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Single-Node Island System

Prerequisites

  • ESFEX installed: pip install esfex
  • A working solver (HiGHS is included by default)
  • Python 3.10+ with h5py, numpy, and matplotlib for results analysis

Scenario

An isolated island currently relies on diesel generators. We want to plan a 10-year transition toward 80% renewable energy by investing in solar PV, wind turbines, and battery storage.

System characteristics:

  • 1 node (single bus)
  • Peak demand: ~200 MW
  • Existing: 250 MW diesel, 50 MW solar PV
  • Candidates: Additional solar PV, wind, Li-ion batteries
  • Target: 80% renewable energy by year 10
  • CO2 budget: 500,000 tonnes/year

Step 1: Create the Configuration

Create island_system.yaml with the configuration below.

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: 1800
  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:
  systems:
    - island

systems:
  island:
    name: island
    demand_path: island_demand.xlsx
    demand_scale: 1.0
    demand_growth: 0.02

    nodes:
      adjacency_matrix: [[0]]
      coordinates: [[-76.80, 18.00]]
      names: ["Main Island"]

    generators:
      solar_pv:
        name: Solar PV
        type: Renewable
        fuel: Solar
        rated_power: [50.0]
        min_power: [0.0]
        invest_cost: [750000.0]
        invest_max_power: [500.0]
        fuel_cost: [0.0]
        fixed_cost: [5.0]
        maintenance_cost: [2.0]
        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: [3]
        degradation_rate: [0.005]
        inertia: [0.0]
        Availability: solar_availability.csv

      wind:
        name: Wind Turbines
        type: Renewable
        fuel: Wind
        rated_power: [0.0]
        invest_cost: [1200000.0]
        invest_max_power: [300.0]
        fuel_cost: [0.0]
        fixed_cost: [8.0]
        maintenance_cost: [5.0]
        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: [20]
        initial_age: [0]
        degradation_rate: [0.005]
        inertia: [0.0]
        Availability: wind_availability.csv

      diesel:
        name: Diesel Generator
        type: Non-renewable
        fuel: Diesel
        rated_power: [250.0]
        min_power: [0.3]
        invest_cost: [500000.0]
        invest_max_power: [0.0]
        fuel_cost: [85.0]
        fixed_cost: [3.0]
        maintenance_cost: [5.0]
        start_up_cost: [5000.0]
        decommissioning_cost: [100000]
        ramp_up: [0.5]
        ramp_down: [0.5]
        min_up_time: [4]
        min_down_time: [2]
        eff_at_rated: [0.40]
        eff_at_min: [0.30]
        life_time: [30]
        initial_age: [15]
        degradation_rate: [0.01]
        inertia: [5.0]

    batteries:
      li_ion:
        name: Li-Ion Battery
        capacity: [0.0]
        max_charge_power: [0.0]
        max_discharge_power: [0.0]
        charge_efficiency: [0.95]
        discharge_efficiency: [0.95]
        soc_min: [0.10]
        soc_max: [0.95]
        soc_initial: [0.50]
        self_discharge: [0.0001]
        invest_cost_power: [200000.0]
        invest_cost_capacity: [150000.0]
        invest_max_power: [200.0]
        invest_max_capacity: [800.0]
        min_duration_hours: 2.0
        max_duration_hours: 6.0
        life_time: [15]
        maintenance_cost: [1.0]
        spillage: false
        degradation_rate: [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: 500000.0

    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

Key Parameters

Parameter Value Purpose
simulation_mode development Economic dispatch without unit commitment binaries (faster LP)
resolution_hours 1 Hourly time steps for operational dispatch
rolling_horizon_hours 48 Each operational window solves 48 hours at a time
overlap_hours 6 6-hour overlap between windows for continuity
representative_days_per_year 5 Master problem uses 5 representative days per year
target_re_penetration 0.80 80% renewable energy target by the final year
max_curtailment_ratio 0.05 No more than 5% of renewable generation can be curtailed
discount_rate 0.08 8% discount rate for NPV calculations

Step 2: Prepare Input Data

Demand File

Create island_demand.xlsx with 8,760 rows (1 year of hourly data) and 1 column (1 node). The values represent load in MW at each hour.

Hour Node 0
1 120.5
2 115.3
... ...
8760 125.0

The demand profile should reflect typical island load patterns: lower overnight (80-120 MW), morning ramp (120-170 MW), afternoon peak (170-200 MW), and evening decline. If you have multiple years of data, concatenate them (17,520 rows for 2 years, etc.).

The demand_growth: 0.02 parameter applies a 2% annual compound growth to this base profile for subsequent years.

Availability Files

Create solar_availability.csv with 8,760 rows, 1 column, values between 0.0 and 1.0. Each value represents the fraction of rated capacity available at that hour.

0.0
0.0
0.0
0.0
0.0
0.05
0.25
0.55
0.75
0.85
0.90
0.88
0.85
0.80
0.65
0.40
0.15
0.02
0.0
0.0
0.0
0.0
0.0
0.0

This example shows a typical tropical solar day: zero output at night, ramping from sunrise (~06:00) to noon peak (~0.90), then declining to zero by ~18:00. The full file continues this pattern for all 365 days, with seasonal and weather variations.

Create wind_availability.csv following the same format. Wind profiles are typically less predictable than solar, with values varying between 0.0 and 1.0 throughout the day and season.

Step 3: Run the Simulation

# Validate the configuration first (catches errors before the long solve)
esfex validate -c island_system.yaml

# Run the 10-year planning study
esfex run -c island_system.yaml --years 10 --verbose

The simulation proceeds in two stages for each year:

  1. Master Problem: Solves the strategic investment/retirement decisions across all years using representative days
  2. Operational Dispatch: Solves detailed hourly dispatch for each year using the rolling horizon approach

Expect the full run to take 15-60 minutes depending on your hardware and solver configuration.

Step 4: Interpret Results

Investment Decisions

import h5py

with h5py.File("results/output.h5", "r") as f:
    investments = f["summary_results/investments"][:]
    print("Year | Solar PV | Wind | Battery Power | Battery Energy")
    for year_data in investments:
        print(f"{year_data}")

Expected pattern:

  • Early years (1-3): Solar PV investment dominates because it has the lowest investment cost ($750,000/MW vs $1,200,000/MW for wind). Small battery additions begin to manage solar intermittency.
  • Mid years (4-7): Wind investment starts for temporal diversity (wind generates when the sun does not). Battery capacity grows to 4-6 hour duration as RE penetration rises above 50%.
  • Late years (8-10): Replacement investments may appear as early solar installations degrade. The diesel generator (initial age 15, lifetime 30) approaches retirement age and its effective capacity declines at 1%/year.

Generation Mix

import numpy as np

with h5py.File("results/output.h5", "r") as f:
    for yr in range(1, 11):
        gen = f[f"detailed_results/island/year_{yr:03d}/gen_output"][:]
        total = gen.sum(axis=(1, 2))  # Sum over nodes and hours
        print(f"Year {yr}: Solar={total[0]:.0f} MWh, "
              f"Wind={total[1]:.0f} MWh, Diesel={total[2]:.0f} MWh")

A typical progression might look like:

Year Solar (GWh) Wind (GWh) Diesel (GWh) Battery (GWh) RE Share
1 85 0 1,300 0 6%
3 350 120 1,000 45 32%
5 550 280 680 95 55%
7 700 400 440 130 72%
10 850 500 250 170 84%

RE Penetration Trajectory

with h5py.File("results/output.h5", "r") as f:
    re = f["summary_results/re_penetration"][:]
    for yr, pen in enumerate(re, 1):
        print(f"Year {yr}: RE penetration = {pen:.1%}")

The RE penetration should follow a roughly linear trajectory from the initial value (~6% from existing 50 MW solar) toward the 80% target. The optimizer determines the most cost-effective pace, constrained by min_annual_increment and max_annual_increment if configured.

LCOE Analysis

with h5py.File("results/output.h5", "r") as f:
    # Per-technology LCOE if available
    if "summary_results/lcoe" in f:
        lcoe = f["summary_results/lcoe"][:]
        tech_names = ["Solar PV", "Wind", "Diesel"]
        for name, cost in zip(tech_names, lcoe):
            print(f"{name} LCOE: ${cost:.1f}/MWh")

Expected LCOE ranges for this scenario:

Technology LCOE ($/MWh) Notes
Solar PV 35-55 Low fuel cost, moderate investment
Wind 50-75 Higher investment, good capacity factor
Diesel 180-250 Dominated by fuel cost at $85/MWh
Li-Ion Battery 120-180 Enables RE integration, reduces curtailment

The system LCOE (blended cost) should decline over the planning horizon as renewable energy displaces diesel.

Cost Breakdown

with h5py.File("results/output.h5", "r") as f:
    objectives = f["summary_results/objectives"][:]
    total_npv = sum(obj / (1.08 ** yr) for yr, obj in enumerate(objectives))
    print(f"Total NPV (10 years): ${total_npv:,.0f}")
    print(f"Average annual cost: ${np.mean(objectives):,.0f}")
    print(f"Year 1 cost: ${objectives[0]:,.0f}")
    print(f"Year 10 cost: ${objectives[-1]:,.0f}")

Alternative: Full Python API Workflow

from esfex import load_config
from esfex.runner import Orchestrator

# Load, run, and analyze - no CLI needed
config = load_config("island_system.yaml")
orchestrator = Orchestrator(config, config_path="island_system.yaml")
results = orchestrator.run(years=10, start_year=2025)

# Print year-by-year summary
for yr in results:
    print(f"Year {yr.year}: "
          f"Cost=${yr.objective:,.0f}  "
          f"RE={yr.re_penetration:.1%}  "
          f"CO2={yr.emissions:,.0f}t  "
          f"Load shed={yr.load_shed:.1f} MWh")

# Plot generation stack for the final year
import matplotlib.pyplot as plt
import numpy as np

yr = results[-1]
hours = np.arange(168)  # First week
fig, ax = plt.subplots(figsize=(14, 5))
ax.stackplot(hours,
    yr.gen_output[0, 0, :168],   # Solar
    yr.gen_output[1, 0, :168],   # Wind
    yr.gen_output[2, 0, :168],   # Diesel
    labels=["Solar PV", "Wind", "Diesel"],
    colors=["#f1c40f", "#3498db", "#7f8c8d"])
if yr.bat_discharge is not None:
    ax.stackplot(hours,
        yr.bat_discharge[0, 0, :168],
        labels=["Battery"], colors=["#2ecc71"], alpha=0.7)
ax.plot(hours, yr.demand[0, :168] if yr.demand.ndim == 2 else yr.demand[:168],
    "k-", linewidth=1.5, label="Demand")
ax.set_xlabel("Hour")
ax.set_ylabel("Power (MW)")
ax.set_title(f"Generation Mix - Year {yr.year} (First Week)")
ax.legend(loc="upper right")
plt.tight_layout()
plt.savefig("island_generation_week.png", dpi=150)

# Compare investment trajectories
print("\nInvestment Decisions:")
for yr in results:
    inv = {k: v for k, v in yr.investments.items() if v > 0.1}
    if inv:
        inv_str = ", ".join(f"{k}: {v:.1f} MW" for k, v in inv.items())
        print(f"  Year {yr.year}: {inv_str}")

Step 5: Results Analysis Deep Dive

Curtailment Analysis

With the 5% curtailment cap, the optimizer invests in storage rather than overbuilding renewables.

with h5py.File("results/output.h5", "r") as f:
    for yr in range(1, 11):
        key = f"detailed_results/island/year_{yr:03d}"
        if f"{key}/curtailment" in f:
            curt = f[f"{key}/curtailment"][:]
            gen = f[f"{key}/gen_output"][:]
            # RE generation is generators 0 (solar) and 1 (wind)
            re_gen = gen[0].sum() + gen[1].sum()
            curt_total = curt.sum()
            ratio = curt_total / re_gen if re_gen > 0 else 0
            print(f"Year {yr}: Curtailment = {curt_total:.0f} MWh "
                  f"({ratio:.1%} of RE generation)")

If curtailment approaches the 5% cap, it signals that additional storage investment would be beneficial.

CO2 Emissions Tracking

with h5py.File("results/output.h5", "r") as f:
    emissions = f["summary_results/emissions"][:]
    budget = 500_000  # tonnes/year
    for yr, em in enumerate(emissions, 1):
        status = "WITHIN" if em <= budget else "EXCEEDED"
        print(f"Year {yr}: {em:,.0f} tCO2 ({status} budget)")

Emissions should decline steadily as diesel generation is displaced. The CO2 budget constraint ensures the transition stays on track, even if the RE target alone would allow higher emissions.

Battery Utilization

with h5py.File("results/output.h5", "r") as f:
    for yr in [1, 5, 10]:
        key = f"detailed_results/island/year_{yr:03d}"
        if f"{key}/bat_charge" in f:
            charge = f[f"{key}/bat_charge"][:].sum()
            discharge = f[f"{key}/bat_discharge"][:].sum()
            cycles = discharge / 800  # Approximate full cycles (800 MWh capacity)
            print(f"Year {yr}: Charged={charge:.0f} MWh, "
                  f"Discharged={discharge:.0f} MWh, "
                  f"~{cycles:.0f} full cycles")

Key Takeaways

  1. Investment timing: The optimizer spreads investments across years to match the RE target progression and minimize NPV. Front-loading all investment is rarely optimal due to discounting and technology degradation.
  2. Storage role: Batteries become essential once RE exceeds ~50% to handle intermittency. The 5% curtailment cap forces storage investment rather than overbuilding RE.
  3. Diesel phase-out: Existing diesel capacity degrades naturally (1%/year) and may not need active retirement. By year 10, its effective capacity is ~225 MW but its utilization drops below 20%.
  4. Curtailment limit: Without the 5% cap, the optimizer might overbuild solar by 30-50% and curtail excess, which is wasteful. The constraint drives economically efficient storage sizing.
  5. Cost trade-offs: Cheaper solar comes first; wind adds value through temporal diversity (evening and nighttime generation). The optimal mix depends on relative availability profiles.
  6. Discount rate sensitivity: At 8%, the optimizer slightly delays investments. Lower discount rates (3-5%) favor earlier, larger RE investments. See the Sensitivity Analysis Tutorial for systematic exploration.

Next Steps