Execution times

The execution times of the algorithms were measured in order to evaluate their suitability for real-time control operation, and also to understand the effect of the different case study systems. Figure 4.16 presents the execution times of the algorithms for the overloaded states in the four case study systems as box-and-whisker plots. In the figure, median execution times of the algorithms on each system are shown with a vertical black line with the value given underneath; mean execution times are shown as a black square; the 25th _{and 75}th

percentiles of the execution time data are shown by the extent of the boxes, while the 5th _and

95th _{percentiles are shown by the whiskers. Outliers are plotted individually.}

The execution times of the three PFSF-based algorithms lie within the same range and do not exceed 1.0 seconds, while the execution times of PFM-CSP and PFM-OPF are typically an order of magnitude higher for each case study system. The minimum median execution times for each algorithm occurs for the 11 kV radial distribution system, which is the simplest of the four case study systems as it contains the least buses, generators and potential overloads. With the exception of PFM-CSP, the maximum median execution times for each algorithm occurs for the IEEE 57-bus system, which has the most buses and potential overloads of all the case study systems. PFM-CSP has its maximum median execution time on the 33 kV meshed distribution system. Although this is not the largest system, it does feature four generators and PFM-CSP scales poorly to increased numbers of generators. The IEEE 14-bus system has the same number of generators, so the lower median execution time for that system must be because it is quicker to execute a load flow on the IEEE 14-bus system model internal to PFM-CSP compared with the internal model of 33 kV system.

The execution times on each system for PFSF-Egal and PFSF-TMA follow a similar pattern to each other, which is to be expected as those algorithms follow the same processes for the majority of their execution. PFSF-LP has the lowest median execution times for each

10

-2

10

-1

10

0

10

1

Execution time [s]

PFSF-LP

PFSF-TMA

PFSF-Egal

PFM-OPF

PFM-CSP

0.234

0.452

0.468

3.229

2.839

0.047

0.094

0.109

0.915

2.777

0.078

0.062

0.078

1.076

3.432

0.016

0.047

0.047

0.608

0.281

11 kV radial

33 kV meshed

IEEE 14-bus

IEEE 57-bus

system except on the 33 kV system, where PFSF-TMA is the fastest algorithm based on median execution time.

This analysis shows that the execution times of the algorithms are relatively small when compared with the length of time each state represents. The PFSF-based algorithms are, on average, and order of magnitude faster than PFM-OPF and PFM-CSP. Although there is variation in the execution times observed across the systems, the algorithms would need to be tested on a larger number of systems in order to determine what characteristics of power systems influence changes in execution times.

4.7

Conclusions

In this chapter, five different power flow management algorithms (as described in Chapter 2) have been applied to four case study power systems, which represent different network topologies (radial, meshed), voltage levels (transmission, distribution) and geographies (UK, US). For each case study system, at least 10,000 different system states have been simulated, with many featuring overloads, to which the algorithms were applied and tested.

PFM-OPF was found to be the most effective algorithm overall for most of the systems, with respect to minimising the number and energy of overloads whilst also minimising the amount of curtailment. However, for the IEEE 14-bus system, PFSF-TMA was more effective at reducing overload energy, whilst minimising the amount of curtailment; and for the 11 kV radial distribution system, PFM-OPF could only provide a performance benefit in terms of reducing the curtailment applied, as there was no statistically significant difference in the number or energy of overloads removed by each of the power flow management algorithms tested. For all of the case study systems, the algorithms were found to execute in a reasonable time when compared with the time period that each simulated state represented; although additional systems would need to be tested in order to draw any empirical conclusions about the scalability of the algorithms.

The performance of each algorithm across all of the case study systems was examined. Design features of the algorithms which were most likely the causes of particular performance traits were identified, and the findings regarding these features could be helpful for research developing improved and novel power flow management algorithms.

This chapter has established the performance of the power flow management algorithms when aggregated across all the states simulated. In the next chapter, the performance of the algorithms is examined for each state, in order to understand if any potential performance benefits can be obtained by selecting different algorithms on a per-state basis.

Potential performance benefits from

per-state selection of algorithms

The previous chapter took the five power flow management algorithms introduced in Chap- ter 2 and assessed their performance on aggregate across all states tested for each of the four case study systems. This chapter aims to complete research objective 1, by examining the performance of the algorithms for each state individually, in order to determine if there is any potential performance benefit if algorithms were selected on a per-state basis, rather than selecting one algorithm to be used for all states.

This chapter is structured as follows: Section 5.1 presents the method used to determine the potential benefit that could be obtained from per-state algorithm selection, Section 5.2 applies that method to assess the potential benefits for each of the case study systems, Section 5.3 examines how frequently each algorithm is the most effective for each sys- tem, Section 5.4 examines how the potential performance benefits vary if different sets of algorithms are considered, and Section 5.5 concludes the chapter.

Some of the work in this chapter has been published previously. The potential per- formance benefits from per-state selection for the 33 kV meshed distribution system were published in [58], the benefits for the IEEE 14-bus system were in [59], while in [60] the benefits for both of those systems and the IEEE 57-bus system were presented.

5.1

Method for assessing the potential performance benefit

The potential performance benefit that could be obtained by selecting algorithms on a per- state basis is calculated using a two-step process, which is repeated for each of the overload performance measures of 1) the number of overloads, and 2) the energy of overloads:

1. First, the optimal algorithm selections are determined for each state. This is achieved by post-processing the performance data of all algorithms, and determining, for each state, the set of algorithms that minimises either the number or energy of overloads for that state. Considering that set of algorithms only, the subset that minimises curtailment is determined, referred to as the “selection set”. If the selection set is a singleton, then there is only a single most effective algorithm for the state with respect to minimising either the number or energy of overloads, while also minimising curtailment; and this algorithm represents the optimal selection. However, if a number of algorithms remain in the selection set, then which represents the optimal selection is arbitrary as the overload and curtailment performances of the remaining algorithms are identical. 2. Second, the optimal selections for each state are used to extract the performance data

of the selected algorithms. This performance data is aggregated to give the theoretical limit for the performance that can be obtained by optimally selecting between the considered set of algorithms on a per-state basis. This performance can be compared with the performance of the individual algorithms to determine if there is any potential performance benefit from selecting different algorithms for each state.

As the sequence of selections is made post-hoc with perfect information about how all the algorithms perform on each state, the selection are referred to as being made by “oracles”, as the selections are always optimal for each state with respect to the performance measures considered. Performance results for two oracles are presented: 1) an oracle that minimises the number of overloads, then the amount of curtailment, and 2) an oracle that minimises the energy of overloads, then also minimises the amount of curtailment.

In the reporting of results for each case study system, the number of times each algorithm appears in the selection sets of each oracle is provided, along with the number of times each algorithm is the sole algorithm in the selection set (when the set is a singleton). This indicates how often each algorithm is uniquely the most effective algorithm.

In the subsequent analysis, the performance of the algorithms is compared to the potential performance that the oracles would allow. The statistical significance of any performance differences are assessed using the same method as used in the previous chapter for comparing the performance of the algorithms, as described in Section 4.1.3. In summary, for each system, the distributions of performance for every performance measure and pair-wise combination of algorithms (including the oracles) are compared using a paired t-test, yielding p-values. The Benjamini-Hochberg procedure is then used to determine which p-values (and therefore which differences in performance) are statistically significant, while correcting for making multiple comparisons.

Table 5.1 Overview of algorithm performance and the potential performance from optimally selecting algorithms on a per-state basis for the 11 kV radial distribution system

performance Algorithm Over-loads

[count] Over- loaded states Overload energy [MVAh] Total cur- tailment [MWh]

Algorithm in selection set (sole algorithm in set) Oracle 1 Oracle 2 Baseline 3344 2462 871.95 0.00 7538 (0) 7538 (0) PFM-CSP 0 0 0.00 2121.40 7538 (0) 7538 (0) PFM-OPF 2 2 0.10 769.94 9997 (2459) 9997 (2459) PFSF-Egal 0 0 0.00 856.20 7454 (0) 7454 (0) PFSF-TMA 0 0 0.00 891.01 7455 (1) 7455 (1) PFSF-LP 0 0 0.00 773.33 7456 (2) 7456 (2) Oracle 1 0 0 0.00 770.08 – – Oracle 2 0 0 0.00 770.08 – –

In document Algorithm selection for power flow management (Page 127-133)