基于集合论估计的电网状态辨识 (二)基于区间约束传播的求解方法

Power System State Identification Based on Set Theory Estimation Part Two Solving Method Based on Interval Constraints Propagation

量测误差有界情况下的状态辨识模型是典型的约束满足问题,且变量和约束均可以区间的形式给出。因此可采用区间分析的方法来求解该约束满足问题。文中首先通过常规的区间约束传播算法来求解该模型,然而得到的结果局部相容且具有较大的保守性。为解决该问题,提出了改进的区间约束传播算法,一方面在区间约束传播算法中引入单调性,有效消除了单调变量出现多次带来的保守性;另一方面通过增加冗余约束,对原有约束集进行扩展,在较大程度上消除了区间约束传播算法的局部相容性所带来的保守性。

The state identification model with only bounded errors is a typical constraints satisfaction problem, and variables and constraints can all be presented in the form of intervals. Thus, interval analysis can be adopted to solve this constraints satisfaction problem. The conventional interval constraints propagation method is first proposed to solve this model. However, the results are locally consistent and have conservative character to a large extent. To deal with this problem, the improved interval constraints propagation method is proposed. On one hand, monotonieity is introduced to an interval constraints propagation algorithm, which can effectively eliminate the conservative character resulting from the many times＇ appearance of monotone variables. On the other hand, by increasing redundant constraints, the original constraint sets are extended, which can eliminate the conservative character resulting from the local consistency of interval constraints propagation algorithm to a great extent.