运用多项式方程系统算法求解电力市场均衡

Computing Equilibrium for Electricity Market Using Solving System of Polynomial Equations Algorithm

在电力市场不完全竞争模型分析中,求解市场的纳什均衡是一个重要任务,其中求解混合策略均衡以及判断是否存在多个均衡都是相当困难的课题。首先建立了考虑网络约束的古诺模型,然后运用属于收益矩阵方法类型的多项式方程系统算法求解市场可能存在的所有均衡。多项式方程系统算法引用支集的特征,将纳什均衡条件转化为多项式方程系统及其不等式约束,并运用软件包PHCpack求解该方程系统,而后通过甄别满足不等式条件的解来求取所有均衡。针对3节点测试系统,构建不同的实验场景来考察所提出算法的有效性,实验结果表明,在一定条件下,多项式方程系统算法能够求解到所有均衡,这表明该方法在实际电力市场分析中有较大潜力。

It is a key problem to calculate the Nash equilibrium for the deregulated electricity market, and the problem mainly has two difficulties： computation of the mixed strategy Nash equilibrium and determination of whether multiple equilibria exist. Cournot model considering the network constraints is presented firstly, then the solving system of polynomial equations algorithm, which is an algebraic method and belongs to the payoff matrix approach, is applied to calculate the all Nash equilibrium for the finite-strategy multi-player game in the electricity market. The proposed approach mostly relies on decomposing the game by means of the support sets, and for each support set, the condition of the Nash equilibrium can be characterized by a system of polynomial equation and inequalities, and a famous software pack PHCpack is applied to solve the equation system, then the all Nash equilibrium could be found through detecting all the solution. Several examples based on the three-bus test system are used to investigate the effectiveness of the proposed approach, and the results show that the approach is capable of finding all Nash equilibrium under certain condition, which indicate that it has the potential to be used in the study of the real-world electricity markets.