In the framework of vigorous promotion of low-carbon power system growth as well as economic globalization, multi-resource penetration in active distribution networks has been advancing fiercely. In particular, distributed generation (DG) based on renewable energy is critical for active distribution network operation enhancement. To comprehensively analyze the accessing impact of DG in distribution networks from various parts, this paper establishes an optimal DG location and sizing planning model based on active power losses, voltage profile, pollution emissions, and the economics of DG costs as well as meteorological conditions. Subsequently, multi-objective particle swarm optimization (MOPSO) is applied to obtain the optimal Pareto front. Besides, for the sake of avoiding the influence of the subjective setting of the weight coefficient, the decision method based on a modified ideal point is applied to execute a Pareto front decision. Finally, simulation tests based on IEEE33 and IEEE69 nodes are designed. The experimental results show that MOPSO can achieve wider and more uniform Pareto front distribution. In the IEEE33 node test system, power loss, and voltage deviation decreased by 52.23%, and 38.89%, respectively, while taking the economy into account. In the IEEE69 test system, the three indexes decreased by 19.67%, and 58.96%, respectively.

With the development of modern society, the speed of economic growth is fast, but energy shortages and environmental pollution becoming increasingly serious, which will create a negative impact on traditional energy generation more and more obvious. Nowadays, with the efforts to build a low-carbon and environment-friendly society all over the world countries [

With a large number of random power loads and DG access, the difficulty of management construction, and scheduling of active distribution networks become intricate, and the disturbance caused by any fault point will have a negative impact on the power system. In special, in case of serious disturbance, it may cause a large-scale power outage with serious and catastrophic consequences [

Location and capacity determination of DG is a complex multi-objective optimization problem, mainly because it is nonlinear and contains discrete optimization variables, etc. When investigating the DG location and sizing planning problem, several scholars prefer the mathematical model to optimize the power loss of the active distribution network or to optimize a series of costs arising from DG location and sizing. Multi-optimization objectives are simply transformed into a single optimization objective by methods such as linear weighting, which causes the optimization results to be mainly determined by weighting coefficients that are defined by experts and scholars according to their expertise, such mathematical models constructed in a single optimization direction cannot guarantee [

On the other hand, wind turbines and photovoltaic systems are more technically mature, which are preferred for DG installations [

Therefore, a multi-objective optimization model based on active distribution network loss, voltage distribution, DG allocation cost, pollutant emission and meteorological conditions is established in this paper. In addition, the original MOPSO algorithm is improved based on the particle distance vector, so that the improved MOPSO algorithm can update the Pareto solution set in multiple iterative directions, so as to obtain better global and uniform Pareto solution set. In this paper, improved ideal point decision method is used to find the best compromise solution from Pareto solution set. In order to verify the effectiveness of the proposed method, simulation experiments based on IEEE33 and IEEE69 nodes are designed.

The main contributions of this paper are as follows:

In this paper, the influence of various indexes has been fully considered in the configuration of DG, such as power loss of active distribution network, voltage distribution, cost of DG, pollutant emission, and meteorological conditions.

This paper adopts the improved multi-objective particle swarm optimization (MOPSO) algorithm to solve the multi-objective optimization model, and the improved MOPSO algorithm can obtain better global and diverse Pareto solution sets in the multi-iteration direction. In addition, the optimal compromise solution is obtained by using the improved ideal point decision method, which can effectively avoid the subjective influence of decision-makers.

Simulation tests based on IEEE33 and IEEE69 nodes are designed in this paper, and the simulation tests show that the improved MOPSO can obtain a more evenly distributed and wider Pareto frontier. The simulation result shows that the power loss and voltage profile can be decreased by 52.23% and 38.89% in IEEE 33 node system and 19.67% and 58.96% in IEEE 69 node system by accessing the DG, respectively.

It is essential to conduct research into the technical, economic, and environmental aspects of DGs to ensure that it is reasonably connected to the distribution network to maximize their effectiveness, with full consideration of the technical and economic characteristics of DGs together with their impact on the distribution network, thus making reasonable decisions on access capacity and access nodes.

The high permeability of DGs into the distribution network may result in the magnitude and direction of the power tide changing, which may have a benign or malignant effect on the active power loss magnitude. The power loss index is employed to measure the size of active power loss in the distribution network. Active power loss indicators are established as follows [

The acceptable connections of DGs to the distribution network perform a critical task in refining the voltage distribution. DG can be well connected to the distribution network to optimize voltage distribution, yet as DG penetration in the distribution network progressively expands, nodal voltages can exceed the rated power. Therefore, this paper employs the voltage distribution index to give a quantitative analysis of the optimization effect, as follows [

For the sake of decreasing the emission of polluting/harmful gases, carbon dioxide, nitrogen compounds, and sulfur dioxide are considered in this paper, as follows [

The economic cost of DG location and sizing is mainly composed of the total cost

It is noteworthy that this paper considers that each unit operates for 20 years and 300 days per year, that is

DG types | Investment cost ($/kW) | Operation and maintenance cost ($/kW·h) | |||
---|---|---|---|---|---|

Fuel cells | 3500–10000 | 0.5–1.0 | 0.502 | ||

Micro-combustion turbines | 700–1100 | 0.5–1.6 | 3.445 | ||

Photovoltaic systems | 4500–6000 | 1% | – | – | – |

Wind turbines | 800–3500 | 1.5% to 2% | – | – | – |

This paper proposes an objective function considering the annual average wind speed

where

Notably, DGs access to the distribution network operation may generate changes in the voltage distribution and tidal current distribution of the nodes in the power system, which directly affects line heating and indirectly diminishes the technical and economic capabilities of the distribution network in terms of security, dependability, and economy, etc. The following limitations are expected to guarantee the reliability and smooth operation of the system [

(1) Transmission line power constraints

(2) Voltage constraints

(3) Distributed power capacity constraints

In this paper, the types of DG considered are photovoltaic systems, wind power systems, fuel cells, and micro-gas turbines. Among them, the output of fuel cells and micro-gas turbines is affected by the input fuel flow rate, the faster the flow rate, the greater the output power. Therefore, the output of fuel cells and micro-gas turbines can be considered constant and adjustable. In addition, the output data of photovoltaic system and wind power generation system in this paper are obtained by fitting the average irradiance and wind speed of typical days in four seasons. Therefore, the output model of photovoltaic system and wind power system can be established as a distributed power supply whose output varies with time scale. The output curve of photovoltaic system and wind power system is shown as

Inspired by previous scholars’ research on the foraging behavior of birds, after setting some rules for the foraging behavior of birds, through modeling and data processing, American social psychologist James Kennedy and electrical engineer Eberhart experimented and completed the research on particle swarm optimization (PSO) through accuracy analysis [

For each generation of individuals, the velocity and position of the particles are updated in the process of searching for the optimum value according to the following equation [

The major differences between the MOPSO [

For

The crowding distance selection strategy is widely used for updating the Pareto solution set. However, the interaction information in the traditional crowding distance is limited to adjacent particles, which simplifies the calculation process but results in poor globality and uniformity of the Pareto solution set. To enhance the globality and uniformity of the Pareto solution set, this paper proposes a dynamic updating strategy for the Pareto solution set using multiple iterative directions: if the Pareto solution set exceeds the scale, the two particles with the smallest values in the crowding distance vector group are deleted until the Pareto solution set meets the scale; the two particles with the maximum values in the crowding distance vector group and the two particles with the maximum values in the opposite crowding distance vector group are selected as the optimal particles, and the Pareto solution set is updated using multiple iterative directions.

Before updating the Pareto solution set, the fitness values of each particle need to be dimensionless, to define and calculate the minimum distance vector group and maximum distance vector group.

The final solution of MOPSO is the Pareto frontier composed of non-dominated solutions. In multi-objective optimization problems, in order to avoid the subjective influence of the decision maker, a decision method is needed to avoid the subjective decision. Ideal point decision based on Mahalanobis distance is a popular decision method, and this method is used in literature [

To confirm the availability of the presented method, this paper performs a sizing and capacitance study in the IEEE 33, 69 bus node system as illustrated in

The active power losses of the IEEE 33, 69 bus nods system can be seen in the literature [

Node | Annual average wind speed (m/s) | Annual average radiation (MJ/m^{2}) |
Node | Annual average wind speed (m/s) | Annual average radiation (MJ/m^{2}) |
---|---|---|---|---|---|

1 | 3.464 | 0.6179 | 18 | 4.437 | 0.6912 |

2 | 2.765 | 0.3120 | 19 | 4.616 | 0.3916 |

3 | 2.315 | 0.1270 | 20 | 4.675 | 0.5796 |

4 | 3.037 | 0.6776 | 21 | 4.893 | 0.5712 |

5 | 4.670 | 0.6893 | 22 | 1.487 | 0.5941 |

6 | 4.016 | 0.6949 | 23 | 4.712 | 0.6056 |

7 | 4.452 | 0.6991 | 24 | 3.967 | 0.6087 |

8 | 2.792 | 0.6963 | 25 | 4.595 | 0.6195 |

9 | 3.359 | 0.6984 | 26 | 3.808 | 0.6862 |

10 | 4.513 | 0.6752 | 27 | 4.156 | 0.6329 |

11 | 2.304 | 0.6981 | 28 | 2.654 | 0.6812 |

12 | 2.882 | 0.4695 | 29 | 2.679 | 0.6020 |

13 | 3.694 | 0.6262 | 30 | 4.458 | 0.6108 |

14 | 2.108 | 0.6695 | 31 | 2.779 | 0.2820 |

15 | 4.566 | 0.6983 | 32 | 3.1125 | 0.6993 |

16 | 3.683 | 0.7054 | 33 | 4.383 | 0.5712 |

17 | 1.333 | 0.6741 |

Nodes | Annual average wind speed (m/s) | Annual average radiation (MJ/m^{2}) |
Nodes | Annual average wind speed (m/s) | Annual average radiation (MJ/m^{2}) |
---|---|---|---|---|---|

1 | 2.575 | 0.8029 | 36 | 2.891 | 0.4583 |

2 | 3.270 | 0.5895 | 37 | 3.157 | 0.5970 |

3 | 4.504 | 0.8487 | 38 | 4.112 | 0.9929 |

4 | 2.833 | 0.2275 | 39 | 3.957 | 0.8437 |

5 | 2.241 | 0.4133 | 40 | 2.279 | 0.4362 |

6 | 1.754 | 0.6670 | 41 | 1.404 | 0.25791 |

7 | 3.791 | 0.7575 | 42 | 3.387 | 0.7879 |

8 | 5.066 | 0.7679 | 43 | 5.762 | 0.9933 |

9 | 4.979 | 0.7717 | 44 | 4.437 | 0.9004 |

10 | 5.15 | 0.7279 | 45 | 4.416 | 0.9204 |

11 | 4.154 | 0.6508 | 46 | 2.151 | 0.5995 |

12 | 3.754 | 0.6141 | 47 | 3.191 | 0.7420 |

13 | 3.079 | 0.5775 | 48 | 3.612 | 0.7454 |

14 | 2.658 | 0.9079 | 49 | 2.041 | 0.6408 |

15 | 1.529 | 0.8395 | 50 | 1.670 | 0.4720 |

16 | 1.312 | 0.4912 | 51 | 1.191 | 0.5133 |

17 | 2.312 | 0.4862 | 52 | 3.133 | 0.5358 |

18 | 4.779 | 0.9379 | 53 | 4.804 | 0.8354 |

19 | 4.233 | 0.6991 | 54 | 2.387 | 0.5945 |

20 | 4.070 | 0.8316 | 55 | 1.879 | 0.2441 |

21 | 4.320 | 0.9141 | 56 | 2.766 | 0.4808 |

22 | 2.875 | 0.8666 | 57 | 1.033 | 0.4033 |

23 | 3.225 | 0.8379 | 58 | 0.908 | 0.1520 |

24 | 2.904 | 0.7133 | 59 | 0.883 | 0.3716 |

25 | 2.116 | 0.5120 | 60 | 2.162 | 0.8954 |

26 | 3.066 | 0.6204 | 61 | 2.216 | 0.5895 |

27 | 2.141 | 0.7229 | 62 | 1.066 | 0.3920 |

28 | 1.875 | 0.33291 | 63 | 1.612 | 0.42166 |

29 | 2.608 | 0.62791 | 64 | 1.125 | 0.66751 |

30 | 1.883 | 0.38254 | 65 | 1.358 | 1.01625 |

31 | 0.416 | 0.19208 | 66 | 1.595 | 0.65666 |

32 | 1.937 | 0.58833 | 67 | 2.058 | 0.64833 |

33 | 3.037 | 0.57666 | 68 | 2.225 | 0.29875 |

34 | 4.037 | 0.68125 | 69 | 1.425 | 0.49208 |

35 | 4.287 | 0.95416 |

Algorithm | IGD | GD | PD | HV | DM | Universality | SP | |
---|---|---|---|---|---|---|---|---|

MOPSO | Ave. | 4.1171 | 0.0202 | 1.0793e+6 | 0.0437 | 0.2244 | 0.9697 | 0.2532 |

Std. | 5.9965 | 0.0965 | 6.2851e+6 | 0.022 | 0.2354 | 0.1797 | 1.5606 |

The results of MOPSO and without optimization are demonstrated in

Algorithms | MOPSO | |
---|---|---|

Photovoltaic system | #1 Capacity (kW) | 188.88 |

#1 Installation node | 27 | |

#2 Capacity (kW) | 60.01 | |

#2 Installation node | 16 | |

Fuel cell | Capacity (kW) | 122 |

Installation nodes | 23 | |

Micro gas turbine | Capacity (kW) | 40.01 |

Installation notes | 31 | |

Wind turbine | #1 Capacity (kW) | 32.49 |

#1 Installation node | 25 | |

#2 Capacity (kW) | 36.41 | |

#2 Installation node | 20 | |

0.027 | ||

0.024 | ||

0.086 | ||

0.032 | ||

0.832 |

Objective | Optimized by MOPSO | Without optimization |
---|---|---|

24.309 | 38.297 | |

0.4236 | 0.6899 | |

1.2032 × |
0 | |

1.8513 × |
0 | |

0.0943 | 0 |

In addition, MOPSO can obtain good meteorological indicators. In order to verify the optimization effect of MOPSO on meteorological indicators, the access positions of photovoltaic systems and wind turbines are exchanged, and the meteorological indicators obtained are 0.1114 p.u. After optimization, it increased by 15.35% (from 0.1114 to 0.0943 p.u.), so that photovoltaic systems and wind turbines can be installed in areas rich in scenery resources.

Generally speaking, as can be seen from

Because this paper optimizes six different metrics (i.e., objective function), the Pareto solution set cannot be plotted in the Cartesian coordinate system. Hence, the Pareto solution set running ten times is mapped from the Cartesian coordinate system to the parallel coordinate system which is shown in

Algorithm | IGD | GD | PD | HV | DM | Universality | SP | |
---|---|---|---|---|---|---|---|---|

MOPSO | Ave. | 8.1910 | 0.0859 | 3.8663e+6 | 0.0236 | 0.4232 | 0.9619 | 0.8324 |

Std. | 5.9965 | 0.0965 | 6.2185e+6 | 0.0220 | 0.2354 | 0.1797 | 1.5606 |

Algorithms | MOPSO | |
---|---|---|

Photovoltaic system | #1 Capacity (kW) | 555.81 |

#1 Installation node | 22 | |

#2 Capacity (kW) | 96.50 | |

#2 Installation node | 14 | |

Fuel cell | Capacity (kW) | 118 |

Installation nodes | 53 | |

Micro gas turbine | Capacity (kW) | 134.92 |

Installation notes | 42 | |

Wind turbine | #1 Capacity (kW) | 58.63 |

#1 Installation node | 43 | |

#2 Capacity (kW) | 146.14 | |

#2 Installation node | 10 | |

0.052 | ||

0.061 | ||

0.029 | ||

0.027 | ||

0.831 |

Objective | Optimized by MOPSO | Without optimization |
---|---|---|

_{1} (kW) |
20.089 | 25.007 |

_{2} (p.u.) |
0.5736 | 1.3979 |

_{3} (kg/h) |
1.6959 × 10^{6} |
0 |

_{4} ($) |
4.9247 × 10^{7} |
0 |

_{5} (p.u.) |
0.0791 | 0 |

Based on the research of meteorological conditions involved in DG location and sizing, this paper proposes a Pareto multi-objective optimization method based on MOPSO. The main contributions are as follows:

(1) A DG location and sizing model considering active power loss, voltage distribution, pollution emissions, economic costs, and meteorological conditions is established. The introduction of meteorological conditions can effectively install photovoltaic systems and wind turbines in areas with rich scenic resources.

(2) MOPSO algorithm based on Pareto multi-objective optimization is proposed, and the implementation and calculation process of MOPSO algorithm are described. In particular, through the IEEE 33 and 69 bus distribution network test, it is proved that the MOPSO algorithm has good convergence and global search ability, and can obtain a widely distributed and uniform Pareto front.

(3) Taking IEEE 33 and 69 bus distribution networks as examples, the simulation results show that the MOPSO algorithm can effectively reduce the active power loss of the distribution network and improve the voltage distribution in a better economic range. Under IEEE 33 bus distribution network, power loss, and voltage deviation are decreased by 52.23%, and 38.89%, respectively. Meanwhile, MOPSO can obtain good meteorological indicators, simulation result shows that the access positions of photovoltaic systems and wind turbines are exchanged, and the meteorological indicators obtained are increased by 15.35%. Under IEEE 69 bus distribution network, the power loss and voltage deviation are reduced by 19.67%, and 58.96%, respectively. Hence, this strategy has been proven to be effective in solving multi-objective programming problems.

For the purpose of operating DGs into the distribution network in a more appropriate manner, the renewable energy sites installed with energy storage systems will be studied in the future. Besides, dynamic load models will be deployed to simulate loads that are more relevant to the actual project, so that DGs can be utilized efficiently. Furthermore, load growth should be considered in the planning of DG.

The authors gratefully acknowledge the support of the Enhancement Strategy of Multi-Type Energy Integration of Active Distribution Network (YNKJXM20220113).

Guobin He: Conceptualization, Writing-reviewing, and editing; Rui Su and Jinxin Yang: Writing-original draft preparation, Investigation; Yuanping Huang and Huanlin Chen: Visualization and contribution to the discussion of the topic; Donghui Zhang, Cangtao Yang, and Wenwen Li: Validation.

The authors declare that they have no conflicts of interest to report regarding the present study.