Spatial optimization of integrated energy system including hydrogen electrolysis center based on mixed integer second‐order cone programming

Hydrogen energy is playing an increasingly important role in integrated energy systems (IES) due to its multiple uses. Green hydrogen can be produced from electricity generated from renewable energy, reducing carbon emissions and environmental pollution. Previous work usually only considers electric vehicles (EVs) as flexible loads, and there are few studies on the production and application process of green hydrogen. In this paper, hydrogen electrolysis centers (HECs) and EVs are simultaneously schedulable loads, integrated into IES, and optimized. The distribution network model is established, and the optimization goal is to minimize network loss while ensuring the safe operation of the power grid. Through the power flow optimization method of mixed‐integer second‐order cone programming, the space optimization scheduling of EVs in the IES is carried out, and the optimal location of the HEC is reasonably planned and set. A simulation instance of IEEE 33 nodes is used to verify the proposed method. The final results show that this method can minimize network loss in the range of safe operation of the system for the spatial scheduling of electrolytic hydrogen centers and EVs. At the same time, it can also provide a reference for HEC addressing.


| INTRODUCTION
With the increasing tension of fossil energy, the attitudes of governments toward the development and utilization of new energy are becoming more active.The integrated energy system (IES) can be seen as an evolution of energy production and consumption cognition.In a certain area, it is very valuable to gather the production and consumption of various energy sources, use advanced communication and control methods to control and schedule the integrated system and find the optimal operation mode of the system in multiple security boundaries.IES contains several flexible loads, among which electric vehicles (EVs) are the most representative.However, the increasing number of EVs brings new problems.][3] Reasonable scheduling of EVs, whether in terms of time or space, has been explored by many scholars.Different optimization goals mean different optimization schemes. 4,5Aiming at the access problems caused by the increasing number of Plug-in EVs, a three-stage scheduling method based on a multiagent-based PEV control strategy, multi-objective genetic algorithm, and adaptive neuro-fuzzy inference system is proposed.Scheduling the charging and discharging of EVs makes the final load flattening, which is beneficial to voltage stability and consumer revenue.Luo 6 studied the model of the AC/DC hybrid distribution network, simplified the object into a Mixed Integer Quadratic Program (MIQP) problem, and optimized the network loss and user convenience. 7roposes a scheduling model based on spatiotemporal bi-layers, formulated a scheduling strategy for upper and lower layers with different objectives, and finally verifies the algorithm through a calculation example, but the energy types considered by the model are not rich enough. 8also divides the scheduling of EVs into two stages.The first stage determines the charging and discharging quantity of EVs.The second stage uses a genetic algorithm to optimize the charging and discharging power of EVs.The simulation results are beneficial to the smooth load curve. 9gives a solution based on the competition over resource (COR) algorithm to optimize the access of EVs, and verify it on 9-bus, 33-bus, and 69-bus respectively.Compared with various algorithms such as the water cycle algorithm (WCA), it proves its superiority. 10integrate the operation strategy of EV charging stations into the MILP model to realize the optimal operation strategy of EVs.Bao et al. 11 considers the problems of power fluctuations and high peak loads caused by high-power charging at charging stations.By controlling the battery energy storage system, a two-layer optimal control strategy is formed, and a calculation example is given to verify that the charging load curve can still be improved under large disturbances. 12studied the method of stochastic optimization to control the uncertain wind power generation system and used the IEEE 118-bus system for numerical calculation, which proved that the operating cost can be reduced. 13ntroduced node power loss sensitivity and electricity price in the optimization goal to reduce network loss and charging costs.A novel interactive network model between the distribution network and EVs was proposed in, 14 which reduces the charging cost and has a smoothing effect on the load curve. 15studied the travel route optimization problem of long-distance EVs and jointly modeled the transportation network and power network.After converting the model into a multiobjective bilevel conic optimization model, it is solved, and finally, the corresponding charging strategy is obtained. 16studied the charging and discharging strategy optimization problem of EVs under the background of virtual power plants (VPP), taking into account carbon transaction costs and various distributed energy sources, and finally effectively guided the charging and discharging behavior of EVs, making the load fluctuation less. 17tudied the coordinated operation of the distribution network and distributed energy, and used the power flow calculation model of convex AC to ensure the convergence of distribution network optimal dispatching results.Aiming at the network loss problem of distribution networks, literature 18,19 deduced it in detail and established a power flow coordination optimization model of distribution networks.Through appropriate relaxation, the complex non-convex nonlinear mixed integer optimization problem is transformed into a convex mixed integer second-order cone optimization problem, which greatly reduces the difficulty of calculation and guarantees accuracy. 20established a gridconnected microgrid model including gas, electricity, and heat, coordinated control of these energy sources, and EVs also participated as dispatchable loads.
In IES, with the continuous enrichment of energy consumption units such as hydrogen energy vehicles, the preparation, storage, transportation, and use of hydrogen are also taken into consideration.2][23] proposes a scheme that completely uses liquid hydrogen as energy storage with renewable energy functions, which enriches the energy consumption mode of the comprehensive energy system. 24incorporated the hydrogen energy storage system into the cross-regional renewable energy consumption system, and explored the reasonable location and scale of HESS.It is foreseeable that hydrogen energy will be deeply integrated into the IES system, and complement the advantages of the grid-centered energy network, playing multiple roles such as energy storage and fuel 25,26 in transportation, power generation, and chemical industry. 27considers the investment and operating costs of the active distribution network at the same time during collaborative optimization, making its model more comprehensive, and verifying its effectiveness with numerical results. 28strives to minimize the net present value of the network investment cost, optimizes the active distribution network in two steps, and achieves good results.
Table 1 compares some references with the work in this paper.In this context, the main work of this paper is to discuss how to reasonably schedule the charging and discharging locations of EVS in the distribution network including hydrogen electrolysis centers (HECs) and a large number of EVS, to reduce the system network loss.At the same time, under the condition of meeting the basic use of green hydrogen, optimize the location of HEC.

| General description
The main goal of this paper is to optimize the spatial location of the charging and discharging of EVs and the electrolysis hydrogen center on the distribution network side of the IES.The model can be represented in Figure 1.Under the safe operation of the power grid, meet the minimum energy requirements of EV owners and hydrogen fuel cell vehicles (HFCVs), and reduce the loss of distribution network lines to obtain maximum economic benefits.In addition, because of the complexity of the grid power flow system, some supplementary assumptions are needed to simplify the description model: 1. Assuming that the construction cost of the electrolytic hydrogen center is the same at any node position, only the factors generated during system operation are considered; 2. The charging and discharging power of an EV are respectively constant.

| Optimization model
The main goal of this paper is to optimize the spatial location of the charging and discharging of EVs and the electrolysis hydrogen center on the distribution network side of the IES.Under the safe operation of the power grid, meet the minimum energy requirements of EV owners and HFCVs, reduce the loss of distribution network lines to obtain maximum economic benefits.
The core energy type in the IES is electric energy, and the objective function of the power line loss in the distribution network is expressed as   where f Ploss is the total energy loss, P loss t , is the energy loss in the period t, T is the number of total scheduling periods, t is the time interval, r ij is the resistance of the branch ij, I ij t , represents the current amplitude of the branch at the time t, i j , represent different nodes respectively, N is the total number of nodes.

| Power balance
Power balance includes active power balance and reactive power balance.Any node needs to satisfy Kirchhoff's law: where P j t s , and Q j t s , are the active power source and reactive power source of the node j at the time t respectively.  i j j e , indicate the direction of power flow respectively, node i is the branch node in the power grid with node j as the end, and e is the branch node with j as the head end.U i t , 2 represents the voltage on the i node.P jEVdischarge,t and P jEVcharge,t represent the charging and discharging power of each EV, respectively.P jHelec t , represents the power used for HEC production at time t.P jload t , Q jload t , represent the active load and reactive load of node j at time t, respectively.

| System safe operation boundary
The operating parameters in the distribution network need to be ensured within a safe range.The constraints The structure of the integrated energy system including IEEE 33 nodes.EV, electric vehicle; HEC, hydrogen electrolysis center; HFCVs, hydrogen fuel cell vehicles.on voltage, current, and maximum power carried by the line are determined using the following equation: where U i t , min and I i t , min are the lower bounds of voltage and current at node i respectively, U i t , max and I i t , max are the upper limits of voltage and current at node i, respectively.P ij t , max is the upper limit of power.

| Constraints for EVs
The number of charging piles is limited.Whether the EV is charging or discharging, it needs to occupy a charging pile.( 4) describes this constraint: .
N ch e i t arg , and N disch e i t arg , , , respectively, represent the number of EVs charged and discharged at the i node and period t.N pile i t , , represents the number of i-node charging piles.

| Constraints for electrolytic hydrogen center
The HEC can be regarded as a flexible load.To facilitate the simulation in the example, the HEC is regarded as an active load in this paper.To meet the consumption demand of hydrogen energy in the region as much as possible, the factory capacity of HEC can be set to not less than the minimum demand.At the same time, there is an upper limit on the power of HEC, and the relevant constraints are as follows: where E jHelec min represents the energy required to produce hydrogen by the minimum HEC, E jHelec represents the total amount of hydrogen energy produced by HEC.

P jHelec t
, represents the actual production power in the period t, and P jHelec t , max represents the maximum production power in the period t.
All objective functions and constraints have been listed, and the model can be transformed into the standard model of MISOCP by bringing (6) into the simplification and performing appropriate relaxation. 18,19 The MISOCP model can be quickly and accurately obtained using a commercial solver (in this paper, Gurobi).

| RESULTS AND DISCUSSIONS
According to the above analysis, an example model is given in this section.This reliable MISOCP model is built in the YALMIP toolbox of the MATLAB platform, and the Gurobi solver is used for subsequent optimization calculations.All calculations are run on a laptop equipped with an Intel Core i7 CPU and 16 GB of RAM.

| Simulation and setup
The IEEE 33-bus model is shown in Figure 2. Considering that the site selection of HEC is usually special, such as needing to be far away from residential areas.Assuming that nodes 0-5, 18-21, and 22-24 are residential areas, the establishment of HEC is prohibited, and 6-17 and 25-32 can be considered as alternative sites for HEC.
The number of EVs that need to be charged and discharged in each time period is randomly generated by the calculation example, as shown in Figure 3.The charging and discharging power of EVs is 20 kW, while the energy consumption of HEC is 1 MW when it is working, and the maximum working time is 13 h a day.
F I G U R E 2 Two regions IEEE 33-bus system.
The voltage fluctuation of all nodes does not exceed 5%, and the number of charging piles for EVs at each node does not exceed 150.The number of EVs that need to be charged and discharged at time t is determined by a random number.For segmented electricity prices, HEC's production time is divided into two types: 8:00 a.m.-8:00 p.m. (case 1) and 8:00 p.m. to 8:00 a.m. the next day (case 2).The production power of HEC is limited to 1 MW.
Taking HEC on node 6 as an example, the scheduling results of case 1 and case 2 are shown in Figure 4. Figure 4 is four 24 × 33 three-dimensional graphics, and the coordinates are Time (24 h), node number, and the number of EVs charged and discharged.The left and right sides represent the charge and discharge quantities of case 1 and case 2, respectively.It can be seen that the time of HEC in the daytime (case1) and nighttime (case2) working modes affect the charging and discharging schedule of EVs, which are also flexible loads.
Figure 5 is also a comparison of cases 1 and 2. It can be seen that the network losses changes within a day after using the MISOCP method, considering the EV as a flexible load, and responding to the scheduling scheme of the system.Respectively, in case 1, the network losses is 2.5419, and 2.5102 MW h in case 2.
Figure 6 shows the voltage amplitude value in cases 1 and 2. It can be seen that the node voltage constraint is working, and no node voltage can break through the constraint limit, which ensures the safe operation boundary of the system.
Extend the possible locations of HECs to the entire manufacturing area in a 33-node system.Then perform network losses optimization calculations for each node individually, and the results are shown in Figure 7.
It can be concluded that the influencing factors of the system network loss include the location of the HEC and the working time of the HEC.As the location of the HEC changes, the network loss also changes: when the HEC is close to node 0, that is, the slack bus, the network loss will gradually decrease, and it will gradually increase when it is far away from the slack bus.At the same time, it can be seen that the network loss of case2 is always lower than that of case1.This is because, under the incentive of the peak-valley electricity price mechanism, HEC deliberately avoids peak power consumption and smoothes the power of the distribution network, resulting in a reduction in network loss.It also means that during the period of low power consumption, HEC manufactures green hydrogen, which can be used to cope with the volatility of a high proportion of new energy connected to the grid.

| CONCLUSIONS
The study in this paper is aimed at the optimization of the spatial dimensions of flexible loads, considering an IES including EVs and HECs.For the optimization of the distribution network, the minimum network loss is selected as the optimization goal, and the model is simplified and transformed into a MISOCP model for computer calculation.Finally, the power flow of the distribution network is optimized and calculated to determine the charging and discharging position of the EV in the spatial dimension, and the optimization results of the location of the hydrogen energy center are compared.Through the calculation example verification of the IEEE 33 bus, it can be seen that this optimization method can effectively schedule the charging and discharging of EVs, reasonably place HEC, and reduce network loss, which means improving the economy of the system.On the basis of this research result, the space scheduling scheme design of flexible loads can be carried out according to the specific requirements and constraints of different IES systems.It can also continue to deeply combine the time and space characteristics of IES for co-optimization to improve the overall performance of IES and can be used to cope with the volatility of a high proportion of new energy access to the grid.

F I G U R E 3
Number of electric vehicles charge and discharge per hour during the day.F I G U R E 4 Electric vehicles (EVs) charging and discharging space scheduling results.

F I G U R E 5
The network loss of cases 1 and 2.F I G U R E 6 Voltage magnitudes of each node in cases 1 and 2.F I G U R E 7The effect of hydrogen electrolysis centers' (HECs) position on network losses in cases 1 and 2.
Comparison of existing work with proposed work.
T A B L E 1