Diversified and high elastic power grid planning method based on two-stage stochastic optimization

. Abstract. With the rapid development of distributed power generation, the study of multi-integrated and highly flexible grid planning methods has become a research hotspot. In multi-resource planning, the planning scheme that considers the active management mode is obviously better than the planning scheme that does not consider the active management mode. In this paper, a diversified and high elastic power grid planning method based on stochastic optimization is proposed, which can effectively deal with the impact of uncertainty caused by the access of distributed generation to the power grid, and provide a method support for the cleaning and efficiency of power system in the future. The IEEE 18 system example proves the feasibility and effectiveness of the proposed method.


Introduction
With the rapid development of smart grid technology, the diversified, integrated and highly resilient grid is based on a modern distribution network to achieve deep integration of information and communication technology and the planning, operation, control, and management of the distribution system, and a high proportion of consumption distribution It is a grid system with features such as green and low-carbon, safe and reliable, efficient interaction, smart openness, and balanced inclusiveness. It is a smart grid, An important part of the Energy Internet. This article summarizes the multiple fusion high-elasticity grid planning methods. Evaluation methods such as fuzzy comprehensive evaluation, ideal point approximation, grey correlation algorithm, entropy weight method [1], data envelopment and analytic hierarchy process are often used in comprehensive evaluation of power systems. The multi-convergence and highly resilient grid can achieve various operations through "source-source complementation", "source-network coordination", "network-load-storage interaction", and "source-networkload-storage coordinated optimization [2] "Energy interconnection and mutual benefit greatly improve the ability to optimize the allocation of energy resources in a wide area and the overall energy efficiency of the society. Diversified integration refers to distributed energy with increasing penetration levels in the distribution network, including distributed power generation, distributed energy storage, demand response, etc [5]. The multiintegrated and highly resilient grid can be attributed to the vertical integration of various elements of the source, network, load and storage, and the horizontal integration of the energy system, physical information, social economy, and natural environment. The multi-integrated high-elasticity grid has the function of resource optimization. It can form a strong receiving-end and sending-end power grid. It is an important power transmission and configuration platform in China. The country's overall investment, environmental protection, and energy production and utilization methods produce huge benefits [6].

Objective function
In order to promote the construction of a diversified and high elastic power grid, a certain number of distributed energy equipment and energy storage equipment will be considered in the process of grid expansion planning to enhance the economy and reliability of system operation. The consideration goal is to minimize the comprehensive cost of the power grid based on two-stage stochastic planning. The comprehensive cost is obtained by summing the investment cost of each stage of the construction decision and the operating cost of each stage during the planning period. Among them, the investment cost of the power grid comes from equipment investment, mainly from the cost of new construction and expansion of lines, distributed power sources such as wind power, photovoltaics, and equipment investment costs such as distributed energy storage; operating costs come from equipment operation and maintenance costs and conventional unit power generation Expenses, specifically, mainly include conventional unit power generation costs, distributed power operation and maintenance costs, energy storage operation and maintenance costs, network loss costs, load shedding costs, the objective function is expressed as: Among them, F is the comprehensive cost during the system planning period, are the investment cost of the y-th stage and the operating cost of the y-th stage respectively, which are both phase index functions, is the discount rate, and Y is the length of the system planning cycle.
(1) Investment cost Where, line NC , EES , WG , PV are the set of line models to be selected, and are to be retrofitted. Line set, line set to be newly built, node set to be selected for energy storage installation, node set to be selected for wind turbine installation, set of node to be selected photovoltaic installation.

Constraints
(1) Line selection constraints When optimizing the planning of the lines in the grid, in order to ensure the economic operation requirements of the system, at most only one line can be replaced or newly built at the same stage, so it can be expressed by line decision variables. Where,

Represents a collection
of new lines to be selected and lines to be upgraded.
(2) Constraints on the number of distributed power installation nodes , 0 max Equations (15) and (16) respectively indicate that the number of nodes for installing wind power and photovoltaics in the system should be less than the allowable number of nodes, and, respectively WG N , PV N are the maximum number of nodes that can be installed with distributed power sources allowed by the system,, x is the sum of the number of nodes installed in the system for wind power and photovoltaic power in the yth planning stage.
(3) Constraints on the number of installed nodes for energy storage equipment There are also restrictions on the amount of energy storage in the system to ensure the minimum investment in the system. x N (7) Where EES N is the maximum number of nodes that can be installed with energy storage devices allowed by the system, and , EES EES i y i x is the sum of the number of nodes that can be installed with energy storage devices in the y-th planning stage.
(4) Distributed power installation capacity constraints Since distributed power sources such as photovoltaics and wind power have strong intermittent and randomness, the safety and stability of the system must be ensured when the distributed power sources are connected. The installed power of the distributed power sources in the system must have a certain capacity limit [9]. Therefore, the following constraints are made: Equations (18) and (19) respectively represent the upper limit of the installed power of wind power at a single node and the sum of all nodes in the y-th planning stage. Equations (20) and (21) respectively Indicates the upper limit of the installed power of the photovoltaic system at a single node and the sum of all nodes in the yth planning stage. Where (5) Installation constraints on the capacity of energy storage equipment In the current situation, the investment in energy storage equipment is expensive, so the installation of energy storage equipment in the system must also meet a certain capacity limit, so the constraint conditions such as equations (22) Equation (12) is that the capacity of a single node in the yth planning stage meets the upper limit constraint, and equation (13) is that all the energy storage in the yth planning stage meets the upper limit constraint.
-max EES y E is the upper limit (kWh) of energy storage allowed by the system.
(6) Output constraints of conventional units The output of a thermal power unit cannot exceed the upper and lower limits of its own output in order to ensure its safe and stable operation. Therefore, there are the following constraints: -min -max , , , , , , In the formula, and are respectively the upper limit and lower limit of output of thermal power unit i (kW, kW).
(7) Distributed energy output constraints The output of distributed energy sources such as wind power and photovoltaics is related to real-time wind speed and light conditions, as shown in equations (15)   The charge and discharge power of an energy storage device is affected by its installed power, and its charge and discharge power must also follow the capacity constraints [10].
Formulas (19) and (20) are the charging power constraint and discharging power constraint of energy storage equipment respectively, and the charging and discharging power cannot exceed the installed power of the energy storage. Formulas (21)-(23) is to constrain the energy storage charging and discharging signs to ensure that only one state can be in progress at the same time. In EES dis i t s y are the symbols indicating the charging and discharging status of the energy storage, when it is 0, it means not charging or discharging, which is 1 o'clock indicates that the energy storage is charging and discharging.
(9) Constraints on remaining energy of energy storage The life of the energy storage device is generally related to the depth of charge and discharge. Overcharge and overdischarge will increase the life loss of the energy storage device. Therefore, the remaining capacity and state of charge of the energy storage device at time t need to be restricted:  (11) Power balance constraints In the coordinated planning of the distribution network and distributed energy, the safe and stable operation of the system must also be ensured, and active power balance and reactive power balance must be met at each node, as shown below:   -dis  , , ,  , , ,  ,  , , ,  , , ,  , , ,  , , ,   -, , ,  , , ,  , , (28) , , , ,

Case Study
3.1 Example of 18-bus power distribution system A regional power distribution system in Huzhou, Zhejiang Province is selected as an example to verify the effectiveness of the proposed method. The network has 10 nodes and 9 lines in the initial year. In the future, it will increase to 18 nodes. The network topology is shown in Figure 1.

Analysis of random planning results
The distribution network planning research is carried out for the calculation examples in the following three situations: Scenario 1: Traditional distribution network planning without RDG; Scenario 2: Consider the traditional distribution network planning of RDG access; Scenario 3: Consider RDG access to the uncertain distribution network planning, and carry out random planning; When the genetic algorithm finds the optimal solution, the initial population size is 100, the crossover probability is 0.8, the redistribution probability is set to 0.2, and the termination algebra T=100. The optimal value does not change for 70 times, which is convergence.
The area to be planned shall be planned according to the traditional distribution network planning without considering DG and RDG access, and the random planning considering the integration and interaction of multiple resources. The planning results are shown in Figure 2, 3, and 4 and  Note: In the planning scheme, "5(3)" means 5 nodes to install 3 corresponding RDGs, and "/" means not to install.   The costs of the three programs are shown in Table 2. From the data in the table, it can be seen that Scenario 1 is a distribution network planning solution that does not consider RDG, Scenario 2 is a traditional distribution network planning solution that considers RDG access, and Scenario 3 is a two-stage stochastic planning solution that considers RDG access. The data can be derived: 1) The annual network investment cost of Scenario 1 is 1.8881 million yuan more than that of Scenario 2 and 2.004 million yuan more than that of Scenario 3. This is because after joining RDG, it can bear part of the load and reduce the investment in the upgrade and construction of the power distribution system, regardless of RDG planning. In the plan, because there is no RDG to bear the load, it is necessary to increase the network investment of the distribution system; and the network investment cost of the plan 2 is 6.11% more than that of the plan 3. This shows that the two-stage stochastic planning plan considering RDG access can better improve the system The ability to accept RDG, and the joint planning of RDG and network can make RDG more reasonable access to the distribution network, and make the grid structure more suitable for RDG access.
2) In the comparison of network loss costs, Scenario 3 is 509,000 yuan, which is 18.1% less than Scenario 1, and 7.48% less than Scenario 2. This is because the two-stage stochastic planning solution considering RDG access can be better utilized RDG plays a positive role in reducing system network loss and improving system operation.
3) In the comparison of the power purchase cost of the higher-level power grid, Scenario 3 is 109.3193 million yuan, which is 23.477 million yuan less than Scenario 1, and 7.199.2 million yuan less than Scenario 2. This is due to the two-stage stochastic planning plan considering RDG access. RDG generates more power and bears a larger load, so it purchases less electricity from the upperlevel grid; in Scenario 2, because RDG is not actively managed, the distribution network's ability to accept RDG output is smaller than that in Scenario 3. Therefore, the RDG's power generation is relatively small, and the power purchase from the upper-level grid is relatively large; similarly, since the influence of RDG is not considered in Scenario 1, all loads in the system must be borne by the substation, so this solution The purchase of electricity from the upper-level grid is the largest.

Conclusion
In this paper, a two-stage stochastic planning model of the diversified and high elastic power grid was proposed, and the joint planning result of the distribution network with distributed power generation under the multi-integration and high flexibility was obtained. The conclusion is as below: Distributed power generation planning and distribution network framework planning are a whole that influences and cooperates with each other. Joint modeling and solving of them can conform to the development trend of active distribution network with large-scale distributed power generation in the future. At the same time, from the perspective of social comprehensive cost, the random planning scheme considering RDG access is the best, which proves that the multi-integrated and highly flexible distribution network can overcome the shortcomings of