Sixième conférence internationale des Sciences et des Techniques de l’Automatique – STA’2005 19 au 21 décembre 2005 – Sousse – Tunisie
Direct voltage stability assessment of large power systems Brahmi Houda, Hasnaoui Othman, Dhifaoui Rachid (1) (1) : INSAT– Centre Urbain Nord – Rue de la Terre- BP 676 - 1080 Tunis Cedex
[email protected]
Abstract: Voltage stability phenomenon have been intensively studied the last two decades because it was the principal factor in the most dangerous blackouts that have streaked many power systems around the world. Various approaches are developed to evaluate if the steady state regime of the power system is at proximity of a saddle node bifurcation (SNB) point or it is sufficiently far from this critical situation. However, because power systems are large systems by nature and they are governed by highly nonlinear models, these approaches are only reliable around the operating point. More investigations in this field are therefore needed and highly encouraged by electrical power companies. The work developed in this paper lies in this field and proposes simple and relatively reliable crisis voltage criterion detection. The criterion integrates not only voltage magnitude profile but also voltage angle influence. Furthermore, the paper indicates how to determine the criterion sensitivities when the SNB problem is treated by continuation power flow (CPF) procedure. Performances of the proposed method are validated on the basis of two power systems respectively of 14 buses and 40 buses.
I. INTRODUCTION Around the world, electric energy companies are today’s faced with various technical constraints and problems generated by the ongoing expansion and growth of energy consumption. These companies are forced on one hand to operate their networks under high stressed conditions and they are asked at the same time to ensure adequate steady state in particular in terms of voltage profile. It becomes in fact well known that voltage stability limits evaluation is of first priority because degradation of voltage level has evident implication in all serious incidents that have streaked many power systems [1, 2, 3]. Excessive decrease in voltage profile can excite very large oscillatory modes on machines and energy transport lines leading to generating unit outages and consumers cancelling [4, 5]. Accurate determination of voltage stability limits, more precisely, accurate evaluation of the remaining distance that separates the actual operating point from the saddle node voltage point is very needed by electric energy companies. Various criteria, generally called voltage stability indices/margins are proposed in the literature
[7, 8, 9]. Generally speaking, these indic es are based on very complicattheoretical procedures and burden time computing routines on one hand and have high nonlinear shapes on the other hand. These voltage indices are therefore very difficult to be used by engineers more interested by general and quick information to predict and plan major actions. Engineers of electrical companies need in fact global judgment, simple information and interpolation tools of reasoning. The work here developed is dressed in this sense. Load flow equations of the multi bus power system are used to build a voltage stability criterion invoking the well known theoretical background of the two bus system case. The criterion is expressed in terms of voltage magnitudes and angles in a very sample way ensuring the possibility of quick sensitivity analysis. The established criterion is shown to have a practically linear shape when tracked versus the actual voltage calculated from a continuation process of increasing power demand. IEEE-14 bus test system and Hawkins’s 40 bus system [10] are used to validate the proposed method. The obtained results are presented and commented. Continuation load flow procedure is realized with PSAT software [11]. II. SADDLE NODE BIFURCATION OF A TWO BUS POWER SYSTEM Fig.1 depicts the elementary case of a two bus power system. Bus 1 is considered as a slack bus with a fixed voltage E and at bus 2 is located an increasing load (P + jQ ) with corresponding voltage denoted by Ve j a . With any loss of generality, we assume that the transmission line is a pure imaginary admittance (- jy ) . 1
Generator
E
Line
2
V
Load P + jQ
Fig.1: Elementary two bus power system
STA05-CM-47
Q
Power balance at bus 1 is governed by load flow equations (1) and (2): P = -yVE sin(a)
(1)
Q = yV (E cos(a) - V )
(2)
V >V
SNB
P
By eliminating the voltage angle at the load bus, one easily derives the following expression: æQ E2 V 4 + 2 çç çè y 2
V
