A Replicator Dynamics method for the Unit Commitment problem

Abstract

A short-term Unit Commitment problem in power systems requires methods that are simple, stable and re- configurable. A Replicator Dynamics based algorithm can be a good candidate in this regard. In this paper, this method is extended to model the unit specific constraints on the fitness function directly and precisely such that the method retains the optimality of the solution. Furthermore, the results are validated by comparison with Newtons Approach for optimal dispatch. The simulation results verify the methodology and implicate the possibility of extending it to complex and coupled constraints. I. I NTRODUCTION Unit Commitment (UC) models the power pool auctions in a market scenario where for a given electricity demand each generation unit proposes a bid (1). This bid consists of a cost function subject to the unit operational constraints. The selection of a bidding strategy can be dependent on the strategies of other units (i.e. players) and environmental variables. This strategic interaction can be modeled using Replicator Dynamics (RD) from the evolutionary game theory. RD models the dynamics of a population playing a specific strategy such that a successful strategy attracts more elements of population (2). RD is an attractive choice for such problems as its benefits include reduced complexity, support for parallel computation and re-configurability. Therefore for system operator, it's important to model the strategic interaction in broader perspective. RD based economic dispatch of distributed generators is discussed in (8), and it is extended to UC problem in this work. Specifically, the methodology of mapping the unit specific constraints on fitness function is presented. The result of optimal resource allocation using RD is validated by com- parison with Newtons Approach (NA) for optimal dispatch. The result increases the confidence of extending the work to multi-objective scenarios. In last the fitness function dynamics are closely observed to explore the rate of convergence and dependency on initial conditions. Based on these results, the stability of the equilibrium is also discussed. The article is organized as follows. The basic concept of RD and analogy with NA is introduced in Sec. II. It is followed by the problem formulation along with a brief discussion on the stability of the desired equilibrium. In Sec. III, results for our test case are presented. The paper is concluded in Sec. IV with a short summary.