^{1}

^{1}

^{1}

^{1}

^{1}

With the increase of penetration of distribution in distribution systems, the problems of power loss increase and short-circuit capacity beyond the rated capacity of the circuit breaker will become more serious. In this paper, a methodology (modified BPSO) is presented for network reconfiguration which is based on the hybrid approach of Tabu search and BPSO algorithms to prevent the local convergence and to decrease the calculation time using double fitness to consider the constraints. Moreover, an average load simulated method (ALS method) considering load variation is proposed such that the average load value is used instead of the actual load for calculation. Finally, from a case study, the results of simulation certify that the approaches will decrease drastically the losses and improve the voltage profiles obviously; at the same time, the short-circuit capacity is also decreased into smaller shut-off capacity of the circuit breaker. The power losses will not be increased too much even if the short-circuit capacity constraint is considered; voltage profiles are better with the constraint of short-circuit capacity considered. The ALS method is simple and the calculation time is fast.

With the large amount of penetration of DGs, reverse power may occur and the quantity of reverse power flow will be also different with the load variation. This will make the power losses change more, whereas it is necessary to consider the load variation during the losses optimization calculation. It has been also discussed that network reconfiguration methods described in previous papers [

Regarding network reconfiguration for loss minimization, one of the first papers published in this field was presented by Merlin and Back [

One conclusion in common of these previous works is that they focus on the improvement of network reconfiguration algorithm, not the load model characteristics during network reconfiguration. For loss minimization calculation for a time based on network reconfiguration, if the method of network configuration changed at unit time is used, it may make the switches change frequently; although the results of losses minimization are the best, for example, for daily load, it will perform 24 operation modes in a day. To avoid this case, in the paper, the method to divide the fluctuant load into several stages is presented. The network configuration is the same at any time in the same stage, and the configuration is built based on the sum of losses minimization in each stage and short-circuit capacity reduction by the network reconfiguration method.

Average load simulated method (ALS method) is proposed for calculation during network reconfiguration considering load variation. It will be illustrated in the next sections in detail.

Mathematically, the problem can be formulated as follows:

_{ij} is the current of branch_{j} is the resistance of branch_{b} is the number of branches in the system,_{s} is the number of divided stages,_{sk} and_{ek} are the start and end time point in stage

Power flow equations:

Voltage limit:

Switch status:

Branches capacity limit:

Short-circuit capacity limit:

Radial distribution system:

_{i}is the status of time point

In the paper, Modified Binary Particle Swarm Optimization (BPSO) is used for switches optimal combination. BPSO is an optimization method of discrete problem based on PSO and was proposed by Kennedy and Eberhart in 1997 [

The constraints must be dealt with especially because the initial BPSO does not take them into account. The equation constraints will be satisfied when the network is configured and power flow is calculated. In this paper, to dispose the inequation constraints, double fitness will be formed; namely, one is the loss minimized fitness and the other is the constraint fitness which is defined according to [

Average load simulated method (ALS method) is a method where the average load value is used instead of the actual load for calculation. In detail, the daily load is divided into several stages according to different loads (such as light, normal, and heavy load stage), and then the average load ratio of every stage is calculated; afterwards, network reconfiguration is done, and the optimal switches combination is got by the MBPSO algorithm. However, the fitness of switch status used to update

The algorithm of ALS method for loss minimization considering SCC reduction and load variation can be described in detail as follows:

Input the data and initial parameters, for example, the impedance of branches, active and reactive power of loads, the number (

Iteration of optimal divided time begins; confirm the divided stages number of each particle.

Get the optimal network in stage

Continue until termination criterion (

Obtain the optimal network in each stage and then calculate the hourly loss using the actual load.

Put out the

Flowchart of network reconfiguration based on average load.

Flowchart of average load simulated method.

Based on the configuration of [

Initial network configuration of test system.

The data of system constants is given in Table

System constants.

| | | | | | | | | Number of particles |
---|---|---|---|---|---|---|---|---|---|

1 MVA | 6.6 kV | 0.95 p.u. | 1.05 p.u. | 143 p.u. | 0.9 | 0.4 | 50 | 2 | 100 |

DG units are rotary generators. In this case study, the DG is the decentralized type and data is given in Table

Data of DG.

DG | Installed node | | | |
---|---|---|---|---|

Decentralized type | 2~17, 22~24 | 0.3 | 0.185 | 0.161 |

In the following simulations, the load variation will be considered when loss and SCC are calculated. The daily load curve in summer used for simulation and data is from [

For the decentralized type of DG, to compare with the results of ALS method, the following three cases are considered: Case I is where the daily load is divided into three stages; Case II is where two stages are divided; and Case III is where there is only one stage in a day. The images of three cases are shown in Figure

Simulated load curves of three cases.

In this section, to confirm the effects of modified BPSO method on convergence and precision of calculated results, the BPSO and Tabu search methods are also done for the test system with decentralized DGs. The losses minimum of each method during iteration is shown in Figure

Losses minimum during iteration.

In Figure

Table

Data of average load in 3 cases.

Case I | Case II | Case III | ||||
---|---|---|---|---|---|---|

Light | Normal | Heavy | Low | High | ||

DR | <0.75 | [0.75, 0.9] | >0.9 | ≤0.65 | >0.65 | — |

AL | 0.64 | 0.79 | 0.94 | 0.57 | 0.87 | 0.74 |

DT | 8, 17, 23 o’clock | 7, 23 o’clock | — |

This time, the network reconfiguration of ALS method is performed for each stage in the 3 cases by using load data shown in Figure

Open switches in each stage for 3 cases.

Open switches in normal | |
---|---|

Case I | |

Stage 1 | S9, S13, S23, S28, S33 |

Stage 2 | S5, S10, S14, S33, S34 |

Stage 3 | S4, S10, S13, S33, S34 |

| |

Case II | |

Stage 1 | S7, S10, S13, S22, S34 |

Stage 2 | S5, S10, S14, S33, S34 |

| |

Case III | — |

Optimization results (ALS method).

TCTOS | SCC1 (MVA) | Loss (kWh) | LRR | |
---|---|---|---|---|

Case I | 20 | 140.7~142.3 | 1319.3 | 70.9% |

Case II | 12 | 138.6~142.3 | 1324.2 | 70.8% |

Case III | — | — | — | — |

However, in Case III, the results could not be obtained. Voltages are over the limitation at some nodes for the actual load in the conditions of the optimal network obtained by average load. The reason is considered as follows: the optimal network is obtained based on average load, during reconfiguration, in order to minimize the losses; the margin of constraint variable to the limitation is small. If the value of actual load in a stage is much bigger or smaller than the value of average load, calculation results using actual load may be over the constraint limitation. The differential of loads in the same stage for ALS method is small as far as possible.

As we know, when large penetration of DGs is connected to the distribution system, the power losses may be increased and it happens probably that the short-circuit current through some circuit breakers is over the interrupting capacity of CB in fault. From the discussion above, the characteristics of average load simulated method (ALS method) proposed can be summarized as follows.

In the paper, network reconfiguration based on MBPSO algorithm is used for power losses minimization and short-circuit capacity. Approaches for losses minimization and short-circuit capacity reduction are proposed considering load variation. MBPSO algorithm uses double fitness to consider the constraints, and it can decrease the calculation time.

The power losses will not be increased too much even if the short-circuit capacity constraint is considered; voltage profiles are better with the constraint of short-circuit capacity considered.

Considering the impacts of load variation on the losses, on account of the model of load used for the network reconfiguration, average load simulated method (ALS method) is approved. The approach is to divide the loads into stages and network reconfiguration in each stage is done to minimize the losses and reduce the short-circuit capacity, finally getting the minimum of losses in the whole interval time. The results of simulation certify that the approaches will decrease drastically the losses and improve the voltage profiles obviously; at the same time, the short-circuit capacity is also decreased into smaller shut-off capacity of the circuit breaker.

The ALS method is simple and the calculation time is fast; however, it is strict with the loads in the same stage.

In the current research, approaches for short-circuit capacity and power losses reduction are on the standpoint of supply system side, at the standpoint of demand side. In the following research, an approach of power losses and short-circuit capacity on the standpoint of demand side will be presented.

The authors declare that they have no competing interests.