The mixed Adams-BDF variable step size algorithm to simulate transient and long term phenomena in power systems

Abstract

AesTRACTA combined simulation of transient and long term phenomena in power systems requires the solution of a large non linear stiff set of differential -algebraic equations.In this paper, we propose the mixed ADAMS-BDF variable step size and variable order algorithm for solving this problem. The Adams method is applied to the differential state variables: It provides a more reliable detection of stable cases from unstable cases than BDF. The BDF, Backward Differentiation Formulae, method is applied to the algebraic state variables. These are less sensitive to the variations in algebraic equations than the Adams method.This combined Adams -BDF method has been sucessfully implemented in the EUROSTAG simulation package and sample results are presented in this paper. I . I "Until recently, it was customary to separate the dynamic behavior of power systems into three different domains : the electromagnetic transient phenomena, the electrical and mechanical transients (transient stability domain) and the long term phenomena. For each domain, independent software had been designed. In at least three recent efforts, [1],[2],[3], the transient stability domain and the long term domain have been combined in a single computer program. In all cases, this has been achieved by the use of a variable step size and variable order integration algorithm.In this paper, we shall present the mixed Adams -BDF variable step size and variable order algorithm. It discriminates between stable and unstable phenomena in a reliable way and tackles efficiently large stiff power systems. Section 2 describes the problem. Section 3 analyses the proposed mixed Adams -BDF variable step size and variable order algorithm and reports differences with other existing algorithms. Section 4 presents the advantages of the algorithm over pure BDF and pure Adams algorithm with examples. Section 5 describes results obtained from a study case. 93 SM 482-0 PWRS by the IEEE Power System Engineering Committee of the IEEE Power Engineering Society for presentation atPower system modeling A unified transient and long term stability simulation software must offer various levels of modeling to the end user. Equations come from four sources, We detail these sources in the case of the EUROSTAG program[l]. First, the bulk of the algebraic equations comes from the network. Pi equivalent model, frequency sensitive branch impedances, frequency and voltage sensitive loads define the 1 = [Y]u admittance matrix equation. Bus voltages define the main algebraical part of the state variables. Generator models, from the simplified up to the complete 6th order Park's equations constitute the first part of the differential equations. The rotor angle, speed and flux linkages state variables are coupled with the network through the interconnection of algebraic equations and are controlled by the mechanical torque and exciter field voltage (EFD).The voltage regulators, speed governors and centralized adjustments control the torque and EFD. They define a new subset of differential an...

A Multirate Approach for Time Domain Simulation of Very Large Power Systems

“…Following [1], we estimate the local error for an attempted step from time t n to t n+1 = t n + τ n as…”

“…In this paper we will use the second-order mixed Adams-BDF method presented in [1] as our basic numerical integration method. In this method second-order Adams method is applied to the differential state variables, whereas algebraic state variables are integrated using second-order BDF method.…”

Time Domain Simulation of Power Systems with Different Time Scales

“…As the basic time integration method we use the mixed Adams-BDF method presented in [1]. The Adams method is applied to the differential state variables and provides a reliable detections of unstable situations.…”

Extensions, simplifications, and tests of synchronic modal equivalencing (SME)

“…3. The group with the machines (21, 15,16,17,22,23) was then selected (Step 5 ) to be the study area (the basis generator appears in boldface). We thus have 6 generators in the study area and 4 external basis generators (with 255 associated state variables altogether, which become the state variables of the equivalenced system), and 13 machines that will eventually be reduced.…”

“…The detailed unreduced model was implemented in the software package EURQSTAG, [15], [16], and its operating point and linearization at this operating point were determined (Steps 1 and 2). All computations with the linearized model were carried out in MATLAB, [17].…”