Electric Power Service (EPS) Business Model¶
Overview¶
The EPS-Electric-Power-Service (PG) model represents an off-grid hybrid energy system combining solar PV, battery storage, and backup generation (genset/grid) to supply electricity to the e-mobility ecosystem. This model is optimized for high PV-to-Battery ratios (2.0-6.0) to maximize direct solar-to-load supply and minimize battery cycling costs.
Business Context¶
Central Question: "How can we minimize energy costs while ensuring 24/7 power availability?"
Critical Modeling Methodology: Integer Unit Constraints¶
Physical Architecture¶
EPS-Electric-Power-Service Unit = 120kW Solar + 261kWh Battery - 1 Unit = 120 kWp solar + 261 kWh BESS + 100 kW inverter (fixed physical constraint) - Modular Expansion: Capacity grows in discrete base unit increments - Cannot deploy partial units: 1, 2, 3... units only (not 1.3 or 2.7 units)
Two-Layer Economic Model¶
The model explicitly separates installed capacity (integer-constrained) from actual usage (demand-driven) to capture the economic impact of modular infrastructure:
Infrastructure Layer (Integer-Constrained):
- Installed units: EPS_SCALE_FACTOR (integer: 1, 2, 3...)
- Installed solar: EPS_SCALE_FACTOR × 120 kWp
- Installed battery: EPS_SCALE_FACTOR × 261 kWh
- Total CapEx: Based on installed units
- Fixed OpEx: Based on installed capacity (maintenance, land, security)
Operational Layer (Demand-Driven):
- Active energy demand: From demand-supply model (ds_total_energy_demand)
- Utilization rate: ds_total_energy_demand / (EPS_SCALE_FACTOR × 541 kWh/day)
- Revenue: Based on actual energy delivered
- Variable OpEx: Based on usage (fuel, grid purchases)
Economic Impact of Integer Constraints¶
Example: Test Case A - Demand: 714 kWh/day energy needed - Supply: Must install 2 units = 2 × 541 kWh/day = 1,082 kWh/day capacity - Utilization: 714/1,082 = 66% - Oversizing penalty: 368 kWh/day unused capacity, diluted fixed costs
Example: If Demand = 600 kWh/day - Demand: 600 kWh/day needed - Supply: Must install 2 units = 1,082 kWh/day (cannot deploy 1.1 units) - Utilization: 600/1,082 = 55% - Oversizing penalty: Larger capacity underutilization, higher LCOE
Key Principle: Off-grid power infrastructure can only expand in discrete modular units (120kW/261kWh base units). When demand doesn't align with unit capacity, you're forced to overbuild, reducing utilization and increasing levelized cost of energy.
Terminology¶
- Base Unit: 120kW/261kWh physical system (indivisible)
- Scale Factor: Integer multiplier (number of units deployed)
- Installed Capacity: Total generation capacity (scale factor × 541 kWh/day)
- Active Demand: Actual energy consumed (from demand model)
- Utilization Rate: Active / Installed (100% = optimal, <100% = oversizing penalty)
- LCOE Impact: Lower utilization → higher fixed cost per kWh → higher LCOE
Key Strategy: - Oversize solar PV relative to battery capacity - Maximize daytime direct-to-load solar supply - Use batteries for night-time load only - Minimize expensive diesel/grid backup usage
Model Parameters¶
Base Unit Configuration¶
| Parameter | Symbol | Value | Unit |
|---|---|---|---|
| Base solar capacity | EPS_SOLAR_CAPACITY_BASE |
120 | kWp |
| Base battery capacity | EPS_BATTERY_CAPACITY_BASE |
261 | kWh |
| Base inverter rating | EPS_INVERTER_RATING_BASE |
100 | kW |
| Number of units | EPS_NUM_UNITS |
1 | units |
| Base unit cost | EPS_BESS_BASE_COST |
156,600 | USD |
| Installation rate | EPS_BESS_INSTALL_RATE |
10% | ratio |
Cost Parameters¶
| Parameter | Symbol | Value | Unit |
|---|---|---|---|
| PV module FOB cost | EPS_PV_COST_FOB |
0.30 | USD/Wp |
| PV installation cost | EPS_PV_INSTALL_COST |
0.20 | USD/Wp |
| Genset capacity | EPS_GENSET_RATING |
50 | kW |
| Genset CapEx | EPS_GENSET_CAPEX |
500 | USD/kW |
| Diesel fuel price | EPS_DIESEL_PRICE |
1.20 | USD/L |
| Grid electricity cost | EPS_GRID_COST |
0.32 | USD/kWh |
| Electricity selling price | EPS_ELEC_PRICE |
0.32 | USD/kWh |
| Annual maintenance rate | EPS_MAINT_RATE |
5% | ratio/year |
Technical Parameters¶
| Parameter | Symbol | Value | Unit | Description |
|---|---|---|---|---|
| Peak Sun Hours (PSH) | EPS_PEAK_SUN_HOURS |
5.5 | hours/day | Location-specific solar resource (Togo: 5-6 hrs, NASA data) |
| System Derating Factor | EPS_SYSTEM_DERATE |
0.82 | ratio | Combined losses: temperature, wiring, MPPT, dust (0.80-0.85) |
| Inverter efficiency | EPS_INVERTER_EFFICIENCY |
95% | ratio | DC-to-AC conversion efficiency |
| Battery round-trip efficiency | EPS_BATTERY_EFFICIENCY |
90% | ratio | Charge-discharge efficiency (10% loss) |
| Genset fuel efficiency | EPS_GENSET_EFFICIENCY |
0.25 | L/kWh | Diesel consumption at rated load |
| Daytime demand ratio | EPS_DAY_DEMAND_RATIO |
60% | ratio | Portion of demand during solar hours |
Asset Lifecycle¶
| Parameter | Symbol | Value | Unit |
|---|---|---|---|
| Solar PV lifespan | EPS_SOLAR_LIFE |
9,125 | days (25 years) |
| Battery cycle life | EPS_BATTERY_CYCLE_LIFE |
6,000 | cycles |
| Electrical equipment life | EPS_ELECTRICAL_LIFE |
3,650 | days (10 years) |
Financial Calculations¶
Key Solar Ratios (Industry Standard)¶
| Metric | Formula | Unit | Description |
|---|---|---|---|
| PV-to-Battery Ratio (PB Ratio) | eps_solar_capacity / eps_battery_capacity |
kWp/kWh | PRIMARY OVES METRIC: 2.0-6.0 for e-mobility |
| Array-to-Load Ratio (ALR) | eps_daily_production_potential / ds_total_energy_demand |
ratio | Solar generation / daily load (1.2-2.5 typical) |
| PV Oversize Ratio | eps_solar_capacity / eps_inverter_rating |
ratio | PV array / MPPT rating (1.2-2.0 typical) |
| Daytime Solar Fraction | eps_solar_to_load / ds_total_energy_demand |
ratio | Load served directly by solar (key economic metric) |
Energy Flow Calculations¶
Daily Production:
eps_daily_production_potential = eps_solar_capacity × EPS_PEAK_SUN_HOURS × EPS_SYSTEM_DERATE
Solar Energy Distribution:
eps_solar_to_load = MIN(eps_daily_production_potential, eps_day_demand)
eps_solar_excess = MAX(0, eps_daily_production_potential - eps_day_demand)
eps_solar_to_battery = MIN(eps_solar_excess, eps_battery_capacity / EPS_BATTERY_EFFICIENCY)
Battery Operations:
eps_battery_stored = eps_solar_to_battery × EPS_BATTERY_EFFICIENCY
eps_battery_discharged = MIN(eps_battery_stored × EPS_BATTERY_EFFICIENCY, eps_night_demand)
eps_battery_cycles_day = eps_battery_stored / eps_battery_capacity
Backup Generation:
eps_shortfall = MAX(0, eps_night_demand - eps_battery_discharged)
eps_grid_purchase = eps_shortfall × 0.3
eps_genset_output = eps_shortfall × 0.7
eps_genset_fuel_consumed = eps_genset_output × EPS_GENSET_EFFICIENCY
Capital Expenditures¶
eps_pv_capex_total = eps_solar_capacity × 1000 × (EPS_PV_COST_FOB + EPS_PV_INSTALL_COST)
eps_bess_capex_total = EPS_BESS_BASE_COST × EPS_NUM_UNITS × (1 + EPS_BESS_INSTALL_RATE)
eps_genset_capex_total = EPS_GENSET_RATING × EPS_GENSET_CAPEX
eps_total_capex = eps_pv_capex_total + eps_bess_capex_total + eps_genset_capex_total
Operating Costs¶
eps_daily_fuel_cost = eps_genset_fuel_consumed × EPS_DIESEL_PRICE
eps_daily_grid_cost = eps_grid_purchase × EPS_GRID_COST
eps_daily_maint_cost = (eps_total_capex × EPS_MAINT_RATE) / 365
eps_daily_opex = eps_daily_fuel_cost + eps_daily_grid_cost + eps_daily_maint_cost
Depreciation¶
eps_pv_daily_depreciation = eps_pv_capex_total / EPS_SOLAR_LIFE
eps_bess_cycle_depreciation = eps_bess_capex_total / EPS_BATTERY_CYCLE_LIFE
eps_bess_daily_depreciation = eps_bess_cycle_depreciation × eps_battery_cycles_day
eps_genset_daily_depreciation = eps_genset_capex_total / EPS_ELECTRICAL_LIFE
eps_total_daily_depreciation = eps_pv_daily_depreciation + eps_bess_daily_depreciation + eps_genset_daily_depreciation
Financial Metrics¶
eps_daily_total_cost = eps_daily_opex + eps_total_daily_depreciation
eps_annual_production = eps_total_supply × 365
eps_lcoe = eps_daily_total_cost / eps_total_supply
eps_daily_revenue = eps_total_supply × EPS_ELEC_PRICE
eps_daily_profit = eps_daily_revenue - eps_daily_total_cost
Output Metrics¶
Key Performance Indicators¶
| KPI | Reference | Unit |
|---|---|---|
| Total Capital Expenditure | eps_total_capex |
USD |
| Daily Energy Supply | eps_total_supply |
kWh/day |
| Annual Production | eps_annual_production |
kWh/year |
| Daytime Solar Fraction | eps_daytime_solar_fraction × 100 |
% |
| Battery Cycles Per Day | eps_battery_cycles_day |
cycles/day |
| Genset Runtime | eps_genset_runtime |
hours/day |
| Levelized Cost of Energy (LCOE) | eps_lcoe |
USD/kWh |
| Daily Revenue | eps_daily_revenue |
USD/day |
| Daily OpEx | eps_daily_opex |
USD/day |
| Daily Depreciation | eps_total_daily_depreciation |
USD/day |
| Daily Profit | eps_daily_profit |
USD/day |
| Profit Margin | (eps_daily_profit / eps_daily_revenue) × 100 |
% |
| Payback Period | eps_total_capex / eps_daily_profit |
days |
| Array-to-Load Ratio (ALR) | eps_array_to_load_ratio |
ratio |
| PV-to-Battery Ratio (PB Ratio) | eps_pv_to_battery_ratio |
kWp/kWh |
| PV Oversize Ratio | eps_pv_oversize_ratio |
ratio |
Interdependencies with Other Models¶
Dependencies FROM Other Models¶
| Source Model | Data Required | Impact |
|---|---|---|
| Demand-Supply | ds_total_energy_demand |
Determines required generation capacity |
| Demand-Supply | DS_PEAK_SUN_HOURS |
Reference for solar resource planning |
| Demand-Supply | DS_INVERTER_EFFICIENCY |
Reference for system sizing |
Dependencies TO Other Models¶
| Target Model | Data Provided | Impact |
|---|---|---|
| Demand-Supply | Electricity pricing (EPS_ELEC_PRICE) |
Energy cost structure for ecosystem |
| SNS-Swap-Network-Service | Power availability | Station operations planning |
Off-Grid Design Strategy¶
Why High PV-to-Battery Ratios?
- Morning/Evening Extension: Oversized PV starts generating earlier and continues later
- Direct-to-Load Supply: Daytime loads bypass battery (no cycling cost)
- Battery Investment Reduction: Smaller batteries + more panels = lower total cost
- Operational Resilience: Multiple energy sources reduce single-point failure risk
Trade-offs: - Higher initial PV CapEx - Some mid-day solar may exceed system absorption capacity - But: Lower battery replacement costs + reduced diesel/grid dependence
Reference¶
For detailed off-grid solar terminology, sizing methodology, and industry best practices, see:
Key concepts covered: - Peak Sun Hours (PSH) and irradiance - PV-to-Battery Ratio (PB Ratio) as primary design metric - Array-to-Load Ratio (ALR) and system sizing - Daytime Solar Fraction and economic optimization - Industry-standard terminology and typical ranges
Version History¶
| Version | Date | Changes | Author |
|---|---|---|---|
| 0.2 | 2025-11-16 | Added full calculations with industry-standard solar metrics | OVES Team |
| 0.1 | 2025-11-02 | Placeholder created | OVES Team |