Small-Signal Stability Assessment of the Cameroonian Southern Interconnected Grid
Abstract
This article investigates the performance of the generator excitation loop equipped with a PID controlled AVR system, and of the dam automaton consisting of a PID controlled water flow regulation system in the southern interconnected grid (SIG) of the Cameroonian power system, when subjected to small perturbations, using linearized state-space models of the power plant. A fifth order model of the synchronous generator with a high gain excitation system and AVR is considered. A detailed formulation of equations comprising the mechanical and electrical swing dynamics of the turbine-generator unit and the load is realized; a multivariable state-space non linear model of the one area single machine system model is obtained. For small-signal performance analysis, the model is linearized around an operating point. The article also presents a state-space model of the water flow system. The effects of PID controlled AVR and water flow regulation systems are examined through performing of extensive MATLAB simulations to analyze the behavior of the proposed models following small disturbances. The simulation results presented in this paper are obtained using a MATLAB computer program developped by the authors; they provide useful insight into the dynamic behavior of the Cameroonian SIG, including stability, speed of response and steady-state accuracy. The paper establishes that the classical control systems do not have very good performance: long settling time, high overshoot, relativly slow response, and many damped oscillations.
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Introduction
Stability is one of the important issues of safe power system operation. Repeated global power outages due to power system instability reveal the importance of the issue [1]. Power system oscillations were first observed as soon as two or more synchronous generators were connected together to provide more generation capacity and reliability. Originally, the fairly closely connected synchronous generators were observed to swing against each other at low frequency; these spontaneous oscillations appeared in mechanical variables like rotor angle and speed [2]. Since synchronous generators are rotating electromechanical devices, mechanical oscillations of their rotor were transmitted by electromagnetic induction to electrical variables like bus voltages, line currents and power. The oscillations are initiated by variations in generation and custom loads, which act upon the systems as perturbations or disturbances. Because power systems have an almost continuously time varying nature – load and thus power demand vary in time, they always suffer from oscillations. Power system oscillations are therefore inevitable and are a characteristic of the system. The perturbations could be normal or abnormal. Normal perturbations are often of small magnitude, and abnormal perturbations like loss of a large generator or custom load, and short-circuit on a transmission line or in a substation are of large magnitude. Power system oscillations become much worse following a large disturbance. In some cases the low frequency growing oscillations cause loss of power supply to custom loads, loss of synchronism among generators, or they reduce transmission capability of long transmission lines; these are expressions of power system instability. Voltage oscillations in a power system indicate a high degree of its vulnerability, because a change in the condition of power system could easily lead to a progressive drop in voltage at all buses in the transmission network, and to voltage collapse. Distribution networks are practically exempted from this problem due to their passive nature. Over the last three decades, the problems of low frequency oscillations in power systems have assumed importance.
The stability issue of power systems can thus be stated in three aspects [3], [4]: (i) rotor (or power) angle stability, (ii) bus voltage stability and (iii) frequency stability. An upset in the balance between power generation and power demand can affect frequency stability; the frequency could no more be maintained within the stability limits. The inability of the power system to meet the demand for reactive power causes voltage instability. However, voltage instability does not always occur alone; often angle and voltage instabilities are associated. One may lead to the other and the distinction may not be clear.
Conclusion
A linearized dynamic model of the Cameroonian southern grid has been developed, using the state-space approach. The model is modular in structure. Intensive MATLAB simulation has been carried out to investigate the behavior of the southern grid of the Cameroon power system, after small disturbances. The simulation results have shown that classical controllers actually in the southern grid of the Cameroon power system ensure stability of the SIG, but they are not accurate, they are slow. The power system is poorly damped. This assessment can serve as a basis for the design of most efficient additional automatic controls to operate in combination with classical controllers present in the SIG.