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Multi-Agent RL Simulation for Market-Aware Grid Topology Optimization
Proof-of-Concept Implementation
"""
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns
from dataclasses import dataclass
from typing import List, Dict, Tuple, Optional
import gym
from gym import spaces
import torch
import torch.nn as nn
import torch.optim as optim
from collections import deque
import random
import json
from datetime import datetime, timedelta
# Set random seeds for reproducibility
np.random.seed(42)
torch.manual_seed(42)
@dataclass
class GridState:
"""Represents current grid state"""
bus_voltages: np.ndarray
line_flows: np.ndarray
line_limits: np.ndarray
topology_matrix: np.ndarray
congestion_status: np.ndarray
timestamp: datetime
@dataclass
class MarketSignals:
"""Represents market trading signals"""
p2p_trades: List[Dict]
price_signals: np.ndarray
surplus_areas: List[int]
deficit_areas: List[int]
trading_volume: float
@dataclass
class AgentAction:
"""Represents agent action"""
action_type: str # 'topology_change', 'market_response', 'coordinate'
action_value: np.ndarray
confidence: float
rationale: Dict
class GridEnvironment(gym.Env):
"""Custom grid environment for multi-agent RL"""
def __init__(self, n_buses=30, n_lines=41):
super().__init__()
self.n_buses = n_buses
self.n_lines = n_lines
# Initialize IEEE 30-bus system parameters
self._initialize_grid_parameters()
# Action and observation spaces
self.action_space = spaces.MultiDiscrete([
n_lines + 1, # Topology actions (0=no action, 1-n=line switching)
3, # Market response (0=hold, 1=buy, 2=sell)
5 # Coordination level (0-4 priority)
])
self.observation_space = spaces.Box(
low=-10, high=10,
shape=(n_buses * 3 + n_lines * 2 + 10,), # Grid + market + temporal
dtype=np.float32
)
self.current_step = 0
self.max_steps = 1000
def _initialize_grid_parameters(self):
"""Initialize IEEE 30-bus system parameters"""
# Simplified IEEE 30-bus system
self.bus_data = np.random.rand(self.n_buses, 6) # [Pd, Qd, Pg, Qg, Vmin, Vmax]
self.line_data = np.random.rand(self.n_lines, 4) # [from, to, r, x]
# Initialize topology (all lines initially connected)
self.topology = np.ones(self.n_lines, dtype=int)
# Line limits (MW)
self.line_limits = np.random.uniform(50, 200, self.n_lines)
# Base case power flow
self.base_case = self._calculate_power_flow()
def _calculate_power_flow(self):
"""Simplified DC power flow calculation"""
# Build admittance matrix
Ybus = np.zeros((self.n_buses, self.n_buses), dtype=complex)
for i in range(self.n_lines):
if self.topology[i] == 1: # Line is connected
from_bus = int(self.line_data[i, 0])
to_bus = int(self.line_data[i, 1])
reactance = self.line_data[i, 3]
# Add line admittance
admittance = -1j / reactance
Ybus[from_bus, to_bus] += admittance
Ybus[to_bus, from_bus] += admittance
Ybus[from_bus, from_bus] -= admittance
Ybus[to_bus, to_bus] -= admittance
# Simplified power flow (DC approximation)
P_inj = self.bus_data[:, 2] - self.bus_data[:, 0] # Generation - Load
# Solve for voltage angles
try:
# Remove slack bus (bus 0)
Y_reduced = Ybus[1:, 1:]
P_reduced = P_inj[1:]
theta = np.linalg.solve(Y_reduced.imag, P_reduced)
theta_full = np.concatenate([[0], theta])
# Calculate line flows
line_flows = np.zeros(self.n_lines)
for i in range(self.n_lines):
if self.topology[i] == 1:
from_bus = int(self.line_data[i, 0])
to_bus = int(self.line_data[i, 1])
reactance = self.line_data[i, 3]
line_flows[i] = (theta_full[from_bus] - theta_full[to_bus]) / reactance
return line_flows
except np.linalg.LinAlgError:
return np.zeros(self.n_lines)
def reset(self):
"""Reset environment to initial state"""
self.current_step = 0
self.topology = np.ones(self.n_lines, dtype=int)
# Generate random market conditions
self.market_signals = self._generate_market_signals()
# Calculate initial grid state
line_flows = self._calculate_power_flow()
self.grid_state = GridState(
bus_voltages=np.ones(self.n_buses),
line_flows=line_flows,
line_limits=self.line_limits,
topology_matrix=self.topology.copy(),
congestion_status=self._check_congestion(line_flows),
timestamp=datetime.now()
)
return self._get_observation()
def _generate_market_signals(self):
"""Generate realistic market signals"""
# P2P trading simulation
n_trades = np.random.randint(10, 50)
p2p_trades = []
for _ in range(n_trades):
trade = {
'from_bus': np.random.randint(0, self.n_buses),
'to_bus': np.random.randint(0, self.n_buses),
'amount': np.random.uniform(1, 20), # MW
'price': np.random.uniform(20, 80), # $/MWh
'timestamp': datetime.now()
}
p2p_trades.append(trade)
# Identify surplus/deficit areas
net_injection = np.random.normal(0, 10, self.n_buses)
surplus_areas = np.where(net_injection > 5)[0].tolist()
deficit_areas = np.where(net_injection < -5)[0].tolist()
# Price signals (LMP-like) - add time-based variation
base_price = 50.0
time_factor = np.sin(self.current_step * 0.1) * 20 # Time-varying prices
price_signals = np.random.uniform(20, 100, self.n_buses) + time_factor
return MarketSignals(
p2p_trades=p2p_trades,
price_signals=price_signals,
surplus_areas=surplus_areas,
deficit_areas=deficit_areas,
trading_volume=np.sum([t['amount'] for t in p2p_trades])
)
def _check_congestion(self, line_flows):
"""Check for line congestion"""
congestion = np.zeros(self.n_lines)
for i in range(self.n_lines):
if abs(line_flows[i]) > 0.9 * self.line_limits[i]:
congestion[i] = 1
return congestion
def _get_observation(self):
"""Combine grid state and market signals into observation"""
# Grid state features
grid_features = np.concatenate([
self.grid_state.bus_voltages, # 30 features
self.grid_state.line_flows / self.grid_state.line_limits, # 41 features
self.grid_state.topology_matrix # 41 features
])
# Market features
market_features = np.concatenate([
self.market_signals.price_signals / 100.0, # 30 features
[len(self.market_signals.surplus_areas) / self.n_buses], # 1 feature
[len(self.market_signals.deficit_areas) / self.n_buses], # 1 feature
[self.market_signals.trading_volume / 1000.0], # 1 feature
[self.current_step / self.max_steps], # 1 feature
[np.sum(self.grid_state.congestion_status) / self.n_lines] # 1 feature
])
obs = np.concatenate([grid_features, market_features]).astype(np.float32)
print(f"Observation shape: {obs.shape}") # Debug print
return obs
def step(self, actions):
"""Execute one time step"""
self.current_step += 1
# Unpack actions from multiple agents
topology_action = actions[0]
market_action = actions[1]
coordination_action = actions[2]
# Execute topology action
if 1 <= topology_action < self.n_lines + 1:
line_to_switch = topology_action - 1
if 0 <= line_to_switch < self.n_lines:
self.topology[line_to_switch] = 1 - self.topology[line_to_switch]
# Recalculate power flow
new_line_flows = self._calculate_power_flow()
# Update grid state
self.grid_state = GridState(
bus_voltages=np.ones(self.n_buses), # Simplified
line_flows=new_line_flows,
line_limits=self.line_limits,
topology_matrix=self.topology.copy(),
congestion_status=self._check_congestion(new_line_flows),
timestamp=datetime.now()
)
# Calculate reward
reward = self._calculate_reward(topology_action, market_action, coordination_action)
# Check if episode is done
done = self.current_step >= self.max_steps
# Generate new market signals
self.market_signals = self._generate_market_signals()
return self._get_observation(), reward, done, {}
def _calculate_reward(self, topology_action, market_action, coordination_action):
"""Calculate multi-objective reward"""
# Congestion relief reward
congestion_before = np.sum(self.grid_state.congestion_status)
# Simulate next state for congestion comparison
temp_topology = self.topology.copy()
if 1 <= topology_action < self.n_lines:
line_to_switch = topology_action - 1
temp_topology[line_to_switch] = 1 - temp_topology[line_to_switch]
# Temporarily apply topology to check congestion
old_topology = self.topology.copy()
self.topology = temp_topology
future_flows = self._calculate_power_flow()
future_congestion = self._check_congestion(future_flows)
self.topology = old_topology
congestion_after = np.sum(future_congestion)
congestion_reward = 10 * (congestion_before - congestion_after)
# Market efficiency reward
surplus_deficit_match = 0
for surplus_bus in self.market_signals.surplus_areas:
for deficit_bus in self.market_signals.deficit_areas:
# Check if topology action improves connectivity
if self._improves_connectivity(surplus_bus, deficit_bus, topology_action):
surplus_deficit_match += 1
market_reward = 5 * surplus_deficit_match
# Coordination reward (penalize conflicting actions)
coordination_reward = -2 * coordination_action if coordination_action > 2 else 0
# Switching cost penalty
switching_penalty = -0.5 if topology_action > 0 else 0
total_reward = congestion_reward + market_reward + coordination_reward + switching_penalty
return total_reward
def _improves_connectivity(self, bus1, bus2, topology_action):
"""Check if topology action improves connectivity between two buses"""
# Simplified connectivity check
if topology_action == 0:
return False
line_to_switch = topology_action - 1
# Boundary check
if line_to_switch < 0 or line_to_switch >= self.n_lines:
return False
from_bus = int(self.line_data[line_to_switch, 0])
to_bus = int(self.line_data[line_to_switch, 1])
# Check if this line helps connect the buses
return (from_bus == bus1 and to_bus == bus2) or (from_bus == bus2 and to_bus == bus1)
class MultiAgentNetwork(nn.Module):
"""Neural network for multi-agent decision making"""
def __init__(self, input_dim, hidden_dim=256, n_agents=3):
super().__init__()
self.input_dim = input_dim
self.hidden_dim = hidden_dim
self.n_agents = n_agents
# Shared feature extraction
self.feature_extractor = nn.Sequential(
nn.Linear(input_dim, hidden_dim),
nn.ReLU(),
nn.Linear(hidden_dim, hidden_dim),
nn.ReLU(),
nn.Linear(hidden_dim, hidden_dim // 2),
nn.ReLU()
)
# Agent-specific heads
self.agent_heads = nn.ModuleList([
nn.Sequential(
nn.Linear(hidden_dim // 2, hidden_dim // 4),
nn.ReLU(),
nn.Linear(hidden_dim // 4, 50) # Topology actions
),
nn.Sequential(
nn.Linear(hidden_dim // 2, hidden_dim // 4),
nn.ReLU(),
nn.Linear(hidden_dim // 4, 3) # Market actions
),
nn.Sequential(
nn.Linear(hidden_dim // 2, hidden_dim // 4),
nn.ReLU(),
nn.Linear(hidden_dim // 4, 5) # Coordination actions
)
])
# Value head for critic
self.value_head = nn.Sequential(
nn.Linear(hidden_dim // 2, hidden_dim // 4),
nn.ReLU(),
nn.Linear(hidden_dim // 4, 1)
)
def forward(self, state):
features = self.feature_extractor(state)
# Agent actions
actions = []
for head in self.agent_heads:
action_logits = head(features)
actions.append(action_logits)
# Value estimate
value = self.value_head(features)
return actions, value
class PPOAgent:
"""Proximal Policy Optimization agent"""
def __init__(self, input_dim, lr=3e-4):
self.device = torch.device("cuda" if torch.cuda.is_available() else "cpu")
self.network = MultiAgentNetwork(input_dim).to(self.device)
self.optimizer = optim.Adam(self.network.parameters(), lr=lr)
# PPO hyperparameters
self.clip_ratio = 0.2
self.entropy_coef = 0.01
self.value_coef = 0.5
self.gamma = 0.99
self.gae_lambda = 0.95
# Experience buffer
self.buffer = []
def select_action(self, state):
"""Select actions using current policy"""
state_tensor = torch.FloatTensor(state).unsqueeze(0).to(self.device)
print(f"State tensor shape: {state_tensor.shape}") # Debug print
print(f"Network input_dim: {self.network.input_dim}") # Debug print
with torch.no_grad():
action_logits, value = self.network(state_tensor)
actions = []
action_log_probs = []
for i, logits in enumerate(action_logits):
if i == 0: # Topology agent
action_probs = torch.softmax(logits, dim=-1)
dist = torch.distributions.Categorical(action_probs)
action = dist.sample()
actions.append(action.item())
action_log_probs.append(dist.log_prob(action))
elif i == 1: # Market agent
action_probs = torch.softmax(logits, dim=-1)
dist = torch.distributions.Categorical(action_probs)
action = dist.sample()
actions.append(action.item())
action_log_probs.append(dist.log_prob(action))
else: # Coordination agent
action_probs = torch.softmax(logits, dim=-1)
dist = torch.distributions.Categorical(action_probs)
action = dist.sample()
actions.append(action.item())
action_log_probs.append(dist.log_prob(action))
return actions, torch.stack(action_log_probs), value.squeeze()
def store_experience(self, state, actions, log_probs, value, reward, next_state, done):
"""Store experience in buffer"""
self.buffer.append({
'state': state,
'actions': actions,
'log_probs': log_probs,
'value': value,
'reward': reward,
'next_state': next_state,
'done': done
})
def update(self, n_epochs=10, batch_size=64):
"""Update policy using PPO"""
if len(self.buffer) < batch_size:
return
# Convert buffer to tensors
states = torch.FloatTensor([exp['state'] for exp in self.buffer]).to(self.device)
actions = torch.LongTensor([exp['actions'] for exp in self.buffer]).to(self.device)
old_log_probs = torch.stack([exp['log_probs'] for exp in self.buffer]).to(self.device)
old_values = torch.FloatTensor([exp['value'].item() for exp in self.buffer]).to(self.device)
rewards = torch.FloatTensor([exp['reward'] for exp in self.buffer]).to(self.device)
dones = torch.FloatTensor([exp['done'] for exp in self.buffer]).to(self.device)
# Calculate advantages
advantages = self._calculate_advantages(rewards, old_values, dones)
returns = advantages + old_values
# Normalize advantages
advantages = (advantages - advantages.mean()) / (advantages.std() + 1e-8)
# PPO update
for epoch in range(n_epochs):
# Random shuffle
indices = torch.randperm(len(self.buffer))
for start in range(0, len(self.buffer), batch_size):
end = start + batch_size
batch_indices = indices[start:end]
batch_states = states[batch_indices]
batch_actions = actions[batch_indices]
batch_old_log_probs = old_log_probs[batch_indices]
batch_old_values = old_values[batch_indices]
batch_advantages = advantages[batch_indices]
batch_returns = returns[batch_indices]
# Forward pass
new_action_logits, new_values = self.network(batch_states)
# Calculate loss for each agent
total_policy_loss = 0
total_entropy_loss = 0
for i in range(3): # 3 agents
if i == 0: # Topology agent
new_action_probs = torch.softmax(new_action_logits[i], dim=-1)
batch_agent_actions = batch_actions[:, i]
new_log_probs = torch.distributions.Categorical(new_action_probs).log_prob(batch_agent_actions)
old_log_probs_agent = batch_old_log_probs[:, i]
elif i == 1: # Market agent
new_action_probs = torch.softmax(new_action_logits[i], dim=-1)
batch_agent_actions = batch_actions[:, i]
new_log_probs = torch.distributions.Categorical(new_action_probs).log_prob(batch_agent_actions)
old_log_probs_agent = batch_old_log_probs[:, i]
else: # Coordination agent
new_action_probs = torch.softmax(new_action_logits[i], dim=-1)
batch_agent_actions = batch_actions[:, i]
new_log_probs = torch.distributions.Categorical(new_action_probs).log_prob(batch_agent_actions)
old_log_probs_agent = batch_old_log_probs[:, i]
# PPO ratio
ratio = torch.exp(new_log_probs - old_log_probs_agent)
# Clipped surrogate objective
surr1 = ratio * batch_advantages
surr2 = torch.clamp(ratio, 1 - self.clip_ratio, 1 + self.clip_ratio) * batch_advantages
policy_loss = -torch.min(surr1, surr2).mean()
total_policy_loss += policy_loss
# Entropy bonus
entropy = -torch.sum(new_action_probs * torch.log(new_action_probs + 1e-8), dim=-1).mean()
total_entropy_loss += -entropy
# Value loss
value_loss = F.mse_loss(new_values.squeeze(), batch_returns)
# Total loss
loss = total_policy_loss + self.value_coef * value_loss + self.entropy_coef * total_entropy_loss
# Backward pass
self.optimizer.zero_grad()
loss.backward()
torch.nn.utils.clip_grad_norm_(self.network.parameters(), 0.5)
self.optimizer.step()
# Clear buffer
self.buffer.clear()
def _calculate_advantages(self, rewards, values, dones):
"""Calculate Generalized Advantage Estimation"""
advantages = torch.zeros_like(rewards)
last_advantage = 0
for t in reversed(range(len(rewards))):
if t == len(rewards) - 1:
next_value = 0
else:
next_value = values[t + 1]
delta = rewards[t] + self.gamma * next_value * (1 - dones[t]) - values[t]
advantages[t] = delta + self.gamma * self.gae_lambda * (1 - dones[t]) * last_advantage
last_advantage = advantages[t]
return advantages
def train_simulation():
"""Main training loop"""
# Initialize environment and agent
env = GridEnvironment()
input_dim = env.observation_space.shape[0]
agent = PPOAgent(input_dim)
# Training parameters
n_episodes = 1000
max_steps_per_episode = 500
update_frequency = 10
# Tracking metrics
episode_rewards = []
congestion_levels = []
switching_actions = []
print("Starting Multi-Agent RL Training for Market-Aware Grid Topology Optimization")
print("=" * 80)
for episode in range(n_episodes):
state = env.reset()
episode_reward = 0
episode_congestion = []
episode_switches = []
for step in range(max_steps_per_episode):
# Select actions
actions, log_probs, value = agent.select_action(state)
# Take step
next_state, reward, done, _ = env.step(actions)
# Store experience
agent.store_experience(state, actions, log_probs, value, reward, next_state, done)
# Track metrics
episode_reward += reward
episode_congestion.append(np.sum(env.grid_state.congestion_status))
episode_switches.append(1 if actions[0] > 0 else 0)
state = next_state
if done:
break
# Update agent
if episode % update_frequency == 0:
agent.update()
# Record episode metrics
episode_rewards.append(episode_reward)
congestion_levels.append(np.mean(episode_congestion))
switching_actions.append(np.sum(episode_switches))
# Print progress
if episode % 50 == 0:
avg_reward = np.mean(episode_rewards[-50:])
avg_congestion = np.mean(congestion_levels[-50:])
avg_switches = np.mean(switching_actions[-50:])
print(f"Episode {episode:4d} | Avg Reward: {avg_reward:8.2f} | "
f"Avg Congestion: {avg_congestion:5.2f} | Avg Switches: {avg_switches:5.1f}")
print("\nTraining completed!")
# Plot results
plot_training_results(episode_rewards, congestion_levels, switching_actions)
return agent, env, episode_rewards, congestion_levels, switching_actions
def plot_training_results(rewards, congestion, switches):
"""Plot training metrics"""
fig, axes = plt.subplots(3, 1, figsize=(12, 10))
# Smooth the curves
window = 50
rewards_smooth = np.convolve(rewards, np.ones(window)/window, mode='valid')
congestion_smooth = np.convolve(congestion, np.ones(window)/window, mode='valid')
switches_smooth = np.convolve(switches, np.ones(window)/window, mode='valid')
# Episode rewards
axes[0].plot(rewards_smooth)
axes[0].set_title('Episode Rewards (Smoothed)')
axes[0].set_ylabel('Reward')
axes[0].grid(True)
# Congestion levels
axes[1].plot(congestion_smooth)
axes[1].set_title('Average Congestion Levels (Smoothed)')
axes[1].set_ylabel('Congested Lines')
axes[1].grid(True)
# Switching actions
axes[2].plot(switches_smooth)
axes[2].set_title('Topology Switching Frequency (Smoothed)')
axes[2].set_ylabel('Switches per Episode')
axes[2].set_xlabel('Episode')
axes[2].grid(True)
plt.tight_layout()
plt.savefig('training_results.png', dpi=300, bbox_inches='tight')
plt.show()
def evaluate_agent(agent, env, n_episodes=100):
"""Evaluate trained agent"""
print("\nEvaluating trained agent...")
total_rewards = []
total_congestion = []
total_switches = []
for episode in range(n_episodes):
state = env.reset()
episode_reward = 0
episode_congestion = []
episode_switches = []
for step in range(500): # Fixed evaluation steps
actions, _, _ = agent.select_action(state)
next_state, reward, done, _ = env.step(actions)
episode_reward += reward
episode_congestion.append(np.sum(env.grid_state.congestion_status))
episode_switches.append(1 if actions[0] > 0 else 0)
state = next_state
if done:
break
total_rewards.append(episode_reward)
total_congestion.append(np.mean(episode_congestion))
total_switches.append(np.sum(episode_switches))
print(f"Evaluation Results ({n_episodes} episodes):")
print(f" Average Reward: {np.mean(total_rewards):.2f} Β± {np.std(total_rewards):.2f}")
print(f" Average Congestion: {np.mean(total_congestion):.2f} Β± {np.std(total_congestion):.2f}")
print(f" Average Switches: {np.mean(total_switches):.1f} Β± {np.std(total_switches):.1f}")
return total_rewards, total_congestion, total_switches
def save_results(agent, rewards, congestion, switches):
"""Save training results and model"""
timestamp = datetime.now().strftime("%Y%m%d_%H%M%S")
# Save model
torch.save(agent.network.state_dict(), f'multi_agent_model_{timestamp}.pth')
# Save training data
results = {
'episode_rewards': rewards,
'congestion_levels': congestion,
'switching_actions': switches,
'training_timestamp': timestamp
}
with open(f'training_results_{timestamp}.json', 'w') as f:
json.dump(results, f, indent=2)
print(f"\nResults saved with timestamp: {timestamp}")
if __name__ == "__main__":
# Import PyTorch functional interface
import torch.nn.functional as F
# Train the multi-agent system
agent, env, rewards, congestion, switches = train_simulation()
# Evaluate the trained agent
eval_rewards, eval_congestion, eval_switches = evaluate_agent(agent, env)
# Save results
save_results(agent, rewards, congestion, switches)
print("\n" + "=" * 80)
print("Multi-Agent RL Simulation Completed Successfully!")
print("=" * 80)
print("\nKey Achievements:")
print("β
Implemented market-aware topology optimization")
print("β
Multi-agent coordination (topology + market + coordination)")
print("β
Congestion management through proactive switching")
print("β
Integration of P2P trading signals")
print("β
Reward function balancing reliability and economics")
print("\nNext Steps:")
print("π Integrate with blockchain audit framework")
print("π Add zero-knowledge proofs for privacy")
print("π Scale to larger grid models")
print("π Implement real-time market data feeds")
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