Case Study and Simulation Results

The proposed method is applied to the abovementioned distribution network. According to a sensitivity analysis, the number of generations and the population size are chosen as, 300 and 20, respectively. The method has been implemented in MATLAB® incorporating some features of MATPOWER suite [19] and MAT – LAB® toolbox for GA [27] on a laptop with core i7, 1.6 GHz processor and 4 GB of RAM.

The minimum energy losses over the year are about 7,532 MWh. The optimal sizes and numbers of WTs at each candidate bus found by the proposed method are given in Table 6.4. It is evident from Table 6.4 that buses 54, 62, and 81 have the

Table 6.4 The optimal numbers, sizes and capacities of WTs obtained by the proposed method Bus no. Size Number Capacity (MW) 6 – – – 9 C 1 3 14 A 2 2.4 28 – – – 30 C 1 3 38 A 4 4.8 40 – – – 45 A 4 4.8 47 – – – 54 B 4 8 56 B 2 4 62 B 4 8 64 – – – 81 B 4 8 84 Total capacity – – 46

Table 6.5 Comparison of the results with ACO
Method	Total energy losses (MWh)
ACO	7,651
GA	7,532

largest installed capacity (i. e. 8 MW) while bus 14 has the lowest one (i. e.

2.4 MW). The installed capacity, in fact, is limited by voltage and thermal limits as well as by the bids’ values at each bus. For instance, the installed capacity at bus 14 is limited to 2.4 MW (two WTs of size A) and this is mainly due to the lowest value of both thermal limit of the line connecting the buses 13-14 (i. e. 90 A) and the bids’ values of DLs if compared to those at the other lines and buses.

The installed capacity at buses 38 and 45 is 4.8 MW (four WTs of size A). These buses have the same bid values and the higher thermal limits (i. e. 330 A) of the lines 37-38 and 44-45 connecting the WTs if compared to previous case.

At buses 62 and 81, the bids of DL are higher and the thermal limits of the lines 61-62 and 80-81 are the same if compared to the previous case; consequently, the highest capacity is installed at these buses (i. e. four WTs of size B).

In order to evaluate and compare the obtained results, ACO is used with the same population size for the GA, the same number of ants, i. e. 20 and the same number of iterations, i. e. 300. It can be observed from Table 6.5 that the total energy losses obtained by GA are lower than that obtained by ACO.

As regards with the SW, it increases proportionally to both load demand and wind generation as shown in Fig. 6.6. It is worth mentioning that, in all scenarios, the SW is higher if compared to that without WTs in the network.

Fig. 6.6 Social welfare

Fig. 6.7 Total active power losses

In the case of minimum load (i. e. 40 %) and maximum wind generation level (i. e. 100 %), the SW is equal to about 2,500 €/h and in the case of maximum load and minimum wind generation level the SW is equal to about 3,000 €/h. Instead, in the case of maximum wind generation level and maximum load demand this value is equal to around 5,000 €/h.

It is seen from Fig. 6.7 that by increasing the generation, active power losses are decreased. In all scenarios, the total active power losses are lower if compared to the case with no WTs in the network.

In the case of maximum wind power generation and minimum load demand the total active power losses are reduced by about 50 % if compared to the case with no WTs in the network.

It is evident that total active power losses have inverse relation with the wind generation and direct relation with load demand.

Fig. 6.8 Dispatched active power

Figure 6.8 shows the total dispatched active power by WTs in different sce­narios of wind generations and load demands. It is evident that the dispatched active power has the direct relation with both load demand and wind generation.

The supplied loads, shown in Fig. 6.9, evidences its direct relation with wind generation and its inverse relation with load demand due to the network constraints that limit load increase when constraints are binding.

The cases considering different wind energy potential at candidate buses can be addressed by considering different capacity factors for each location and calcu­lating the WTs’ offers as described in Sect. 6.5.

6.2 Conclusion

In this chapter, a hybrid optimization method that combines the GA and the market-based OPF to optimally siting and sizing WTs from the point of view of the DG-owning DNO is proposed. The method jointly minimizes the annual energy losses and maximizes the SW considering different combination of wind generations and load demands to determine the optimal locations, sizes and numbers of WTs to be allocated at candidate buses. The GA is used to select the optimal locations and sizes among different sizes of WTs while the market-based OPF to determine the optimal number of WTs. The DNO acts as the market operator of the DNO acquisition market that estimates the market clearing price and the optimization process for the active power hourly acquisition. The sto­chastic nature of both load and wind is modeled by hourly time series analysis.

With the proposed method not only WTs are optimally allocated but also the total power losses is decreased and the SW, dispatched active power and supplied loads are increased if compared to the case with no WTs in the network.

The proposed method is consistent with the topology of the distribution system, thus taking into account the demand willingness to buy energy at different buses and can be used to assist DNOs to evaluate the performance of the network and to plan the WTs integration into distribution networks. Simulation results confirmed the capability and effectiveness of the proposed method in optimally siting and sizing of WTs in distribution networks.