Summary for all case study systems

Table 5.5 summarises the potential performance for each case study system that could be achieved if the algorithms are selected optimally on a per-state basis. The oracles represent the potential performance that could be achieved if the optimal selections minimise the number (oracle 1) or energy (oracle 2) of overloads, whilst minimising curtailment. The potential performances are compared with the algorithms that are most effective overall with respect to the same objectives used when determining the optimal selections. Where the performance represented by the two oracles is the same, and one algorithm is most effective at both reducing the number and energy of overloads – such as for the 11 kV and 33 kV systems – then the results are grouped together to save duplication.

Bold values in Table 5.5 indicate where there is a statistically significant difference in the distribution of performance between the potential performance from per-state algorithm

selection and the algorithm it is compared against. For example, for the IEEE 14-bus system the potential performance that could be obtained if algorithms are optimally selected for each state to minimise the number of overloads, whilst also minimising curtailment (represented by oracle 1), is compared with PFM-OPF, which is the most effective algorithm overall for those objectives. The bold values for performance represented by oracle 1 indicate that the potential performance if algorithms are optimally selecting on a per-state basis is statistically significantly different to the performance of PFM-OPF.

Figure 5.1 presents the data from Table 5.5 in terms of the potential performance gain from per-state algorithm selection, relative to the performance of the algorithms that are most effective overall. As in the table, the potential performance represented by each oracle is compared against the algorithms that are most effective overall with respect to the same objectives as used when determining the optimal selections. The result of this comparison is shown by the percentage performance gain (or loss). Positive values represent improved performance; for example, if algorithms are optimally selected on a per-state basis for the IEEE 14-bus system, there is potential to remove 100% of the overloads that the most effective algorithms would otherwise leave in the system.

For the 11 kV radial distribution system, all the algorithms tested except PFM-OPF could remove all overloads. Amongst these, PFSF-LP applied the least curtailment, so it is used to compare with the performance represented by the oracles. As it is possible to remove all overloads with a single algorithm, there is no performance gain in terms of reducing the number or energy of overloads. Per-state algorithm selection could potentially result in a 0.42% reduction in the amount of curtailment applied to achieve no overloads; however, as explained in Section 5.2.1, this is not a statistically significant performance improvement.

For the 33 kV meshed distribution system the potential performance from per-state algorithm selection is compared against PFM-OPF, as it was able to remove all overloads. Due to this, there is no potential performance gain in terms of reducing the number or energy of overloads. There is, however, the potential for a small but statistically significant improvement in the amount of curtailment applied, which can be reduced by 0.91% if algorithms are selected optimally for each state.

For the IEEE 14-bus system, every algorithm leaves some overloads remaining, but optimally selecting algorithms for each state can allow for all overloads to be removed. The potential performance represented by oracle 1 is compared with PFM-OPF as that algorithm minimised the number of overloads, whereas the potential performance represented by oracle 2 is compared with PFSF-TMA, which is the algorithm that minimised overload energy. Algorithm selection on a per-state basis potentially offers a statistically significant performance benefit in terms of minimising the number and energy of overloads on the

11 kV radial

33 kV meshed

IEEE 14-bus

IEEE 57-bus

0.0%

20.0%

40.0%

60.0%

80.0%

100.0%

% gain for number of overloads

0.00%

0.00%

100.00%

43.82%

0.00%

0.00%

100.00%

43.75%

Oracle 1

Oracle 2

11 kV radial

33 kV meshed

IEEE 14-bus

IEEE 57-bus

-300.0%

-250.0%

-200.0%

-150.0%

-100.0%

-50.0%

0.0%

50.0%

100.0%

% gain for overload energy

0.00%

0.00%

100.00%

-250.58%

0.00%

0.00%

100.00%

20.65%

11 kV radial

33 kV meshed

IEEE 14-bus

IEEE 57-bus

-15.0%

-10.0%

-5.0%

0.0%

5.0%

10.0%

15.0%

% gain for total curtailment

0.42%

0.91%

1.19%

-9.49%

0.42%

0.91%

11.41%

-10.24%

Fig. 5.1 Potential performance gains for each system that could be achieved by optimally selecting algorithms on a per-state basis

IEEE 14-bus system. Additionally, per-state algorithm selection can also allow statistically significantly less curtailment to be applied compared with the most effective algorithms for the two overload performance measures.

Similar to the IEEE 14-bus system, for the IEEE 57-bus system no algorithm can remove all overloads. The potential performances represented by both oracles are compared with PFM-OPF, as it is the most effective algorithm with respect to both minimising the number and energy of overloads. Per-state algorithm selection can potentially reduce the number of overloads by up to 43.82% and the overload energy by up to 20.65%, although it is not possible to remove all overloads completely. If minimising the number of overloads is prioritised (oracle 1), there is potentially a significant performance loss in terms of overload energy, with a 250.58% increase compared to PFM-OPF. This is because the optimal selections represented by oracle 1, though they minimise the number of overloads, also minimise the amount of curtailment applied, which can lead to larger overloads remaining for states where no algorithm can remove the overloads. However, if the optimal selections prioritise minimising the overload energy (oracle 2), there is a potential performance gain for both the number and energy of overloads, with the performance gain for the number of overloads being almost exactly the same as that represented by oracle 1. Per-state algorithm selection does not offer a potential performance benefit regarding the amount of curtailment applied, although this can be expected as reductions in overloads is associated with the application of additional curtailment.