Multi-objective Planning for Distributed Power Considering Low Carbon Benefits

Distributed power can effectively alleviate the problems of environmental pollution and energy shortage. Based on the consideration of the low-carbon benefits of DG, a multi-objective mathematical model with minimal system carbon dioxide emissions, minimum annual network loss cost, and minimal system voltage deviation of the distribution network is established for multi-type DG access location and capacity. This model is solved using a MOPSO algorithm, which gives the planners a scientific decision-making basis. The analysis results show that the DG configuration scheme obtained by this method can effectively reduce carbon dioxide emissions, reduce network loss costs, and reduce voltage deviation, which verifies the usefulness of the model and algorithm.


Introduction
Recently, people are paying attention to the protection of the environment.However, the excessive increase in the capacity of distributed power sources can also have a negative impact on the distribution network.Therefore, it is necessary to optimize the allocation of distributed power sources scientifically and reasonably [1][2].At present, as more and more scholars study the optimal configuration of distributed power supply, many factors are being considered, making the optimization problem of distributed power supply has now become a multi-objective problem.In the face of multi-objective optimization problems, many scholars have solved them by adding weights to make them into single objectives.[3] normalizes the dual objectives by subjective self-weighting to realize the siting of distributed power; [4] takes the minimization of the loss of the entire grid line as the objective function and unifies the voltage constraint and current constraint Although the above literature is superior to single-objective optimization, the method of determining weights is generally subject to human intervention, and in reality these weights are often difficult to determine, and the results are usually not selective.
Therefore, in recent years, some algorithms that can handle multi-objective optimization problems are increasingly widely used.In [5], the MOPSO algorithm is used to solve the Pareto non-inferiority solution set and give typical and ideal solutions.The Pareto non-inferiority solution set is obtained by the MOPSO algorithm, which is no longer a single optimization solution and greatly increases the number of planning options available in different situations.
Considering the low-carbon benefits, this paper establishes a multi-objective mathematical model with the smallest system carbon dioxide emissions, the smallest annual network loss cost, and the smallest system voltage deviation of the distribution network, and uses the MOPSO algorithm to solve the model to obtain the multi-objective optimal Pareto solution, which provides a basis for the decision of site selection and volumetric scheme.

Objective function
A multi-objective model is established with the lowest system CO2 emissions, the smallest annual network loss cost of the distribution network, and the lowest system voltage deviation { } 1) The smaller the distribution network low carbon indicator 1 f , the lower the impact of the network on the environment, which is calculated as follows: where e is the CO2 emissions per unit of electricity supplied by the distribution network; is the active loss of line j in the scenario i; , i j P is the active load power of the jth node in the scenario i; , DG i j P is the active output of the jth distributed power in the scenario i, respectively.
2) The economic index 2 f of the distribution network is composed of the network loss cost loss C of the annual value of the distribution network.
where m C is the cost per unit of purchased electricity; , i j P Δ is the active loss of line j in scenario i.
3) Grid safety indicators 3 f , for system voltage deviation 3 1 where N is the total number of nodes; N U is the nominal system voltage; i U is the voltage at each node during operation.

Constraints
1) Distribution network tidal constraints: ( ) ( ) where DG P  is the total installed distributed power capacities; μ is the maximum penetration rate of clean energy into the distribution network; L P  is the sum of the active loads; DG i P and ,max DG i P are the installed distributed power capacities and the maximum installed capacity of the DG node to be selected respectively.

Improved MOPSO algorithm
PSO algorithms are widely used.However, standard particle swarm algorithms usually use a decreasing weight strategy and a fixed learning factor, which will lead to a tendency to fall into local optima and slow convergence.MOPSO algorithm can search for multiple non-inferior solutions simultaneously in a parallel manner.In summary, the improvements of the MOPSO algorithm are usually in the population update strategy and population fitness ranking.
1) Improvements in adaptive population renewal strategies It has been found from previous research that the value of the inertia weights plays a crucial role in the search for an optimal solution.The tangent function y = tan(x) can be introduced into the variation of inertia weights, which can maintain the population diversity in the early stage of the algorithm and the convergence characteristics in the later stage of the algorithm.
The improved iteration equation is.
( ) ( ) ( )  x are the particle velocity and the current position of the particle i at the kth iteration; gen is the number of counts; t is the current number of counts; k is the control factor; 0.9 2) Improvement of population fitness ranking The fitness of the i-th particle is defined as follows , s k i j denotes the inter-particle fitness sharing function defined as.
where share σ is the radius of the microhabitat; α is generally expressed as a constant.

Case Studies and Results Analysis
In this paper, IEEE33 nodes are used for example analysis.In the MATLAB 2021a environment, the Pareto solution set diagram is obtained, as shown in Figure 1.The diagram reflects the mutually restricting relationship between the three objectives.The multi-objective function can provide decisionmakers with more alternative schemes through one solution, and planners can choose appropriate planning schemes according to their actual needs, which greatly improves the efficiency of optimization.

Figure 1 Pareto solution set diagram
To provide decision-makers with a more scientific decision-making scheme, the optimal compromise solution obtained when using fuzzy decision theory for selection is shown in Table 1.In this case, is 14632.29 tons, is 21.92 million, and is 40.30.

Conclusion
The conclusion is as follows.(1) The improved algorithm has better global search ability and convergence during operation, and the Pareto frontier graph obtained by using this algorithm is more uniformly distributed.(2) The solution obtained by using the multi-objective solution algorithm is a series of Pareto solution sets, which can only solve a set of solutions compared with the traditional solution algorithm, providing decision-makers with free choice space, and decision-makers can choose the appropriate optimization solution according to their actual needs, to make more scientific decisionmaking schemes, which provides certain guidelines for the economic and reliable access of DG righteousness.

where 1 f
is the low carbon indicator of the distribution network, indicating the carbon dioxide emissions generated by the network; 2 f is the economic indicator, indicating the network loss cost and other annual values; 3 f is the safety indicator, indicating the voltage deviation.
are the voltage amplitudes at nodes i and j and the voltage phase angle differences between the nodes, respectively; ij i Q are the active and reactive power injected into the i node, respectively; DG i P θ