Weather Conditions and Modelling Parameters

The cost of security is influenced by the weather conditions because these conditions affect the component failure rates. The Monte Carlo simulation can thus take the weather conditions into account when estimating the cost of security. Three weather conditions have been considered: fair, average and adverse weather. When the weather is fair, the probability of component failure due to weather-related incidents is very small. On the other hand, during adverse weather conditions, the component failure rates can be very high. Average weather reflects a theoretical weather condition, which lies between fair and adverse weather and where the failure rates is equal to the average value calculated over a year.

Details of the modelling of weather are given in Chapter 3 of this thesis. The proportion of failure during adverse weather conditions was computed using data collected in Canada during the period 1991-1995 [5]. According to [5], 67% of the permanent failures take place during adverse weather conditions at 300kV to 400kV for any type of

supporting structures. 72% of 110-149kV line failures occur in adverse weather. When modelling the adverse weather the proportion factor of failures is chosen as 70% throughout the network. When modelling the average weather the proportional factor of failures of Area-1 is chosen as 20% and Area-2 and Area-3 are chosen as 15% each. [6]. 5.9.3 Cost of Security With Fair Weather and Considering System Blackouts

When considering system blackouts, the cost of security is estimated using the Monte Carlo simulation. The stratified sampling with shed load stratification is used to reduce the variance of the estimate. Figure 5.3 shows the smoothed values of probabilistic cost of security with fair weather effects considering the system blackouts. The method of estimating the cost of security is described in Chapter 3 of this thesis.

Figure 5.3: Probabilistic cost of security levels of modified 24-bus IEEE Reliability Test System for fair weather and considering system blackouts. The numbers along the contour lines indicate the cost of security (in thousands of pounds). This figure also shows the deterministic security boundary.

It can be observed from Figure 5.3 that the probabilistic cost of security is densely populated at the highest operating points, which are defined by the highest values of study parameters. Cost of security can be varied from £200 to £35,000 within the feasible limits of operation. In here the feasible limit is referred to the operating conditions beyond which power flow diverges. There is a region where the system can be operated compromising a cost of security of £200 to £400. Beyond this region the incremental cost of security tends to increase significantly.

The probabilistic method used in [1] is based on a resulting risk due to constraint violations, instead in our analysis it is the cost of security. Reference [1] change the generation pattern according to the criteria in Equations (5.1) and (5.2) where as our analysis adjust the generation pattern with respect to the criteria in Equations (5.1) and (5.2) together with an economic despatch. This is the reason why there is a difference between our results of probabilistic assessment and the results reported in [1].

Figure 5.4 shows the raw values of cost of security with fair weather effects considering system blackouts. When compared Figures 5.4 and 5.3, it can be seen that the smoothed values more close to the raw values.

Figure 5.4: Raw values of the cost of security with fair weather effects when system blackouts are considered.

When the operating point moves from lower to higher ‘North to South flow’, because of a change in generation pattern, some of the plants in South (i.e., Area-1 in Figure 5.1) are switched off as the Northern generation is fully committed to supply the Southern demand. This is because the criterion in Equation (5.2) adjusts any change in generation in Area-1 with Area-3 and a reduction in generation at Area-1 causes occasionally requires the shut down of certain expensive plants, which also carries a significant amount of reactive power. Although the active power balance is maintained with respect to the criteria in Equations (5.1) and (5.2), these equations do not take into account reactive power control.

Increasing the ‘North to South flow’ reduces the reactive margin and increases the cost of security considerably at the highest levels of ‘North to South flow’ and the highest levels of ‘Generation at bus 23’. Therefore under such operating conditions of the network, load disconnections are needed to get system back to normal operation. In addition, the plants in Area-1 & Area-3 do not have same generation capacity including the reserve to interchange the generation to follow the criterion in Equation (5.2). This imbalance also disturbs the change in generation pattern when the ‘North to South flow’ and ‘Generation at bus 23’ approach their boundary limits.

Figure 5.5 shows the number of system blackouts that are considered for the estimation of cost of security in Figure 5.4.

Figure 5.5: Number of system blackouts that are considered for the estimation of probabilistic cost of security in Figure 5.4.

It can be seen from Figure 5.5 that the insufficient reactive power control at the higher levels of ‘North to South flow’ triggers a large number of system blackouts. According to Figure 5.5, when the ‘North to South flow’ is highest, the cost of security is entirely dominated by system blackouts. Ignoring this effect distorts the estimate. The reason for larger number of system blackouts at these operating points is the lack of reactive reserve to compensate for the increase in reactive demand that results from line outages. When changing the generation pattern according to the criterion in Equation (5.1), the influence of system blackouts is not significant as this region experiences a small number of system blackouts. This is because this criterion is defined between the generators connected at two busses (i.e., bus 13 and bus 23 in Figure 5.1) and the imbalance between the reactive powers of the generators connected at these two busses can be compensated from the reserve in Area-3. Area-3 has the largest reserve and it can be controlled only by the criterion in Equation (5.2).