^{1}

^{1}

^{2}

^{1}

^{1}

^{2}

Aiming at the instability of voltage and large network loss of dispersed wind farms (DWFs) integration into distribution network (DN), an optimal power factor regulation method based on improved firefly algorithm is proposed. Firstly, the generalized load model based on the static voltage characteristics is analyzed. Then reactive power capabilities of DWFs are thoroughly discussed and the influences of DWFs with variable power factor on network loss and voltage profile are presented. In order to reduce network loss and enhance power quality, optimal power factor regulation of DWFs based on improved firefly algorithm (IFA) is proposed. Finally, results of the benchmark IEEE-33 node system show the feasibilities and validities of the proposed method and the superiorities of proposed IFA are revealed by comparison with the existing algorithms.

As the development of distributed energy, dispersed wind farms (DWFs) are expected to comprise a significant portion of future power generation. However, high penetration level of DWFs integration into the distribution network (DN) presents major challenges in terms of planning and operation of the power grid. According to traditional “fit and forget” practice, DWFs usually operate at maximum power point and unity power factor, which are mostly treated as negative fluctuant loads in the conventional DWF management [

To facilitate an active DN operation, how to reestablish and resolve system optimization function with the introduction of such active participators is essential. On one hand, operation related problems mostly focus on the optimization of typical indexes under a single load type condition in the literature [

On the other hand, various optimization techniques have been suggested in recent decades. The solution techniques could be classified into conventional, intelligent searches, and fuzzy set applications. Compared to other intelligent algorithms, the firefly algorithm is faster and the variable parameter adjustment is simplified. But the common disadvantages of these algorithms are premature convergence of the population and slow convergence rate [

To address these issues, optimal operation of DWFs considering reactive power support capabilities and load types is proposed for network loss reduction and power quality enhancement. In this paper, the generalized load model based on the static voltage characteristics is first introduced. Afterwards, the reactive power capabilities of DWFs are thoroughly discussed. On this basis, the multiobjective optimization function is established, considering the various load and stochastic wind conditions as well as the system equality and inequality constraints. Furthermore, the improved firefly algorithm (IFA) is introduced to solve the given optimization function. Finally, results in the benchmark IEEE-33 node radial distribution system validate the effectiveness of the proposed method.

The typical topology of DWFs in distributed network system is shown in Figure

Typical topology of DWFs in DN.

In (_{0} and _{0} are both zero for the constant power load._{1},_{1},_{1}, and_{1} are the active power weight coefficients,_{2},_{2},_{2}, and_{2} are the reactive power weight coefficients, which are determined by the percentages of active and reactive power consumption or demand.

Voltage characteristic coefficients for different load types.

Season | RL | CL | IL | |||
---|---|---|---|---|---|---|

_{1} | _{1} | _{2} | _{2} | _{3} | _{3} | |

Spring | 1.2 | 4.38 | 1.26 | 3.35 | 0.18 | 6 |

Summer | 0.72 | 2.96 | 1.26 | 3.5 | 0.18 | 6 |

Autumn | 0.98 | 3.52 | 0.98 | 3.95 | 0.18 | 6 |

Winter | 1.04 | 4.18 | 1.5 | 3.15 | 0.18 | 6 |

Doubly-Fed Induction Generator (DFIG) based wind generator is widely used in DWFs, which mainly consists of a wind turbine, a gearbox, DFIG, and back-to-back converters, as shown in Figure

DFIG based wind generator.

The back-to-back converters interfacing the DFIG based wind turbines to the grid play a significant role in the whole system, which are composed of grid-side converter (GSC) and rotor-side converter (RSC). The GSC is connected to the grid and is usually controlled to provide a steady DC-link voltage and meet the power quality requirements, while the RSC is connected to the rotor windings of the DFIG and control the active and reactive power injected into the grid. The total generated power is divided into the power from the stator and the power from the rotor controlled by the back-to-back converter. Therefore, their reactive power support capabilities are complicated since they could be generated by both stator and rotor sides via back-to-back converters, which are thoroughly discussed in this Section [

By using stator voltage oriented vector control [_{s} has no component on the d axis, which is the direct component of the stator voltage _{s} is the peak value of stator voltage.

Therefore, the total active power

The maximum and minimum reactive power

Similarly, the maximum and minimum reactive power

Combining (

It can be seen from (_{s}_{m}/_{s}.

Figure _{rc} with paralleled capacitor is much smaller than_{r} at the operating point (_{0},_{0}), which means that the reactive power capabilities could be enhanced by implementing proper control and capacitors. Furthermore, with the increasing of active power, reactive power capabilities are decreased gradually, which are mainly restricted by

Reactive power capabilities of DFIG.

In an M-node distribution network, the total active and reactive power network loss_{L} and_{L} could be expressed as [

In (_{i},_{j},_{i,} and_{j} are the active and reactive power injections at the ith and jth nodes, respectively;_{i} and_{j} are the _{ij} is power angle difference between nodes_{ij} and_{ij} are resistance and reactance between nodes

When the DWFs are integrated into the M-node distribution network, the total active and reactive power network loss are updated as (_{LDWF} and_{LDWF}.

In (_{Gi} and_{Gi} are the injecting active and reactive power from grid at node_{ei} (see (_{i} are the injecting active power and power factor angle of DWF at node_{Li} and_{Li} (see (

Indexes of active and reactive power network loss APL and RPL could be further derived as

Obviously, the active power and power factor (PF) of DWFs have great influences on network loss. In this paper, negative power factor represents capacitive reactive power while positive power factor is on behalf of inductive reactive power according to the convention. For a given PF, the network loss will first decrease and then increase with the increase of the integrated power as shown in Figure

Impacts of maximum integrated power and PF on network loss.

Compared to the conventional DN, the voltage profile is quite different with the introduction of both the diverse load types and stochastic wind power. In traditional DN, the voltage profile is simple. The node voltage usually decreases as the electrical distance from the node to the main utility increases and may become lower than the minimum voltage at the end of the feeder. However, with the integration of DWFs, the voltage profile is complicated. Three DWFs were connected into IEEE 33 system, located in the points 14, 24, and 30, and the voltage curves are shown in Figure

33-bus network voltage profile in the four PF scenarios.

It can be concluded that the PF can make a big difference on the voltage profile. If power factor or reactive power of DWFs can be adjusted, the voltage profile may be improved. The comparative results also indicate that constant fixed power factor values are not always the preferred solutions.

Based on the above analysis, we can know the network loss and voltage profile can be further optimized by adjusting PF.

In order to get the optimal results, considering various load types and stochastic wind conditions, multiobjective optimal function is constructed, whose equation is_{APL} is the degree of active power loss,_{RPL} means the degree of reactive power loss, and_{v} is voltage deviation, whose calculation is

Form the above equations, it can be known that the network loss and voltage deviation are considered to construct MOF. The optimal value is the minimum MOF. Besides, all weight factors in (_{APL} gets the highest weight of 0.45 and_{RPL} gets the second highest weight of 0.38, while

The constraints should be set to solve the equations, which include power flow, output power, node voltage, branch current, and climbing rate. The details are shown as follow:

_{ij} and_{ij} are, respectively, susceptance and conductance between nodes_{Gi} and_{Gi} are, respectively, injected active and reactive power from grid,_{ei} and_{ei} are the active and reactive power of DWF at node_{1} is the first node voltage.

The conventional Firefly algorithm (FA) is a metaheuristic proposed by Xin-She Yang and inspired by the flashing behaviour of fireflies. FA has many advantages, such as simple operation, strong robustness, easy implementation, etc. compared with the existing genetic algorithm and particle swarm optimization algorithm, FA owns better ability to search the global optimal solution, what’s more, whose convergence speed is faster. FA has been successfully applied to the optimization of nonlinear issues [

_{0} is the maximum light intensity at_{ij} = 0 and_{ij} is the Euclidean distance between two fireflies

_{0} is the maximum attractiveness.

_{i} and_{j} are the positions of fireflies

Based on its pattern, the chaos motion can traverse all states in a certain range without repeating and optimization search using chaos variables is better than blindly and disorderly random search. To avoid premature convergence of the population and slow convergence rate, improved FA (IFA) is introduced, where the chaos theory is integrated into optimization parameters of the firefly algorithm.

Equations (

Here chaos parameter

After each iteration, a set of random parameter values

The comprehensive procedures for the multiobjective optimal function using IFA are given through the flowchart of Figure

The flow chart of improved firefly algorithm.

In Figure

At each iterative step, the light intensity and the attractiveness of each firefly are calculated.

The purpose is to obtain the optimized power factor. Therefore, the position variable in (

The benchmark IEEE-33 node radial distribution system is used for validating the proposed optimization method as shown in Figure

Terminologies and parameter settings of IFA and DN system with integration of DWFs.

Parameter | Value | Description |
---|---|---|

Population size | 50 | Number of Fireflies/Particles |

| 200 | Number of generations |

| | Randomization parameter |

_{0} | 0.1 | Initial attractiveness |

| 0.2 | Absorption coefficient |

IEEE-33 node radial distribution system with 3 POIs of DWFs.

Typical active power profiles of diverse load types and DWF used.

As shown in Figure

In order to demonstrate the effectiveness of network loss under diverse load type conditions by using four constant PFs (0.95, unity power factor, -0.95, -0.85) and proposed optimal PF control method, respectively, both single load type and mixed load type are conducted, where three single load types (IL, RL, and CL) are with the same peak active and reactive power values 3.72 MW and 2.30 MVar, and the mixed load type consists of 40% industrial load, 45% residential load, and 15% commercial load. The results

Comparative results of network loss under diverse load type conditions by using constant PFs and optimal PF regulation.

APL index

RPL index

It can be seen in Figure

To further investigate the effectiveness of the proposed method on voltage profile, one-day voltage profile is under mixed load condition by using four constant PFs (0.95, unity power factor, -0.95, and -0.85), and proposed optimal PF regulations are comparatively presented in Figure

Voltage profile and power factor by using constant PFs and optimal PF regulation under mixed load condition.

Voltage profile

Power factor

It can be easily known that the voltage profile is around 1 based on the proposed optimal PF method, which is to say that the voltage deviation is around 0 and the stability is the best. Compared with the positive power factor, when the values of PFs are 0.95 and 1, the DFWs need reactive power and the voltage deviation is large (>0.02). The voltage curve of Cons -0.95 is improved because the DWFs are providing reactive power and then the reactive power injected by the upstream branch will be diminished, but the difference still exists obviously. If the DWFs generate excess reactive power, the voltage profile will be also deteriorated, as demonstrated by the curve of Cons -0.85. Anyhow, as loads are real-time changed, the constant power factor could not give a good voltage profile all the time. Figure

In summary, the varieties of loads would affect the reactive power for practical conditions and the fixed power factors cannot meet the actual distribution networks. Through the optimal PF which is calculated by the IFA algorithm, the network loss and voltage stability issues can be improved significantly.

The output power of conventional wind farm is high in the daytime and low at night, while the dispersed wind farms are different, whose power is easily affected by surrounding environment and shows the stochastic fluctuation; the regular of output power of dispersed wind farms is similar; thus any moment can be chosen as an example, and here we chose “Time 18h” as an example.

Reference [

Convergence curves of network loss and voltage deviation by using different algorithms under mixed load condition.

Network loss

Voltage deviation

It can be known from Figure

When best results are obtained, the computation time is counted, and the comparative results are shown in Table

Computation time of different algorithms.

Algorithms | Computation time (s) |
---|---|

IFA | 28.07 |

ABC | 52.69 |

FA | 59.87 |

PSO | 65.53 |

It can be concluded that compared with other algorithms, since IFA algorithm has less program occupation and simplified variable parameter adjustment, computation time is 28.07s, much lower than ABC (52.69s), FA (59.87s), and PSO (65.53s). Therefore, the time is much saved up by using IFA. In a word, the proposed IFA has more advantages than the existing optimal algorithms, especially in network loss, voltage deviation, and calculation time.

High penetration level of dispersed wind farms integration into distribution network presents great challenges and an optimal power factor regulation method based on improved firefly algorithm is proposed to ensure the instability of voltage and reduce network loss of dispersed wind farms. This paper proposes an optimal power factor regulation method under diverse load and stochastic wind conditions based on improved firefly algorithm and after discussion and verification, the conclusions are as follows:

The authors promise that all the data used in our manuscript are available and other researchers can access the data supporting the conclusions conveniently.

The authors declare that there are no conflicts of interest related to this paper.

This work was supported by National Natural Science Fund (51407186) of China.