The previous section has described the influence of capacitors on voltage and losses independently. For networks with poor voltage regulation, if capacitors are used strictly to enforce minimum voltage limits only, it may typically result in increased losses as compared to the optimal loss configuration for that network. This implies that a combined strategy is required.
5.3.1 Methodology to size and locate capacitors based on peak feeder load
1. Networks with power factor < 0.95 and total reactive power demand (Qmax) > 300kvars should be considered for shunt compensation [68].
2. The power system simulation model needs to be scaled to the peak load where the λ load distribution should be determined using (5.26).
3. Determine the optimal location and size of the shunt capacitor using Figure 5-6 and Figure 5-7 for the given λ. The model is then re-adjusted by applying the capacitor on the network where this becomes the base model for further analysis.
4. If the minimum voltage of the network after the placement of the capacitor in step 3 is greater than the statutory voltage limit (Vstatutory), then the optimal location (𝑥) and sizing (Qopt) has been determined. In this instance the installation of the capacitor is dictated by loss minimisation only. The final size of the capacitor then needs to be modulated to the closest integer multiple of the smallest available bank size available on the market. This will cater for any switching requirements during the low load scenario. Please note that this step,
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although not stated, is required in all the assessments that follow when determining the C ratio and sizing at peak load.
5. If the minimum voltage of the network (Vtailend) is less than the statutory voltage limit after the placement of the capacitor in step 3 and λ > 0.4, then the installation of the capacitor is dictated by raising the minimum feeder voltage to the statutory limit. As illustrated in Figure 5-7, for feeders with λ > 0.4, the optimal location is at the tail end and thus the assessment entails determining the appropriate capacitor size only. From (5.5), if (Vstatutory− Vtailend) <
[(Qmax10∗ V−Qopt)∗xltail
p−p2 ] then the rating of the capacitor is given by [10∗ Vp−p2∗(Vstatutoryxl −Vtailend)
tail ] +
Qopt, else the rating is equal to Qmax which implies a C factor of 1 is used. Note xltail represents the inductive reactance in Ohms between the source and tail end of the feeder.
6. If the minimum voltage of the network is less than the statutory voltage limit after the placement of the capacitor in step 3 and c, two assessments must carried out and compared for the optimal sizing and positioning of the shunt capacitor.
7. The first assessment is to determine if by increasing the C ratio at the optimal location, whether the minimum voltage objective could be met. From (5.5), it follows that if (Vstatutory− Vtailend) < [(Qmax10∗ V−Qopt)∗xlopt
p−p2 ], then the rating of the capacitor is given by [10∗ Vp−p2∗(Vstatutory−Vtailend)
xlopt ] + Qopt, else the rating is equal to Qmax which implies a C factor of 1 is used. Note the C ratio is capped at 1 so as not to impact the upstream Sub-Transmission voltage regulation.
8. The second assessment is to determine if by increasing the location with the optimal C ratio applied, whether the minimum voltage objective could be met. Note increasing the location implies increasing the reactive impedance through which the leading capacitive current is injected. Again from (5.5), if (Vstatutory− Vtailend) < [Qopt∗xltail
10∗ Vp−p2], then the new location can be found at that point on the backbone where the inductive impedance equals [10∗ Vp−p2∗(VstatutoryQ −Vtailend)
opt ]. If the condition is not satisfied, then it follows that the location should be moved to the tail end in order to maximize the reactive impedance. In this case, the assessment as listed in step 5 above needs to be carried out to determine if the size of the capacitor can be further optimized to less than Qmax at the tail end location. For completeness, if (Vstatutory− Vtailend) < [(Qmax10∗ V−Qopt)∗xltail
p−p2 ] then the rating of the capacitor is given by [10∗ Vp−p2∗(Vstatutoryxl −Vtailend)
tail ] + Qopt, else the rating is equal to Qmax which implies a C factor of 1 is used.
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9. The final step is then to compare the results of the two assessments such that the new calculated parameters results in [ Vmin _new
1−PuPlossred] being the maximum. This final assessment ensures that the tail end voltage is maximized with maximum power loss reduction.
10. Mobile capacitor banks [68] should be considered for all cases where the C ratio required is 1 and the location set to the tail end of the feeder. The network should be strengthened to improve tail end voltages where permanent placement of capacitors for loss minimization can be reassessed.
The steps to size and locate capacitors have been summarised in the algorithms in Figure 5-11 and Figure 5-12.
Figure 5-11: Overall algorithm for capacitor placement based on combined voltage and loss objectives
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Figure 5-12: Algorithm for assessment to be carried out if minimum voltage less that statutory limit and λ > 0.4
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5.3.2 Methodology to determine the switching requirements for shunt capacitor
1. To determine the switching requirements of a capacitor bank, the impact of the capacitor needs to be studied on the network under varying load conditions with keeping the location fixed as determined in section 5.3.1 above. Thus a typical day profile of the network is to be obtained.
2. Using the profiles the network can be simulated under the varying load. Take for example, a particular instance in time T = i, the power system simulation model needs to be scaled and simulated without any compensation for this instance.
3. If the minimum voltage of the network at time T = i without any compensation is greater than the statutory voltage limit, then the size of the capacitor required is solely based on minimisation of losses on the network where using equation (19) the optimal C ratio can be calculated. The size of the capacitor then needs to be modulated to the closest integer multiple of the smallest available bank size available on the market as discussed in step 4 of section 5.3.1.
4. If the minimum voltage of the network at time T = i without any compensation is less than the statutory voltage limit then the sizing of the capacitor should be dictated by raising the minimum feeder voltage to the statutory limit. The size of the capacitor required at time T = i is given by [10∗ Vp−p2∗(Vxlstatutory−Vmin _i)
tail ]. However to ensure no increase in losses on the network if the capacitor size required is greater than the reactive power consumption of the network then the size of the capacitor required is equal to the reactive power consumption.
5. Steps 2 to 4 needs to be repeated for the various time periods in the day and the size of capacitors required under each time period should be analysed to determine the minimum, maximum and incremental step sizes required for the capacitor to ensure optimal capacitor sizing under all instances.
The algorithms for the switching requirements have been summarised in Figure 5-13.
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Figure 5-13: Algorithm to determine switch requirements of the capacitor installation.