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...

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The authors have developed a new type of program for the numerical simulation of dynamic phenomena in power systems.This program unifies the conventional fields of transient, mid-term and long-term stabilities.The integration algorithm ensures a constant level of accuracy in the calculation of fast o r slow transients through a continually variable step and through suitable numerical stability properties.The performance levels reached, both as regards ease of utilisation and the size and complexity of the simulated systems, allow the majority of cases to be covered so far as the dynamic system behaviour study requirements of the Belgian power companies are concerned. * System black start simulation.* Centralized control design. 0885-8950/89/0200-0129$01 .00@ 1989 IEEE * All long-term stability problems (load shedding schemes, ... ) .* All mid-term stability problems, with simulation of large transients until full return to steady state conditions, with representation of overload protection, emergency shutdown devices and so on, particularly those equipping nuclear power units.* The user requirement of entering his own process and control system models and of disposing of convenient means for checking out these models. *The replacement and unification of all the transient and long-term stability programs used by the power utilities in Belgium, as well as the mathematical process and regulation models, in Order to maximize model building profitability and to facilitate the exchange of results between specialists.