Optimal power flow incorporating renewable uncertainty related opportunity costs

In this paper, an optimal power flow solution method incorporating a cost model that associates the uncertainty-related expense incurred with the use of renewable energy sources, viz., solar and wind, is demonstrated. Wind speed and solar radiation are assumed to follow Weibull and normal distributions and the uncertainty is simulated using Monte-Carlo approach. Wind turbine mathematical model is used to estimate the wind generator output, while the same for solar PV is estimated using PV-inverter models. The uncertainty-induced opportunity cost for both the renewable sources is composed of the costs due to both power excess and deficit. These cost components are indicative of the reserve requirement and loss of benefit, due to the unavailability of the corresponding generation. This research models and integrates the opportunity costs of renewable generation into a conventional OPF formulation, which is then solved using four variants of particle swarm optimization method. Among these, mutation-based PSO approach provided better results than others. The test system used is modified IEEE 39-bus network and the performance of the method as well as the effect of the uncertainty cost is evaluated under multiple renewable penetration levels. The results also indicate that solar generation is preferred over wind in terms of the uncertainty cost, while the use of stochastic natured renewable systems is economically justified and preferred over thermal generators.