IEEE Transactions on Power Systems, Vol. 11, No. 1, February 1996 303 Low-Order Black-Box Models for Control System Design in Large Power Systems I. KAMWA, MEMBER, IEEE G. TRUDEL, MEMBER, IEEE L. GERIN-LAJOIE Institut de recherche d’Hydro-Qukbec IREQ, 1800 montke Ste-Julie, Varennes, Qc, Canada J3X IS1 Rkseau de transport, Hydro-Qukbec 855 Est Ste-Cathe’rine, Place Dupuis Montrkal, Qc, Canada H2L 4P5 Etudes de rkseaux, Hydro-Qukbec 855 Est Ste-Cathe‘rine, Place Dupuis Montrkal, Qc, Canada H2L 4P5 ABSTRACT - The paper studies two multi-input multi-output (MIMO) procedures for the identification of low-order state-space models of power systems, by probing the network in open loop with low-energy pulses or random signals. Although such data may result from actual measurements, the development assumes simu- lated responses from a transient stability program, hence benefit- ing from the existing large base of stability models. While pulse data is processed using the eigensystem realization algorithm, the analysis of random responses is done by means of subspace identi- fication methods. On a prototype Hydro-Qu6bec power system, including SVCs, DC lines, series compensation, and more than 1100 buses, it is verified that the two approaches are equivalent only when strict requirements are imposed on the pulse length and magnitude. The lmh-order equivalent models derived by random- signal probing allow for effective tuning of decentralized power system stabilizers (PSSs) able to damp both local and very slow inter-area modes. KEYWORDS: small-signal stability, minimal realization, subspace identification, reduced-order models, damping controller,stabilizer I. INTRODUCTION Low-order state-space or transfer function model sufficiently representative of the nominal system behavior are prerequisite to the systematic design of control systems. Recent trends toward decentralized multivariable dynamic pole-placement [ 11 and robust control through H, optimization [2] further empha- size the critical need for accurate small-signal models with less than 20 states, irrespective of the size of the involved power system [3]. The mainstream approach uses a small-signal stabil- ity package 141to build the linearized state-space representation of the whole network from which any subset model of interest can be deduced. However, with the MASS [2,4] or MANSTAB/ POSSIM [3,5] software, this approach is restricted by the size of the network. On the other hand, the state-space modeling capabilities of PEALS [2,4], which specifically targets bulk power systems, are insufficientfor the present aim. Whatever the case, even if it were feasible to build, like in MASS, a complete (A,B,C,D} linearized state-space represen- tation of say, a 12, 000-bus system, such a model would be impractical for control design without extensive order reduc- tion. So far, the practice has been to carefully reduce the large- scale system to manageable dimensions through dynamic equiv- alency [Sj prior to small-signal analysis. But when the inter-area modes of concern involve widely distributed geographical areas, it is not always possible to build a consistent medium- scale equivalent preserving its frequency and shape [6]. This paper was presented at the 1995IEEE Power Industry Computer Applications Conference held in Salt Lake City, Utah, May 7-12 1995. Consequently, designers are often bound to make direct use of the complete, large-scale system as the basis for building the required low-order control design models. One emerging approach in this context is based on identification techniques applied to signal responses generated by time-domain simula- tions of the large-scale model [3,7-111. In long-term planning studies, this may be the only way to capture the dynamic behav- ior of the bulk network, from the existing base of standard sta- bility models and using the same configurations as for transient stability assessment. However, the approach is also applicable to actual measured signals, provided the estimation procedures used are sufficiently robust to cope with colored noise [8,9]. In this paper, we study two identification techniques for deriving numerically balanced, state-space black-box models suitable for control design. Poles and zeros are merely by-prod- ucts of the identification, computed in the last stage if neces- sary, after a robust order reduction [ 121 of the raw model. From the start, these methods have encompassed MIMO systems to deal effectively with the possible loss of controllability andlor observability of some modes, depending on which selected locations are excited and/or monitored. While eigensystem real- ization E131 is limited to pulse response data, Numerical algo- rithms for Subspace State-Space System Identification,the so- called N4SID [ 141 or more simply, S41D [15], can use any type of excitation, as long as it is persistent. Besides illustrating some applications of low-order black-box models in controller tuning, one aim of this study was to use N4SID as a benchmark for assessing the pitfalls, if any, of the pulse-response based Prony or state-space realization methods. The paper is organized as follows. In Section 11, testing pro- cedures easy to incorporate into a transient stabilityprogram are presented. Section I11 summarizes the two state-space estima- tion methods used. Section IV deals with single-inputmulti-out- put (SIMO) applications to a representative future Hydro- Qukbec network and Section V reports on decentralized single- input, single-output (SISO) stabilizer tuning in a wide fre- quency range, based on the heuristic flexible PSS structure first introduced by Grondin et al. [ 161. 11. mSTING IN A WNSIENT-STABILITY PROGRAM A major problem in developing a time-domain identification experiment for small-signal model derivation is that a compro- mise has to be made between two conflicting goals with regard to the excitation signal [8]: it must be of a high enough level to provide signal responses of sufficientmagnitude, e.g., above the background noise floor for actual tests, but sufficiently weak to avoid nonlinear effects, especially within the test machine. 0885-8950/96/!$05.00 0 1995 IEEE