A Distributionally Robust Optimization Approach for the Optimal Wind Farm Allocation in Multi-Area Power Systems

Abstract

This dissertation presents a distributionally robust planning model to determine the optimal allocation of wind farms in a multi-area power system, so that the expected energy not served (EENS) is minimized under uncertain conditions of wind power and generator forced outages. Unlike conventional stochastic programming approaches that rely on detailed information of the exact probability distribution, this proposed method attempts to minimize the expectation term over a collection of distributions characterized by accessible statistical measures, so it is more practical in cases where the detailed distribution data is unavailable. This planning model is formulated as a two-stage problem, where the wind power capacity allocation decisions are determined in the first stage, before the observation of uncertainty outcomes, and operation decisions are made in the second stage under specific uncertainty realizations.

In this dissertation, the second-stage decisions are approximated by linear decision rule functions, so that the distributionally robust model can be reformulated into a tractable second-order cone programming problem. Case studies based on a five-area system are conducted to demonstrate the effectiveness of the proposed method. The model is extended to deal with the hybrid system by including the solar power as a third source of uncertainty besides the wind power and conventional generation forced outages. The correlation between the wind and solar power is investigated to capture the diversity and the availability of all included power resources.

Capacity credit is calculated to measure the effective load carrying capacity of the allocated renewable resources. The probabilistic method including Monte Carlo simulation is used to calculate the loss of load expectation (LOLE) at different peak loads and analytically determined the capacity credit of wind and solar power generation for several installed wind capacities. The penetration factor and the availability of the renewable power generation are major factors influencing the capacity credit value, besides the overall power system reliability level.

The results reflect the usefulness of utilizing the distributionally robust optimization approach in the data-driven decision making. It positively responds with the amount of the information provided regarding the uncertain variables in the renewable power generation allocation problem and sequentially in the system reliability and the yielded capacity credit values of the allocated renewable generation units.