CAJ | 학술논문

针对电力系统无功优化确定性算法在处理离散变量时有困难及收敛域小的问题，提出把基于互补约束的全光滑牛顿算法用于含离散控制变量的电力系统无功优化。该方法使用光滑松弛函数，以避免海森（Hessian）矩阵的奇异性，将优化模型的1阶优化条件（Karush．Kuhn．Tucker，KKT）中的互补约束条件转化为光滑非线性方程，从而把非线性优化问题重构成一组非线性方程组的根求解问题，并用牛顿法进行求解。在此基础上，进一步提出以离散变量的2个边界构造其互补约束条件，并将约束条件直接嵌入到牛顿法中，实现离散变量在优化过程中的逐次逼近。算例表明：该无功优化方法具有大范围收敛性，突破了基于内点法等的无功优化技术要求系统初始点必须位于系统可行域之内的限制；采用互补约束条件处理离散变量，简单有效，能够可靠地同时得到连续变量及离散变量的最优解。
침대전력계통무공우화학정성산법재처리리산변량시유곤난급수렴역소적문제，제출파기우호보약속적전광활우돈산법용우함리산공제변량적전력계통무공우화。해방법사용광활송이함수，이피면해삼（Hessian）구진적기이성，장우화모형적1계우화조건（Karush．Kuhn．Tucker，KKT）중적호보약속조건전화위광활비선성방정，종이파비선성우화문제중구성일조비선성방정조적근구해문제，병용우돈법진행구해。재차기출상，진일보제출이리산변량적2개변계구조기호보약속조건，병장약속조건직접감입도우돈법중，실현리산변량재우화과정중적축차핍근。산례표명：해무공우화방법구유대범위수렴성，돌파료기우내점법등적무공우화기술요구계통초시점필수위우계통가행역지내적한제；채용호보약속조건처리리산변량，간단유효，능구가고지동시득도련속변량급리산변량적최우해。
Focusing on the difficulty of processing the discrete variables and the small convergence region for the current deterministic methods of reactive power optimization, a new method based on complementarity constraint smooth Newton method was applied to reactive power optimization with discrete variables in this paper. In the method, the complementarity constraints sub-condtions in the Karush- Kuhn-Tucker （KKT） conditions were transformed to be a set of smooth nonlinear equations by introducing smooth relaxation function, which ensured the nonsingularity of Hessian matrix, and the nonlinear optimization problem was reconstructed as the solution of a set of smooth nonlinear equations, and solved by smooth Newton method. On this basis, the upper and lower integer bounds of the discrete variables are constructed to be complementarity constraints conditions, and embedded with smooth Newton method to approach its integer solution successively during the Newton iteration. The results of the samples demonstrate that the method proposed for reactive power optimization owns following advantages： firstly, it has large convergence region, which breakthroughs the requirement and restriction of reactive power optimization method based on the interior point algorithm that the initial point must be located in the feasible region of the system; secondly, the strategy of adopting complementarity constraints conditions to address discrete variables is simple and efficient, and can make the optimal solutions respectively for continuous variables and for discrete variables being reliably obtained at the same time.