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Multi-System Interconnection

Prerequisites

Scenario

Two island systems connected by a submarine cable:

  • System A (Main Island): 3 nodes, ~500 MW peak demand, diverse generation mix (diesel, solar, wind). Relatively developed grid with transmission between nodes.
  • System B (Small Island): 1 node, ~50 MW peak demand, limited generation (diesel + small solar). High electricity costs due to small scale and fuel dependency.

The submarine cable allows power transfer between Node 2 of the Main Island and Node 0 of the Small Island.

Step 1: Complete Configuration

Create multi_system.yaml:

simulation_mode: development
date_start: "01/01/2025 00:00"

temporal:
  resolution_hours: 1
  use_rolling_horizon: true
  rolling_horizon_hours: 48
  overlap_hours: 6

solver:
  name: highs
  threads: 4
  time_limit: 3600
  gap: 0.01
  verbose: false

n1_security:
  enabled: false

master_problem:
  stochastic: false
  representative_days_per_year: 5
  min_day_separation: 7

enable_primary_energy: false

# --- Meta-Network: defines which systems exist and how they connect ---
meta_network:
  systems:
    - main_island
    - small_island
  dynamic_transfer_pricing: false

  systems_links:
    submarine_cable:
      systems: [main_island, small_island]
      from_nodes: [2]           # Node 2 of main_island
      to_nodes: [0]             # Node 0 of small_island
      capacity: [30.0]          # MW existing submarine cable capacity
      invest_cost: [800000.0]   # $/MW for cable expansion
      invest_max: [100.0]       # MW maximum cable expansion
      losses: [0.03]            # 3% transmission losses

# --- System A: Main Island (3 nodes) ---
systems:
  main_island:
    name: main_island
    demand_path: main_island_demand.xlsx
    demand_scale: 1.0
    demand_growth: 0.02

    nodes:
      adjacency_matrix:
        - [0, 100, 50]
        - [100, 0, 80]
        - [50, 80, 0]
      coordinates:
        - [-76.80, 18.00]     # Node 0: Capital
        - [-77.50, 18.20]     # Node 1: West Coast
        - [-76.20, 17.80]     # Node 2: East (cable landing)
      names: ["Capital", "West Coast", "East"]
      reserve_static: [5.0, 2.0, 2.0]
      reserve_dynamic: [3.0, 1.0, 1.0]
      reserve_duration: [2, 2, 2]
      losses: [0.02, 0.02, 0.02]

    generators:
      solar_pv:
        name: Solar PV
        type: Renewable
        fuel: Solar
        rated_power: [30.0, 20.0, 40.0]
        min_power: [0.0, 0.0, 0.0]
        invest_cost: [750000, 750000, 700000]
        invest_max_power: [200, 150, 250]
        fuel_cost: [0.0, 0.0, 0.0]
        fixed_cost: [5.0, 5.0, 5.0]
        maintenance_cost: [2.0, 2.0, 2.0]
        start_up_cost: [0.0, 0.0, 0.0]
        decommissioning_cost: [0, 0, 0]
        ramp_up: [1.0, 1.0, 1.0]
        ramp_down: [1.0, 1.0, 1.0]
        min_up_time: [0, 0, 0]
        min_down_time: [0, 0, 0]
        eff_at_rated: [1.0, 1.0, 1.0]
        eff_at_min: [1.0, 1.0, 1.0]
        life_time: [25, 25, 25]
        initial_age: [3, 2, 4]
        degradation_rate: [0.005, 0.005, 0.005]
        inertia: [0.0, 0.0, 0.0]
        Availability: solar_availability.csv

      wind:
        name: Wind
        type: Renewable
        fuel: Wind
        rated_power: [0.0, 40.0, 0.0]
        min_power: [0.0, 0.0, 0.0]
        invest_cost: [1200000, 1100000, 1300000]
        invest_max_power: [100, 300, 50]
        fuel_cost: [0.0, 0.0, 0.0]
        fixed_cost: [8.0, 8.0, 8.0]
        maintenance_cost: [5.0, 5.0, 5.0]
        start_up_cost: [0.0, 0.0, 0.0]
        decommissioning_cost: [0, 0, 0]
        ramp_up: [1.0, 1.0, 1.0]
        ramp_down: [1.0, 1.0, 1.0]
        min_up_time: [0, 0, 0]
        min_down_time: [0, 0, 0]
        eff_at_rated: [1.0, 1.0, 1.0]
        eff_at_min: [1.0, 1.0, 1.0]
        life_time: [20, 20, 20]
        initial_age: [0, 0, 0]
        degradation_rate: [0.005, 0.005, 0.005]
        inertia: [0.0, 0.0, 0.0]
        Availability: wind_availability.csv

      diesel:
        name: Diesel
        type: Non-renewable
        fuel: Diesel
        rated_power: [200.0, 80.0, 50.0]
        min_power: [0.3, 0.3, 0.3]
        invest_cost: [500000, 500000, 500000]
        invest_max_power: [0.0, 0.0, 0.0]
        fuel_cost: [80.0, 80.0, 80.0]
        fixed_cost: [3.0, 3.0, 3.0]
        maintenance_cost: [5.0, 5.0, 5.0]
        start_up_cost: [5000, 5000, 5000]
        decommissioning_cost: [100000, 100000, 100000]
        ramp_up: [0.5, 0.5, 0.5]
        ramp_down: [0.5, 0.5, 0.5]
        min_up_time: [4, 4, 4]
        min_down_time: [2, 2, 2]
        eff_at_rated: [0.40, 0.40, 0.40]
        eff_at_min: [0.30, 0.30, 0.30]
        life_time: [30, 30, 30]
        initial_age: [12, 8, 10]
        degradation_rate: [0.01, 0.01, 0.01]
        inertia: [5.0, 5.0, 5.0]

    batteries:
      li_ion:
        name: Li-Ion Battery
        capacity: [0.0, 0.0, 0.0]
        max_charge_power: [0.0, 0.0, 0.0]
        max_discharge_power: [0.0, 0.0, 0.0]
        charge_efficiency: [0.95, 0.95, 0.95]
        discharge_efficiency: [0.95, 0.95, 0.95]
        soc_min: [0.10, 0.10, 0.10]
        soc_max: [0.95, 0.95, 0.95]
        soc_initial: [0.50, 0.50, 0.50]
        self_discharge: [0.0001, 0.0001, 0.0001]
        invest_cost_power: [200000, 200000, 200000]
        invest_cost_capacity: [150000, 150000, 150000]
        invest_max_power: [100, 100, 100]
        invest_max_capacity: [400, 400, 400]
        min_duration_hours: 2.0
        max_duration_hours: 6.0
        life_time: [15, 15, 15]
        maintenance_cost: [1.0, 1.0, 1.0]
        spillage: false
        degradation_rate: [0.02, 0.02, 0.02]

    penalties:
      LOSS_DEMAND_TRHESHOLD: 10000.0
      curtailment_penalty: 50.0
      loss_reserve_static_penalty: 500.0
      fre_penalty: 600.0

    co2_budget:
      annual_limit: 800000.0

    target_re_penetration: 0.80
    initial_re_penetration: 0.0
    max_curtailment_ratio: 0.05
    discount_rate: 0.08
    MAX_ANNUAL_SYSTEM_COST: 500000000.0

  # --- System B: Small Island (1 node) ---
  small_island:
    name: small_island
    demand_path: small_island_demand.xlsx
    demand_scale: 1.0
    demand_growth: 0.03      # Higher growth on small island

    nodes:
      adjacency_matrix: [[0]]
      coordinates: [[-75.50, 17.50]]
      names: ["Small Island"]

    generators:
      solar_pv:
        name: Solar PV
        type: Renewable
        fuel: Solar
        rated_power: [10.0]
        min_power: [0.0]
        invest_cost: [800000.0]
        invest_max_power: [80.0]
        fuel_cost: [0.0]
        fixed_cost: [6.0]
        maintenance_cost: [3.0]
        start_up_cost: [0.0]
        decommissioning_cost: [0]
        ramp_up: [1.0]
        ramp_down: [1.0]
        min_up_time: [0]
        min_down_time: [0]
        eff_at_rated: [1.0]
        eff_at_min: [1.0]
        life_time: [25]
        initial_age: [2]
        degradation_rate: [0.005]
        inertia: [0.0]
        Availability: solar_availability.csv

      diesel:
        name: Diesel
        type: Non-renewable
        fuel: Diesel
        rated_power: [40.0]
        min_power: [0.3]
        invest_cost: [500000.0]
        invest_max_power: [0.0]
        fuel_cost: [120.0]        # Higher fuel cost (shipping premium)
        fixed_cost: [5.0]
        maintenance_cost: [8.0]
        start_up_cost: [3000.0]
        decommissioning_cost: [80000]
        ramp_up: [0.5]
        ramp_down: [0.5]
        min_up_time: [3]
        min_down_time: [2]
        eff_at_rated: [0.35]
        eff_at_min: [0.25]
        life_time: [25]
        initial_age: [18]
        degradation_rate: [0.015]
        inertia: [4.0]

    batteries:
      li_ion:
        name: Li-Ion Battery
        capacity: [0.0]
        max_charge_power: [0.0]
        max_discharge_power: [0.0]
        charge_efficiency: [0.93]
        discharge_efficiency: [0.93]
        soc_min: [0.15]
        soc_max: [0.90]
        soc_initial: [0.50]
        self_discharge: [0.0002]
        invest_cost_power: [250000.0]
        invest_cost_capacity: [180000.0]
        invest_max_power: [50.0]
        invest_max_capacity: [200.0]
        min_duration_hours: 2.0
        max_duration_hours: 4.0
        life_time: [12]
        maintenance_cost: [2.0]
        spillage: false
        degradation_rate: [0.025]

    penalties:
      LOSS_DEMAND_TRHESHOLD: 10000.0
      curtailment_penalty: 50.0
      loss_reserve_static_penalty: 500.0
      fre_penalty: 600.0

    co2_budget:
      annual_limit: 100000.0

    target_re_penetration: 0.70
    initial_re_penetration: 0.0
    max_curtailment_ratio: 0.08
    discount_rate: 0.10         # Higher risk premium for small island
    MAX_ANNUAL_SYSTEM_COST: 100000000.0

Key Design Decisions

Why separate systems instead of one big multi-node system?

Multi-system modeling is appropriate when:

  • The systems have separate regulatory environments, budgets, or RE targets
  • They are connected by a limited, discrete interconnector (submarine cable)
  • Each system has its own demand file, discount rate, and planning constraints
  • You want to analyze the value of interconnection vs. autarky

Inter-system link parameters:

Parameter Value Meaning
capacity 30 MW Existing submarine cable capacity
invest_cost $800,000/MW High cost due to submarine installation
invest_max 100 MW Maximum cable expansion
losses 3% Transmission losses over the submarine cable

Step 2: Prepare Input Data

Main Island Demand

Create main_island_demand.xlsx with 8,760 rows and 3 columns (one per node). Total peak demand should be approximately 500 MW distributed across the three nodes.

Small Island Demand

Create small_island_demand.xlsx with 8,760 rows and 1 column. Peak demand is approximately 50 MW.

Shared Availability Files

Both systems can use the same solar_availability.csv and wind_availability.csv if they are geographically close enough to share similar weather patterns.

Step 3: Run the Simulation

esfex validate -c multi_system.yaml
esfex run -c multi_system.yaml --years 15 -v

The multi-system simulation takes longer because the Master Problem creates investment variables for both systems plus the inter-system link. Expect 45-120 minutes.

Step 4: How Multi-System Optimization Works

The optimization proceeds in three layers:

  1. Master Problem: The multi-system master problem (create_multi_system_master_problem()) creates investment variables for each system and adds inter-system link constraints. It sees all years simultaneously and decides:
  2. How much generation/storage to invest in each system
  3. Whether to expand the submarine cable

  4. The optimal timing for each investment

  5. Investment coordination: The optimizer trades off between:

  6. Building local generation on the Small Island (expensive: higher fuel costs, smaller scale)
  7. Building excess RE on the Main Island and exporting via the cable (requires cable expansion)

  8. A hybrid approach that balances local resilience with export economics

  9. Operational dispatch: Each system is dispatched independently for each year, with inter-system transfers modeled as fixed import/export schedules determined by the Master Problem.

Step 5: Results Analysis

Per-System Investments

import h5py
import numpy as np

with h5py.File("results/output.h5", "r") as f:
    for sys_name in ["main_island", "small_island"]:
        print(f"\n=== {sys_name.upper()} ===")
        if f"summary_results/{sys_name}/investments" in f:
            inv = f[f"summary_results/{sys_name}/investments"][:]
            print("Investments (MW per year):")
            print(inv)

        if f"summary_results/{sys_name}/objectives" in f:
            obj = f[f"summary_results/{sys_name}/objectives"][:]
            print(f"Total NPV: ${obj.sum():,.0f}")

Inter-System Transfer Analysis

with h5py.File("results/output.h5", "r") as f:
    if "summary_results/inter_system_transfer" in f:
        transfer = f["summary_results/inter_system_transfer"][:]
        print(f"\nSubmarine cable transfer profile:")
        for yr, val in enumerate(transfer, 1):
            direction = "Main -> Small" if val >= 0 else "Small -> Main"
            print(f"  Year {yr}: {abs(val):.1f} MW avg ({direction})")

Cable Expansion Decisions

with h5py.File("results/output.h5", "r") as f:
    if "summary_results/inter_system_investment" in f:
        cable_inv = f["summary_results/inter_system_investment"][:]
        print(f"\nCable expansion: {cable_inv.sum():.1f} MW total")
        for yr, val in enumerate(cable_inv, 1):
            if val > 0.1:
                print(f"  Year {yr}: +{val:.1f} MW")

Comparative Cost Analysis

with h5py.File("results/output.h5", "r") as f:
    main_obj = f["summary_results/main_island/objectives"][:].sum()
    small_obj = f["summary_results/small_island/objectives"][:].sum()
    cable_cost = 800000 * cable_inv.sum()  # Approximate cable investment cost

    print(f"\nTotal system cost breakdown:")
    print(f"  Main Island NPV:  ${main_obj:,.0f}")
    print(f"  Small Island NPV: ${small_obj:,.0f}")
    print(f"  Cable investment:  ${cable_cost:,.0f}")
    print(f"  Combined total:    ${main_obj + small_obj + cable_cost:,.0f}")

Value of Interconnection

To quantify cable value, compare with an isolated scenario (set capacity: [0.0] and invest_max: [0.0] in the link).

# After running both scenarios:
# isolated_results/output.h5 (no cable) vs results/output.h5 (with cable)
with h5py.File("isolated_results/output.h5", "r") as f_iso:
    with h5py.File("results/output.h5", "r") as f_linked:
        iso_cost = (f_iso["summary_results/main_island/objectives"][:].sum() +
                    f_iso["summary_results/small_island/objectives"][:].sum())
        linked_cost = (f_linked["summary_results/main_island/objectives"][:].sum() +
                       f_linked["summary_results/small_island/objectives"][:].sum())
        savings = iso_cost - linked_cost
        print(f"Value of interconnection: ${savings:,.0f} "
              f"({savings/iso_cost:.1%} cost reduction)")

Expected result: interconnection saves 5-15% of total system cost by:

  • Allowing the Small Island to import cheap RE instead of running expensive local diesel ($120/MWh)
  • Reducing storage needs on the Small Island (imports provide flexibility)
  • Enabling the Main Island to build slightly more RE than needed, exporting the surplus

Key Takeaways

  1. System independence: Each system maintains its own RE targets, CO2 budgets, and investment constraints. The interconnection provides economic coordination without forcing identical policies.
  2. Inter-system coordination: The Master Problem jointly optimizes investments across systems. It may invest more RE on the Main Island specifically to export to the Small Island.
  3. Transfer investment: The optimizer expands the submarine cable when the marginal cost of cable capacity ($800,000/MW) is less than the avoided cost of local generation on the Small Island.
  4. Asymmetric benefit: The Small Island typically benefits more from the interconnection because its local generation costs are higher. However, the Main Island also benefits from economies of scale in RE investment.
  5. Losses matter: The 3% cable losses mean that 30 MW exported from the Main Island delivers only 29.1 MW to the Small Island. High losses reduce the value of long-distance interconnection.
  6. Resilience trade-off: Heavy reliance on the cable makes the Small Island vulnerable to cable outages. The target_re_penetration on the Small Island ensures some local generation capacity is maintained.

Next Steps