Developing Piecewise Damping Terms For The Fifth-Order Generator Model And Applications

It is essential to adopt an appropriate synchronous generator model in power system dynamic simulation and stability analysis.The seventh-order or higher order generator model can be sufficiently accurate,but it requires small time-steps in dynamic simulation due to the co-existence of the electro-magnetic and the electromechanical transients,which incurs tremendous calculation burden.In the modern power system,synchronous generators are numerous in parallel operation.Due to the high order of the seventh-order generator model,the high order of differential equations will bring the "curse of dimensionality" problem,so that the analysis and calculation can not be carried out.In order to reduce the computational complexity and improve the analysis efficiency,the fifth-order generator model,which neglects the stator transients,is adopted in the power industry.But one key problem with the fifth-order generator model is that it may lead to over-estimation or conservativeness in stability analysis,making it inadequate at times in terms of accuracy.Traditional approach proposes to append a linear damping term in the reduced-order model.However,methods for determining an appropriate damping factor are still under development and an empirical value has to be employed.It is a common practice in the power industry to employ a zero damping coefficient for the 5th-order generator model in performing time-domain simulation.The rationale behind this practice may be for the sake of conservativeness in stability analysis.However,the compensation effect for the electromagnetic torque difference by appending a zero damping term does not improve the model accuracy of the 5th-order generator model.In this paper,a piecewise damping term is proposed and developed into the fifthorder generator model,which can greatly improve the stability analysis accuracy when the fifth-order generator model is employed.An iterative method for calculating the damping coefficient of the piecewise damping term is proposed and validated via numerical studies on two test systems.Our numerical studies show that the 5th-order model with the proposed piecewise damping term is sufficiently close to those of the 7th-order model in simulating rotor dynamics.The proposed piecewise damping schemes offer higher accuracy than the traditional constant damping coefficient scheme.The regularity of the proposed piecewise damping coefficient under different dynamic conditions is also investigated.It has been found that variations of the proposed piecewise damping coefficients under different operating conditions reveal certain patterns,such as linearity and robustness under different loading conditions.In addition,the group property under different fault locations is also revealed.These nice features,in combination with the proposed piecewise damping scheme,have high potential in practical applications.Practical applications of the proposed piecewise damping terms are presented.