**5. Conclusion**

40 Simulated Annealing – Single and Multiple Objective Problems

electrical system would be worthwhile considering.

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

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

• Concluding remarks

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

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 numerous configurations.



Optimal Sizing of Harmonic Filters in Electrical Systems: Application of a Double Simulated Annealing Process 43

The analysis of every one can provide several equivalent solutions in terms of total power but shows different voltage distributions. The practical cases discussed in this chapter conclude that for a similar filtering power, some other practical considerations like the minimum cost of the filter installation, the available place aboard ship, the expected power quality at the moment and the further system evolution, must also be taken into account so

Consequently, the optimisation method associated with the implemented software must be considered as an interesting support for the engineer in charge of the placement of harmonic filters onto the grid. Also given practical purposes, the use of the calculation tool should make easier the harmonic filters sizing and provide a good starting point to make the right decision in terms of filtering solutions. Improvements of power quality together with the optimisation of the power to install in electrical distribution systems are today a critical

The specifications of the power system described in figure 3 are summarised in the following table 8 and table 10. The impedance of the cables is neglected due to their small length. The harmonic analysis is achieved from the currents injected by the non linear loads

ref. Un (V) P (kW) Q (kvar)

*Zeq1* 690 160 126

*Zeq2\_BD* 400 315 237

*Zeq3\_TD* 400 300 225

*Zeq4* 230 56 #0

*Zeq5* 230 40 #0

*Zeq6* 230 56 #0

*DA1-DA3* 690 1180 11800 (SCC)

*DA4* 690 OFF OFF

that the best solution can be suitably identified.

challenge that deserves our undivided attention.

**Appendix** 

given in the table 9.

**Table 8.** Linear load parameters

**Table 7.** Filtering of the 5th harmonic order on the 690V/400V/230V busbar – Configuration B

**Figure 7.** Filtering power and harmonic voltages – Combination {4,6} for h = 5 - (Conf. B)

The analysis of every one can provide several equivalent solutions in terms of total power but shows different voltage distributions. The practical cases discussed in this chapter conclude that for a similar filtering power, some other practical considerations like the minimum cost of the filter installation, the available place aboard ship, the expected power quality at the moment and the further system evolution, must also be taken into account so that the best solution can be suitably identified.

Consequently, the optimisation method associated with the implemented software must be considered as an interesting support for the engineer in charge of the placement of harmonic filters onto the grid. Also given practical purposes, the use of the calculation tool should make easier the harmonic filters sizing and provide a good starting point to make the right decision in terms of filtering solutions. Improvements of power quality together with the optimisation of the power to install in electrical distribution systems are today a critical challenge that deserves our undivided attention.
