Multiagent, multitimescale aggregated regulation method for demand response considering spatial-temporal complementarity of user-side resources

0 Introduction

In the construction of new power systems, the flexible integration of a large number of renewable energy and controllable resources into the distribution grid has led to increasingly frequent and complex interactions between the supply side and users.Consequently,the operation and regulation of the distribution grid exhibit a high degree of volatility and instability [1-4].Demand response involves extensively exploring the flexible adjustment potential of user-side resources, modifying users’ electricity consumption behaviors to respond to changes in the power system demand, and supporting the coordinated operation of the distribution grid [5-7].However, owing to the dispersed distribution, small capacity, diverse response characteristics, and complex user behavior of user-side resources,the differences in physical locations between multiagents need to be considered.By fully exploiting the spatial--temporal complementary characteristics, the implementation of cluster regulation of loads at the distribution station area level will not only aggregate and regulate resources from multiple stakeholders, but also enhance grid resilience [8,9].This strategic approach can facilitate spatial--temporal coordinated demand response, significantly improving the operational efficiency and stability of the distribution grid [10-12].

Considering the diverse time requirements of different stakeholders in demand response, the distribution grid adopts multitimescale regulation strategies for both dayahead and intraday operations.Day-ahead regulation strategies plan future electricity demand and supply based on forecasts, whereas intraday regulation strategies adjust these plans based on real-time conditions.Existing studies have explored specific aspects of demand response but often fail to comprehensively address multitimescale dynamics.For example, Wei et al.[13] proposed a pricebased demand response method to optimize the energy management of multienergy buildings.Although effective for demand-side management,this approach primarily targets single-timescale optimization.Tarnate et al.[14]introduced a predictive control method for residential load regulation in intraday markets.Although this method incorporates uncertainty, it lacks integration with dayahead planning.Such single-timescale approaches limit the accuracy and flexibility of demand response.

Some researchers have considered multitimescale characteristics.Pandey et al.[15]employed hierarchical control methods using game theory to optimize the interactions between demand response providers;however,the connection between day-ahead and intraday strategies remained weak.Chen et al.[16] developed a joint optimization model that links thermal power generation and user-side resources across timescales, achieving cost minimization and peak--valley reduction at the day-ahead level.Wang et al.[17]proposed multitimescale peer-to-peer(P2P)trading strategies for demand response to promote collaboration between aggregators.However, these studies do not fully address the spatial--temporal complementarity of user-side resources across timescales, which is essential for improving coordination and reducing overall costs.

For the day-ahead regulation stage, the particle swarm optimization (PSO) algorithm exhibits strong global search capabilities and performs exceptionally well in addressing nonlinear and nonconvex problems [18,19].For example,Dou et al.[20]used PSO to optimize the economic dispatch strategy of microgrids by integrating combined heat and power generation with the demand response.However, the PSO algorithm relies on information sharing between particles to guide the search process,which only applies to day-ahead regulation predictions.In the fast-changing environment of intraday markets, realtime information sharing may be limited, resulting in a slow convergence of the algorithm.To enhance intraday optimization,the alternating direction method of multipliers (ADMM) algorithm is renowned for its distributed optimization capabilities and parallel computation effi-ciency [21,22].Kou et al.[23] proposed a comprehensive regulation framework that leveraged the strengths of the ADMM algorithm in handling uncertainties and distributed computation.However,they failed to dynamically adjust the penalty factors based on real-time load variations,thereby limiting their optimization accuracy in practical applications.

Even though progress have been made in aggregated regulation research, the following challenges remain:

Firstly, existing studies on user-side resourceaggregated regulation overlook spatial--temporal complementarity and coordination for the day-ahead and intraday stages, leading to ineffective integration between different regulation stages and high aggregated regulation costs.Secondly, in the traditional PSO algorithm, the number of particles is fixed and the search space is limited,resulting in slow convergence and low precision for dayahead regulation.In addition, the inertia weights cannot be dynamically adjusted,which further contributes to slow convergence.Finally, existing ADMM-based intra-day regulation methods overlook the influence of spatial--temporal coordination on the load output, leading to low precision and high regulation costs because of the inability to adaptively adjust penalty factors based on load changes, thereby affecting the ability of the grid to maintain stability under variable loads.

To address these challenges, we propose a multiagent,multitimescale aggregated regulation method for spatial--temporal coordinated demand response of userside resources in this work, focusing on enhancing smart grid resilience.Firstly,we constructed an aggregated regulation architecture that considers the spatial--temporal coordinated demand response of user-side resources.Next,we formulated the day-ahead and intraday optimization problems for distribution station areas to minimize the weighted sum of the total regulation costs and distribution grid losses at large and small timescales.Finally,we developed an aggregated regulation algorithm that considers the spatial--temporal coordinated demand response of user-side resources, including an improved PSO-based day-ahead optimization regulation strategy and an improved ADMM-based intraday regulation strategy.Our contributions are outlined as follows:

IPSO-based Day-ahead Regulation Strategy Optimization:We propose an improved PSO(IPSO)algorithm that features the dynamic adjustment of inertia weights to enhance the global and local search capabilities.Global search is applied to accelerate convergence when the weighted sum of the regulation costs and grid losses is high, whereas local search improves the optimization precision when the weighted sum is low.In addition,the states and number of particles are dynamically adjusted based on historical intraday regulation results, preventing the algorithm from being stuck at the local optima and increasing the efficiency and accuracy of the day-ahead regulation strategy.

IADMM-based Intraday Regulation Strategy Optimization: We propose an improved ADMM (IADMM) intraday regulation strategy that considers the spatial differences between the distribution station areas.By adaptively adjusting the penalty factors for each distribution station area based on historical day-ahead optimization results,the method achieves demand response aggregation with spatial--temporal coordination of user-side resources.This approach improves the precision and convergence speed of intraday regulations, reduces optimization costs,and corrects deviations caused by the randomness of controllable loads in day-ahead scheduling.

1 System model

The multiagent, multitimescale aggregation regulation framework for spatial--temporal coordinated demand response of user-side resources is shown in Fig.1.The response aggregation process of resources consists of three layers: (1) the distribution grid regulation center, (2) the regional control centers,and(3)the controllable resources.The distribution grid regulation center releases demand response requirements to the regional control centers,which collect controllable resource data from each distribution station area and develop demand response plans.Subsequently,the regional control centers use a communication network to send the demand response plan to the controllers in each distribution station area.Each distribution station area is equipped with a controller, which is responsible for aggregating and coordinating the response of multiple types of resources within its area.The controllers interact with the distributed generators, energy storage devices,and controllable loads through communication methods such as Ethernet, wireless networks, and power carrier communication.

In this work,we used a discrete time slot model for multitimescale regulation.Specifically, the regulation time is divided into E regulation periods, representing the large timescale, which is denoted as E= {1，2，···，e，···，E}.Each period consists of T0 time slots of length τ,representing the small timescale, which is denoted as τ= {1，2，···，t，···，T }.The set of time slots within the eth period is denoted as T （e ）= {（e-1）T0+1， （e-1）T0+2，···，eT0}.Considering the spatial and temporal differences in the demand response capabilities of the user-side resources, the resources are unevenly distributed in space and time.The day-ahead optimal scheduling is performed at a large timescale,while the intraday scheduling is performed at a small timescale.In the day-ahead stage,the distribution grid regulation center collects the spatial information of the userside resources and state information such as response capacity and load power, and carries out centralized day-ahead optimization regulation of the demand response.Since the resource potential of intraday controllable loads is unknown, the day-ahead regulation of userside resources can be optimized based on the intraday forecast values.In the day-ahead stage, only the decision instructions for day-ahead controllable loads are executed,while the instructions for intraday controllable loads are not yet issued or executed, and serve only as a reference for intraday decision-making.Considering the spatial distribution differences of resources between multiple distribution station areas, each distribution station area adjusts its local load output by using the day-ahead regulation strategy to reduce deviations between the planned day-ahead regulation and the actual intraday measurements, thereby enhancing the demand response accuracy of the user-side resources.

1.1 Load model

Fig.1.Multiagent, multitimescale aggregated regulation framework for spatial--temporal coordinated demand response of user-side resources.

In this section,the loads are categorized into interruptible loads,transferable loads,and shiftable loads considering the load flexibility [24], with their sets denoted asrespectively.There are some differences in the response times between the three types of loads.For loads that require some preparation time before responding, the regulation instructions must be provided well in advance, whereas loads that can respond quickly require a shorter advance notice.Therefore,the controllable loads exhibit different advance notification characteristics.Based on the differences in the advance notification characteristics, the above loads can be further classified into dayahead and intraday controllable loads.The day-ahead controllable loads exhibit strong predictability and plannability.The users declare the controllable parameters to the grid ahead of the day, which include interruptible periods, interruptible power, transfer-out periods,transfer-out power, transfer-in periods, transfer-in power,shiftable periods, and shiftable power.The users are notified of their electricity usage adjustment behavior in advance for the time slots of the following day.In contrast, the intraday controllable loads are characterized by high randomness, where the users declare the controllable parameters to the grid during intraday regulation periods,including interruptible periods, interruptible power,transfer-out periods, transfer-out power, transfer-in periods, and transfer-in power.Subsequently, the grid makes regulation decisions and notifies the users to respond to the regulation.

1.1.1 Interruptible loads

Interruptible loads refer to loads that can be reduced according to actual needs.Owing to the predictable nature of interruptible loads in terms of advance planning for production and daily life as well as the temporary nature of adjusting electricity consumption, interruptible loads include both day-ahead and intraday controllable loads.The regulation characteristic model can be represented as

1.1.2 Transferable loads

Transferable loads refer to loads in which the total electricity consumption remains constant over a time period;however, the electricity consumption in each time slot can be adjusted within a certain range.Transferable loads also include both day-ahead and intra-day controllable loads.The regulation characteristic model can be represented as

Shiftable loads refer to loads that are constrained by production lines and cannot change the overall shape of the load curve, but can only shift the overall load from one time period to another.Shiftable loads involve scheduling the next-day production activities in advance and signing contracts with the grid, and they belong to day-ahead controllable loads.The regulation characteristic model can be represented as

1.1.3 Load regulation cost model

The load cost of distribution station area sk consists of day-ahead controllable load regulation cost and intraday controllable load regulation cost.The day-ahead controllable load regulation cost C（t ） for distribution station area sk is given by

where cIN denotes the interruptible load cost coefficient,cT denotes the transferable load cost coefficient, and cs denotes the shiftable load cost coefficient.

This model ensures the coverage of diverse user-side resource characteristics and is widely recognized in the field for its applicability and generality.

Electric vehicles can be modeled as transferable loads,

whereas industrial loads can be treated as interruptible or shiftable loads, depending on their operational flexibility.

1.2 Distribution station area day-ahead regulation cost model

The day-ahead regulation cost Fk （t ）of distribution station area sk consists of day-ahead controllable load regulation costs, intraday controllable load regulation costs,distributed energy storage regulation costs, distributed generator regulation costs, and the cost of purchasing and selling electricity from and to higher-level distribution station areas, which is given by

1.3 Distribution station area intraday regulation cost model

The cost function ^Fk （t ） for the intraday regulation of distribution station area sk is composed of intraday controllable load regulation costs, distributed energy storage regulation costs, distributed generator regulation costs,and the cost of purchasing and selling electricity from and to higher-level distribution station areas,which is represented as

1.4 Distribution station area power balance constraint model

The power balance model of distribution station area sk is divided into day-ahead and intraday regulation stages.In the day-ahead regulation stage, the distribution station area power balance constraint for the distribution station area sk is represented as

In the intraday regulation stage,the distribution station area power balance constraint for station area sk is expressed as

1.5 Distribution grid loss model

Considering the complexity of the distribution grid topology [26,27], the distribution grid loss is defined as Closs （t ）, which is given by

where Nnode is the total number of nodes in the distribution grid, γloss is the unit loss cost, Rij （t ） is the resistance value between node i and node j in the distribution grid in time slot t,v（i）is the set of branch end nodes in the distribution grid with node i as the starting node, Pij （t ） and Qij （t ） are the active and reactive powers, respectively,transmitted from the upstream node i to node j in time slot t, and V i （t ） is the voltage magnitude at node i.

The distribution grid flow constraint is represented as

The voltage equation of node j is given by

where V i （t ）and V j （t ）are the voltages at node i and node j.

Furthermore, considering the influence of voltage fluctuations on the security of the distribution grid in the loss,the voltage constraint for node i is established as

2 Problem formulation

We comprehensively considered the differentiated advance notification times of controllable loads and the spatial--temporal coordinated demand response capabilities of multiple agents in the distribution grid.Hence, we formulated a multiagent, multitimescale aggregated regulation optimization problem for the spatial--temporal coordinated demand response of user-side resources, with the aim of enhancing the resilience of smart grids.This problem is divided into two parts:(1)day-ahead optimization regulation at a large timescale and (2) intraday optimization regulation at a small timescale.

For the day-ahead part, we formulated a largetimescale day-ahead regulation optimization problem.By considering the response characteristics of the user-side resources at different time periods and geographical locations, the day-ahead regulation optimization can optimize the operation plans of controllable loads, distributed generators, and energy storage devices, thereby reducing the peak--valley difference in the power grid and improving the operational efficiency.For the intraday part, we formulated a small-timescale intraday regulation optimization problem.By adjusting the day-ahead regulation optimization results, the intraday regulation optimization can correct the deviations from day-ahead forecasting and optimize the operation status of the power grid through real-time response.

2.1 Large-timescale day-ahead regulation optimization

2.2 Small-timescale intraday regulation optimization

The intraday regulation optimization involves optimizing the power transactions to higher-level grids, as well as the intraday interruptible load interruption power, intraday transferable load transfer power, distributed energy storage regulation power, and distributed generator regulation power for different time slots in the distribution station area.The objective is to minimize the weighted sum of the total intraday regulation cost and grid loss, which is formulated as

where C1 represents the constraints of the intraday controllable loads, including intra-day interruptible load constraints and intraday transferable load constraints, C2 represents the energy storage regulation power constraint,C3 represents the distributed generator regulation power constraint, C4 ～C6 represent the upper and lower limits for power transactions in the distribution station area,C7 represents the power balance constraint of the distribution station area in the intraday regulation stage, and C8 represents the branch flow and voltage constraints.

3 Multiagent, multitimescale aggregated regulation algorithm for demand response considering spatial--temporal coordination

The multiobjective optimization method is typically adopted as the traditional aggregated regulation method in the day-ahead regulation stage for user-side resource demand response.When the differences in the spatial allocation of resources between the distribution station areas are not considered, this method results in poor applicability of the day-ahead regulation strategy and is prone to getting stuck in the local optima.Meanwhile, the traditional aggregated regulation method overlooks the influence of the spatial--temporal coordinated characteristics of load regulation in the intraday regulation stage, resulting in a low intraday regulation accuracy, slow convergence speed, and difficulties in fulfilling the actual demand response requirements.

To address the aforementioned issues, we developed a multiagent, multitimescale aggregated regulation method for demand response, where we considered the spatial--temporal coordination.By effectively utilizing the spatial--temporal complementary characteristics of the user-side resources,the regulation accuracy of the demand response in the distribution grid is improved and the regulation cost is reduced.The principle of the proposed algorithm is illustrated in Fig.2.We developed a day-ahead regulation decision optimization method on a large timescale based on the IPSO algorithm.In this method, the control center collects the spatial information of the user-side resources distinguished by multiple distribution station areas in order to formulate the day-ahead regulation decisions.By considering the influence of the spatial--temporal complementary characteristics of intraday regulation, a corresponding search pattern is adopted in the day-ahead regulation process according to the magnitude of the regulation cost and distribution grid loss.Based on the historical intraday regulation decision results, the number of particles in the multistation area is dynamically adjusted to realize a dynamic trade-offbetween the search space and search speed.Therefore,the IPSO algorithm can prevent getting stuck in the local optima, as well as improves the accuracy of the dayahead regulation optimization and reduces costs.The IPSO algorithm also improves the accuracy and efficiency of the model search process and satisfies the practical operational requirements of the day-ahead regulation optimization.

We developed an intraday regulation decision optimization method on a small timescale based on the IADMM algorithm by considering the differences in the spatial distribution of resources in multiple distribution station areas.The IADMM algorithm is used to allocate regulation tasks to each edge station area for distributed optimization.Meanwhile, the penalty coefficients of the dispatch timeslots of the current day in each distribution station area are adaptively updated according to the historical dispatch results of the previous day.Hence, it is possible to realize the demand response aggregation regulation by considering the spatial and temporal cooperative demand response of the user-side resources.Therefore,the IADMM algorithm can effectively improve the accuracy and convergence speed of the model for intraday regulation and effectively reduce the optimization cost.

In addition, the IADMM algorithm corrects the deviations due to the randomness of the actual controllable loads in the day-ahead optimization scheduling results,thus improving the accuracy and convergence speed of the intraday regulation and reducing the intraday regulation cost.

3.1 Day-ahead regulation decision based on the IPSO algorithm

The conventional PSO algorithm suffers from low optimization accuracy and susceptibility to becoming trapped in the local optima.Moreover,the conventional PSO algorithm overlooks the influence of intraday optimal regulation results on day-ahead regulation, leading to a significant deviation between the day-ahead regulation strategy and the actual day-ahead regulation results,making it difficult to balance regulation costs and benefits.Therefore, we developed an optimization method for day-ahead regulation decisions based on the IPSO algorithm.By dynamically adjusting the number of particles based on historical intraday regulation results and adaptively adjusting the particles’inertia weights subject to the day-ahead constraints, we aim to improve the day-ahead optimization accuracy and reduce the regulation cost.The proposed method consists of four parts: (1) initialization of the particle swarm parameters, (2) computation of the particle’s fitness value,(3)update of the particle’s state,and (4) adaptive adjustment of the number of particles.These are described in the following subsections.

Fig.2.Multiagent, multitimescale aggregated regulation method for demand response considering the spatial--temporal coordination of the user-side resources.

3.1.1 Initialization of the particle swarm parameters

3.1.2 Computation of the particle’s fitness value

The fitness value of a particle during the search process will determine the mass of the solution corresponding to the particle.In this work,we obtain the fitness value based on the constraints of the day-ahead optimal regulation for each distribution station area.The penalty function concept is introduced to penalize the solutions that do not satisfy the constraints.A particle with a higher fitness value indicates a superior solution, implying a higher possibility of being the optimal solution.The fitness value Ha （d ） of the a-th particle in the d-th search of the e-th time period is given by

where σ is a negative number, which is significantly less than 0.

3.1.3 Update of the particle’s state

where ωmax and ωmin denote the maximum and minimum values of the inertia weight, respectively.By dynamically adjusting the inertia weight ωa （d ）,the proposed algorithm can effectively balance the global and local search abilities of the IPSO algorithm, which improves the search accuracy,prevents getting stuck in the local optima,and accelerates the convergence speed.

3.1.4 Adaptive adjustment of the number of particles

The IPSO algorithm determines whether the maximum number of iterations has been reached, i.e., e=E.When the iteration constraint is reached, the IPSO algorithm outputs the global best positions Bbest of all particles.Meanwhile, the day-ahead regulation strategy is executed.Otherwise, e=e+1.Considering the influence of the spatial--temporal complementary characteristics of the user-side resources of multiple distribution station areas,the number of particles in the next time period is dynamically adjusted based on the average historical intraday optimal regulation cost.If the average historical intraday optimal regulation cost is larger than the current intraday optimal regulation cost,this indicates that the current dayahead optimization effect is poor.Therefore, it is essential to expand the number of particles to broaden the search space and improve the global optimization capability of the algorithm.Conversely, the number of particles can be reduced to accelerate the convergence speed of the algorithm.The number of particles in the （e+1）-th time period is adjusted according to

where μ is the sensitivity coefficient of the particle number relative to the intraday regulation result.SN-（e ）is the average of the sum of all distribution station area intraday optimal regulation costs in the previous e-1 time periods,andrepresents the ceiling function.

Adjusting the number of particles based on the spatial--temporal complementary characteristics of the user-side resources can improve the global search ability of the IPSO algorithm, prevent the particles from getting stuck in the local optima,and enhance the day-ahead regulation accuracy in the initial phase of the algorithm when the weighted sum of the regulation cost and grid loss is relatively high.In the later stage of the algorithm, when the weighted sum of the regulation cost and grid loss is relatively low, the local search is strengthened such that the algorithm converges to the optimal solution faster and reduces the day-ahead regulation cost.

3.2 Intraday regulation decision based on the IADMM algorithm

We developed an intraday regulation decision method on a small timescale based on the IADMM algorithm by considering the differences in the spatial distribution of resources in multiple distribution station areas.The IADMM algorithm is used to allocate regulation tasks to each edge station area for distributed optimization.Meanwhile, the penalty coefficients of the regulation time slots of the current day in each distribution station area are adaptively updated according to the historical regulation results of the previous day.Thus,it is possible to realize the demand response aggregation regulation by considering the spatial and temporal cooperative demand response of the user-side resources.Therefore, the IADMM algorithm can effectively improve the accuracy and convergence speed of the model for intraday regulation and effectively reduce the optimization cost.The basic form of the multiregion ADMM algorithm is given by

The augmented Lagrangian function corresponding to the multiregion optimization objective (31) based on the ADMM is given by

where x1，···，xn，···，xN represent the decision variable matrices for each region.λ is the augmented Lagrange multiplier vector.ρe （t ） is the penalty coefficient for the tth time slot for intraday regulation located in the e-th period for day-ahead regulation.

To ensure that the optimization objectives meet the above intraday optimal regulation inequality constraints,we introduced the station area auxiliary variable z and two auxiliary functions,i.e.,the equality constraint indicator function h（z ） and the inequality constraint indicator function y （z ）, which are expressed as

where Z1 and Z2 represent the two sets of auxiliary variables.The auxiliary variables in Z1 satisfy the equality constraints, whereas the auxiliary variables in Z2 satisfy the inequality constraints related to the controllable loads,station area power transactions, and node voltage limits.

Based on the above auxiliary functions, the improved multiregion optimization objective of (31) is expressed as

By setting u=λ/ρe （t ）, further manipulation yields the augmented Lagrangian function corresponding to the optimization problem in the above equation, which is expressed as

The iterative process of the improved augmented Lagrangian function is given by

where k is the number of iterations.

It shall be noted that the unreasonable setting of ρe （t ）often increases the number of iterations required for the distributed optimization computation to converge,or even makes convergence difficult.We addressed the difficulty of converging of the distributed optimization model by adaptively updating the value of the penalty coefficient.The penalty coefficient is updated according to

where rk+1 and sk+1 represent the primal and dual residuals after the （k+1） th iteration, respectively.εprime and εdual represent the primal and dual infeasibilities, respectively.

4 Simulations

4.1 Simulation description

Fig.3.Topological structure of the distribution grid based on the IEEE33-node distribution system.

Table 1
User-side resource configuration for each distribution station area.

Distribution station area Transformer capacity Distributed generator capacity Energy storage power and capacity 400 kVA 400 kW 60 kW, 300 kWh 2 400 kVA 300 kW 40 kW, 150 kWh 3 400 kVA 380 kW 80 kW, 300 kWh 4 400 kVA 300 kW —1

We conducted a case study of four distribution station areas within a certain regional distribution grid.MATLAB R2022b was used for the analysis based on the IEEE 33-node distribution system.For the simulations,we incorporated distributed generators with variable outputs,as indicated by the probabilistic nature of renewable energy inputs such as solar and wind power.The topological structures of the distribution grid and station areas are shown in Fig.3,where each station area includes various differentiated resources,such as distribution transformers, distributed generators, and energy storage devices, as shown in Table 1.Each distribution station area consists of various controllable loads for day-ahead and intra-day operations.Their compositions and proportions of the total load are presented in Table 2.The spatial characteristics were reflected by setting different differentiated resources and controllable loads in different distribution station areas.The unit regulation costs for transferable loads, interruptible loads, shiftable loads,and distributed energy storage were 0.018, 0.195, 0.087,and 0.018 $/kWh, respectively.Considering the peak--valley electricity prices, the purchasing price during peak hours(08:00-24:00)was set as 0.168$/kWh and the selling price was set as 0.142$/kWh.During off-peak hours(0:00-08:00), the purchasing and selling prices were set as 0.060and 0.038 $/kWh, respectively.The values of the other simulation parameters are tabulated in Table 3 [28,29].

Table 2
Composition of the controllable loads for each distribution station area.

Time interval Distribution station area Transferable loads Interruptible loads Shiftable loads Controllable loads/Total 50 % 50 % 0 % 12 %Dayahead Dayahead 1 60 % 40 % 0 % 12 %Dayahead 2 25 % 25 % 50 % 15 %Dayahead 3 0 % 0 % 100 % 10 %Intraday 5 50 % 50 % 0 % 5 %Intraday 6 60 % 40 % 0 % 5 %Intraday 7 50 % 50 % 0 % 5 %Intraday 8 100 % 0 % 0 % 3 %4

We employed three baseline algorithms to validate the effectiveness of the proposed algorithm.Baseline 1 is a PSO-based resource-aggregated regulation method.In this method, the traditional PSO algorithm was used for centralized regulation in both the day-ahead and intraday stages [30].Baseline 2 is a PSO consensus-based resource-aggregated regulation method.In this method,the traditional PSO algorithm was used for centralized regulation in the day-ahead stage, whereas the classical consensus algorithm was used for locally distributed regulation in each distribution station area during the intraday stage [31].Baseline 3 is a the PSO-ADMMbased resource-aggregated regulation method.In this method, the traditional PSO algorithm was used for centralized regulation in the day-ahead stage, whereas the classical ADMM algorithm was used for local distributed regulation in each distribution station area during the intra-day stage[32].It is worth noting that neither of these algorithms considers the influence of constraints such as the distribution grid node voltage.

4.2 Regulation optimization results

Fig.4 shows the day-ahead regulation performance for each distribution station area,demonstrating the temporal complementarity of the user-side resources.It can be seen that during peak electricity consumption periods, there was a general decrease in the total load across all distribution station areas, whereas during off-peak periods, there was a slight increase in the total load.In addition, owing to the variations in consumption behaviors between the distribution station areas, there was a certain deviation between the off-peak and peak electricity consumption periods in each distribution station area.This indicates that the flexible adjustment of controllable loads effectively alleviates the load pressure during peak consumption periods.Taking the distribution station area 3 as an example,before the inclusion of controllable loads in the optimization, the peak--valley difference in the system reached 484 kW.After the inclusion of controllable loads in the optimization, the peak--valley difference decreased to 397 kW, corresponding to a reduction of 17.97 %.This indicates that by introducing controllable loads in the day-ahead optimization,the system can more flexibly meetthe load demands during peak consumption periods,thereby achieving the goal of peak shaving and valley filling in the grid.Furthermore, owing to differences in the distributed resources and adjustable loads across stations,the peak-shaving capacity varied between areas.As shown in Fig.4(d),distribution station area 4 lacked energy storage and had limited peak-shaving capability.However,this station ultimately achieved peak shaving through controllable loads and electricity trading.This indicates that the system can leverage the differentiated spatial characteristics of areas to achieve spatial regulation, thereby enabling peak shaving and valley filling across the grid.

Table 3
Simulation parameters.

Parameter Value Parameter Value K 4 T0 4 π 0.3 E 25 dmax 100 A 25 μ 0.4σ -103 ϖ1，ϖ2 [0,1] ωmin，ωmax 0.4, 0.8 εprime 10-4 εdual 10-4

Fig.4.Day-ahead regulation performance for each distribution station area.

Fig.5 shows the involvement of the five types of controllable loads in the day-ahead optimization scheduling process for distribution station areas 1 and 3.As shown in the figure, considering the spatial--temporal complementary characteristics of user-side resources in the distribution station areas, the transferable and shiftable loads could shift the electricity consumption from peak periods to off-peak periods,achieving load balance across different time periods within the distribution station areas.For instance, in distribution station area 1, some of the loads during the evening peak period were shifted to non-peak periods such as 11:00-13:00 and 23:00-01:00.Similarly,in distribution station area 3, some of the loads during the evening peak period were shifted to the nighttime period (00:00-07:00).The interruptible load regulation was more flexible, allowing successive reductions in electricity consumption across multiple time periods.This indicates that the proposed day-ahead demand regulation optimization method can formulate an optimal day-ahead strategy based on the output constraints of the controllable loads in each distribution station area and the spatial--temporal complementary characteristics of the user-side resources,effectively supporting peak shaving and valley filling in the power grid.

Fig.5.Day-ahead controllable load response for each distribution station area.

Fig.6 shows the deviation between the actual measured load values and day-ahead regulation values in distribution station areas 1 and 3 during the intraday regulation process.The response results of intraday controllable loads and the adjustment of energy storage devices and other resources are also presented.Owing to the spatial and temporal variability of the user-side resource output,there was a certain deviation between the predicted load curve and the theoretically calculated day-ahead regulation values during the intraday stage.When the predicted intraday load value was higher than the day-ahead regulation value, the deviation was positive.When the predicted intraday load value was lower than the day-ahead regulation value, the deviation was negative.We interpreted the results in this section by taking distribution station area 1 as an example.

Fig.6.Intraday controllable load response for distribution station areas 1 and 3.

1) As shown in Fig.6(a), during the periods 23:00-00:00, 04:00-05:00, 07:00, 12:00-13:00, and 15:00,the power deviation in distribution station area 1 was less than 0.Considering the transfer characteristics of loads over time,this power deficit can be compensated for by transferring the transferable loads to other periods,charging the energy storage devices,or adjusting the purchase and sale of electricity.Conversely, during the periods 01:00-02:00, 06:00,08:00-10:00,14:00,and 16:00-22:00,the power deviation in distribution station area 1 was greater than 0.The transfer of power can be further optimized based on the spatial--temporal complementary characteristics of the user-side resources.In terms of temporal measures, the electricity purchase and sale can be adjusted for different periods.This shifts the loads in the peak periods to off-peak periods.The spatial measures include reducing interruptible loads in the peak load areas of substations, transferring shiftable loads,or releasing stored energy to satisfy the power balance requirements.

2) Intraday transferable loads and interruptible loads can respond to short-term intra-day regulations.Comparison of Figs.4 and 6 reveals that the intraday regulation corrected the results of the long-term dayahead regulation.During the period 00:00-08:00(Fig.6(a)), further adjustments were made to the energy storage regulation values to reduce the deviation between the day-ahead regulation optimization solutions and the actual intraday measured values.This adjustment leverages the spatial--temporal coordination of the user-side loads.By optimizing intraday electricity transactions and managing shiftable and interruptible loads, the precision of the demand response on the user side can be enhanced.Moreover, the rational scheduling of loads across substation areas further balances the system.

4.3 Comparative analysis

Table 4 presents an economic comparison of the different regulation algorithms.Compared with the baseline 1 and baseline 2 algorithms,the proposed algorithm reduced the intraday regulation costs by 63.16 % and 52.22 %,respectively, and reduced the total regulation costs by 6.41%and 3.69%,respectively.During the day-ahead regulation stage, the proposed algorithm dynamically adjusts the number of particles for day-ahead optimization based on the historical intraday regulation results, fully exploiting the response potential of multiagent user-side resources by considering the spatial--temporal coordination between distribution station areas.This enhances the precision of the day-ahead regulation optimization, resulting in higher regulation costs for controllable loads, energy storage devices, and other resources compared with those for the baseline algorithms.In the intraday stage, considering the aforementioned factors in the day-ahead optimization and the feedback of intraday regulation results, the deviation between the day-ahead regulation results and actual intraday operations are further reduced, leading to a significant reduction in the intraday regulation costs.In sum-mary, the spatial--temporal coordination of the user-side resources is fully considered in the proposed algorithm,which exploits the demand response potential of the user-side resources and formulates reasonable aggregated regulation strategies in advance, thereby reducing costs and achieving better economic benefits.

Table 4
Economic comparison of different regulation algorithms.

Regulation algorithm Regulation cost of controllable loads,energy storage devices,etc./$Baseline 1 3,120.3 Day-ahead Intraday Total regulation cost /$Regulation stage 64.6 128.9 Baseline 2 3,032.1 Day-ahead Intraday 61.6 99.4 Proposed algorithm 2,920.2 DayaheadIntraday 182.8 47.5

Fig.7 shows the comparison of the distribution grid loss with respect to the number of iterations during a specific day-ahead regulation process between the proposed algorithm and baseline algorithms.It can be observed that the optimized distribution grid loss values for the baseline 1, baseline 2, and baseline 3 algorithms were higher than those of the proposed algorithm.This is because the day-ahead regulation for the baseline algorithms does not consider the influence of the intraday optimization results, leading to convergence to the local optima,whereas the proposed algorithm coordinates the dayahead and intraday regulations, enhancing regulation precision by fully utilizing the spatial--temporal coordination.In addition,it can be seen that from iterations 1 to 35,the distribution grid loss values for the proposed algorithm and baseline 1, baseline 2, and baseline 3 algorithms decreased by 39.19, 21.28, 26.53, and 28.23 kW respectively.The proposed algorithm exhibited a faster convergence rate in terms of unit grid loss optimization, where the proposed algorithm improved the convergence rate by 84.16%,47.72%,and 38.82%compared with the baseline 1, baseline 2, and baseline 3 algorithms, respectively.Furthermore,the proposed algorithm and baseline 1,baseline 2, and baseline 3 algorithms converged at iterations 35, 55, 45, and 40, respectively.This is because the proposed algorithm considers the influence of the intraday optimization results, constructs fitness functions based on constraints,and dynamically adjusts the particle exploration weights to accelerate convergence.

Fig.7.Comparison of the distribution grid loss with respect to the number of iterations between different algorithms.

Fig.8.Number of node voltage limit violations versus the number of distribution station areas.

Fig.8 shows the variations in the number of node voltage limit violations with respect to the number of distribution station areas for the proposed algorithm and baseline algorithms.For the same number of distribution station areas, the proposed algorithm exhibited fewer instances of node voltage limit violations.As the number of optimized distribution station areas increased, the proposed algorithm showed a slower increase in the number of node voltage limit violations.When the number of distribution station areas increased to 10, the proposed algorithm reduced the number of node voltage limit violations by 57.1 %, 62.5 %, and 70 % compared with the baseline 1,baseline 2, and baseline 3 algorithms, respectively.This is attributed to the increased complexity of the network with a higher number of distribution station areas, which makes it more prone to voltage constraint violations during the optimization process.However,the proposed algorithm dynamically adjusts the number of particles in the swarm to expand the search space,which facilitates in fulfilling the constraints during grid loss optimization.This does not only reduce the number of node voltage limit violations, but also significantly enhances the resilience and stability of the smart grid under varying operating conditions.

5 Conclusion

A multiagent, multitimescale aggregated regulation method that integrates the spatial--temporal complementarity of the user-side resources was proposed in this work.The effectiveness of the proposed method in optimizing grid operation was verified through simulations.The conclusions drawn based on the key findings of this work are as follows.

Reduction in Distribution Grid Losses:By leveraging the spatial--temporal complementarity of the user-side resources, the proposed method optimizes the day-ahead and intraday regulation strategies, significantly reducing distribution grid losses and improving the operational effi-ciency of the distribution network.

Cost Reduction:Through coordinated regulation across day-ahead and intraday timescales, the proposed method effectively reduces the total regulation costs, demonstrating its economic advantages over existing approaches.

Improvement in Voltage Stability: The spatial and temporal coordination of user-side resources ensures voltage stability across different distribution station areas,thereby enhancing the reliability and robustness of the grid.

In future work,we will focus on extending the proposed method by incorporating robust optimization and exploring complex load behavior models to improve its adaptability to uncertainties and applicability in practical scenarios.

CRediT authorship contribution statement

Tingzhe Pan: Writing - original draft,Validation, Software, Methodology, Investigation. Chao Li: Writing -original draft, Software, Methodology, Investigation.Chen Yang:Methodology,Investigation,Funding acquisition. Zijie Meng: Software, Methodology. Zongyi Wang:Methodology, Investigation. Zean Zhu: Software.

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.

The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: Tingzhe Pan and Zongyi Wang are currently employed by China Southern Power Grid Scientific Research Institute Co.; Chao Li and Zean Zhu are currently employed by Electric Power Dispatching &Control Center of Guangdong Power Grid; Chen Yang is currently employed by China Southern Power Grid Co., Ltd.The research project is funded by Science and Technology Program of China Southern Power Grid Corporation under grant number 036000KK 52222004 (GDKJXM20222117).

Acknowledgments

This work was supported by Science and Technology Program of China Southern Power Grid Corporation under grant number 036000KK52222004(GDKJXM20222117) and National Key R&D Program of China for International S&T Cooperation Projects(2019YFE0118700).