Security distance analysis of active distribution network considering energy hub demand response☆

0 Introduction

1) Motivation and literature review

The rapid socio-economic development in China has led to a continuous annual increase in residential electricity demand, with air conditioning (AC) loads emerging as the primary temperature-controlled contributor to total energy consumption [1].Globally, the use of AC systems and electric fans now accounts for approximately onefifth of the electricity consumed in buildings and around 10 % of total global electricity consumption [2].

Simultaneously, the advent of the 5th generation (5G)mobile communication era has brought significant convenience to residential life and infrastructure development.However, the widespread adoption of 5G technology has resulted in an exponential growth in mobile communication data volume[3],leading to an increase in base station(BS)loads and a consequent rise in mobile network energy consumption.Flexible loads, such as AC and BS loads,have become critical resources for participating in the demand response of Active Distribution Networks(ADNs) [4-9].

Numerous studies have focused on modeling techniques for Energy Hubs (EHs) interacting with ADNs.For instance, research has explored EH modeling with wind power and its optimization [10,11], the impact of EHs on distribution network power flow and its optimization[12-14], and energy hubs centered on combined cooling,heating,and power supplies[15-18].Additionally,BS load modeling has been studied, including Internet data center load modeling based on spatiotemporal transferable characteristics [19] and energy management modeling for 5G BSs [20].However, the method for considering the common characteristics of the BS load and EH and exploring a method to transfer the impact of the BS on the interactive power between the EH and ADN still needs to be researched.The transfer of base station (BS) loads influences renewable energy consumption and the operational costs of distribution networks.To address these challenges, the concept of green wireless communication has been proposed in the literature [21].This approach integrates distributed power generation into the energy supply of 5G networks to reduce electricity costs and carbon emissions.However, the intermittent and fluctuating nature of distributed clean energy output affects the power supply capacity [22-24].It is urgent to study how to balance the load transfer of the BS, renewable energy consumption, and safe power consumption, with the consideration of random wind power, and to establish a multi-objective optimization model that considers the above.

The effect of flexible load regulation, such as AC load curtailment and BS load transfer, on security distance is a critical factor in assessing the power supply reliability of an ADN.Current research on security distance in distribution networks primarily focuses on security evaluations and the conceptualization of security distance.

Reference[25]categorizes security distances in distribution networks into feeder and geometric security distances and evaluates their implications for network reliability.Reference[26]introduces the concept of security distances in ADNs, accounting for the influence of distributed power sources.Similarly, Reference [27] presents a model and the concept of a security region for all-quadrant distribution systems in ADNs.

However,there has been limited research on the impact of flexible load regulation on security distance,particularly in scenarios where energy hubs (EHs) with stochastic wind-solar power and flexible loads are integrated into ADNs.Further study is needed to explore the relationship between flexible load regulation and security distance in such contexts.

Research on enhancing the security distance of Active Distribution Networks (ADNs) must account for renewable energy integration and flexible loads.Additionally,the challenges associated with renewable energy consumption and the active network losses induced by its integration cannot be overlooked.

Reference [28] proposes an optimal power flow model that addresses the static security margin objective, considering imbalances in current distribution within the power system.Reference [29] develops a multi-objective optimal power flow model based on a direct-current power flow controller for hybrid systems comprising alternating and direct currents.Reference [30] validates a multi-objective optimal power flow model that considers three key objectives: system network loss, generator power generation cost, and carbon emissions.

Using the NSGA-II algorithm, Reference [31] solves a model focusing on network losses,system generation costs,and voltage offsets.Reference [32] explores the participation of flexible renewable energy hubs (EHs) equipped with wind farms,biowaste units,and storage systems,such as hydrogen, thermal, and compressed air, in energy markets using a market-clearing price model.Reference [33]examines the total expected operating cost of networks,adhering to constraints from optimal power flow equations,EH operation models,and EH flexibility limits.Reference [34] applies scenario-based stochastic optimization to address uncertainties, providing a novel approach to modeling and evaluating the performance of integrated systems.Despite these advancements, a comprehensive multi-objective optimization model that simultaneously addresses energy efficiency, clean energy utilization, and the secure operation of ADNs remains unexplored.

2) Research gaps and contributions

A summary of the studies reviewed in the literature is presented in Table 1.Research [30,33,35] focused on the economic and environmental operation of distribution networks but largely overlooked the security indices of Active Distribution Networks (ADNs).In contrast, studies[28,29,31] included distribution network security indices,such as dynamic thermal rating and current load levels,in their optimization objectives.However, these indices did not account for three-phase conditions, nor did they analyze the impact of stochastic wind-solar power and flexible load regulation on security indicators.In this study, the three-phase security distance EH was used as the safety optimization index, and a multi-objective optimization regulation model was established by considering the BS load transfer and AC load reduction.

Considering the aforementioned literature review, the main contributions of this study are summarized as follows.

· Combined with the traditional EH, this study incorporates the impact of stochastic wind-solar power and flexible loads on the EH and established an EH model containing stochastic wind-solar power and flexible loads.

Table 1 Summary of recent related studies.

Ref.IndicesAC load reductionBS load transferRandom wind-solar powerThree-phase safety distances OperationSafetyEconomic[19]YesNoYesNoYesNoNo[28]YesYesYesNoNoNoNo[29]YesYesYesNoNoNoNo[30]YesNoYesNoNoNoNo[31]YesYesYesNoNoNoNo[33]YesNoYesNoNoYesNo[35]YesNoNoYesNoYesNo PSYesYesYesYesYesYesYes

· The effects of changes in flexible loads (BS and AC loads) on the safety distances were analyzed.

· Taking the BS load as the decision variable and considering the security distance, active network loss,energy cost objective, and voltage safety constraints,a multi-objective optimization model of the BS load transfer is established,and the corresponding solution algorithm is proposed.

1 EH modeling containing stochastic wind-solar power and flexible load

1.1 Random wind-solar power modeling

The random wind power output is related to the wind speed, and this section incorporates the Weibull distribution to model the random wind power output [35] as follows:

where vr is the rated wind speed of the wind turbine;vci and vco are the cut-in and cut-out wind speeds,respectively;Pwtr is the rated power of the wind turbine.

Photovoltaic power generation mainly relies on solar arrays, their output size, and light irradiation intensity;the total area of solar arrays S and photoelectric conversion efficiency have a direct relationship with the output model [36], as follows:

The light intensity followed a beta distribution depending on the α and β, which is not repeated here.

1.2 BS power load modeling

The 5G BS load has a large demand response potential because it includes a large number of communication loads.The power-consumption load of the 5G BS has an approximately linear relationship with the communication load [37], as shown in (3).

where Lb is the electrical load of the BS;Tb is the communication load of the BS;αb and βb are constant coeffi-cients;Qb is the reactive power of the BS; and ϕb is the power factor angle of the BS.

The power consumption of the BS loads varies under different communication conditions.In addition,considering the spatial transfer characteristics of the communication load, realizing BS load regulation helps solve the peak overload problem.

The communication load is mainly in the form of servers, and the power expression for the communication load can be written as follows:

where Mi,j is the number of the jth type of servers in the ith BS, is the power of the jth type of server, PUE - i is the power utilization efficiency of BS i, and Ωt is the set of the first server types.

1.3 EH interactive power model with random wind-solar power and BS load

Based on existing research on EH, an EH model incorporating stochastic wind-solar power and flexible loads was established,as shown in Fig.1.This model introduces new base station (BS) loads and AC loads, collectively referred to as flexible loads.The original electrical loads of the EH are divided into flexible loads and other electrical loads, with the latter being collectively referred to as electrical loads hereafter.The output ports of the flexible loads and electrical loads are connected to the transformer, while the distributed wind-solar power is directly linked to the EH’s electrical loads, flexible loads, and central AC system through a converter.The interaction between the EH and the ADN is inherently stochastic due to the variability of the distributed wind-solar power output.

Fig.1 EH model with random wind-solar power and flexible load.

As illustrated in Fig.1, the left side of the EH model comprises distributed wind power, distributed photovoltaic power, and the ADN, which serve as the input energy sources.The output energy of the EH is delivered in the form of electrical loads, flexible loads, and cooling/heating loads.The EH consists of components such as a wind power conversion device, a power transformer,and a central AC system.Due to the inherent randomness of distributed wind power and photovoltaic power generation, the active interactive power between the EH and the ADN also exhibits stochastic behavior.

Let the cooling/heating load-allocation factor of distributed wind power be vw,the flexible load-allocation factor be（1-vw）vwt,the power supply load-allocation factor be （1-vw）（1-vwt）; the cooling/heating load-allocation factor of distributed wind power be vPV, the flexible loadallocation factor be （1-vPV）vPVt, the power supply loadallocation factor be （1-vPV）（1-vPVt）; the cooling/heating load-allocation factor of ADN be ve, the flexible load-allocation coefficient be （1-ve）vet, and the supply load-allocation coefficient be （1-ve）（1-vet）.The coupling relationship between the original input and the converted output energy of the EH model containing random wind-solar power and flexible loads is shown in (5).

where Le is the EH electrical load,Lt is the EH flexible load,Lh is the EH cooling/heating load,ηC is the efficiency of the wind power converter,ηPV is the efficiency of the photovoltaic converter,ηT is the efficiency of the power transformer,and ηAC is the cooling and heating efficiencies of the central AC system.

The above (5) can be written in matrix form as shown below:

The EH is defined as a power state when the interactive power between the EH and the ADN is positive,while it is defined as a load state when the interactive power is negative.

Two main types of flexible loads are considered: a cuttable load(AC load) and a spatially transferable load(5G BS load).When the AC load is curtailed or the BS load is transferred,the interactive power between the flexible load and the EH/ADN must satisfy the relationship defined in(6)above.However,when the BS load is transferred,it not only affects the interactive power between the EH and the ADN where the BS is located,but also induces changes in the interactive power between the EHs and the ADN of other EHs.This occurs if the transferred load exceeds the capacity of the current EH and is redistributed to other EHs containing the BS.

2 Impact of EH containing flexible loads on security distances

2.1 Security distances for ADN with flexible loads

In this study, the impacts of AC and BS loads on the security distance of a distribution network were considered.The security region [38] model is established as (7)below:

where Sφ denotes and is the power of any branch i except for the component that is withdrawn from operation due to a fault; is the power of any main transformer i except for the component that is withdrawn from operation due to a fault;CB.i is the rated capacity of branch i;CT.i is the rated capacity of main transformer i; B is the set of all branches; T is the set of all main transformers;SA,SB, and SC are loads of branch or main transformers of the three-phase of A, B, and C,respectively; refers to the total load of the A, B, and C phases at the three-phase node; is the total three-phase BS loads of A, B, and C; is the total three-phase AC loads of A, B, and C;ΩB.i（k） is the set of all nodes downstream of the branch i after the component is taken out of operation at the time of the N-1 fault;ΩT.i（k） is the set of all nodes downstream of the main transformer i after the component ϕk is taken out of operation at the time of the N-1 fault.

In this case,the security distance between the phases of the distribution network can be written as

where, andare the security distances of phases A, B, and C, respectively, containing flexible loads.

2.2 ADN security distance with EH containing flexible load

Considering the EH power factor angle, the interactive power between the EH and the ADN is obtained as

where is the reactive power interaction between the EH and ADN;ϕEH is the power factor angle of the EH containing flexible loads.

The AC and BS loads were added to the EH, and the three-phase loads containing random wind-solar power and flexible loads accessing the ADN should satisfy the following security region constraints:

where is the total three-phase interactive power between the EH and the ADN.

Due to the access to distributed wind-solar power in the EH, the distributed wind-solar power is random, and therefore, the interactive power between the EH and ADN is also random.The ADN security distance model with an EH containing a flexible load is as follows:

When the BS load is transferred after the AC load reduction,the distribution interval of the security distance is calculated to determine whether the work point meets the security distance requirement.

3 Multi-objective optimization and regulation model for energy saving, clean and safe ADN containing EH

3.1 Research on the mechanism of security distance regulation of EH containing wind-solar power and flexible loads

Random wind-solar power affects the security distance of the ADN, resulting in a random security distance.At the same time, the reduction of AC loads and the transfer of BS loads have a significant impact on the security distance.Therefore, active management of the security distance in the ADN is required after the regulation of wind-solar power and flexible loads.For this reason, this paper proposes connecting energy storage to the EH node of the ADN to improve the energy consumption rate of distributed wind-solar power, reduce the amount of abandoned wind and solar energy, and regulate the interactive power between the EH containing random wind-solar power, flexible loads, and the ADN.Additionally, energy storage and static reactive power compensators are connected to the ADN.Thus,the ADN must satisfy the security constraints in (12).

where ΔSe is the amount of interactive power change between the EH and ADN after considering the AC load reduction, BS load transfer, and optimizing the amount of abandoned wind and solar energy under random wind-solar power;Qsvc is the amount of reactive power compensation of the static reactive power compensation device accessing the ADN; and Pbess is the charging and discharging power of the energy storage accessing the ADN.

In this case, the security distance of the ADN with an EH containing random wind-solar power and a flexible load is shown in (13).

whereare the three-phase interactive powers between the optimized EH considering AC load curtailment, BS load transfer, and the amount of abandoned wind and solar energy, respectively;,and are the three-phase reactive power compensation amounts of the optimized static reactive power compensation device accessing the ADN;, and are the three-phase charging and discharging powers of the optimized energy storage accessing the ADN, respectively.

3.2 Multi-Objective optimal regulation model for ADN with EH

3.2.1 Objective function

The three objective functions of the multi-objective optimal power flow model with random wind-solar power and a flexible load ADN security distance are as follows:

1) Security distance target

The security distance objective is to carry out AC load curtailment and BS load transfer under random wind-solar power, optimized by the EH interacting power with the ADN, energy storage, and reactive power compensation devices to ensure the maximum security distance for the ADN.

The objective function is shown in (14) below:

2) Energy cost targets

Considering the ADN electricity cost and BS load transfer cost, the objective function of the energy cost is established, as shown in (15).

where nEH is the number of EH accessed by the ADN;Pi.bess is the ith EH node energy storage charging and discharging power;Pi.a and ΔPi.a are the ith EH node AC aggregation power and its reduction,respectively;Pi.h is the ith EH node cooling and heating load;Pi.e is the ith EH node other electrical loads;Pi.b and ΔPi.b are the ith EH node BS load and transfer, respectively; and Ploss is the active network loss power of the ADN;Cbess,Ca,Ch,Ce,Cb,Closs, are energy storage charging and discharging, AC load, cooling, and heating electric load, BS load, and network loss cost factor, respectively.

3) Active network loss target

The active network loss objective is to minimize the active network loss of the entire ADN after considering the AC load reduction and BS load transfer through ADN security distance optimization.Its objective function is shown in the following (16):

where Γ is the set of all nodes connected to the node i.

3.2.2 Restrictive condition

1) Power balance constraints

where and are the random interactive active and reactive power of the EH of the ith node with the ADN,respectively, if the node does not contain an EH, the variable is 0;ΔPi.e and ΔQi.e are the change values of the random interactive active and reactive power of the EH of the ith node with the ADN, respectively, if the node does not contain an EH, the variable is 0;ΔPi.bess is the storage charging and discharging power of the ith node after the optimization;Qi.svc is the initial amount of the compensation of the stationary reactive power compensation device before optimization of the ith node; and ΔQi.svc is the amount of the change of the compensation of the static reactive power compensation device after the optimization of the ith node.

2) BS electrical load capacity constraints

The BS load needs to satisfy the upper limit constraint,that is, it cannot be overloaded, as shown in (18).

where Lb max is the rated capacity of the electrical load of the BS.

3) Total BS power load constraints

The total value of all the BS loads in the ADN must remain unchanged when the BS loads are transferred.If the total electrical load of the BS is L, the total capacity constraint of the ADN should satisfy (19).

where Li.b is the electrical load of the ith BS.

4) Reactive power compensation device constraints

where Qsvc.max is the rated capacity of the reactive power compensation device.

5) Energy storage charge/discharge capacity constraints

where Pbess.min and Pbess.max are the lower and upper limits of the charging and discharging of the energy storage device, respectively.

6) AC load reduction constraints

The AC loads should satisfy an aggregated power reduction that does not exceed the maximum allowable AC aggregated load reduction before the reduction, with the constraints shown in (22).

where αi.a is the maximum allowable reduction ratio of AC aggregated load at the ith node.

7) Security distance constraints

The ADN security distance constraint is satisfied with a main transformer security margin of at least 30 %, as shown in (23).

3.2.3 Best compromise solution

For the ADN peak load scenario,to improve the ADN load and security distance margins,the amount of BS communication load transfer and AC load reduction were considered as the main decision variables, while simultaneously ensuring the security distance of the ADN,the amount of new energy storage charging and discharging power, and the amount of reactive power compensation of the static reactive power compensation device were considered as the decision variables.The decision variables are shown in (24) below:

where Li.b is the BS load of the ith energy-containing hub node,Pi.a is the AC aggregated load of the ith energycontaining hub node, and , and are the A, B, and C phases of reactive power compensation of the jth reactive power compensation device, respectively.

The multi-objective optimization model was solved using a combination of power flow calculations and the NSGA-II algorithm.To evaluate the solutions,a fuzzy satisfaction function was employed, calculating the satisfaction levels for the nondominated solutions based on security distance, abandoned wind and solar energy, and active network loss.Based on the Pareto-optimal solution set, the optimal compromise solution is solved using the maximum fuzzy satisfaction method, as shown in (25).

The satisfaction of the ith objective function(μni)for the nth nondominated solution is given by the following equation, where i takes values 1, 2, 3;fi.n is the value of the ith objective function for the nth nondominated solution;fi.max is the maximum value of the ith objective function among the set of Pareto-optimal solutions, and fi.min is the minimum value of the ith objective function among the set of Pareto-optimal solutions.

Based on the satisfaction values of the objective functions, the standardization of each nondominated solution is calculated using (25).After standardizing the satisfaction, the solution corresponding to the maximum standardized satisfaction value is identified as the optimal compromise solution.

where μn is the satisfaction value after normalization of the nth nondominated solution, and N is the number of nondominated solutions in the Pareto optimal solution set.

3.2.4 Solution process

The multi-objective optimization model was solved by combining the forward back-generation trend calculation method, NSGA-II algorithm, and maximum fuzzy satisfaction method.Security distance constraint changes were added to the objective function based on the penalty function of the voltage security constraint.For the ADN BS load overload scenario, the BS load capacity constraint is used as the control condition to ensure that the BS load satisfies the capacity constraint.Furthermore, the ADN security distance, amount of abandoned wind and solar energy, and active network loss are optimized.

The ADN multi-objective optimization model solution process is as follows:

Step 1: Obtain information on distributed wind-solar power, BS load, AC load, and EH parameters for the ADN.

Step 2: Determine whether the BS load satisfies the capacity constraint.If it does, proceed to Step 6.If it does not, the forward-back generation algorithm and the initial BS electrical load are combined to perform the ADN trend calculation.

Step 3: Based on the NSGA-II, calculate the values of the three objective functions of security distance,amount of abandoned wind and solar energy, and active network loss,and obtain the Pareto optimal solution set.

Step 4: Decision making using the fuzzy maximum satisfaction algorithm to select the optimal compromise solution from the Pareto optimal solution set.

Step 5: Obtain the decision variables under the optimal compromise solution and calculate the transfer amount of the BS load and AC load reduction amount.

Step 6: Update the currents based on the forward back generation trend calculation method and calculate the ADN security distance.

Step 7: output the calculation results and end.

The flowchart is shown in Fig.2.

4 Example simulation analysis

4.1 Parameters of the algorithmic system

Fig.2 Algorithm flowchart.

To verify the validity of the method proposed in this section, the calculation method and model were tested using the improved IEEE33 node distribution system.In this setup, five nodes—node 1, node 8, node 15, node 20,and node 29—are connected to EHs containing random wind-solar power and flexible loads, each configured with energy storage with a rated capacity of 100 kW.Additionally,three nodes—node 1,node 18,and node 22—are connected to static reactive power compensators, each with a capacity of 100 kVar.The IEEE33 node distribution system is shown in Fig.3 below.The distributed wind-solar power and EH parameters are listed in Tables 2 and 3.

4.2 Results analysis

4.2.1 Analysis of EH interactive power variation with flexible loads

To verify the influence of the AC load and BS loads on the interactive power between the EH and ADN,the initial thermal load was set to 150 kW, and the other electrical loads were set to 100 kW.The initial AC load was set to 180 kW, and the initial BS load was set to 150 kW.

The variation in interactive power with changes in flexible loads is shown in Fig.4, where the change in flexible load can result from either AC load reduction or BS load transfer.As the amount of AC load curtailment or BS load transfer increases, the flexible load of the EH decreases,which leads to an increase in the interactive power between the EH and the ADN.Therefore, the changes in BS and AC loads are linearly related to the interactive power,respectively.Meanwhile, unlike the AC load reduction,the BS load transfer has an impact on the loads of the other BS, that is, the other EHs containing BS loads have a smaller interactive power with the ADN.

The interactive power change for the EH with random wind-solar power and flexible load is shown in Fig.5.Considering the random wind-solar power, when the AC load is curtailed or the BS load is transferred, the interactive power between the EH and ADN gradually increases.This change no longer follows a linear relationship between the amount of change in flexible load and the interactive power between the EH and ADN.In addition, the EH gradually changes from the load state before the load changes to the power state.

Fig.3 IEEE33 node system.

Table 2 Distributed wind and photovoltaic parameters.

ParametersValueParametersValue vci/(m/s)3Pwtr/kW400 vco/(m/s)25K4.44 vr/(m/s)13c/(m/s)14.3 α 0.85η0.1365 β 0.90S/m21,200 × 2.16

Table 3
EH parameters.

ParametersValueParametersValue ηC0.95vw0.2 ηT0.95vPV0.2 ηPV0.9ve0.5 ηAC0.75vet0.9 vPVt0.9vwt0.9

Fig.4 Interactive power between EH and ADN under flexible load change.

Fig.5 Interactive power between EH and ADN with random wind-solar power and flexible load.

4.2.2 Analysis of the impact of EH containing flexible loads on security distances

To analyze the impact of the EH regulation strategy containing flexible loads on the security distance of the ADN, the scenarios before and after the change in flexible loads in the EH were set, as shown in Table 4.

Scenario 1 was performed before the flexible load reduction.Scenario 2 considers AC load reduction.Scenario 3 considers only the BS load transfer.Scenario 4 considers AC load reduction and BS load transfer.The other electrical and cooling/heating loads did not change in any scenario.

First, only the effect of flexible load regulation on the security distance of the ADN is analyzed,that is, the relationship between the flexible load and security distance under the determination of wind-solar power is considered, as shown in Table 5.

As shown in Table 5,comparing Scenarios 1 and 2,the security distances of all three phases (A, B, and C) are increased when only AC load curtailment is considered.For example, the security distance of Phase A increases by 17.0 %, Phase B by 17.2 %, and Phase C by 17.6 %.Comparing Scenarios 1 and 3, the security distances of all three phases also increase when only the BS load transfer is considered.For example, the security distance of Phase A increases by 19.5%,Phase B by 18.0%,and Phase C by 18.5 %.Compared with the security distance in Scenario 2 (where only AC load reduction is considered), the three-phase security distances after BS load transfer increase more.However, the total BS load between EHs remains unchanged when the BS is transferred, indicating that the security distance of the ADN does not correlate with the total load of the EH in a linear manner.Scenario 4 shows the results after considering both AC load reduction and BS load transfer, where the security distance increases by 17.1 % for Phase A, 17.2 % for Phase B,and 17.7 % for Phase C.The security distance in Phase C increased by 17.7 %.The change in security distance in Scenario 3 was more pronounced than in Scenario 4,with the changes in security distance in Scenarios 2 and 4 being closer.The power access to the ADN, after performing random simulations of wind-solar power for n times, was recorded as work point n, with Table 4 serving as work point 0 for each scenario.The three-phase security distance of work point n in each scenario is shown in Figs.6-8.The three-phase security distance of the ADN,under the influence of random wind-solar power in different scenarios,is random.The relationship between the EH containing flexible loads and security distances for stochastic wind-solar power is consistent with the conclusions obtained in Table 4 for deterministic wind-solar power.

4.2.3 Multi-objective optimization analysis

To verify the actual reduction and transfer effects of AC load and BS load, it is assumed that the maximum reduction ratio of the AC load is 8%,and the maximum allowable capacity of the BS load is 150 kW.It is also assumed that the BS load of EH3 exceeds the limit, with the initial sizes of its AC load and BS load shown in Fig.9.From Fig.9,it can be observed that the BS load exceeds the limit during the 12:00-20:00 time period, and thus, the BS load must be transferred.This is addressed using the multiobjective optimal power flow model and algorithm.By applying the forward-backward power flow algorithm,the NSGA-II multi-objective optimization model solution,and the maximum fuzzy satisfaction method, the optimal results are obtained as follows:

Table 4 BS load and AC load data in the EH.

ScenarioEHBS load/kW AC load/kW Scenario 11100180Scenario 21100167.4 2 1202002120184.0 3 1502403150202.4 Scenario 31120180Scenario 41120167.4 2 1252002125184.0 3 1252403125202.4 AC load/kW ScenarioEHBS load/kW

Table 5 Relationship between flexible load variation and security distance.

ScenarioPhasesecurity distance/MVAScenarioPhasesecurity distance/MVA Scenario 1A2.4015Scenario 2A2.8102 B 2.3672B2.7740 C 2.3113C2.7190 Scenario 3A2.8301Scenario 4A2.8116 B 2.7937B2.7753 C 2.7388C2.7204

Fig.6 Security distance of phase A at working point.

Fig.7 Security distance of phase B at working point.

Fig.8 Security distance of phase C at working point.

The algorithm sets the NSGA-II population size to 100,the Pareto frontier factor to 0.3,and the number of generations for genetic variation to 200.The Pareto frontier solved based on NSGA-II for a single period is shown in Fig.10 below.

The Pareto front distribution is relatively uniform and exhibits good convergence, indicating that the model and algorithm proposed in this study can effectively achieve multi-objective coordinated optimization and obtain the corresponding Pareto solution set.

The amount of BS load transfer for all the EH is shown in Fig.11.

Fig.9 Initial value of EH3 flexible load.

Fig.10 Pareto frontier in a single period.

Fig.11 Load transfer amount of each EH BS.

As shown in Fig.11, for each BS load transfer amount, and as illustrated in Fig.9, during the periods of 00:00-08:00 and 20:00-23:45, the BS load has not reached the overrun condition of 150 kW.In these periods,the ADN is not optimized by the multi-objective model,so the load transfer amount for all BS loads is 0.During the 08:00-20:00 period, when the BS communication load is excessively large, the model and method proposed in this study begin to optimize it.At this time, EH3 has the largest BS load transfer, with a maximum transfer of up to 50 kW, and the transfers from other EHs are overwhelmingly negative, indicating that they accept the load transferred from EH3.To ensure the security distance, active network loss, and energy cost constraints, the transfer amount of EH4 appears in a small number of positive cases, resulting in the optimal transfer scheme.

As shown in Fig.12, AC loads are curtailed during the 08:00-20:00 period, with all EHs experiencing AC load curtailment.The maximum curtailment value is approximately 19 kW, although the curtailment of AC loads in the different EHs varies during each period.

The optimization results with the total three-phase security distance of the ADN as the objective function are shown in Fig.13.During the periods of 00:00-08:00 and 20:00-23:45, the optimization algorithm was not carried out because the BS load did not exceed the limit.In these periods, the security distance before and after optimization did not change.However, during the 08:00-20:00 period, the algorithm begins to optimize as the BS load exceeds the limit.Before optimization, the total three-phase security distance of the ADN is between 7.8-11.3 MVA, while after optimization, it ranges from 7.8-11.4 MVA.As shown in the figure, the security distance of the ADN is significantly increased during the period in which optimization is applied.

The ADN active network loss before and after optimization is shown in Fig.14.During the periods of 00:00-08:00 and 20:00-23:45, the optimization algorithm is not carried out because the BS load does not exceed the limit.In these periods, the active network loss before and after optimization does not change.However, during the 08:00-20:00 period, when the algorithm is applied,the ADN active network loss ranges from 0.026-0.095 MW before optimization, and from 0.025-0.090 MW after optimization.As seen in Fig.14,there is a significant reduction in ADN active network loss during the periods in which optimization is performed.

Fig.12 Amount of AC load reduction for each EH.

Fig.13 Comparison of the security distance before and after optimization.

Fig.14 Comparison of active network loss before and after optimization.

Table 6 Optimize energy costs before and after.

ScenarioPre-Optimization Reduction Rate/%Cost/10,000 Yuan3.51573.42480.026 Post-Optimization

The ADN energy cost before and after optimization is shown in Table 6, where the total energy cost for one day is reduced by 0.0909 million yuan compared with pre-optimization.The saving is 0.026 %.

The changes in the node voltage magnitude and voltage phase angle of each node across 96 time periods of a day after optimization are shown in the attached Fig.A1 from Appendix A.The node voltage magnitudes for phases A,B, and C are maintained between 0.96-1.00 pu, satisfying the voltage magnitude constraint of 0.95-1.05 pu.The voltage phase angles, shown on the right side of Fig.A1,are as follows: the phase angle of phase A is betweenand ; the phase angle of phase B is betweenand ; and the phase angle of phase C is between and .These phase angles satisfy the three-phase phase angle transformation conditions.All node voltages in each period meet the voltage security constraints.

In summary, the method proposed in this paper effectively reduces the AC load,transfers the BS load,improves ADN security distance, reduces active network loss,ensures voltage security constraints, and contributes to energy-saving,safe,and economical power grid operation.

5 Conclusion

In this paper,a security distance analysis method for an ADN that considers the demand response of an EH is proposed.The main conclusions are as follows:

1) By establishing an EH model with random windsolar power and flexible loads, the relationships between changes in random wind-solar power, flexible loads,and interactive power between the EH and ADN were revealed.

2) The security distance model of the ADN with a flexible load in an EH was established,and the influence of flexible load changes on the security distance of the ADN was discussed.The results show that, after considering AC load curtailment and BS load transfer,the phase security distances for phases A,B,and C increased by 17.1 %, 17.2 %, and 17.7 %,respectively.

3) To optimize the security distance, energy consumption cost, and active network loss, a multi-objective optimization and control model for energy-saving,economics,and security of the ADN was established.This model enhances the security distance of the ADN, facilitates BS load transfer, and reduces AC load.The optimized one-day total energy cost savings were 0.026%, and the total three-phase security distance boundaries of the ADN improved by 0.1 MVA.

However, the effects of other flexible loads, such as EV charging loads, on the security distance were not considered in depth in this study.Future studies will include this as a factor in the multi-objective optimization, and its impact on the security distance will be further explored.Moreover, the optimization algorithm used in this study has room for improvement in accuracy.Future research will consider using solvers to achieve higher precision.

CRediT authorship contribution statement

Rui Ma:Writing-review&editing.Qi Zhou:Writingoriginal draft.Shengyang Liu:Writing-original draft.Qin Yan: Writing - review & editing.Mo Shi: Resources.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This study was supported in part by the National Natural Science Foundation of China (No.51977012, No.52307080).

Appendix A

Fig.A1.Voltage of each node in the 96 periods after optimization