''' Negative Locational Marginal Prices (LMPs) Example - PyConvexity Version This example demonstrates how negative locational marginal prices (LMPs) can occur in electricity systems due to line congestion. Using a simple 3-bus linearised DC power flow model, we reproduce the phenomenon where cheap generation is trapped behind a congested line, causing LMPs to drop below zero as the system redistributes power flows to meet demand. This is the PyConvexity version of the PyPSA example. PyConvexity stores the model in a SQLite database and then builds/solves PyPSA networks from it. Key differences from PyPSA: 1. Model is stored in a SQLite database instead of in-memory PyPSA network 2. Components (buses, generators, loads, lines) are created using create_component() 3. Attributes are set using set_static_attribute() and set_timeseries_attribute() 4. Network time periods must be explicitly created 5. Carriers must be created before components 6. Solving uses solve_network() which builds a PyPSA network from the database Source (original PyPSA): Based on Kyri Baker's "3bus_LMP" example ''' import pyconvexity as px import numpy as np from datetime import datetime, timedelta import os # Database path - save in examples/dB directory db_path = os.path.join(os.path.dirname(__file__), "dB", "002_three_bus_lmp_example.db") os.makedirs(os.path.dirname(db_path), exist_ok=True) # Create database with schema px.create_database_with_schema(db_path) with px.database_context(db_path) as conn: # Create network with 24 hourly time periods # Time periods are automatically created from start_time, end_time, and time_resolution start_time = datetime.now().replace(hour=0, minute=0, second=0, microsecond=0) end_time = start_time + timedelta(hours=23) network_req = px.CreateNetworkRequest( name="Three Bus LMP Example", description="3-bus system demonstrating negative LMPs due to line congestion", start_time=start_time.strftime("%Y-%m-%d %H:%M:%S"), end_time=end_time.strftime("%Y-%m-%d %H:%M:%S"), time_resolution="PT1H", # ISO 8601 duration format for hourly ) px.create_network(conn, network_req) # Create carriers carrier_id = px.create_carrier( conn, name="AC", co2_emissions=0.0, color="#1f77b4", nice_name="Electricity", ) # Texas coordinates for the three buses # Using approximate locations in Texas to form a triangular layout bus_coords = { "Bus1": {"latitude": 30.3, "longitude": -97.7}, # Austin area (top-left) "Bus2": {"latitude": 30.3, "longitude": -95.4}, # Houston area (top-right) "Bus3": {"latitude": 29.4, "longitude": -98.5}, # San Antonio area (bottom, load) } # Create buses with coordinates bus_ids = {} for bus_name, coords in bus_coords.items(): bus_id = px.create_component( conn, component_type="BUS", name=bus_name, carrier_id=carrier_id, latitude=coords["latitude"], longitude=coords["longitude"], ) bus_ids[bus_name] = bus_id # Set bus voltage px.set_static_attribute(conn, bus_id, "v_nom", px.StaticValue(400.0)) # Create generators # Gen1 at Bus1: 100 MW, marginal cost 10 €/MWh (cheap) gen1_id = px.create_component( conn, component_type="GENERATOR", name="Gen1", bus_id=bus_ids["Bus1"], carrier_id=carrier_id, latitude=bus_coords["Bus1"]["latitude"] + 0.05, # Slightly offset from bus longitude=bus_coords["Bus1"]["longitude"] + 0.05, ) px.set_static_attribute(conn, gen1_id, "p_nom", px.StaticValue(100.0)) px.set_static_attribute(conn, gen1_id, "marginal_cost", px.StaticValue(10.0)) # Gen2 at Bus2: 100 MW, marginal cost 20 €/MWh (medium) gen2_id = px.create_component( conn, component_type="GENERATOR", name="Gen2", bus_id=bus_ids["Bus2"], carrier_id=carrier_id, latitude=bus_coords["Bus2"]["latitude"] + 0.05, longitude=bus_coords["Bus2"]["longitude"] + 0.05, ) px.set_static_attribute(conn, gen2_id, "p_nom", px.StaticValue(100.0)) px.set_static_attribute(conn, gen2_id, "marginal_cost", px.StaticValue(20.0)) # Gen3 at Bus3: 100 MW, marginal cost 100 €/MWh (expensive) gen3_id = px.create_component( conn, component_type="GENERATOR", name="Gen3", bus_id=bus_ids["Bus3"], carrier_id=carrier_id, latitude=bus_coords["Bus3"]["latitude"] + 0.05, longitude=bus_coords["Bus3"]["longitude"] + 0.05, ) px.set_static_attribute(conn, gen3_id, "p_nom", px.StaticValue(100.0)) px.set_static_attribute(conn, gen3_id, "marginal_cost", px.StaticValue(100.0)) # Create load at Bus3 with 24 hours of randomly varying load # Base load is 100 MW with ±20% variation base_load = 100.0 load_variation = base_load * (1 + np.random.uniform(-0.2, 0.2, size=24)) load_id = px.create_component( conn, component_type="LOAD", name="Load3", bus_id=bus_ids["Bus3"], carrier_id=carrier_id, latitude=bus_coords["Bus3"]["latitude"] + 0.1, # Offset from bus longitude=bus_coords["Bus3"]["longitude"] + 0.1, ) # Set timeseries attribute for load px.set_timeseries_attribute(conn, load_id, "p_set", load_variation.tolist()) # Create lines (transmission lines) # Line12: Bus1 to Bus2, x=1, s_nom=100 MW line12_id = px.create_component( conn, component_type="LINE", name="Line12", bus0_id=bus_ids["Bus1"], bus1_id=bus_ids["Bus2"], carrier_id=carrier_id, # Line coordinates at midpoint latitude=(bus_coords["Bus1"]["latitude"] + bus_coords["Bus2"]["latitude"]) / 2.0, longitude=(bus_coords["Bus1"]["longitude"] + bus_coords["Bus2"]["longitude"]) / 2.0, ) px.set_static_attribute(conn, line12_id, "x", px.StaticValue(1.0)) px.set_static_attribute(conn, line12_id, "s_nom", px.StaticValue(100.0)) # Line23: Bus2 to Bus3, x=1, s_nom=100 MW line23_id = px.create_component( conn, component_type="LINE", name="Line23", bus0_id=bus_ids["Bus2"], bus1_id=bus_ids["Bus3"], carrier_id=carrier_id, # Line coordinates at midpoint latitude=(bus_coords["Bus2"]["latitude"] + bus_coords["Bus3"]["latitude"]) / 2.0, longitude=(bus_coords["Bus2"]["longitude"] + bus_coords["Bus3"]["longitude"]) / 2.0, ) px.set_static_attribute(conn, line23_id, "x", px.StaticValue(1.0)) px.set_static_attribute(conn, line23_id, "s_nom", px.StaticValue(100.0)) # Line13: Bus1 to Bus3, x=1, s_nom=10 MW (BOTTLENECK - this is the key constraint!) line13_id = px.create_component( conn, component_type="LINE", name="Line13", bus0_id=bus_ids["Bus1"], bus1_id=bus_ids["Bus3"], carrier_id=carrier_id, # Line coordinates at midpoint latitude=(bus_coords["Bus1"]["latitude"] + bus_coords["Bus3"]["latitude"]) / 2.0, longitude=(bus_coords["Bus1"]["longitude"] + bus_coords["Bus3"]["longitude"]) / 2.0, ) px.set_static_attribute(conn, line13_id, "x", px.StaticValue(1.0)) px.set_static_attribute(conn, line13_id, "s_nom", px.StaticValue(10.0)) # Bottleneck! # Set up dashboard configuration from pyconvexity.dashboard import set_dashboard_config, DashboardConfig, auto_layout charts = [{ "id": "lmp-main", "title": "Locational Marginal Prices", "visible": True, "view": { "timeseries": { "component": "Bus", "attribute": "marginal_price", "group_by": None } } }] config = DashboardConfig(charts=charts, layout=auto_layout(charts)) set_dashboard_config(conn, config) conn.commit() print("✅ Model created successfully!") print(f" 📍 Location: Texas, USA") print(f" 🚌 Buses: 3 (Bus1: Austin area, Bus2: Houston area, Bus3: San Antonio area)") print(f" ⚡ Generators: 3 (Gen1: 10 €/MWh, Gen2: 20 €/MWh, Gen3: 100 €/MWh)") print(f" 🏠 Load: 1 at Bus3 (100 MW base, ±20% variation over 24 hours)") print(f" 🔌 Lines: 3 (Line13 is bottlenecked at 10 MW)") print(f" ⏰ Time periods: 24 hours") # Solve the network print("\n🔧 Solving network...") result = px.solve_network( db_path=db_path, solver_name="highs", progress_callback=lambda progress, msg: print(f" {progress}%: {msg}"), ) print(f"\n✅ Optimization complete!") print(f" Success: {result.get('success', False)}") print(f" Objective: {result.get('objective_value', 'N/A')}") print(f"\n💡 Note: This example demonstrates negative LMPs when cheap generation") print(f" (Gen1 at Bus1) is trapped behind the congested Line13 (10 MW limit).") # Export to Excel print("\n📊 Exporting to Excel...") from pyconvexity.io.excel_exporter import ExcelModelExporter xlsx_path = db_path.replace('.db', '.xlsx') exporter = ExcelModelExporter() export_result = exporter.export_model_to_excel( db_path=db_path, output_path=xlsx_path, progress_callback=lambda progress, msg: print(f" {progress}%: {msg}") if progress else None, ) print(f"✅ Excel export complete: {xlsx_path}")