Dynamic Load Models for Power Systems - Estimation of Time-Varying Parameters During Normal Operation

Sammanfattning: Economic and environmental concerns will slow down the expansion of the transmission system in many countries. The addition of new transmission lines will be few and far between. The de-regulation of the power supply will introduce new power flow patterns on the bulk transmission systems. The net result is that the power systems will operate much closer to their transfer limits and operate there much longer time than has been necessary. The risk for voltage collapse determines the transfer limits in many bulk transmission systems. The accurate determination of the transfer limits will be an increasingly important task to maintain the operational security and economic operation of the power system. Many studies have shown the importance of the load representation in voltage stability analysis. Static load models are not accurate enough for capturing the dynamics of the network. Therefore dynamic load models are needed even if voltage collapse, in many cases, is a slow phenomenon. iii Due to the large amount of electric heating loads in Sweden and its effect on voltage stability, Hill and Karlsson have proposed a load model with exponential recovery. The model is expressed as a set of nonlinear differential equations, where the real and reactive load powers have a nonlinear dependency with voltage. The standard dynamic active load model is characterized by three parameters, steady state load-voltage dependence, transient load-voltage dependence and a load-recovery time constant. The same applies to reactive load. As an extension of the mentioned work, the present author proposes an automatic method for the determination of parameters in standard dynamic load models. The dynamic set of nonlinear equations has been linearised and the problem has been reduced to a linear identification problem. The Least Squares criterion is used for minimizing the error function between measured and simulated data. Field measurements from continuous normal operation at the 20 kV and 50 kV-level from a substation in the South East of Sweden have provided over 1 GByte of data covering all seasons during the time period July 2001-June 2002. The determination of the load parameters based on this data has resulted in valuable information. The parameters’ time-varying characteristic and their dependency with weather and season of the year have been studied; there is correlation between the active and reactive recovery time constants, and between them and the corresponding steadystate characteristic of the load. Strong dependency of the transient active and reactive characteristic of the load with the temperature has been found. Furthermore, some unexpected deviations in the reactive load parameters have led to a new representation of the reactive load. The reactive power level, which was previously used as normalization factor, is inappropriate. If instead apparent power level is used, the variability in the parameters that describe the reactive load response is drastically reduced.