Analysis And Control Methods Of The Switching-Type Ultra-Low Frequency Oscillation In High Hydroelectric Sending-End Power System

In recent years,ultra-low frequency oscillations(ULFOs)have occurred many times in sending-end power grids with high proportion of hydropower at home and abroad.At present,the cognitions of the ULFOs are not comprehensive enough.Based on the mechanism of negative damping oscillation and forced oscillation in traditional smooth dynamic system,it is impossible to explain the ULFO phenomenon when the system with positive damping or without equilibrium point.On the other hand,the dead zone and limit non-smooth switching links of the hydrogovernor(the corresponding system is a non-smooth dynamic system)have important effects on the occurrence and characteristics of the ULFOs.In view of this,the paper proposes a new oscillation classification and studies the mechanism,bifurcation characteristics,approximate analysis methods and control methods of the ULFOs engaged with dead zone and limit,based on the relevant theories of the non-smooth dynamic systems.The main work and innovations of the paper are as follows:Based on the mathematical representations,i.e.,mathematical characteristics such as system model and trajectory form when oscillations occur,a new classification of oscillations is proposed,including negative damping oscillations,forced oscillations,switching-type oscillations,and other complex oscillations.It is pointed out that the ULFOs engaged with the governor dead zone and limit belong to the switching-type oscillations,which correspond to the oscillations occurring after the occurrence of a non-smooth bifurcation in a non-smooth system,and are different from the oscillations occurring after the occurrence of a smooth bifurcation in a traditional smooth system.The mechanism and corresponding non-smooth bifurcation characteristics of the switching-type frequency oscillation engaged with dead zone and limit in a single hydro-machine power system(SHPS)are analyzed.In the non-smooth SHPS,two different types of switching-type frequency oscillation phenomena are found when the system with positive damping or negative damping,and the reasons of oscillation are analyzed based on the phase portrait method.Further,when the load parameters change,the boundary equilibrium bifurcation,the Hopf-like bifurcation,and the C-bifurcation of dynamic structure,together with the dynamic properties after disturbance and other non-smooth bifurcation characteristics of the SHPS are analyzed.The influence of the dead zone and limit non-smooth switching links of hydrogovernor and the different fault impact on the ULFO characteristics of a large power grid with high proportion of hydropower is analyzed.The power grid oscillates when the system with dead zone and limit,while recovers stability when the system without dead zone and limit,and oscillates when the fault duration is long(large disturbance),while recovers stability when the fault duration is short(small disturbance),indicating that one of the reasons for the switching-type ULFOs(ST-ULFOs)in the power grid with positive damping is that sufficient fault disturbance makes multiple dead zones and limits work.In the non-smooth SHPS,four different types of ST-ULFOs are found,which can respectively correspond to the ULFOs in the actual power grid.Based on the description function method,an approximate analysis method of the ST-ULFO is provided,which is applicable to the frequency oscillation with center not deviating from the rated frequency.This method is based on a piecewise description function considering both dead zone and limit,which can approximately analyze the switching-type frequency oscillation phenomena and their characteristics of the non-smooth SHPS with positive damping after large disturbance.In the approximate smooth system,it is shown that the non-smooth system can have an unstable limit cycle and a stable limit cycle(corresponding to the switching-type oscillation engaged with dead zone and limit)outside the stable equilibrium point.The adaptability analysis of the description function method shows that when the low-pass filtering performance of the system becomes poor,the accuracy of the analysis results of using smooth systems to approximate non-smooth systems will also become poor.Based on the improved Popov harmonic linearization,an approximate analysis method of the ST-ULFO is proposed,which is applicable to the frequency oscillation with center deviating from the rated frequency.This method firstly applies the Popov harmonic linearization theory to analyze the ULFOs engaged with the dead zone and limit of hydrogovernor and improves the traditional Popov harmonic linearization analysis method based on the characteristic law that the stable limit cycle is basically symmetrical about the frequency of the unstable equilibrium point.For the system with dead zone and limit multiple switches,the improved method does not need to assume all the situations of the switches that may work during oscillation in turn,which reduces the complexity of calculation.Simulation results show the effectiveness of the proposed method.A control method of ST-ULFO is proposed,which considers both the system stability and the performance of primary frequency modulation.Compared with the existing method,which only considers the optimization of the PID general control parameters of primary frequency modulation,the proposed method considers the optimization of the dead zone and limit non-smooth structure parameters at the same time.According to the conditions for weakening switching-type oscillation,the proposed optimization method takes increasing the suppression effect of the non-smooth part and reducing the amplification effect of the smooth part as the evaluation indicators,and considers the influence of dead zone and limit on the performance indicators of primary frequency modulation,so as to solve the optimization parameters based on the particle swarm optimization algorithm.Compared with the existing optimization method,the simulation results of the SHPS,a reconstructed four-machine two-area system and a large power grid show that the system optimized by the proposed method has better primary frequency modulation performance and anti-disturbance performance.