Multi-Source Energy Storage Stations Control Strategy Considering Implicit Linearization of The Power Flow Manifold

With the development of distributed new energy and multi-type loads, in order to realize the effective management of distributed power sources by multi-microgrids and better play the supporting role of microgrids on distributed power sources, we consider the dynamic changes of power flow in the distribution network caused by the power interaction between multi-microgrids and shared energy storage and propose an optimal dispatching strategy of multi-microgrids considering multi-source synergy considering the constraints of power flow. Since the constraint of the distribution network is a highly nonlinear mixed integer programming problem with power terms, a linearized approximation model is adopted for the power flow of the distribution network, and then a multi-objective model with minimal wind power and photovoltaic abandonment and minimum total operating cost of multi-microgrid is established. The improved IEEE18 node system is used to verify the model, and the results show that the proposed method comprehensively considers the linkage of grid-load-storage, which makes the dispatching results more realistic and more applicable.


Introduction
In the context of new energy development, new energy sources will usher in more rapid development.In addition, a large number of electric vehicles and flexible loads connected to the microgrid will increase the impact of new energy power fluctuations on the safety and stability of the microgrid [1].The energy storage system is a means to solve the trouble of new energy consumption, and its rapid charge and discharge characteristics are used to smooth the load fluctuation of the microgrid.Shared energy storage is an energy storage operation mode that decouples the ownership and use of energy storage [2], which effectively solves the problems of high cost and limited space resources of distributed energy storage through economies of scale, and can provide services for multiple subjects [3].The shared energy storage fully considers the differential complementary characteristics of energy storage behavior and energy production and sales complementary characteristics of multi-microgrid energy storage behavior, which can further reduce energy storage investment costs, and facilitate service users [4].
At present, the research on multi-collaborative energy storage optimal scheduling mainly includes multi-energy system collaborative scheduling, multi-user subject shared energy storage optimal scheduling, demand response, and shared energy storage collaborative optimization.[5] proposes a comprehensive energy-sharing energy storage optimization scheduling method based on collaborative games.[6] proposes a collaborative optimization operation strategy.[7] proposes an optimal dispatch of shared energy storage in microgrids considering the uncertainty of new energy generation to achieve win-win benefits for multiple subjects.[8] proposes a multi-park integrated energy system strategy considering electric vehicle auxiliary shared energy storage power stations.[9] proposes a two-layer optimal dispatching strategy for multi-microgrid systems that takes into account both energy-consuming user demand response and shared energy storage to promote power interaction between microgrids.However, the above research only focuses on the various user subjects that interact with the energy generated by shared energy storage, mainly focusing on economic operation, and rarely considers its role in the stable operation of the distribution network, which is not conducive to the overall realization of the optimal dispatch of various energy sources and the dynamic balance of multiple objectives.
Therefore, this paper considers the changes in network node voltage and branch current caused by the power interaction between multi-microgrid and shared energy storage and constrains the power flow of the distribution network.Based on this power flow constraint and multi-source load, a dual-objective model of minimum wind and solar curtailment and minimum operating cost when multi-microgrid shared energy storage is established.Since the power flow equation and constraint model of the distribution network are highly nonlinear, they are linearized similarly, and mixed integer linear programming is used to solve the dual-objective problem.Finally, the improved IEEE-18 node system is analyzed to verify the effectiveness of the proposed model.

2.
Multi-microgrid shared energy storage system architecture 2.1.System architecture It is supposed that there are multiple microgrid users in a distribution network who jointly lease a shared energy storage system (SESS).This paper takes the daily scheduling cycle to consider the power interaction behavior between users and shared energy storage.The system architecture diagram is shown in Figure 1 below.Each microgrid contains conventional loads, wind and solar resources, and controllable loads, and each microgrid is connected to the distribution network.
where EMG,i,t is the actual capacity of the microgrid i in t period, and Emax MG,i,t is the dynamic rated capacity of shared energy storage to microgrid i in t period.
where Pmax MG,i,c and Pmax MG,i,d represent the upper and lower limits of the power of microgrid i using shared energy storage for charging and discharging in t period, and c and d are the charging and discharging efficiency of shared energy storage.c MG,i,t and d MG,i,t represent the battery charge and discharge state.
∂ is the scale coefficient.

Distribution network power flow constraints
It is assumed that the distribution network where N microgrids are located contains B nodes and L lines, and the node set α={1,2,...... B}, Line β={1,2,...... L} [10].This paper represents the node complex voltage as ub=ub'ejb, b∈α, where ub' is the voltage amplitude, b is the voltage phase angle, and the node injection complex power meter is sb=pb+jqb, where pb is injected active power and qb is injected reactive power.
where Y∈CB×B (CB×B represents the B×B matrix) with complex numbers as elements as the node admittance matrix of the distribution network, u∈CB (CB represents the B-dimensional column vector with complex numbers as elements) is the node complex voltage vector, s∈CB injects the complex power vector into the node, and Yu represents the conjugate of Yu.In addition to meeting the power flow balance during operation, the range of voltage amplitude of all nodes should be reasonable: In order to facilitate the derivation of the branch current of the distribution network, we define the node-branch association matrix A∈RB×L (RB×L represents the B×L matrix with real numbers as the element), where f(l) represents the first end node of the branch and t(l) represents the end node of the branch.
We define the matrix Y1b∈CL×B based on matrix A and the tributary admittance matrix Y1∈CL×L (diagonal matrix composed of tributary admittance): Through this equation, the original system branch admittance matrix Y1 can derive an indirect matrix that can calculate the branch current from the node voltage based on Ohm's law under the action of the node-branch correlation matrix A, so that the current vector i1∈CL of the branch can be directly converted from the complex voltage vector u of the node and written as: Considering the operation of the distribution network, all branch currents need to be met: where i max l is the maximum mode value of the branch L that allows current to flow.
4. Multi-microgrid shared energy storage dispatching model considering the power flow constraint of the distribution network

Objective function
Since photovoltaics and wind power make full use of natural conditions to generate electricity, their power generation costs are generally ignored [11].The cost of fuel units includes fuel, start-up and maintenance costs, the charging and discharging of SESS requires a certain rental cost, and the internal resource scheduling of the microgrid considers giving certain subsidies to electric vehicles.
where F1 means that the operating cost of the microgrid is the smallest, and F2 means the abandonment of photovoltaic and wind power in the microgrid at the minimum. ( Since there are two states of charge and discharge in a single electric vehicle, the 0-1 variable ch i,t and dis i,t indicate the state of the electric vehicle.
Assuming that the electric vehicle can be guided to meet the power load demand by adjusting the charging and discharging electricity price [12].The relationship between user charging power and electricity price is as follows: where k1 is the ratio of the charging electricity price to the grid time-of-use electricity price at that moment; k2 is the ratio of the charging power to the reference charging power at that moment.
Price incentives are provided directly for the unit discharge of electric vehicles at the time of discharge.According to the above relationship, the charging and discharging electricity price at each moment is obtained.MG, ,EV, where F is the total number of electric vehicles participating in the dispatch, St is the time-of-use price of the grid, and EV is the unit dispatch subsidy cost.
(2) Shared energy storage costs The total shared energy storage capacity of each microgrid is Emax SESS , and the service fees required to use shared energy storage in a typical day microgrid i in the t period are: where SESS indicates the service unit price of energy storage charging and discharging.

Constraints
The constraints on the optimal operation of the microgrid are basically the same as the constraints on calculating the output range of the microgrid, and include the following constraint.
where PMG,i,W,t is the microgrid node power, PMG,i,pv,t and PMG,i,wt,t are the predicted output of photovoltaic and wind turbines in each period, and Pi,other,t is the transmission power with other microgrids.

Model solving
The constraints of multi-microgrid shared energy storage optimization dispatch problems can be converted into linear constraints, so they can be converted into mixed integer linear programming for solving.Among them, the secondary fuel cost of micro-combustion engines can be processed by the segmented linearization method.It is supposed that there is a balance node in the distribution network where the user is located, and the rest are PQ nodes, the voltage amplitude and phase angle of the balance node are expressed as UR' and R respectively, and remain unchanged, and the voltage amplitude vector and phase angle vector of the PQ node are expressed as UPQ' and PQ, respectively.V is a vector composed of node designation order, which indicates the voltage amplitude of all nodes and  indicates the voltage phase angle of all nodes of the distribution network.
Given a running point (u', ), a first-order Taylor expansion of the power flow equation yields:

Parameter settings
The 18-node distribution network data in the standard example in matpower 7.1 is selected as the distribution network parameters where the microgrid is located, the structure is as follows: the power benchmark value is 10 MVA, node 18 is the first node and a balance node, and the remaining nodes are PQ nodes, and the distribution line parameters, natural load data of each node and new energy output data are shown in [13].Three microgrids share energy storage optimization dispatch for simulation.The microgrids are located at nodes 9, 12, and 14.The optimization period T is 24 h, and the interval is 1 h.The internal electric vehicle travel law of each microgrid was sampled according to the function of the commercial area, and 100 electric vehicles were selected to participate in the dispatch of each microgrid, with an installed capacity of 60 kWh for a single electric vehicle, a charge and discharge power of 20 kW, a charge and discharge efficiency of 0.9, and a unit discharge subsidy of 1.1 yuan/kWh for electric vehicles.SESS provides energy storage charging and discharging services for each microgrid, and its parameters are shown in Table 1 This paper considers two scenarios: Scenario 1: multi-microgrid shared energy storage without considering the power flow constraint of the distribution network; Scenario 2: multi-microgrid shared energy storage considering the power flow constraint of the distribution network.For the power flow constraint parameters of the distribution network, the parameters are set as follows: we set the node voltage amplitude to meet 0.95~1.05pu, and the branch current mode value to meet 1.8 pu.
The following is a case test of the model proposed in this paper according to the scenario settings, and the tests are solved on the MATLAB2020b platform with the help of commercial optimization software Gurobi 9.5.1.
The power flow of the distribution network also changes at different times.The node voltage amplitude and branch current modulus values of each period of the distribution network in scenario 1 are shown in Figure 4.The node voltage exceeds the upper limit, reaching 1.07 pu, and the maximum current of the confluence branch reaches 2.0 pu.Scenario 2 considers the power flow constraints of the distribution network, which limits the power interaction between the multi-microgrid and the shared energy storage, but the controllable load inside the microgrid will reduce the load output of the microgrid itself to a certain extent.Moreover, this scenario is closer to the actual operation situation, so the scheduling results are also more practical reference value.
The results of the shared energy storage output and internal output of each microgrid in scenario 2 are shown in Figures 6-7.When the renewable energy in the microgrid is surplus, the aggregate electric vehicle will successively arrive at each microgrid for charging.When the wind and solar output does not meet the load requirements, we consider the price of natural gas and use the polymerized electric vehicle or micro-combustion engine for discharge.

Conclusion
Considering the coordinated control strategy of a multi-source coordinated energy storage power station to support distribution network operation can avoid the waste of capacity caused by ignoring the physical constraints to a certain extent, and ensure that the power flow of the distribution network is always within the feasible range when the energy storage optimization dispatch is carried out, which makes the optimization results of shared energy storage more reliable.The results show that since the controllable load within each microgrid will reduce the load demand of the microgrid itself to a certain extent, the curtailment of wind and photovoltaic and the total operating cost of multi-microgrid still have certain advantages.

Figure 2 .
Figure 2. Schematic diagram of 18-node distribution network topology Three typical microgrid output curves are selected, and the load output of each microgrid is shown in Figure 3.

Figure 3 .
Figure 3. Load diagram of a typical microgrid

Figure 4 .
Figure 4. Node voltage amplitude and Branch current modulus

Figure 5 .
Figure 5. Node voltage amplitude and Branch current modulus

Figure 7 .
Figure 6.Shared energy storage output The cost of electric vehicles Electric vehicle constraints are as follows: .

Table 2
shows the wind and light abandonment and operating costs in the two scenarios.