transformer-warmstart-unit-commitment

# Transformer Warm-Start Framework for Unit Commitment Methodology for accelerating Unit Commitment (UC) optimization using transformer-based deep learning with MILP warm-starting, based on arXiv:2604.21891. ## Problem Context ### Unit Commitment (UC) Problem **Objective**: Schedule generator on/off states to meet electricity demand at minimum cost. **Mathematical Formulation**: ``` Minimize: Σ_t Σ_g (C_g^on u_g(t) + C_g^var p_g(t)) Subject to: Power balance: Σ_g p_g(t) = D(t) ∀t Generator limits: u_g(t) P_g^min ≤ p_g(t) ≤ u_g(t) P_g^max ∀g,t Ramp limits: |p_g(t) - p_g(t-1)| ≤ R_g ∀g,t Min up/down: u_g(t) satisfies min up/down time constraints Reserve requirements: Σ_g u_g(t) P_g^max ≥ D(t) + R(t) ∀t ``` **Complexity**: NP-hard, high-dimensional, tightly constrained. ### Challenges - **Scale**: 72+ hour horizons, hundreds of generators - **Renewables**: Variable wind/solar integration - **Storage**: Long-duration energy storage coordination - **Time limits**: Operators need solutions in minutes ## Proposed Solution: Multi-Stage Pipeline ### Architecture Overview ``` ┌─────────────────┐ ┌──────────────────┐ ┌─────────────────┐ ┌─────────────┐ │ Transformer │ → │ Post-Processing │ → │ Warm-Start │ → │ MILP │ │ Predictor │ │ (Feasibility) │ │ + Fixation │ │ Solver │ └─────────────────┘ └──────────────────┘ └─────────────────┘ └─────────────┘ (Stage 1) (Stage 2) (Stage 3) (Stage 4) ``` ## Stage 1: Transformer-Based Prediction ### Model Architecture ```python class UCTransformer(nn.Module): """ Transformer for generator commitment prediction Input: Demand forecast, renewable forecast, generator parameters Output: Binary commitment schedule u_g(t) ∈ {0,1} """ def __init__(self, n_generators, horizon, d_model=256, n_heads=8): super().__init__() # Encoder: Process input features self.input_encoder = nn.Linear(input_dim, d_model) # Temporal attention across horizon self.temporal_attn = nn.TransformerEncoder( nn.TransformerEncoderLayer(d_model, n_heads), num_layers=6 ) # Generator-specific attention self.generator_attn = nn.MultiheadAttention(d_model, n_heads) # Decoder: Predict commitments self.commitment_head = nn.Sequential( nn.Linear(d_model, d_model // 2), nn.ReLU(), nn.Linear(d_model // 2, 1), nn.Sigmoid() # Probability of commitment ) def forward(self, demand, renewable, gen_params): # Encode inputs x = self.input_encoder(torch.cat([demand, renewable, gen_params], dim=-1)) # Temporal attention x = self.temporal_attn(x) # Predict commitments probs = self.commitment_head(x) return probs # Shape: (batch, n_generators, horizon) ``` ### Training ```python def train_uc_transformer(model, train_loader, epochs=100): """ Train transformer on historical UC solutions Loss: Binary cross-entropy with optimal solutions as labels """ optimizer = Adam(model.parameters(), lr=1e-4) for epoch in range(epochs): for batch in train_loader: demand, renewable, gen_params, optimal_commit = batch # Forward pass pred_probs = model(demand, renewable, gen_params) # Binary cross-entropy loss loss = F.binary_cross_entropy(pred_probs, optimal_commit) # Backward pass optimizer.zero_grad() loss.backward() optimizer.step() ``` ## Stage 2: Deterministic Post-Processing ### Problem: Raw Predictions are Infeasible ML predictions often violate: - Minimum up/down times - Physical constraints - Reserve requirements ### Post-Processing Heuristics ```python def post_process_commitments(raw_predictions, gen_params): """ Enforce physical feasibility constraints Returns: Feasible commitment schedule """ schedule = raw_predictions.clone() n_gen, horizon = schedule.shape # Enforce minimum up/down times for g in range(n_gen): min_up = gen_params[g]['min_up_time'] min_down = gen_params[g]['min_down_time'] schedule[g] = enforce_min_up_down(schedule[g], min_up, min_down) # Enforce power balance (greedy repair) for t in range(horizon): shortage = calculate_shortage(schedule[:, t], demand[t]) if shortage > 0: # Commit additional generators schedule[:, t] = commit_additional(schedule[:, t], shortage) # Minimize excess capacity for t in range(horizon): excess = calculate_excess(schedule[:, t], demand[t]) if excess > 0: # Decommit generators if possible schedule[:, t] = decommit_excess(schedule[:, t], excess) return schedule ``` ### Minimum Up/Down Time Enforcement ```python def enforce_min_up_down(commitment, min_up, min_down): """ Ensure commitment satisfies minimum up/down constraints Algorithm: 1. Identify violations 2. Extend commitments forward (min_up) or backward (min_down) 3. Resolve conflicts """ result = commitment.copy() # Track state transitions transitions = np.diff(result, prepend=0, append=0) # Fix short up periods for i, t in enumerate(transitions): if t == 1: # Startup # Check if runs long enough if i + min_up < len(result) and np.all(result[i:i+min_up] == 0): # Extend startup result[i:i+min_up] = 1 # Fix short down periods (similar logic) return result ``` ## Stage 3: Confidence-Based Variable Fixation ### Concept Fix high-confidence predictions to reduce MILP search space. ```python def confidence_based_fixation(predictions, confidence_threshold=0.9): """ Fix variables with high prediction confidence Returns: fixed_vars: Dictionary of fixed variable values free_vars: Set of variables to be optimized """ fixed_vars = {} free_vars = set() for g in range(n_generators): for t in range(horizon): confidence = max(prediction[g, t], 1 - prediction[g, t]) if confidence > confidence_threshold: # Fix this variable fixed_vars[(g, t)] = round(prediction[g, t]) else: # Keep variable free for optimization free_vars.add((g, t)) return fixed_vars, free_vars ``` ### Search Space Reduction | Threshold | Variables Fixed | Search Space Reduction | |-----------|-----------------|----------------------| | 0.95 | ~80% | 10⁵× | | 0.90 | ~70% | 10³× | | 0.85 | ~60% | 10²× | ### Warm-Start Strategy ```python def warm_start_milp(problem, fixed_vars, post_processed_schedule): """ Initialize MILP solver with ML predictions 1. Fix high-confidence variables 2. Use post-processed schedule as initial solution 3. Solve reduced MILP """ # Create modified problem with fixed variables reduced_problem = fix_variables(problem, fixed_vars) # Set warm-start solution solver.set_initial_solution(post_processed_schedule) # Solve solution = solver.solve(reduced_problem) return solution ``` ## Stage 4: MILP Solver Integration ### Complete Pipeline ```python def uc_ml_warmstart_pipeline(demand, renewable, gen_params, model, solver): """ Complete multi-stage UC pipeline Returns: Optimal commitment schedule """ # Stage 1: Transformer prediction raw_predictions = model(demand, renewable, gen_params) # Stage 2: Post-processing for feasibility feasible_schedule = post_process_commitments(raw_predictions, gen_params) # Stage 3: Confidence-based fixation fixed_vars, free_vars = confidence_based_fixation(raw_predictions, threshold=0.9) # Stage 4: Warm-start MILP optimal_schedule = warm_start_milp( problem=build_uc_problem(demand, renewable, gen_params), fixed_vars=fixed_vars, post_processed_schedule=feasible_schedule ) return optimal_schedule ``` ## Performance Results ### Key Metrics | Metric | Traditional MILP | ML Warm-Start | Improvement | |--------|-----------------|---------------|-------------| | Feasibility | 100% | 100% | - | | Computation Time | 300s | 45s | 6.7× faster | | Optimality Gap | 0% | <1% | Near-optimal | | Cost (20% cases) | Baseline | -5% | Better solutions | ### Validation - **Test System**: Single-bus system with 10-50 generators - **Horizon**: 72 hours - **Renewable Integration**: 30% penetration - **Feasibility**: 100% guarantee via post-processing ## Implementation Considerations ### Data Requirements ```python # Training data generation # For each instance: training_data = { 'demand_forecast': [...], # 72-hour demand 'renewable_forecast': [...], # Wind/solar forecast 'generator_params': [...], # Costs, limits, ramp rates 'optimal_commitment': [...] # From exact solver (label) } ``` ### Model Variants 1. **Single-Bus Model** (Current): Aggregated demand/supply 2. **Multi-Bus Model**: Network constraints, transmission limits 3. **Stochastic UC**: Scenario-based uncertainty 4. **Multi-Period**: Rolling horizon implementation ### Deployment ```python class UCOptimizationService: """ Production service for UC optimization """ def __init__(self, model_path, solver_config): self.model = load_model(model_path) self.solver = configure_solver(solver_config) def optimize(self, demand_forecast, renewable_forecast, gen_params): """ Real-time UC optimization Target: < 5 minutes for 72-hour horizon """ start_time = time.time() # Run pipeline schedule = uc_ml_warmstart_pipeline( demand_forecast, renewable_forecast, gen_params, self.model, self.solver ) elapsed = time.time() - start_time logger.info(f"UC solved in {elapsed:.1f}s") return schedule ``` ## Extensions and Future Work ### Multi-Objective Optimization ```python # Beyond cost minimization objectives = { 'cost': minimize_operating_cost(), 'emissions': minimize_emissions(), 'flexibility': maximize_ramping_capability() } # Pareto frontier exploration solutions = multi_objective_uc(objectives, weights) ``` ### Online Learning ```python # Adapt model to new grid conditions def online_update(model, new_data): """ Fine-tune model with recent operational data """ model.train(new_data, epochs=5, lr=1e-5) ``` ## References - **Paper**: arXiv:2604.21891 [eess.SY, cs.AI] - **Authors**: Za'ter, Van Boven, Hodge, Baker - **Date**: April 2026 - **Application**: Power system optimization, renewable integration ## Related Skills - `power-systems-optimization` - `milp-solving` - `transformer-architectures` - `warm-start-optimization`