The distribution network planning considering distributed power supply and battery energy storage station

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Introduction
Distributed generation (DG) has developed rapidly in recent years, which can not only realize the effective use of renewable energy, but also adjust the peak-valley difference and can improve the reliability and flexibility of power system, in this way DG can be the development direction of electric power industry in the 21st century [1,2]. However, due to the intermittence and randomness of renewable energy power generation in DG, it is necessary to build energy storage devices to ensure the smooth utilization of distributed power [3]. Traditional distribution network planning method is to reasonably design expanded grid structure and capacity according to the load forecasting results of local as well as the built power grid structure in a certain planning period, which aims to meet the demand of load growth and the safety of power grid conditions and make the distribution network construction and the running economy to achieve the optimal goal [4]. The access of distributed power generation and energy storage equipment changes the type of source load that are not considered in the traditional planning of distribution network [5].
At present, there are many literatures about the mathematical model of distribution network planning, many of which have introduced the planning problems of distribution network with the connection of distributed power supply and energy storage equipment. An improved multi-objective hybrid quantum genetic algorithm based on the distributed power planning method is established in [6], which can make the processing results of distributed power distribution network planning more rationality and feasibility. The improved multi-population genetic algorithm proposed in [7] is applied to the multi-objective distribution network planning problem, which provides a specific repair scheme for the infeasible solution generated under the genetic operation. In [8], a distribution network planning mathematical model with comprehensive consideration of substation planning and feeder planning is proposed and established, which has good results for global optimization of distribution network comprehensive planning. However, most of the researches only considered the distributed generation or storage device individual interconnection of power distribution network planning problem, and most of them only focused the distribution network planning with one year planning period. This paper constructs a comprehensive distribution network planning model with the consideration of the new substation, new lines, distributed generation and energy storage device interconnection together and extends the fixed number of the planning period in the model. Besides, by considering the distribution network construction and the time value of operation maintenance cost, the goal of distributed generation and energy storage equipment access of the medium and long-term planning can be achieved, and the results of the research will provide decision support for the regional long-term distribution network planning.

Model construction
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Objective function
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Where FCO represents the investment expenses of the distribution network construction and upgrading; FPD represents the cost of distribution network operation; FC represents government subsidies for renewable energy generation. In this paper, the total investment costs of various components can be divided into two categories according to whether the investment costs are associated with design capacity. Taking FSS for example, the mathematical expressions can be expressed as shown below:

FCO: Investment expenses of distribution network construction and upgrading
Where, where u represents internal rate of return; Ct represents present value coefficient of the year t discount to the start of the planning period; Fi represents total amount of capital not related to substation construction capacity for initial investment; Ti represents tax rate related; i represents average interest rate during the service life of a substation; S represents the annual growth rate of construction investment costs; , have the same derivation and similar form as SS F , so they will not be explained separately in this paper.

FPD: Cost of distribution network operation
In this paper, when calculating the operating cost of distribution network, the purchasing cost of substation and the reduced generation cost of power generation using renewable energy are mainly considered. The calculation formula is as follows: Where PSSE represents electricity purchasing cost of substations; PSSD represents the extra charge that a power company needs to pay to the generator during peak hours; PRES represents reduced electricity purchasing costs of DGs for using renewable energy; PDG represents electricity purchasing costs of DGs for using traditional energy.

Electricity purchasing costs
, , (1 ) Where pf represents average power coefficient of the power grid; t C represents the present value coefficient of capital discount from year t to the beginning of the planning period;  represents the proportion of electricity consumption for the valley time of the total electricity consumption; represents the installed capacity of renewable energy DGs at node i in year t(MVA); RES P represents reduced electricity purchasing cost for using renewable energy.

Electricity purchasing costs
Represents reduced electricity purchasing cost for using renewable energy The government subsidies for renewable energy power generation in this paper is that the government issued relevant policies and standards to provide certificates for renewable energy generation under the electricity market environment, which has gradually matured in the European and American power markets. The development of renewable energy has played a good incentive and guiding role. Referring to the relevant foreign standards, the specific calculation formula is as follows: Where, q repersents the market price of a unit certificate; r repersents capacity coefficient of renewable energy generation; M repersents installed capacity for using renewable energy sources;
For built substations in the distribution network: For all nodes in the grid: Where, , ON ji t S represents the apparent power value of node j entering node i through line ij in the peak and hours of year t (MVA/phase); , , Where M represents three-phase capacity of components in a distribution network; U represents max three-phase capacity allowed to be installed at the node;  is a decision variable.
(3) Node voltage constraint For built lines in the distribution network: Where , i t V represents phase voltage at node i in year t (kV); t V represents average voltage amplitude in year t.
For new lines in the distribution network: , , , Where, G is a control variable; FR  is a 0-1 decision variable of building new transmission lines. For all nodes in the distribution network: Where , i t V is the phase voltage amplitude of node i in year t(KV); min V and max V are the minimum and max allowable phase voltage in the grid(KV).
(4) Grid security constraint For power generation safety constraints: Where,  represents the proportion of electricity consumption for the valley time of the total electricity consumption; i  repersents storage efficiency of battery storage stations; (6)Other constraints This set of constraints is to ensure that there is at most one new substation, one distributed power source, and one new circuit between one node or two nodes during the planning period.

Case and results analysis
All manuscripts must be in English, also the table and figure texts, otherwise we cannot publish your paper. Please keep a second copy of your manuscript in your office. When receiving the paper, we assume that the corresponding authors grant us the copyright to use the paper for the book or journal in question. Should authors use tables or figures from other Publications, they must ask the corresponding publishers to grant them the right to publish this material in their paper. As show in Fig. 1 and Table 1, three scheme comparing.
References are cited in the text just by square brackets [1]. Two or more references at a time may be put in one set of brackets [3,4]. The references are to be numbered in the order in which they are cited in the text and are to be listed at the end of the contribution under heading references, see our example below.
The case is that in the initial network there are 11 nodes and 9 transmission line of 25kV. The aim is to expand to a network including 16 nodes and 16 transmission lines with DGs and renewable energy generation. The initial network frame structure is shown in figure 1: Assume that the extension planning life of distribution network is 5 years; the load growth rate of each load node is 4%. The service life of substations and transmission lines is 30 years. The service life of distributed power is 15 years. The life of a renewable power source is 10 years. The market price of a renewable energy certificate is 700 yuan /MWh. The max voltage allowed by the load node is 5%. The max load of substations and transmission lines shall not exceed 10% of their rated capacity; the average annual increase in energy prices is 5%. Construction and equipment costs increase by 7% annually; the internal rate of return is 10%. The tax rate is 3%. The bank rate is 8% a year.
The technical parameters and construction costs of each component in the distribution network are shown in table 1-12:        According to the parameters and the load of each node, after linearization of constraint condition, the traditional genetic algorithm (GA) with the tool of Matlab is used to simulate the example. It isconcluded that the distribution network extended decision shown in the following table: represents the capacity of components (MVA/three-phase); XX is the type of element that the variable represents; i is the number in the category element; t represents construction time. At the end of the planning life, the network structure is shown in figure 2

Conclusion
This paper constructed a PDEP programming model which considers DG, especially renewable energy as an energy distributed power supply and battery energy storage station connecting to the power distribution network. The Model takes the capital cost present value of distribution network construction and expansion as the objective function and meets the requirements of load growth and power grid safe operation indicators, and will support to establish a comprehensive distribution network planning decision support system.