理论分析与实际现状均表明了电力系统电压非平衡问题会引发传统频率估计算法的有偏及震荡，造成频率调整过程的不收敛。本项目围绕非平衡系统电压的统计模型开展工作，力图将迅速发展的完备二阶统计理论及最大似然估计理论应用于非平衡电力系统的电压故障分析以及高精度频率估计算法的研究。研究工作包括：建立基于非平衡电压的椭圆分布特征参数与完备二阶统计特性的电压故障判定方法；在复数高斯白噪声的联合概率密度函数的基础上，开展基于Cramer-Rao下界的非平衡电力系统电能质量参数估计的归一化性能测试标准、以及根据非平衡系统电压的特性，提出基于系统电压及其复数共轭的离散傅立叶联合功率谱最大化的高精度频率无偏估计算法的研究；搭建基于实时数字仿真器的小型电网硬件在环仿真环境进行频率估计算法在频率调整机制中的性能测试。

It has been illustrated in both theory and practice that the unbalanced system voltage causes the estimation bias and oscillation of conventional frequency estimation methods, resulting in the unconvergence of frequency control process. This project is based on the statistical model of the unbalanced system voltage and aims to apply the fast developping complementary second order statistics and maximum likelihood estimation theory to the voltage unbalance analysis and accurate frequency estimation analysis of the unbalanced power systems. The content of this project includes: building up the elliptical characteristics and complementary second order statistics based voltage problem detection method; based on the joint probability density function of complex valued white Gaussian noise, building up the Cramer-Rao Lower Bound (CRLB) to provide a normalized test standard for power quality parameter estimation of unbalanced power systems and studying accurate unbiased frequency estimation problem based on maximizing the combined discrete Fourier power spectrum of the system voltage and its complex conjugate according to the special statistical property of the unbalanced system voltage; implementing a small-scale power system in hardware-in-the-loop simulation based on real-time digital simulator to test the proposed frequency estimation methods within the real-time frequency control process.