A non-iterative method for power system state estimation and a PMU-based method for assessing generator damping contributions

Abstract

In the proposed state estimation method, the measurement equations, which are the bus voltage magnitude, line power flow, and bus power injection equations, are formulated using rectangular coordinates of the bus voltages. With this formulation, the non-linear measurement equations become quadratic polynomials of the voltage variables. Because there are usually more measurements than what is necessary for observability, the system is over-determined and Kipnis-Shamir relinearization can be applied. The relinearization technique transforms the quadratic equations to a higher dimension system which allows the quadratic variables formed by the states to be solved in a direct, non-iterative manner. The technique requires keeping track of the indices of bus voltages that make up each quadratic variable. After solving for the quadratic variables, the real and imaginary parts of the bus voltages can be extracted.

This dissertation develops a method of assessing the damping contributions from generators based on synchronized measurements of the generator rotor angle and its terminal bus voltage phasor. The method is based on an extension of the deMello-Concordia synchronizing and damping torque decomposition method. This method can be applied if unstable or lightly damped oscillations are observed on a power system after major disturbances, without the need to do specific generator testing. The method can also be applied locally to individual generators. It can also be applied to time responses from simulation programs. Thus for inter-area modes, this method is useful in determining which PSSs are providing damping torque and which PSSs are not. Testing on the method using linear analysis and non-linear simulations on small systems has shown good results.

Second, this dissertation describes a new method of assessing the damping contributions from generators to power systems swing modes. Damping torques for power system swing modes are typically provided by power system stabilizers (PSSs) acting through voltage regulation of generators. Once these PSSs are tuned and commissioned by the vendors, their control parameter settings are not normally changed. However, as the power system evolves and the power transfer patterns change, some of the PSS settings are no longer appropriate. It is not trivial to check whether a PSS is providing positive damping contribution in a power system simulation program, let alone using field tests or measured data from generator testing.

This new state estimation method provides the same results as traditional iterative methods when given accurate measurements, and the method does not require an initial guess or have issues with solution convergence. The method has been programmed using MATLAB and has been tested on system of up to over 1400 buses. The computation speed of the new method is found to be competitive with the classical iterative weighted least-squares state estimation method, especially when parallel processing/multi-threading techniques are used. Synchronized phasor measurements can also be incorporated to speed up the solution time.

This dissertation presents two new methods in the area of power systems monitoring. These methods extract useful information from the readings of power systems measurement devices and can help utilities operate their power systems in a more efficient and stable manner.

First, this dissertation describes a new method for solving for the state estimation problem of a non-linear AC power system in a non-iterative manner when given an adequate set of sufficiently accurate measurements. This method is based on the Kipnis-Shamir relinearization technique that is used to solve over-determined systems of polynomial equations. The new method has no issues with convergence and does not require a starting guess. The non-iterative method was first proposed by Dr. Bruce Fardanesh of the New York Power Authority, and this dissertation describes further research into this solution method.