Study of linear models in steady state load flow analysis of power systems

Steady state analysis techniques use linear phasor circuit models, but power flow calculations require the solution of nonlinear algebraic equations. Small-signal linear models form the basis of solution algorithms such as the Newton-Raphson method and decoupled load flows. Since linear models are attractive from the viewpoint of gaining significant insight into system behavior under different operating scenarios, large-signal models such as ´DC models´ are commonly employed. Results obtained from linear models are approximate, but they provide easy comparison between different operating conditions. Contingency ranking using a DC model, and generation shift and line outage distribution factors is highly satisfactory in many instances. Studies requiring steady state analysis such as security analysis, optimal power flow and economic dispatch, and voltage stability can significantly reduce computational burdens by assuming linear models. The main objective of this paper is to study quantitatively the relative merits of commonly used linear models in steady state power system analysis. The ´DC model´ assumes negligible resistances and flat voltage profiles, and relates the bus phase angles to real power injections. A new linear model which accounts for the voltage and reactive power flows is developed, and compared to the results from ´DC model´ and ´small-signal´ models. The figure of merit for comparison is taken as the root mean square difference of similar quantities such as bus voltages and line active and reactive flows. IEEE 14-bus is used for the testing. Results show significant potential for the new linear model.