考虑发电机安全运行极限的非固定分段无功优化模型及其算法

针对目前无功优化中没有根据不同发电机运行区域建立相应的无功辅助费用的问题，考虑了发电机安全运行极限约束，按照无功输出能力的不同，把发电机运行域分为了4个区，并给出了各个区域的发电机无功辅助费用计算函数。建立了以系统有功网损费用与发电机无功辅助费用之和最小为目标函数的无功优化模型，其对应的优化问题是一个具有非固定分段特点的非线性混合整数规划问题。文中提出了2种优化算法来求解该优化问题：结合启发式规则的混合整数规划内点法HEUIPM，其计算速度虽快，但为局部优化算法，并且在某些情况下存在不收敛的可能性；基于非线性内点法和免疫遗传算法所提出的启发式混合随机优化算法IPMIGA，该算法是全局优化的, 没有收敛性问题, 但其计算速度比HEUIPM慢很多。所以文中将2种方法结合起来，在程序设计时, 先用HEUIPM算法, 遇到不收敛时自动转到IPMIGA算法。对节点数从14到171的5个测试系统进行了仿真计算，结果验证了所提算法的有效性。

An Unfixed Piecewise Model of Reactive Optimization and Its Algorithms Considering Generator Capability Limits

To deal with the problem that the corresponding reactive power costs in the different generator areas have not been researched in the optimal reactive power flow (ORPF), the generator operation area is divided to four parts according to the reactive power bound, and the corresponding reactive power costs are given based on the generator capability limits. By minimizing the costs of reactive power and the system active power loss, the novel ORPF model is proposed. The model is an unfixed and piecewise mixed-integer nonlinear programming problem. Two optimization algorithms are developed in this paper. The first one is a heuristic and mixed-integer interior point method (HEUIPM) which owns the high speed. But in some time HEUIPM has the convergence problem. By integrating an immune genetic algorithm (IGA) with an interior point method (IPM), a heuristic hybrid stochastic search method (IPMIGA) is proposed as the second algorithm. Although IPMIGA has no convergence problem and can search the global optimal solution, HEUIPM has notable advantage in speed over IPMIGA. In the program to solve the proposed model, HEUIPM is used firstly, switch to IPMIGA only when HEUIPM is unconvergent. The numerical results of five test systems that rang in size from 14 to 171 buses indicate the effectiveness of proposed algorithms.