考虑发电机阀点效应的改进拉格朗日松弛有功调度策略

发电机阀点效应导致的非凸非光滑特性增加了有功经济调度模型的复杂度,从而增大了求解难度.文中提出一种考虑发电机阀点效应影响的改进拉格朗日松弛有功调度算法.首先,提出一种二次多项式分段拟合算法,从而将发电机阀点效应成本分解为多个分段二次多项式形式;其次,将拟合后的表达式代入拉格朗日松弛子问题中,从而将原问题转化为分段二次规划问题,并采用比较对称轴及优化变量上下限的方法快速求解,避免了引入整数变量造成的求解效率偏低问题.同时,为防止多个局部最优解导致的优化过程不收敛问题,提出一种基于近端梯度法的增广求解策略,通过在目标函数中引入辅助变量及惩罚项来加强子问题的凸性,加快收敛速度.最后,基于40机和48机测试系统对所提方法的有效性进行了测试.

Improved Lagrangian Relaxation Active Power Dispatching Strategy Considering Valve-point Effect of Generator

The non-convex and non-smooth characteristics caused by generator valve-point effect increase the complexity of active power economic dispatching modelS, which increases the difficulty of solving the model. An improved Lagrangian relaxation active power dispatching algorithm considering the influence of generator valve-point effect is proposed. Firstly, a quadratic polynomial piecewise fitting algorithm is proposed to decompose the cost of generator valve-point effect into multiple piecewise quadratic polynomials. Secondly, the fitted expression is brought into the Lagrange relaxation subproblem, so that the original problem is transformed into a piecewise quadratic programming problem, which is solved rapidly by comparing the axis of symmetry and the upper and lower limits of optimization variables, so as to avoid the problem of low solution efficiency caused by the introduction of integer variables. At the same time, in order to prevent the convergence stagnancy of the optimization process caused by multiple local optimal solutions, an augmented solution strategy based on the proximal gradient method is proposed. The convexity of the subproblem is strengthened by introducing auxiliary variables and penalty terms into the objective function to accelerate the convergence speed. Finally, the effectiveness of the proposed method is tested based on 40-machine and 48-machine test systems.