Voltage Stability – Modelling and System Protection Scheme

This report describes power system component and system modelling for voltage stability studies, as well as a protection system against voltage collapse installed in Sweden. The importance of detailed and accurate models for dynamic loads, tap changer control, generator current limiters and distribution systems is demonstrated in the paper. The necessity to go into details and to do experiments is also emphasised and illustrated. Introduction Voltage stability, as a phenomenon, has been studied for some decades now. There is however no generally accepted stringent definition of voltage stability or voltage collapse. Both IEEE and CIGRÉ have their respective definitions [1,2]. Voltage stability can be interpreted as the capability of the power system to maintain voltage equilibrium at reasonable voltage levels. There are essentially three types of voltage collapse: 1) Transient voltage collapse, time scale of a few seconds, which occurs immediately after a very severe disturbance. In this case it is not possible to find any equilibrium point after the disturbance. The typical example is a brush fire, across a number of parallel transmission lines. Example: South Florida, May 1985 [1]. 2) Longer term voltage collapse, time scale of 10 seconds to 10 minutes. The system survives the initial disturbance, e. i. an equilibrium point is reached immediately after the disturbance, but due to load recovery and control system actions (such as on-load tap changer operation) the power demand is increased and the weak system will finally collapse. Example: Sweden, December 1983 [3,4], France January 1987 [5]. 3) Longer term voltage collapse due to load growth, time scale tens of minutes. Without any initial disturbance a rapid load growth can slowly bring the system to a collapse. Example: Tokyo, July 1987 [6]. Beside the phenomenon of voltage stability and collapse itself, stability margins and indices have been defined and methods to derive such quantities have been developed [7]. Some researchers in the field use simulations in order to include the dynamics of load, tap changers, and generator reactive power capacity limits in the voltage collapse studies [8,9,10]. Good surveys of the voltage stability discipline can be found in references [1,4,11], where theory as well as analytical tools and industrial experience are presented. The phenomenon of voltage stability is very often illustrated by the so called nose-curve, see Figure 1, where the receiving end voltage in a transmission system is plotted against the receiving end real power (the power factor or the reactive power is often used as a parameter). Figure 1. Nose-curve for voltage stability illustration. It has to be remembered that the nose-curve is a static description of the transmission system capability. If dynamic aspects are taken into consideration, which is necessary for a complete analysis, the nosecurve has to be modified. As the demands concerning return on investment for power systems around the world increases, different ways to utilise the system harder and closer to its limits are studied. Since the risk of voltage collapse is the limiting factor for the transmission capacity in many power systems, detailed studies, based on accurate models are requested. On-line real-time simulation tools to keep track of the operational risks have been developed, as well as protection systems against voltage collapse [10,12]. Having a protection system against voltage collapse installed, the operational requirements could be changed from “the system should withstand the most severe single fault” to “the system should withstand the most severe single fault followed by protective actions from the voltage collapse protection system”. Load Modelling The modelling of power system loads has been shown to be extremely important for voltage stability studies. For transient angular stability studies, impedance characteristic load models are mostly accurate enough. For long term planning and loadability, studies constant power load models are used. The phenomenon of voltage stability is in the time scale from just a few seconds to tens of minutes. Therefore accurate load models for the entire time frame are necessary. Depending on the type of load, degree of reactive power compensation and load control system a corresponding load model has to be chosen. Sometimes even on-load tap changers and shunt capacitors in the distribution system are included in the load. For longer term voltage stability studies (longer than a few seconds) induction machines can be regarded as constant power load objects. For shorter term studies a short load relief, a few seconds, can be achieved. Special attention has however to be paid to reactive power compensation close to the motors, the capacitors will behave like constant impedances. Therefore low voltage in induction motor dominated load areas will keep the real power close to the nominal value, but additional reactive power have to be transmitted from neighbouring areas, with further voltage drop and perhaps a collapse as a consequence. Detailed load model studies have been performed in Swede, where quite extensive field measurements were included [13,14,15]. Two substations, each one feeding about 10,000 households, were used. One substation fed a pure residential area with dominating household load, while the other substation fed a small town and a rather large industry. The recordings, to find out the dynamic behaviour of the load with respect to the applied voltage, were made during winter, spring and summer as well as for different times of the day. No on-load tap changers were activated in the load area and no shunt compensation was connected. For the excitation of the dynamic load response different shapes of the applied voltage magnitude were used, such as step, ramp, sine (staircase approximation) and pseudo random binary sequence. The voltage variations were achieved by quick manual operation of the tapchanger on the feeding transformer (ramp and sine) and by switching the transformer circuit-breaker on one out of two parallel transformers with tap changers at different positions, see Figure 2. Figure 2. Arrangement for the voltage step-change recordings. The two tap changers were set at different tap positions. The circuit-breaker for one of the transformers was used to create the step. The analysis was concentrated to the voltage step change. Results from the recordings are shown in Figure 3. The basic behaviour of the load was similar, irrespective of the time of the year and the day. It was also similar for both load areas. The amount of load recovered, the time constant, etc. differed however between the recordings. Figure 3. Active and reactive power recording from the pure residential area; June; daytime. From Figure 3 we see that a voltage drop of about 10% (from 22 to 20 kV) cause an initial drop in real power of about 20%, which corresponds to the impedance load model. But after about 5 minutes the real power has recovered to a level that is just slightly below the pre-disturbance level, which corresponds to the constant power load model. The initial drop in reactive power is larger than for the real power, but the recovery is less pronounced. For both real and reactive power, it seems reasonable to assume that a dynamic load model comprising the transient and steady state level, combined with a time constant, according to Equation 1.