of the absolute error of the
forecast. That ensures it is not too distinctive from other errors, preventing
potential problems that are currently unforeseen but still large enough to
bring the batte ry load back within boundaries . 𝛼= 1
2max (𝑃𝑐,𝑃𝑑) (17)
(𝐸𝑡> 𝐿𝑖𝑚 𝑢𝑝𝑝𝑒𝑟 ) →𝐹𝑡+1𝑛𝑒𝑤=𝐹𝑡+1+α
(𝐸𝑡< 𝐿𝑖𝑚 𝑙𝑜𝑤𝑒𝑟 ) →𝐹𝑡+1𝑛𝑒𝑤=𝐹𝑡+1−α (18) Analysis
3.
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Zero -Mean Adjustment
Followingly the effect of the zero -mean adjustment is visualized and explained. Below in Figure 6 a series of boxplot showing the true error based on hour of the day
of the forecast composition with original unadjusted data is displayed . Generally, the
boxplot displays the distribution of errors, the box itself , called interquartile range
(IQR), represents the range from the 25% -quartile (Q1) to the 75% -quartile (Q3) and
the black continuous lines, called whiskers, repr esent the range from 𝑄1−1.5∗𝐼𝑄𝑅
to 𝑄3+1.5∗𝐼𝑄𝑅, all dots are considered outliers and represent single datapoints,
while the IQR and whiskers do not convey information about the number of datapoints
within them . Most important for the present case of battery determination is the median
and mean. The median (Q2) is marked by the black bar within the box, while the mean
is represented is marked by the red cross. In this unadjusted case all the mean values
for all the hours of the day are below zero. Thi s implies the model has tendency to
underpredict. Note that this excludes the hour 0 to 4 and hour 19 to 23 where all points
lie directly on zero. As the used data is solar data, the production and forecasts will be
zero during those times, consequently al so resulting in an error of zero, which causes
these hours to appear as flat lines within the boxplot. All following boxplot will have
this characteristic inherent.
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The issue resulting from that is that is easier to understand
when looking at Figure 7. Consistent underprediction also would mean the battery
needs to be consistently charged and would only be rarely discharged, which is not a
practical scenario. Analysis
41 Figure 6: Error based on dayti me
Figure 7: Cumulative Error over Time
Analysis
42 Since a balanced number of charges and discharges is preferred, the zero mean -
adjustment is employed. The impact of this adjustment on the error distribution of the
forecast composition can be seen in Figure 8. The mean of the error for hour 5 to 9 and
hour 14 to 18 is a lot closer to zero than it was before the adjustment. For hour 10 to 13
the mean is now slightly above zero. Presumably that is due t he mean error of the test -
data during these hours not being as high as for the train -data. Figure 8: Adjusted error based on daytime
Analysis
43 That case implies trend or seasonality of the error, in other words the error
distribution ch anges over time, which causes the chosen approach to not be perfectly
able to balance the error. But to factor in seasonality properly multi -year data would be
necessary which is not present. Regardless, as shown in Figure 9, the error of the
adjusted data is more balanced than before. The cumulative error of the unadjusted data
was at roughly -10,000 at the end of the two-month period, after the adjustment after
the same period it is at about -250. Optimally it woul d be hovering close to zero
consistently. Figure 9: Cumulative Error over Time (Adjusted data)
Analysis
3.2. Forecast Compositio n
To validate the established hypothesis of reducing errors by combining multiple
forecasts, a total of 36 indivi dual dataset and respective forecasts are used. Figure 10
shows the progression of errors with increas ing set size.
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Each step along the x -axis
represents an increase of the set size , while the y -axis represents the magnitude of error . The first datapoint therefore is distribution of the individual datasets. For example, t he
second datapoint describes the error distribution of all sets consisting of two combined
datasets, increasing further with each step. The last da tapoint is the combination of all
datasets, and therefore only a single value , as there is only one possible combination . Figure 10: Forecast Composition – Percentage Error Progression
Analysis
45 Out of the initial 36 forecasts, the minimu m MAPE is 3.066%, while the
maximum MAPE is 10. 693% and the overall average is 5.0 19%. As seen in Figure 10
all three metrics tend to generally decrease with increasing number of combined
forecasts. While the median and minimum decrease s relatively smoothly, the maximum
fluctuates until it is experiencing a more gradual curtailment from 1 8 combined
forecasts onwards. Also, it is to be observed that magnitude of decreases for median
and minimum error is largest in the beginning, but is quickly converging at around a
set size of 10 -15 combined forecasts. In fact, the exact numbers presented in Appendix
1., reveal that after 1 2 combined forecasts the mean stop continuously decreasing but
still reaching its overall minimu m of 1.9 61% at 36 combined forecasts. The overall
smallest minimum error of 1. 708% is found at 1 2 combined forecasts, while afterwards
the minimum error ranges from 1.7 44% to 1.9 61%, actually reaching its highest values
after the minimum at the point where all datasets are combined. For the last set where
all forecasts are combined , the MAPE for all metrics is 1.9 61%. Another useful property of the composition is revealed when, looking at the
progression of the maximum percentage error (all numbers in Appen dix 2.) displayed
in Figure 11. The figure is similar to previous but this time displaying the maximum
error of each forecast along the y -axis. Note that the scale is logarithmic, so the
reduction in maximum errors is more significant than they first appear by proportion. While within the individual datasets, percentage errors as high as 12,482% appeared,
when combining the forecasts these errors are compensated for through the other
individuals. The range of maximum errors seems to continuously decrease, which
would suggest that with increasing number of set -size this compensation effect
becomes more reliable to take place . The maximum error is important to battery
capacity planning due to the condition of maximum Do D. High errors would either Analysis
46 mean large battery capacity to not violate the DoD condition or only covering a certain
degree of error, meaning not all errors would be compensated, which would in turn not
ease the operation of the grid, as the goal of negatin g the uncertainty is not fulfilled. In connection to this, the distribution of errors is also of significance to the
battery capacity planning as high errors mean higher charges or discharges to the battery
affecting the battery’s lifetime. As can be see n in Figure 12, the share of errors above
5% decreases with increasing set size (all numbers in Appendix 3.). While of the
individual forecasts the highest one of them had 17% of its errors above 5%, but even
the lo west one has share of 11.3%. Figure 11: Forecast Composition – Maximum Percentage Error Progression
Analysis
47 Figure 12: Forecast Composition - PE Distribution Progression
For the composition with all forecasts combined it was just 6.74% of the errors. As the share of errors above 5% is so distinctively higher for the first few composition
sizes, below in
Figure 13, the change from set -size 11 and onwards is displayed. Thi s clearly
shows that the median share of high errors keeps decreasing almost continuously with
increasing composition size. Analysis
48 Figure 13: Forecast Composition - PE Distribution Progression (11 onwards)Analysis
3.3. Battery Capacity Simulation
Using the composite forecast, the simulation process described in the Chapter
Simu lation Method is followingly applied to the dataset to determine the required
battery size to counteract all inherent errors. Beyond t he forecast data it is also
necessary to define the values of roundtrip efficiency and maximum DoD of the battery. These values vary depending between different manufactures and models. Therefore, it
is necessary to test presented approach on multiple mode ls with different specifications. Further this might provide insight to how different battery properties affect the final
capacity and also the reliable functioning of the battery. Maybe certain specification
thresholds are required to ensure reliability. Two models with available specifications
are the “Tesla Powerwall 2 ”1 and the “sonnen eco ”2, with a roundtrip efficiency of 90%
and 81.6%, as well as a maximum DoD of 100% and 90%, respectively. Since the
manufactures only specify the roundtrip efficiency (η𝑟) it will be assumed that the
charging and discharging efficiency are equal. η𝑐= η𝑑= √η𝑟 (19)
The simulation will be run with the values of these two batteries. This should
also help to create a better underst anding of the effect these parameters have on the
final capacity of the battery. For the self -discharge factor 𝜏𝑆𝐷 and the buffer -size 𝛽, a
value of 2 % per month and 25% is assumed, respectively, which both can be considered
as common dimension for these variables [Swierczynski, Stroe et al. 2014] .
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A 𝜏𝑆𝐷 of
2% per month is equal to about 0.000463 % per ten minutes. The numerical inputs and results of the simulation are displayed in
1https://www.tesla.com/sites/default/files/pdfs /powerwall/Powerwall%202_AC_Datasheet_en_northam
erica.pdf
2https://sonnenusa.com/en/eco/#specifications Analysis
50 Analysis
51 Table 2, the third column showing the values of the Tesla Powerwall 2 and th e
last column the values of the sonnen eco . To put results into the proper perspective,
note that the total power production of the systems considered lies at 2,340,049 W
(~2.34 MW) for a time period from the 30th April to the 30th June or a total of 62 da ys. To separate the procedure more clearly, the different parameters are grouped into
stages. Stage 0 are the inherent properties of the battery models – Stage 1 are the
parameters initially determined – Stage 2 are the numerical results of the simulation –
Stage 3 shows the required capacity to reach different desired cycle life goals. The lesser 𝛿𝑑𝑜𝑑 and lower efficiency of the sonnen eco results in a higher initial
capacity of the battery. As a side effect that actually causes the boundaries to b e
exceeded less often, the upper boundary is exceeded 70 times by the Tesla Powerwall
2, while only 66 times for the sonnen eco. The lower boundary is exceeded 79 times by
the Tesla Powerwall 2, while only 75 times for the sonnen eco. This difference could
be considered neglectable though. For both batteries models the simulation of the load
never exceeds the capacity and also never falls below zero, which is the main condition. The 𝛿𝑑𝑜𝑑 is exceeded only once by 5,9% . As the capacity of the sonnen eco is larger,
the load of the battery is also higher on average, resulting in a higher total amount of
self-discharge, while ∑𝜏𝑆𝐷 in the two -month period for the Tesla Powerw all 2 is 7.45
W, it is 8.42 W for the sonnen eco, around 13% more. Regardless the se lf-discharge in
both cases is neglectable small compared to the overall production. The difference in
conversion losses is more significant, the sum of conversion losses of the sonnen eco
are 9.66% higher than those of the Tesla Powerwall 2, an absolute difference of 2,007
W. The three desired cycle life are the defined based on the specification sheet of
the battery models, the sonnen eco has a warranty for 10,000 cycles (estimated usage Analysis
52 is 10 years ), retaining 80% of the original capacity afterwards. The Tesla Powerwall 2
does not have a rated number of cycles but also specifies a 10-year warranty. In addition
to the specification provided for the sonnen eco, two more conse rvative values will be
tested, 6,000 and 8,000 cycles over 10 years . In all three cases the required capacity to comply with the defined desired cycle
life, is lower than the already determined initial capacity. Since the cycle life condition
is only optional, instead computing the cycles with initial capacity might be more
interesting. For the Tesla Powerwall 2 the sum of charges and discharges are equal to
37,452.48 W, which is 96.28 times the capacity, propagated for one year this would
correspond to 577.68 cycles. In the case of the sonnen eco the sum of charges and
discharges propagated for one year would correspond to 516.3 cycles. The visualization of the simulated battery load for the Tesla Powerwall 2 and
sonnen eco, is given in Figure 14 and Figure 15, respectively. The overall pattern is
very similar as it is mainly determined by the error made by the forecast, which is the
same in both cases.
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Due to the employed loa d adjustment policy, both stay well within the limit of the total
capacity and above zero. Analysis
53 Table 2: Capacity Simulation
Stag
e Parameters Tesla Powerwall 2 sonnen eco
0 𝛿𝑑𝑜𝑑 (For 10min) 16.6667% 15%
η𝑐= η𝑑 94.868% 90.0333%
1 𝐵𝐸𝑆𝑆 𝑐𝑎𝑝𝑖𝑛𝑖𝑡 389 W 433 W
𝐿𝑖𝑚 𝑢𝑝𝑝𝑒𝑟 291.75 W 324.75 W
𝐿𝑖𝑚 𝑙𝑜𝑤𝑒𝑟 97.25 W 108.25 W
𝛿𝑑𝑜𝑑 (𝑖𝑛 𝑘𝑊) 64.83 W
𝛼 32.4478 W
2 # (𝐸𝑡> 𝐿𝑖𝑚 𝑢𝑝𝑝𝑒𝑟 ) 70 66
# (𝐸𝑡< 𝐿𝑖𝑚 𝑙𝑜𝑤𝑒𝑟 ) 79 75
max (𝐸𝑡) 329.3567 W 362.14 W
min (𝐸𝑡) 58.8617 W 77.692 4 W
max (𝑃𝑐) 50.37 W
max (𝑃𝑑) 68.66 W
∑𝜏𝑆𝐷 7.4458 W 8.4197 W
∑𝑐𝑜𝑛𝑣𝑒𝑟𝑠𝑖𝑜𝑛 𝑙𝑜𝑠𝑠𝑒𝑠 20,770.87 W 22,777.67 W
3 ∑𝑃𝑐𝑡
𝑡+ ∑𝑃𝑑𝑡
𝑡 37,452.48 W 37,260.76 W
𝐵𝐸𝑆𝑆 𝑐𝑎𝑝(𝐶𝐿= 6,000
10𝑦𝑟) 375 W 372 W
𝐵𝐸𝑆𝑆 𝑐𝑎𝑝(𝐶𝐿= 8,000
10𝑦𝑟) 281 W 280 W
𝐵𝐸𝑆𝑆 𝑐𝑎𝑝(𝐶𝐿= 10,000
10𝑦𝑟) 225 W 224 W Analysis
Figure 14: Simulated Battery Load (Tesla Powerwall 2)
Analysis
55
Figure 15: Simulated Battery Load (sonnen eco)
Results
4. Results
4.1.
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Zero-Mean Adjustment
As shown the zero-mean adjustment is a simple but effective method for
correcting forecasts with an inherent tendency to either under - or overpredict. In Table
3 a comparison of the error distrib ution between the composition of the non -adjusted
data and adjusted data is given. The overall mean is significantly closer to zero after
adjusting. But the previously presented cumulative error throughout time ( Figure 9)
also showed that the simplicity of the approach comes with caveats as well. While might
being able to achieve a long -term balance of negative and positive errors, it fails to
ensure that the error is balanced short -term. Temporal characteristics wer e present,
meaning the overall tendency of underprediction is not consistent throughout time. Table 3: Comparison of Error Distribution
Metric Non-adjusted data Adjusted data
Minimum -72.261 -68.661
1st Quartile -1.945 -0.271
Median 0 0
Mean -1.153 -0.028
3rd Quartile 0 1.242
Maximum 46.834 50.374 Results
4.2. Forecast Composition
The effective overall mean percentage error for the 36 forecasts has been
reduced by roughly 60% simply by adjusting their true error to be centered around zer o
and consecutively combining them. Another benefit is that extreme errors in individual
forecast are cancelled out. While the overall highest single percentage error out of all
the individual forecast lies at 12,482%, the highest single error of the combi nation that
includes all forecasts lies only at 110% , a reduction by about 113.47 times . When
looking at the share of percentage errors that was higher than 5% (subjectively
considered as significant error), the worst individual had a share of 17%, while t he final
composition had a share of just 6,74%. Besides this quantitative evaluation of the improvement, the effects can also be
seen when visualizing the forecast, which allows for a less abstract insight to the results. In Figure 16 and Figure 17 we can see the power forecasts for the 16th of May, the prior
figure is the forecast of a single system while the latter is the forecast for the
composition. Note how the single sys tem forecasts struggles with correctly predicting
sudden changes when power generated is fluctuating, as it occurs from 13:00 to 15:00. The gap between the blue line (actually produced power) and green line (predicted
power) is clearly visible. When lookin g at the forecast for the composition the lines
appear to be almost matching, only small gaps are visible even when sudden changes
in power produced occur. As both plots are on a different scale, absolute error might
differ for equal gap sizes but the rela tive error is still accurately represented and can be
compared through this method. Results
58
Figure 16: Power Forecast of Station 1 - Inverter 7
Figure 17: Power Forecast Composition
The results also show that the error metrics do not improve linearly with
increasing set -size. While not exactly matching, an exponentially decreasing function
Results
59 seems to be fitting, meaning the improvement decreases gradually with each increase
of set size.
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The fluctuation of the max imum and minimum value of each metric between
set-sizes can be explained through the chosen approach of randomly drawing datasets
to create a limited number of combinations within each set. The number of samples
obtained is extremely small compared to the number of possible combinations.
|
Therefore, the samples within this set do not accurately reflect the distribution of all
possible combinations of the respective set size. But this also highlights that the chance
of experiencing a significant improvement w ithin a given error metric increases with
an increasing number of individual forecasts, corroborating the importance of this
multi -system composition approach. The reason for that is that with increasing number
forecasts in the composition not just the cha nce of balanced number of over - and
underprediction at every point in time increases, but also each individual forecast has
less of a weight. For example, w hen a n individual forecast has a relatively high error at
one point in time, then this is compensate d for by all other forecasts within the
composition. Nevertheless, the minimum value for each metric over all set sizes, always
occurred at a set -size smaller than all forecasts combined. A value for any given metric
will be lower the more equally the over- and underpredict ions within the composition
are distributed . As the pool of possible combinations within each size is quite large, it
basically depends on chance how well the forecasts selected for the composition, do
equal each other out.Results
4.3. Battery Capaci ty Simulation
The simulation results show that determining the capacity of a BESS with the
purpose of compensating forecasting errors can be achieved with a simple constraint of
maximum discharge. The prerequisite to do so is a reliable forecast where the maximum
errors are consistent and expectable. Beyond simply delivering a capacity estimation
for a BESS that reliable compensates for errors, the provided buffer and management
policy, ensure reasonable cycle life of the batteries. The sum of charges and d ischarges
(or full charge equivalents) appear to be below what is expected for both the Tesla
Powerwall 2 and the sonnen eco. As computed in the analysis, the full cycles of the
BESS would be just be over 500 a year. As the sonnen eco’s cycle life is speci fied to
10,000 cycles that would allow for theoretical operation of 20 years, while it’s specified
warranty lies at only 10 years , which probably also aligns with its expected lifespan in
a residential application . Both battery models tested for simulatio n are able to fulfill all set conditions
besides the maximum dis -/charge condition.
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This condition though is not a hard
condition, meaning not fulfilling it will not break the operation of the BESS. As
mentioned earlier exceeding the maximum DoD can cause permanent reduction of the
battery’s capacity. While the relative excess does not seem to be major, n umerically
evaluating the exact consequences of a single occasion to the degree present in the
conducted simulation is not possible to the best of the auth or’s knowledge . Regardless
based on this observation it is most likely beneficial to add some security buffer when
estimating the initial size of the battery, e.g., adding an additional 10% to the initial
capacity determined through the maximum DoD conditi on, presented in equation (15). Results
61 But while from the viewpoint of reliability, which is the main focus of this
research, the models are not distinguishable, an economical comparison of different
models would might lead to a different result. The difference in conversion losses is
significant even for a period of just two months (about 2,000 W). This is not too
surprising at 36 inverters are considered. Presumably this difference could be a major
factor when comparing operation cost.
|
The main drawback of the presented approach is the relative long period of data
needed to ensure reliability . The zero -mean adjustment already relies on a split of the
data, meaning the simulation can only be run with the second set. But the simulation
itself also needs to be validated, meaning it requires two sets of data is well. This also
affects the validity of this research, the data used for validation only spans a month. The results are therefore only meaningful under the assumption that the relevant error
metrics of the forecasts used will stay consistent throughout time.
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5. Conclusion and Discussion
The goal of the research to provide a solution to determining battery capacity in
such a way that it is capable of fully compensating all forecast errors and thereby
indirectly making forecast reliable. Or in other words from the viewpoint of an operator
in the bidding market, making the supply from RES plannable ahead in time. As shown
even for large array of solar power systems a battery that is many time s3 smaller than
the daily output is sufficient to fully compensate all forecasting errors . Beyond simply
fulfilling the compensation purpose even the strain on the battery is minimal, as based
on the results of simulation a cycle life of around 10,000 cycl es over 20 years could be
expected. Notably m ore so than high accuracy, reliability and consistency of the errors
is the essential property that the forecast must meet to keep the capacity of the battery
small . This is due to the fact that maximum amount o f energy that can be charged or
discharged within in a given time (which is directly tied to the size of the error) appears
to be driving factor of the required capacity. Doubling of the maximum absolute error
does basically results in doubling of the requ ired capacity. The advantages of the approach in regards to the forecast composition (in
combination with the zero -mean adjustment) as shown are an effectively reduced mean
percentage error, a significant reduction in the height of maximum errors and overa ll a
smaller proportion of high errors. Although the reduction of error metrics does not
continuously decrease with additionally inputs to the composition, the chance that the
composition is effective does continuously improve . Basically, how well the grou p of
3 37,743 W/389 W = 97.03 | Daily Production = 2,340,049 W / 62 days = 37,743 W/day | Capacity =
389W
63 individuals does cancel each other errors out does depend on chance to a degree, but
regardless of that it always offers improvement compared to looking at forecasts in
isolation. Another benefit of the composition is the reduced need for quality of each
individual forecast and thereby reduced time for training and optimization , as a generic
approach for model creation as used in this research might already be sufficient .
|
Whatever the reason might be, systems with forecast that have overall worse
performance are compensated through the more well performing systems. The
subsequent impact for the battery capacity is a reduction in required capacity , and
prolonged life time. Th e lower maximum errors impact the capacity as the maximum
occurring charges or discharges are relatively smaller. The overall reduction of the
average error and in connection distribution of errors, profits the cycle life, as less
charging and discharging in sum occurs. The zero -mean adjustment as used in this research, while suffic iently functional
in this case, might not be sophisticated enough for longer periods of data. This issue is
in direct connection with another issue, the relatively short period of data used. The
whole does not even span full seven months and the test data used for the battery
capacity determination does cover just two months. While based on the results, the
range of errors seems to be stable and reliable, certainly more data would be beneficial
to further corroborate any claims in regards to long -term appli cability of the approach. Further t he presented approach does not consider location of the BESS which
could lead to the argument that not all the system in the composition are co-located and
as such a single BESS can’t not cover them all or if so, transpor tation losses must be
considered. But this could be argued against, as the assumption is that all these systems
feed to the same grid, therefore the placement is not relevant. The BESS just must be
64 located with one of the systems in the composition. Whatev er the total mismatch and
its origin may be the charging is only provided through the system located with the
BESS. The other systems always fully feed their electricity into the grid. As mentioned,
this is only true when the different systems feed into th e same grid. Also, in case if the
power producing systems that are co -located with the BESS have a failure, they could
also not provide charging when necessary. But complete failure of multiple inverters in
the case of solar power is unlikely, and if so wo uld also be only temporarily [Green
2012] . 6.
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Future Work
The presented work provides merely a fundamental idea. From the discussion
in last chapter a few potential ideas arise, which could extend this research are
followingly provided. Translating the findings into an economic model would be of benefit to a
potential operator of such a battery system. Opposite to the upfront cost for capacity,
construction and the maintenance cos t, is the cost associated with prediction errors. Underpredicting means underselling in a bidding market, only the agreed upon amount
of power can be sold. Overpredicting on the other hand incurs fees, as the too little
power is delivered. Potentially , being able to provide set amounts of power reliably,
even could improve asking price for the power provided. Beyond that the model could
be extended to buy power when buying price is cheaper than selling price at another
time and the current capacity of the b attery allows for it. Testing the provided approach with long -term data would help verifying the
presented results, as factors like seasonality or time depended changes might affect
forecasting performances and critical conditions like maximum DoD could be violated. If so then mechanism for time -dependent retraining or readjustment must be added,
ensuring that the performance of the forecast does not deteriorate too strongly over
time. It also would help to invent more sophisticated approaches to the zero -mean
adjustment which could lead to even higher improvements when utilizing the forecast
composition, which in turn reduces the required battery capacity. As mentioned within the results of the forecast composition, it depends of
chance how well chosen fore cast within a composition compensate for each other. It
66 might be possible by using a training and testing dataset to find group of forecasts that
compensate for each other well consistently throughout time. This would lead to even
further improvement of th e error metrics. The condition would be that out of a pool of
forecasts, each of them must belong to exactly one group and the combined result of all
groups is still better than grouping just all of them together. Finding a solution to transfer results of this approach to other battery systems,
would allow to determine battery capacity without the need of collecting and analyzing
data. Basically, the goal would to build up BESS as quickly as possible. To do so the
shown approach could be first applied to multiple system s and forecasts. Subsequently
correlation between the properties of the systems and the results could be analyzed. If
a strong correlation is present than potentially the capacity of the BESS could be
roughly determined without the need of extensive data. Lastly while factors, like buffer size, have been addressed , but their impact on
battery life and performance is not measured. Also, temperature of the battery has not
been considered under the assumption that the partial (and with majority relatively
small) charges and discharges would not cause issues in this dimension. Certainly,
considering the impact of these factors on the cycle life of the battery can lead to more
optimal solutions, when viewed in conjunction with an economic model. 67 Bibliography
U.
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Pode (2015). "Potential of lithium -ion batteries in renewable
energy." Renewable Energy 76: 375 -380. EPRI (2011). "Estimating the Cost s and Benefits of the Smart Grid: A Preliminary
Estimate of the Investment Requirements and the Resultant Benefits of a Fully
Functioning Smart Grid ." Electric Power Research Institute . Green, P.
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(2004). "Self -discharge losses in lithium -ion cells." Aerospace and
Electronic Systems Magazine, IEEE 19: 19-24. 70 Appendix 1. Forecast Composition – MAPE Distributions
Table 4: Forecast Composition – MAPE Distributions
n forecasts
combined MAPE Distribution
Maximum (%) Mean (%) Median (%) Minimum (%)
1 10.6931 5.0192 4.4171 3.0663
2 8.6427 3.4691 3.4518 2.3093
3 7.9713 3.2153 2.9547 2.1647
4 7.5357 3.2236 2.7182 2.0251
5 4.2057 2.6797 2.5335 1.9981
6 4.6913 2.5724 2.3868 2.0029
7 3.0218 2.4104 2.4450 1.8464
8 3.1417 2.3331 2.3444 1.8211
9 4.8647 2.3338 2.2539 1.8450
10 4.6717 2.3176 2.1992 1.7920
11 2.6541 2.2167 2.1899 1.8736
12 2.8257 2.1921 2.1851 1.7077
13 3.3880 2.2130 2.1758 1.8532
14 3.0548 2.2157 2.1602 1.7441
15 3.2365 2.1616 2.1354 1.8127
16 2.8014 2.1298 2.0767 1.8206
17 2.4617 2.0546 2.0312 1.8104
18 2.8545 2.0895 2.0789 1.7759
19 2.5266 2.0902 2.0819 1.7879
20 2.4154 2.0663 2.0144 1.8814
21 2.3579 2.0712 2.0594 1.8602
22 2.4303 2.0589 2.0291 1.7996
23 2.4235 2.0620 2.0437 1.8760
71 n forecasts
combined MAPE Distribution
Maximum (%) Mean (%) Median (%) Minimum (%)
24 2.3912 2.0400 2.0241 1.8081
25 2.2857 1.9940 1.9977 1.8166
26 2.2001 1.9858 1.9694 1.8288
27 2.2528 2.0081 1.9917 1.8323
28 2.2655 2.0002 1.9840 1.8368
29 2.2641 2.0053 2.0004 1.8601
30 2.1236 1.9962 2.0089 1.8660
31 2.1827 1.9935 1.9910 1.8879
32 2.0877 1.9660 1.9574 1.8931
33 2.0770 1.9711 1.9711 1.8974
34 2.0850 1.9764 1.9680 1.9264
35 2.0489 1.9673 1.9636 1.9333
36 1.9614 1.9614 1.9614 1.9614
72 Appendix 2. Forecast Composition – Maximum PE Distribution
Table 5: Forecast Composition – Maximum PE Distributions
n forecasts
combined Maximum P E Distribution
Maximum (%) Mean (%) Median (%) Minimum (%)
1 17720.9 3005.5 709.7 100.0
2 7731.4 603.3 269.7 83.4
3 7814.8 702.8 234.4 111.2
4 7040.0 908.3 284.0 84.5
5 3195.4 381.3 239.2 83.4
6 3634.9 411.1 271.6 72.6
7 595.7 221.9 193.7 79.1
8 328.5 180.9 174.8 79.9
9 634.6 183.8 154.6 79.6
10 644.3 208.1 187.1 72.5
11 398.5 187.8 169.0 114.0
12 322.0 163.9 162.1 94.9
13 385.2 162.8 150.3 70.2
14 300.4 163.2 151.3 67.0
15 308.6 166.5 163.1 83.4
16 277.5 155.0 149.2 73.7
17 246.1 146.1 143.3 59.0
18 248.8 144.8 127.4 90.5
19 227.1 139.6 119.7 87.6
20 260.1 144.1 140.8 72.6
21 220.8 151.1 151.4 79.8
22 227.5 140.3 135.9 77.2
23 234.6 143.5 150.7 61.4
24 185.7 129.9 119.4 85.6
73 n forecasts
combined Maximum P E Distribution
Maximum (%) Mean (%) Median (%) Minimum (%)
25 174.1 130.5 133.8 91.6
26 178.0 125.4 123.9 54.2
27 172.3 128.0 131.4 85.4
28 156.9 124.1 129.8 89.9
29 155.8 123.6 128.2 81.0
30 156.1 121.3 125.3 83.9
31 148.8 117.3 119.6 85.5
32 138.1 118.9 120.4 83.7
33 135.3 115.5 119.7 79.5
34 125.2 112.8 115.4 82.9
35 123.1 111.2 112.2 87.5
36 110.3 110.3 110.3 110.3
Appen dix 3. Forecast Composition – Share PE over 5%
Table 6: Forecast Composition – Distribution of PE over 5%
n forecasts
combined Share PE over 5%
Maximum (%) Mean (%) Median (%) Minimum (%)
1 11.30% 14.31% 14.31% 17.00%
2 8.33% 11.27% 10.84% 15.22%
3 7.36% 10.29% 10.25% 14.21%
4 7.20% 9.38% 9.48% 11.65%
5 7.78% 9.44% 9.43% 11.68%
6 7.38% 8.90% 8.82% 11.29%
7 7.12% 8.72% 8.55% 11.21%
8 7.34% 8.59% 8.51% 10.42%
9 6.98% 8.55% 8.39% 10.92%
10 7.34% 8.27% 8.01% 10.29%
11 6.91% 8.15% 8.06% 9.94%
12 6.98% 8.00% 7.86% 10.07%
13 6.96% 7.91% 7.93% 8.96%
14 7.13% 8.12% 7.98% 9.40%
15 6.97% 7.96% 7.99% 9.32%
16 6.82% 7.69% 7.64% 9.09%
17 6.92% 7.75% 7.73% 9.26%
18 6.86% 7.74% 7.68% 9.01%
19 6.74% 7.76% 7.74% 9.40%
20 6.86% 7.78% 7.72% 9.05%
21 7.15% 7.77% 7.68% 8.83%
22 6.89% 7.67% 7.57% 9.03%
75 n forecasts
combined Share PE over 5%
Maximum (%) Mean (%) Median (%) Minimum (%)
23 7.04% 7.72% 7.58% 8.58%
24 6.80% 7.63% 7.55% 8.73%
25 6.94% 7.53% 7.53% 8.74%
26 7.07% 7.57% 7.50% 8.15%
27 7.04% 7.60% 7.62% 8.34%
28 7.19% 7.57% 7.56% 8.01%
29 7.02% 7.46% 7.42% 8.46%
30 7.03% 7.51% 7.54% 8.01%
31 7.19% 7.47% 7.47% 7.90%
32 7.14% 7.52% 7.50% 8.05%
33 7.11% 7.41% 7.38% 7.97%
34 7.16% 7.45% 7.40% 7.91%
35 7.22% 7.37% 7.35% 7.70%
36 7.35% 7.35% 7.35% 7.35%
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