Q10Power System Planning

(a) Optimal Power System Expansion Planning and WASP Memory Limitations

Optimal power system expansion planning is the process of determining, from among a very large number of technically feasible combinations of new generating plant additions over a multi-year horizon, the specific sequence, size, technology and commissioning year of new units that minimizes the total discounted system cost while ensuring that a minimum acceptable level of system reliability (commonly expressed as loss of load probability, LOLP, not exceeding a specified threshold, or expected energy not served, EENS, remaining below a target) is maintained in every year of the study. The total cost considered includes the capital investment cost of new plants, their fixed and variable operating and maintenance costs, fuel costs, and the economic cost associated with any unserved energy due to residual unreliability.

Because the number of possible combinations of candidate plant additions across many years grows combinatorially, a direct exhaustive search is computationally impractical for realistic systems; this is why packages such as WASP use dynamic programming, which breaks the multi-year problem into a sequence of single-stage decisions linked by a recursive cost function, dramatically reducing the computational burden while still guaranteeing an optimal (or near-optimal, given the discretization) solution.

WASP, being an older-generation dynamic-programming based package, has practical memory and computational limitations that bound the size of problem it can handle within a reasonable computation time and available computer memory. Typical limitations include a maximum number of study years that can be considered in a single run (commonly cited as up to about 30 years), a maximum number of candidate plant types that can be considered simultaneously (commonly a handful, e.g., up to about 10-14 types), and a maximum number of discrete states/configurations retained at each stage of the dynamic programming recursion. When a real system's planning problem exceeds these limits, the planner must either break the study into shorter overlapping horizons, pre-screen and reduce the candidate plant list to the most promising types, or use a coarser discretization of capacity states, at some cost to the theoretical optimality of the solution.

(b) Flow Chart of Least-Cost Planning and Formulation of the Optimization Problem

Least-cost planning is the overall methodology of selecting a generation expansion plan (and, in an integrated resource planning context, demand-side measures as well) that minimizes the total present-worth cost of meeting forecast demand over the study horizon, subject to reliability and other operational constraints.

• Load forecast: establish the peak demand and energy forecast for every year of the study horizon.
• Characterize candidate plants: compile capital cost, fixed/variable O&M cost, fuel cost/heat rate and availability data for every candidate generating technology.
• Generate expansion configurations: for each year, enumerate feasible combinations of existing plus candidate plants that could meet the forecast demand.
• Evaluate reliability: for each configuration, calculate reliability indices (LOLP, EENS) using probabilistic production simulation.
• Calculate total cost: compute the discounted sum of capital cost, operating cost and expected unserved-energy cost for each configuration in each year.
• Optimize via dynamic programming: search across years and configurations for the minimum total discounted cost sequence that satisfies the reliability constraint in every year.
• Output optimal expansion plan: report the selected sequence of plant additions, their timing, and the associated cost and reliability profile over the horizon.

In this formulation, Z is the total discounted cost to be minimized over the study horizon of T years at discount rate r; C_cap, C_O&M and C_fuel are respectively the annual capital (annuitized), operating/maintenance and fuel costs of the plants in service in year t; C_EUE is the economic cost associated with expected unserved energy in year t; and the constraint requires the loss-of-load probability in every year t to remain at or below a specified maximum acceptable threshold, ensuring that cost minimization never compromises system reliability below the policy-defined minimum standard.

Because WASP applies dynamic programming to a discretized representation of the expansion problem, the memory and time limitations translate directly into practical constraints on study design: planners must aggregate similar candidate technologies, limit the study horizon to a manageable number of years per run (extending the overall study through successive overlapping runs if a longer horizon is required), and pre-screen candidate plant types using simpler screening-curve techniques before submitting only the most promising few types to the full WASP optimization, so that the combinatorial state space explored by DYNPRO remains within the package computational limits.

The least-cost optimization formulation is also sensitive to the assumed discount rate: a higher discount rate favours technologies with lower capital cost and higher operating cost (since future operating costs are discounted more heavily relative to upfront capital), while a lower discount rate favours capital-intensive, low-operating-cost technologies such as hydro or nuclear; sensitivity analysis around the discount rate is therefore a standard part of interpreting the output of any least-cost expansion study, since the choice of discount rate itself reflects a policy judgement about the relative weight given to near-term versus long-term costs.

A further consideration in interpreting WASP-based results is that the optimal plan produced is only as good as the input data and discretization used; planners routinely conduct sensitivity runs varying key uncertain inputs such as demand growth, fuel price and candidate-plant capital cost, and examine whether the recommended near-term capacity additions remain robust across this range, since near-term decisions are the ones that must actually be committed to soon, while far-horizon decisions can reasonably be left for revision in the next planning cycle.

The reliability constraint in the optimization formulation is most naturally expressed as a chance constraint - requiring the probability of a shortfall event to remain below a specified threshold - which fits directly with the probabilistic simulation output already produced by the MERSIM-type reliability evaluation module, allowing the dynamic-programming search in DYNPRO to simply discard or heavily penalize any candidate configuration whose simulated LOLP exceeds the specified maximum before comparing the cost of the remaining, reliability-compliant configurations.

In addition to the formal WASP memory limits, practical expansion-planning studies are also constrained by data quality: capital-cost estimates for candidate technologies more than a decade into the future carry substantial uncertainty due to unpredictable changes in commodity prices, technology learning curves (especially for renewable and storage technologies) and financing conditions, so the numerical optimum produced by the least-cost formulation should always be interpreted as a guide to the broad shape of the optimal plan rather than as a precise, unquestionable prescription for exact future capacity additions.