*4.2.1. Eleventh harmonic order in the configuration A*

• Filters on the 690V busbar

The present study considers a single filter connected to the main 690V busbar *(TPF1)*, at the same location than the propulsion system injecting the greatest harmonic currents. The optimal filtering power provided by the proposed algorithm amounts to 158.9kVA, as mentioned in the table 4.

Optimal Sizing of Harmonic Filters in Electrical Systems: Application of a Double Simulated Annealing Process 37

**Figure 4.** Filtering power and harmonic voltages – Combination {1,4,5,6} for h = 11 – (Conf. A)


**Table 4.** Filtering of the 11th harmonic order on the 690V busbar – Configuration A

It can be then noticed that the resultant harmonic voltage is very low at the filtering node whereas it becomes very close to the specified limits at the other nodes 4 and 6. The voltage requirements are however met at every busbar, even though the limit value of 1.2% is reached on the 230V busbars that are the farthest from the filter's location.

From the sixty-three possible combinations, thirty-two of them assume that one filter at least is to connect at *TPF1*. These solutions however offer different results according to the filtering nodes considered. For example, three filters connected to the 690V and 400V busbars require a lower total power of 109.5kVA as displayed in the table 4, with harmonic voltages at the nodes 4 and 6 still maintained within the specified limits. This solution is actually the best one. When considering another possible combination with harmonic filters on the 690V and 230V busbars respectively, the proposed solution shows a large filter to connect at *TPF1* in addition with smaller ones distributed on the three 230V busbars, in compliance with the harmonic voltages within the specified requirements of the table 1. Even though the total filtering power is slightly lower than that obtained with a single filter placed on the 690V busbar, common sense tell us that the global cost of the filtering system may be higher due to a minimum cost required by the placement of filters with their associated equipment such as cables and breakers. Then, the connection of too small filters might be no economically interesting.

Figure 4 indicates the progress of the main variables during the SA procedure. The graphs show a convergence of the voltage up to the fixed limit while the filtering power decreases towards an optimal value corresponding to the power distribution that minimises the total power. It must be however noticed that the filtering power represents only the magnitude of the current *jh* that would be injected by an active filter. The variations of its phase angles which are not reported herein, could explain the greatest fluctuations of the harmonic voltages while power remains constant.

• Filters on the 690V busbar

might be no economically interesting.

voltages while power remains constant.

mentioned in the table 4.

*4.2.1. Eleventh harmonic order in the configuration A* 

The present study considers a single filter connected to the main 690V busbar *(TPF1)*, at the same location than the propulsion system injecting the greatest harmonic currents. The optimal filtering power provided by the proposed algorithm amounts to 158.9kVA, as

*Filtering power (kVA)* Harmonic voltage (%Vn)

*1 2 3 4 5 6 total* 1 2 3 4 5 6 *158,9 - - - - - 158,9* 0,39 0,93 0,93 1,20 0,97 1,20 *15,0 50,4 44,1 - - - 109,5* 1,79 0,93 1,10 1,20 0,97 1,20 *143,1 - - 0,8 1,2 2,0 147,1* 0,67 1,20 1,20 1,03 0,99 0,90

It can be then noticed that the resultant harmonic voltage is very low at the filtering node whereas it becomes very close to the specified limits at the other nodes 4 and 6. The voltage requirements are however met at every busbar, even though the limit value of 1.2% is

From the sixty-three possible combinations, thirty-two of them assume that one filter at least is to connect at *TPF1*. These solutions however offer different results according to the filtering nodes considered. For example, three filters connected to the 690V and 400V busbars require a lower total power of 109.5kVA as displayed in the table 4, with harmonic voltages at the nodes 4 and 6 still maintained within the specified limits. This solution is actually the best one. When considering another possible combination with harmonic filters on the 690V and 230V busbars respectively, the proposed solution shows a large filter to connect at *TPF1* in addition with smaller ones distributed on the three 230V busbars, in compliance with the harmonic voltages within the specified requirements of the table 1. Even though the total filtering power is slightly lower than that obtained with a single filter placed on the 690V busbar, common sense tell us that the global cost of the filtering system may be higher due to a minimum cost required by the placement of filters with their associated equipment such as cables and breakers. Then, the connection of too small filters

Figure 4 indicates the progress of the main variables during the SA procedure. The graphs show a convergence of the voltage up to the fixed limit while the filtering power decreases towards an optimal value corresponding to the power distribution that minimises the total power. It must be however noticed that the filtering power represents only the magnitude of the current *jh* that would be injected by an active filter. The variations of its phase angles which are not reported herein, could explain the greatest fluctuations of the harmonic

**Table 4.** Filtering of the 11th harmonic order on the 690V busbar – Configuration A

reached on the 230V busbars that are the farthest from the filter's location.

**Figure 4.** Filtering power and harmonic voltages – Combination {1,4,5,6} for h = 11 – (Conf. A)

• Filters on the 400V busbars

The second group of combinations presented below assumes that filters are placed on the 400V busbars together with some additional ones connected to the 230V busbars. The table 5 and Figure 5 show the resultant harmonic voltages and the filtering power progress during the optimisation procedure. When only one filter is connected to *TPF2* or *TPF3*, the specified limits on harmonic voltages cannot be respected. The optimisation procedure returns then the optimal power sizing associated with the lowest maximal harmonic voltage observed in the electrical system. An alternative is to place two filters on the both 400V busbars: then, the harmonic voltages are within the limit values, whatever the voltage levels throughout the electrical system. Compared with the placement of a single filter on the 690V busbar *(TPF1)*:

Optimal Sizing of Harmonic Filters in Electrical Systems: Application of a Double Simulated Annealing Process 39

**Figure 5.** Filtering power and harmonic voltages – Combination {2,4,6} for h = 11 - (Conf. A)

the requirements set by the IEC Standard (i.e. 3.5% for h=11).

The analysis of the combinations involving one, two or three harmonic filters on the 230V busbars as displayed in the table 6, leads to the same conclusion: whatever the number of filters connected, none of the proposed solutions are able to fit the harmonic voltage requirements. It can be however noticed that a filtering solution on the 230V busbars could be considered if the harmonic voltage limits were less severe. For example, the table 6 shows that the combination of three filters connected to the nodes 4, 5, 6 respectively could meet

• Filters on the 230V busbars


When filtering the 230V busbar (node 4 or 6) in addition with the both 400V busbars, the results compared with the previous one do not change significantly regarding the total power. Only the distribution of the maximal harmonic voltages is different according to the nodes. Besides, when only one filter is connected to the 400V busbar (TPF2 or TPF3) and several smaller ones to the 230V, the voltage limit observed on the 400V busbar with no filter is exceeded. It can be however noted in Figure 5 the progress in reducing the involved harmonic voltages. Initially, when the annealing temperature is high, some large increases in the harmonic voltages are accepted and some areas far from the optimum are explored. As execution continues and the temperature falls, fewer uphill excursions are tolerated with smaller magnitude. This performance is typical of the SA algorithm. Even if the voltage amplitudes remain greater than the specified limits, the returned values are the best expected ones.


**Table 5.** Filtering of the 11th harmonic order on the 400V busbar – Configuration A

**Figure 5.** Filtering power and harmonic voltages – Combination {2,4,6} for h = 11 - (Conf. A)

• Filters on the 230V busbars

38 Simulated Annealing – Single and Multiple Objective Problems

The second group of combinations presented below assumes that filters are placed on the 400V busbars together with some additional ones connected to the 230V busbars. The table 5 and Figure 5 show the resultant harmonic voltages and the filtering power progress during the optimisation procedure. When only one filter is connected to *TPF2* or *TPF3*, the specified limits on harmonic voltages cannot be respected. The optimisation procedure returns then the optimal power sizing associated with the lowest maximal harmonic voltage observed in the electrical system. An alternative is to place two filters on the both 400V busbars: then, the harmonic voltages are within the limit values, whatever the voltage levels throughout the electrical system. Compared with the placement of a single filter on the 690V busbar



When filtering the 230V busbar (node 4 or 6) in addition with the both 400V busbars, the results compared with the previous one do not change significantly regarding the total power. Only the distribution of the maximal harmonic voltages is different according to the nodes. Besides, when only one filter is connected to the 400V busbar (TPF2 or TPF3) and several smaller ones to the 230V, the voltage limit observed on the 400V busbar with no filter is exceeded. It can be however noted in Figure 5 the progress in reducing the involved harmonic voltages. Initially, when the annealing temperature is high, some large increases in the harmonic voltages are accepted and some areas far from the optimum are explored. As execution continues and the temperature falls, fewer uphill excursions are tolerated with smaller magnitude. This performance is typical of the SA algorithm. Even if the voltage amplitudes remain greater than the specified limits, the returned values are the best

*Filtering power (kVA)* Harmonic voltage (%Vn)

*1 2 3 4 5 6 total* 1 2 3 4 5 6

*- 114,5 - - - - 114,5* 1.66 1.40 2.25 1.03 1.34 2.34

*- - 119,5 - - - 119,5* 1.51 2.11 1.49 2.34 2.14 1.35

*- 55,1 49,5 - - - 104,6* 1.94 0.92 1.10 1.20 0.96 1.20

*- 49,7 51,9 0,3 - - 101,9* 2.02 1.16 1.10 1.20 1.19 1.20

*- 56,6 46,0 - - 0,7 103,3* 1.98 0.93 1.20 1.20 0.97 1.16

*- 73,6 - 3,0 - 17,8 94,4* 2.37 1.21 2.44 1.20 1.23 1.35

**Table 5.** Filtering of the 11th harmonic order on the 400V busbar – Configuration A

• Filters on the 400V busbars

*(TPF1)*:

expected ones.

The analysis of the combinations involving one, two or three harmonic filters on the 230V busbars as displayed in the table 6, leads to the same conclusion: whatever the number of filters connected, none of the proposed solutions are able to fit the harmonic voltage requirements. It can be however noticed that a filtering solution on the 230V busbars could be considered if the harmonic voltage limits were less severe. For example, the table 6 shows that the combination of three filters connected to the nodes 4, 5, 6 respectively could meet the requirements set by the IEC Standard (i.e. 3.5% for h=11).

#### • Concluding remarks

Among the different solutions discussed above for the configuration A, the optimal filtering solution that offers a minimal total power is achieved with three filters, connected to the nodes 2, 3, 4 respecttively, as shown in Figure 6. However, when thinking about some other considerations like the cost involved by the connection of an additional filter (outputs, protecting devices, etc…), the decision to make can be greatly influenced. Then, a comparison with the gain offered on the total filtering power and the power quality of the electrical system would be worthwhile considering.

Optimal Sizing of Harmonic Filters in Electrical Systems: Application of a Double Simulated Annealing Process 41

*Filtering power (kVA)* Harmonic voltage (%Vn)

*1 2 3 4 5 6 total* 1 2 3 4 5 6

*- - - 9,4 - - 9,4* 4.66 4.93 5.21 2.04 4.93 5.28

*- - - - 30,4 - 30,4* 4.08 3.73 4.64 3.88 3.02 4.72

*- - - - - 29,9 29,9* 4.08 4.62 3.76 4.72 4.63 2.82

*- - - 6,5 22,7 23,9 53,1* 3.50 3.22 3.38 1.36 1.76 1.79

Except in the situation where only one filter is located at the node 4 or 5 (230V), every other filters combination allows to meet the harmonic voltage specifications. The table 7 and Figure 7 illustrate the main results for the new configuration. Nevertheless, it can be noted that the filtering power can vary greatly in a ratio from 1 to 4 according to the selected connection point. Then the maximum power level near to 51kVA is achieved with a filter connected to the node 1 or 2 while the minimum value of 14.5kVA is obtained with a

The proper working of the optimisation process can be then appreciated: the implemented procedure allows to assess a suitable filtering power in compliance with the specified limits set to 3.5% for the fifth harmonic while minimising the total power involved. This also highlights the interest to search for the optimal number and placement of harmonic filters to connect to the grid. In the proposed example, the placement of two filters at the nodes 4 and 6 allows to solve the matter whereas a single filter connected to the node 4 cannot meet the

This chapter deals with a new technique to optimise the both placement and sizing of the harmonic filters to connect to a distribution system. Then, the problem is solved by a combinatorial optimisation method using successively two SA processes. The objective is to reduce the harmonic voltages with respect to the standards and to achieve a minimum

The optimisation technique has been implemented into a software package and tested on several real power systems. The tables of results giving information about the optimal filtering power and the resultant harmonic voltages allow fast comparisons between

**Table 6.** Filtering of the 11th harmonic order on the 230V busbar – Configuration A

voltage requirements for a similar filtering power near to 14 kVA.

power size in view of maximum savings in the equipment cost.

*4.2.2. Fifth harmonic order in the configuration B* 

• Filters on the 690V / 400V / 230V busbars

filtering applied to the nodes 4 and 6.

**5. Conclusion** 

numerous configurations.

**Figure 6.** Filtering power and harmonic voltages – Combination {2,3,4} for h = 11 - (Conf. A)


**Table 6.** Filtering of the 11th harmonic order on the 230V busbar – Configuration A
