Stability Analysis Of Delayed Power System And Design Of Time Delay Compensator

In order to reduce the adverse impact of low frequency oscillations on the stability of modern large-scale interconnected power grids,wide-area control system(WACS)based on wide-area measurement system(WAMS)is applied to power system.Due to the signal acquisition,processing,transmission and control delays in WACS,traditional power system becomes a delayed cyber-physical power system(DCPPS).The time delays in WACS will degrade the control performance of wide-area damping controller(WADC)for the inter-area low frequency oscillation modes of the system.In severe cases,the system may even lose its stability.Therefore,in order to avoid the unstable operation mode of DCPPS and ensure the reliability of power supply,it is necessary to study accurate and efficient methods for analyzing the small signal stability of DCPPS.In addition,in order to suppress the deterioration of control performance of WADC caused by the delays in DCPPS,the delays can be compensated by designing a reasonable time delay compensator.The second and third chapter of the dissertation studies the solution operator discretization(SOD)based eigenvalue calculation methods of DCPPS that are based on the DCPPS model described by delayed differential equation(DDE)and the DCPPS model described by delayed differential-algebraic equation(DDAE),respectively.The fourth chapter of the dissertation considers the delays in DCPPS as a random time delay that meets a variety of normal distributions.An adaptive time delay compensator is designed to compensate the phase lag of control signals caused by the delay.The main research work and the results achieved of the dissertation are as follows:(1)An eigenvalue calculation method based on partial SOD with pseudo-spectral differencing(PSOD-PS-?)method of DDE model is proposed.Firstly,the partial pseudo-spectral discretization scheme is adopted to obtain the DDE model based discretization matrix.Then,the IRA method is utilized to calculate the partial eigenvalues with the highest modulus values of the preconditioned discretization matrix.And the obtained eigenvalues are transformed to the eigenvalues of DCPPS.In IRA algorithm,the sparse triangular factorization is adopted to calculate the matrix inversion and vector product.Lastly,the accuracy and efficiency of DDE model based PSOD-PS-? are validated on the two-area four-machine system and Shandong grid.(2)An eigenvalue calculation method based on partial PSOD-PS-? method of DDAE model is proposed.Firstly,the partial pseudo-spectral discretization scheme is adopted to obtain the DDAE model based discretization matrix.Then,the IRA method together with the properties of Kronecker product are utilized to calculate the partial eigenvalues with the highest modulus values of the preconditioned discretization matrix.And the obtained eigenvalues are transformed to the eigenvalues of DCPPS.In IRA algorithm,the sparse triangular factorization is adopted to calculate the matrix inversion and vector product.Lastly,the accuracy and efficiency of DDAE model based PSOD-PS-II are validated on the two-area four-machine system and Shandong grid.(3)An adaptive time delay compensator is designed,which can improve the deterioration of control performance of WADC caused by the delays in DCPPS to some extent.Firstly,the PSOD-PS-II method and eigenvalue tracking technology based on perturbation theory are used to verify that the time delay compensator can improve the damping ratio of the low-frequency oscillation modes of DCPPS.Secondly,consider random delays that satisfy several normal distributions and set the upper and lower bounds of the random delays.Then,the delay interval is divided into several equilong sub-intervals,and the median value of each time delay sub-interval and the angular frequency of a certain oscillation mode are used to design the corresponding fixed delay compensators.Thirdly,a switching strategy for the delay compensator is designed,and the fixed delay compensator is switched automatically and timely according to the time delay sub-interval that online measured delay locates in.Then,the effective compensation for random delays is realized.Finally,The effectiveness of the designed adaptive time delay compensator in suppressing the degradation of WADC control performance caused by time delay is validated on the two-area four-machine system and Shandong grid.The PSOD-PS-I1 method based on DDE model proposed in the dissertation is capable to accurately and efficiently calculate the critical eigenvalues of DCPPS and enhances the calculation efficiency of the SOD-PS-I1 method.The PSOD-PS-? method based on DDAE model improves the calculation efficiency of the DDE model based PSOD-PS-? method when calculating the critical eigenvalues of the DCPPS whose feedback signal is related to algebraic variables.The adaptive time delay compensator designed in this paper can reduce the adverse effect of delay on WADC control performance to some extent.