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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。
In the incomplete market competition model analysis, it is an important task to solve the market Nash equilibrium. It is a very difficult task to solve the equilibrium of the hybrid strategy and to judge whether there are multiple equalizations. First, a Cournot model considering network constraints is established, and then all equilibria that may exist in the market are solved using the polynomial equation system algorithm that belongs to the type of income matrix method. Polynomial equation system algorithm refers to the characteristic of support set, transforms Nash equilibrium condition into polynomial equation system and its inequality constraints, and uses software package PHCpack to solve the system of equations, and then obtains all equilibria by discriminating solutions that satisfy inequality conditions. The experimental results show that under certain conditions, the polynomial equation system algorithm can solve all equilibria, which shows that the method in the actual power market analysis, there are Great potential.