Planning Modes¶

MicroGridsPy supports two complementary modelling modes, addressing different levels of temporal complexity and data availability:

• Multi-year planning mode (dynamic);
• Typical-year planning mode.

Both are investment-oriented and rely on an annuity-based cost formulation, making them suitable for long-term, multi-scenario techno-economic planning. In both cases the model minimizes the expected total system cost — annuitized investment costs (with capital recovery), operating costs, and optional externalities.

The optimization runs at hourly resolution and can account for multiple scenarios representing alternative realizations of demand, renewable availability, or grid conditions, each with a probability. The resulting problem is a two-stage stochastic optimization with recourse, solved in deterministic-equivalent form: sizing and investment are here-and-now decisions shared across scenarios, while operational decisions are scenario-dependent recourse actions. Both modes can represent a fully off-grid or a weakly grid-connected system through a grid-availability matrix.

What the total system cost includes¶

• Investment costs — annualized using a technology-specific WACC to reflect the opportunity cost of capital, financing conditions, and risk premia. Here the WACC is used solely within the annuity formulation and does not model private bankability.
• Operating costs — fuel, maintenance, and replacement expenditures.
• Externalities (optional) — social or environmental damages such as CO₂ emissions, internalized through cost adders.

In the multi-year formulation, a social discount rate discounts future costs to present value. This rate is conceptually distinct from the WACC: the WACC captures the cost of financing capital equipment, while the social discount rate reflects society's valuation of future expenditures and long-term benefits.

This structure captures the key long-term trade-offs in mini-grid planning: CAPEX vs OPEX substitution (e.g. PV + battery vs diesel), renewable integration and emissions reduction under externality pricing, grid interaction under variable pricing and availability, and reliability vs cost.

Multi-Year Planning¶

The multi-year mode is the most comprehensive formulation. It is defined over a horizon \(y = 1,\dots,H\), where both system decisions and exogenous parameters may evolve over time. Time-dependent inputs — demand, renewable availability, prices, grid conditions — are indexed by year and scenario.

It is formulated as a two-stage stochastic capacity-expansion problem with recourse and captures three key effects:

• Monotone capacity expansion. Investments are phased across predefined planning steps, letting the system grow over time while enforcing non-decreasing installed capacity and modelling technology roll-out through cohort-specific capacity additions.
• Intertemporal economic valuation. All system costs are evaluated in present-value terms using a dual-rate logic: capital recovery uses technology-specific financial discount rates (\(\text{WACC}_j\)), while system-level discounting uses a social discount rate \(r_s\).
• Cohort-based annuity persistence. Once an investment cohort is activated, its annualized cost stream remains active over the remaining modelled horizon through an implicit like-for-like replacement logic. Replacement expenditures are therefore represented through the persistence of the annuity stream rather than separate overnight reinvestment terms.

The objective is the discounted expected system cost within the modelled horizon — see Objective Function → Multi-Year.

Investment cohorts¶

Capacity expansion is not restricted to the initial year but can occur at discrete investment steps \(\tau\) (equivalently, cohorts \(k\)), each commissioned at a specific year. Each cohort is characterized by its installation time, technical lifetime, and financial parameters, and contributes annualized costs from its commissioning year onward.

Typical-Year Planning¶

The typical-year mode is a tractable steady-state approximation of long-term economics. The system is described by a single representative operating year assumed to repeat identically over time, so the objective reduces to minimizing the expected annual (welfare) cost.

It is well suited to systems assumed to have reached long-term equilibrium, where key time-varying parameters (most notably demand) are not expected to evolve significantly. It can be interpreted as a collapsed version of the multi-year model under single-year operation: load, resource availability, performance, and operating conditions are identical every year; inter-annual variability, demand growth, technology learning, and degradation are neglected.

Under this assumption, the annuity-based investment cost becomes mathematically equivalent to an infinite discounted sequence of identical replacements — the system is implicitly assumed to operate indefinitely in steady state, each asset replaced by an identical one at end of life. The objective is the expected equivalent annual cost (EAC) — see Objective Function → Typical-Year.

Choosing a mode¶

Both modes rely on the same bottom-up cost structure, so the typical-year model is the steady-state limit of the multi-year one under time-invariant conditions.