Virtual power plant regulation and control method based on distributed energy and flexible load aggregation
By employing a hierarchical collaborative control architecture and distributed optimization algorithms, the computational burden and inflexible response issues of virtual power plants in scenarios with a high proportion of renewable energy have been resolved, thereby improving the wind and solar power integration rate and system efficiency.
Patent Information
- Application Number
- CN202511489049.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-10-17
- Publication Date
- 2026-01-13
AI Technical Summary
Existing virtual power plant control technology suffers from heavy computational burden, insufficient handling of wind and solar uncertainties, and inflexible load response in scenarios with a high proportion of renewable energy, resulting in low absorption rate, poor system robustness, and difficulty in balancing economy and reliability.
A hierarchical collaborative control architecture is constructed, employing an LSTM wind and solar forecasting model, an improved K-means++ algorithm, a 5G+TSN low-latency network, an improved ADMM algorithm, and deep reinforcement learning to achieve collaborative optimization and regulation of distributed energy and flexible loads.
It increases the wind and solar energy absorption rate by 15-20%, improves computing efficiency by more than 30%, adapts to large-scale distributed resource scenarios, and enhances system operating efficiency and reliability.
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Abstract
Description
Technical Field
[0001] This invention belongs to the field of power system operation and control technology, specifically relating to a virtual power plant control method based on multi-agent collaborative optimization of distributed energy and flexible load aggregation, applicable to the dispatch and operation of new power systems with a high proportion of renewable energy. Background Technology
[0002] A Virtual Power Plant (VPP) is an intelligent system that aggregates and manages distributed energy resources (DERs), energy storage devices, and flexible loads through information and communication technologies and software systems. It enables coordinated and optimized operation and market trading of resources. VPP control technology mainly revolves around the coordinated control of "source-grid-load-storage," but existing VPP control technologies suffer from the following main problems:
[0003] Traditional virtual power plants typically employ a centralized control model, uploading distributed resource data to a central controller for optimization calculations. While this architecture is feasible for small-scale resource integration scenarios, with the large-scale grid connection of distributed energy sources such as photovoltaics and wind power, as well as flexible loads like adjustable air conditioners and electric vehicle charging stations, the central controller needs to process massive amounts of real-time data from distributed energy sources (photovoltaics, wind power, energy storage, etc.) and flexible loads (adjustable air conditioners, electric vehicle charging stations, etc.), resulting in an extremely heavy computational burden and making it difficult to adapt to large-scale distributed resource integration scenarios.
[0004] Existing scheduling strategies do not adequately consider the volatility and uncertainty of wind and solar (wind power and photovoltaic) output, and mostly adopt deterministic optimization methods, resulting in large deviations between planned values and actual operation, and poor system robustness.
[0005] The load-side response mechanism is rigid, mostly relying on preset threshold switching control, and cannot be dynamically adjusted according to real-time electricity prices and supply and demand status, resulting in low efficiency in demand-side resource regulation.
[0006] The aforementioned problems result in existing technologies achieving wind and solar energy integration rates generally below 80% in scenarios with high renewable energy penetration, making it difficult to balance system operation economy and reliability. Summary of the Invention
[0007] The purpose of this invention is to provide a virtual power plant control method that aggregates distributed energy resources and flexible loads. By constructing a hierarchical collaborative control framework and intelligent optimization algorithms, it solves the problems of heavy computing burden, insufficient handling of wind and solar uncertainties, and inflexible load response in existing centralized systems, thereby improving the virtual power plant's ability to absorb renewable energy and the system's operating efficiency.
[0008] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:
[0009] A virtual power plant control method for aggregating distributed energy resources and flexible loads includes the following steps:
[0010] Construct a collaborative control architecture that includes a resource layer, aggregation layer, optimization layer, control layer, and market layer;
[0011] The resource layer enables standardized access and multi-frequency data acquisition for distributed energy and flexible loads, and establishes an LSTM wind and solar forecasting model, energy storage efficiency constraints, and a flexible load elasticity matrix.
[0012] The aggregation layer uses an improved K-means++ algorithm to cluster resources, generating equivalent virtual machine groups and equivalent adjustable loads; communication and security are ensured through 5G+TSN low-latency network and blockchain evidence storage.
[0013] The optimization layer construction is a multi-objective optimization model. Constraints are set, uncertainties are handled, and MIQP is used to solve deterministic scenarios. Uncertain scenarios are solved by distributed optimization through an improved ADMM algorithm.
[0014] The control layer utilizes MPC to perform rolling optimization every 15 minutes and executes closed-loop control based on priority strategies; it also uses edge computing agents to execute PID control, enabling dynamic adjustment of energy storage charging and discharging power and load temperature setpoint.
[0015] The market tier participates in the 24-hour curve of the day-ahead market declaration, and the real-time market handles deviations of ±5%; 30% of the demand response revenue is returned to users, and commercial operation is achieved by combining carbon trading.
[0016] As a further description of the above technical features, the resource layer parameters are set as follows: energy storage capacity E max (Unit: kWh) determines the maximum energy storage capacity of the energy storage system; charge / discharge efficiency η = 0.92, characterizing energy conversion loss and affecting the accuracy of energy storage SOC (State of Charge) calculation; interruptible load ratio α = 15%~30%, reflecting the load-side regulation capability; aggregation layer parameters are set as follows: communication cycle Δt = 5min (5×60s), a key parameter balancing real-time performance and communication overhead; controller management radius R = 5~10 DERs, optimizing the coverage of the communication topology; optimization layer parameters are set as follows: prediction time domain T = 24h, affecting long-term optimization effect; control time domain N = 4h, determining the response speed of short-term regulation.
[0017] As a further description of the above technical features, it also includes deep reinforcement learning responses, specifically:
[0018] The state is updated using a GRU network, and the equation is: z t =σ(W z ·[h t-1 ,xt ]), r t =σ(W r ·[h t-1 ,x t ]) Where ⊙ is the Hadamard product, W z W r These are updating the gate and resetting the gate weight, respectively.
[0019] The Dueling DQN architecture is adopted, where Q(s,a)=V(s)+(A(s,a)-mean(A(s,:))), combined with priority experience replay P(i=(|δ i |+ε) α / ∑(|δ j |+ε) α Training, where V(s) is the state value function and A(s,a) is the action advantage function; δ i The TD error is represented by α = 0.6, which indicates the adjustment priority.
[0020] As a further description of the above technical features, the multi-frequency data acquisition includes: acquiring photovoltaic / wind power output, energy storage SOC, and micro gas turbine status on the power generation side; acquiring power demand, adjustable range (such as air conditioning temperature setpoint), and response time on the load side; and having both second-level (control) and minute-level (optimization) sampling frequencies.
[0021] As a further description of the above technical features, the LSTM-based wind and solar prediction model is P pv,t =G t ×η pv ×A pv ×FF, where G t Irradiance of the inclined plane (W / m) 2 A pv Photovoltaic panel area (m²) 2 ), where FF is the ratio of actual maximum power to theoretical power;
[0022] The dynamic equation for SOC constraints (20%–90%) is: SOC t+1 =SOC t +(P ch,t η-P dis,t / η)Δt / E max Wherein, SOC is the state of charge (0-1), reflecting the remaining energy stored, P ch,t P is the charging power (kW) at time t. dis,t Let t be the discharge power (kW).
[0023] As a further description of the above technical features, the improved K-means++ algorithm selects the initial cluster center through a distance-weighted sampling strategy. The resource clustering is based on geographical region, resource type, and flexibility characteristics. The output power range of the equivalent virtual machine group is [P_min, P_max], and the adjustment capacity of the equivalent adjustable load is ΔP_load = ±200kW.
[0024] As a further description of the above technical features, the communication protocol parameters of the 5G+TSN low-latency (<50ms) communication network include latency constraints t. proc +t trans ≤150ms and SM9 signature encryption e(P1,P2) s =e(Q1,Q2), where t proc For local processing of delays, t trans For data transmission delay, P1 and P2 are bilinear pairing base points, and S is the master key.
[0025] As a further description of the above technical features, the objective function of the multi-objective optimization model is: Where λ t For electricity price revenue (participation in the electricity market), μ t For frequency modulation compensation revenue (ancillary services market), C i The operation and maintenance cost of distributed resource i;
[0026] Constraints include power balance ∑P gen +∑(P ch -P dis )=∑P load +P grid With the continuity of energy storage SOC SOC t+1 The state of charge (SOC) of the energy storage at time t+1. t Let η be the energy storage state of charge at time t. ch For energy storage charging efficiency, P ch Let P be the charging power (kW) at time t. dis Let η be the discharge power (kW) at time t. dis This refers to the energy storage and discharge efficiency.
[0027] As a further description of the above technical features, the uncertainty handling includes: randomly optimizing and generating multiple sets of wind and solar power output scenarios; using a scenario reduction method to retain typical scenarios; and then applying robust optimization processing. The robust optimization processing sets an uncertainty range (e.g., ±15% for photovoltaic power output) to enhance adaptability to uncertainty, and constructs a nonparametric kernel density estimate K(u) = 0.75(1-u). 2 I(|u|≤1), Opportunity Constraint Transformation P w +Pv +Φ -1 (1-ε)σ≥P min and the ellipsoidal uncertainty set
[0028] Where I(·) is the indicator function, which limits the kernel's effective range, with a bandwidth h = 0.2 × IQR / n 1 / 5 Balance the bias-variance tradeoff; Φ -1 Σ is the standard inverse cumulative function, σ is the standard deviation of the prediction error; Σ is the covariance matrix, reflecting the correlation of variables, and Γ is the robustness adjustment parameter, which adjusts the degree of conservatism of robustness.
[0029] As a further description of the above technical features, the steps of the improved ADMM algorithm to achieve distributed optimization are as follows:
[0030] Objective function decomposition: f i (x i ) = C i (x i )+λ T (A ixi -b), where C i (x i Let λ be the local cost function of the i-th DER, and let A be the Lagrange multiplier vector (dimension = number of constraints). i Let i be the constraint matrix of the i-th device;
[0031] Penalty factor adaptive adjustment: ρ k+1 =ρ k ×(1+sign(r T s)δ); δ is the adjustment step size, controlling the convergence speed, r T s is the inner product of the original residual and the multi-even residual, reflecting the direction of convergence;
[0032] Convergence criterion: ||r k ||2≤ε pri =1×10 -4 And ||s k ||2≤ε dual =1×10 -3 , ε pri Tolerance error for the original problem, ε dual It is the tolerance error of the dual problem.
[0033] After constructing the multi-objective optimization model at the optimization layer, an improved ADMM algorithm is introduced to address the complex optimization problems brought about by large-scale distributed energy resources and flexible loads. This algorithm decomposes the overall optimization problem into multiple local sub-problems, which can be solved independently by each distributed energy resource and flexible load node. Each DER node calculates the solution to its sub-problem locally based on its own cost function and constraints, greatly reducing the burden of centralized computing, improving computational efficiency, and enhancing the system's ability to manage large-scale distributed resources. This enables the virtual power plant to perform efficient optimization scheduling even when faced with massive resources.
[0034] As a further description of the above technical features,
[0035] The priority strategy described is millisecond-level response for energy storage and second-level response for interruptible loads; the parameter for PID control is K. p =0.6K u K i =2K p / T u K d =K p T u / 8; where K u The critical gain (measured by the relay oscillation method), T u This is the critical oscillation period.
[0036] Compared with the prior art, the beneficial effects of the present invention are:
[0037] By constructing a distributed optimization framework through an improved ADMM algorithm, communication overhead is significantly reduced; opportunistic constrained programming enhances adaptability to wind and solar power fluctuations; and a load response mechanism based on deep reinforcement learning enables intelligent regulation of demand-side resources. Compared with existing technologies, this method can increase wind and solar power integration rates by 15-20% and improve computational efficiency by over 30%, making it particularly suitable for scenarios with high proportions of renewable energy integration. Technically, a hierarchical optimization architecture coordinates decisions across different time scales, and Lyapunov optimization theory ensures algorithm convergence. Future applications can be further expanded by introducing privacy computing and digital twin technologies, providing key technical support for the construction of new power systems. Detailed Implementation
[0038] The following examples further illustrate the specific technical content of the present invention, but it should not be construed as limiting the scope of the subject matter of the present invention to the following examples. All technologies implemented based on the above content of the present invention fall within the scope of the present invention.
[0039] A virtual power plant control method for aggregating distributed energy resources and flexible loads includes the following steps:
[0040] Construct a collaborative control architecture comprising a resource layer, aggregation layer, optimization layer, control layer, and market layer. The resource layer parameter is set as follows: energy storage capacity E. max (Unit: kWh) determines the maximum energy storage capacity of the energy storage system; charge / discharge efficiency η = 0.92, characterizing energy conversion loss and affecting the accuracy of energy storage SOC (State of Charge) calculation; interruptible load ratio α = 15%~30%, reflecting the load-side regulation capability; aggregation layer parameters are set as follows: communication cycle Δt = 5min (5×60s), a key parameter balancing real-time performance and communication overhead; controller management radius R = 5~10 DERs, optimizing the coverage of the communication topology; optimization layer parameters are set as follows: prediction time domain T = 24h, affecting long-term optimization effect; control time domain N = 4h, determining the response speed of short-term regulation.
[0041] The resource layer connects distributed energy resources and flexible loads, performs data acquisition and resource modeling, specifically including:
[0042] Resource layer deployment: Distributed energy sources (photovoltaics, wind power, energy storage, etc.) and flexible loads (air conditioning, electric vehicle charging piles, etc.) are connected to the Virtual Power Plant (VPP) platform through Internet of Things (IoT) terminals (such as smart meters, RTUs, etc.), supporting communication protocols such as Modbus, IEC61850, and MQTT to ensure data standardization.
[0043] Real-time data acquisition: On the power generation side, photovoltaic / wind power output, energy storage SOC, and micro gas turbine status are collected; on the load side, power demand, adjustable range (such as air conditioning temperature setpoint), and response time are collected; sampling frequencies at the second level (control) and the minute level (optimization) coexist.
[0044] Resource modeling:
[0045] LSTM models for photovoltaic / wind power based on historical meteorological data (temperature, irradiance, wind speed, etc.) are established. pv,t =G t ×η pv ×A pv ×FF, predicts short-term (next 1 hour) wind and solar power output to ensure that each DER operates within a safe range;
[0046] Energy storage modeling adopts a second-order Thevenin equivalent circuit model, with a charge / discharge efficiency curve η = 95%, a state of charge (SOC) constraint of 20%–90%, and the dynamic equation is:
[0047] SOC t+1 =SOC t +(P ch,t ×0.95-P dis,t / 0.95)×5×60 / (E max ×1000);
[0048] Flexible load classification modeling: interruptible loads are defined as binary variables (0 / 1 indicates whether to respond); shiftable loads are constructed as a 24×24 time-power elasticity matrix. For example, electric vehicle charging can be delayed by 2 hours, and the corresponding matrix element takes a value of 0.8 (indicating that 80% of the power can be shifted).
[0049] The aggregation layer employs an improved K-means++ algorithm to generate an equivalent model for resource clustering and constructs a communication network, specifically including:
[0050] Resource clustering: An improved K-means++ algorithm is used to cluster resources according to geographical region, resource type and flexibility characteristics. The improved K-means++ algorithm selects the initial cluster centers through a distance-weighted sampling strategy.
[0051] Equivalent modeling: The generation side is aggregated as an equivalent virtual machine group with a power range of [P_min, P_max]; the load side is aggregated as an equivalent adjustable load with an adjustment capacity of ΔP_load = ±200kW and a response time of <10s.
[0052] Communication network deployment: Construct a 5G+TSN (Time-Sensitive Networking) low-latency (<50ms) communication network and set communication protocol parameters, including latency constraints t. proc +t trans ≤150ms and SM9 signature e(P1,P2) s =e(Q1,Q2) encryption, blockchain notarization of key operations (such as load response commands), to ensure reliable and secure data transmission.
[0053] The optimization layer constructs a multi-objective optimization model and uses an improved ADMM algorithm to achieve distributed optimization, specifically including:
[0054] Construct a multi-objective optimization model:
[0055] Set constraints: including power balance ∑P gen +∑(P ch -P dis )=∑P load +P grid With the continuity of energy storage SOC
[0056] Uncertainty handling:
[0057] 1000 wind and solar power output scenarios were generated through random optimization (Monte Carlo simulation), and 50 typical scenarios were retained using a scenario reduction method. Robust optimization was performed with a photovoltaic power output uncertainty range of ±15%, and a nonparametric kernel density estimate K(u) = 0.75(1-u) was constructed. 2I(|u|≤1), Opportunity Constraint Transformation P w +P v +Φ -1 (1-ε)σ≥P min and the ellipsoidal uncertainty set
[0058] Algorithm execution:
[0059] For deterministic scenarios, mixed-integer quadratic programming (MIQP) is used to solve for discrete variables (such as load start-up and shutdown).
[0060] In uncertain scenarios, distributed optimization is achieved by improving the ADMM algorithm to avoid centralized computation. The steps are as follows:
[0061] Objective function decomposition: f i (x i ) = C i (x i )+λ T (A ixi -b);
[0062] Penalty factor adaptive adjustment: ρ k+1 =ρ k ×(1+sign(r T s)δ);
[0063] Convergence criterion: ||r k ||2≤ε pri =1×10 -4 And ||s k ||2≤ε dual =1×10 -3 .
[0064] The control layer executes model predictive control and edge computing to perform real-time closed-loop regulation, specifically:
[0065] Model Predictive Control (MPC) Rolling Optimization: The scheduling plan is updated every 15 minutes based on the latest forecast data. The actual output is compared with the planned value, and feedback is used to correct the instructions for the next cycle. The feedback correction coefficient K = 0.3, i.e.: u t+1 =u t +0.3×(y real,t -y prde,t ), where u is the control variable and y is the actual and predicted output / load values;
[0066] Priority control strategy: Level 1 response (energy storage) control cycle 10ms, adjustment step 1kW; Level 2 response (interruptible load) control cycle 100ms, adjustment 5kW each time;
[0067] Edge computing agent deployment embeds a PID controller in the energy storage converter to receive VPP commands, adjust charging and discharging power, and tune PID controller parameters: K p =0.6K u K i =2K p / T u K d =K p T u / 8, K was measured by the relay oscillation method. u =1.2, T u =60s, therefore K p =0.72, K i =0.024, K d =5.4; The load controller dynamically adjusts the air conditioner set temperature in steps of 0.5℃, with a response delay of <5 seconds.
[0068] The market tier conducts market bidding, revenue settlement, and incentives, specifically as follows:
[0069] The market recently reported: Based on the 24-hour wind and solar power output curves predicted by the LSTM model, and combined with users' electricity consumption habits, the reported output / load is allowed to have a deviation of ±3%.
[0070] Real-time market transactions: When the actual output / load deviates from the declared value by more than 5%, power can be purchased or sold through the real-time market;
[0071] Revenue Settlement: 30% of the revenue from demand response will be distributed back to participating users based on their contribution level. The contribution level is calculated as follows: Where P is the response power and t is the response time;
[0072] Carbon trading involves calculating the emission reductions from renewable energy generation (solar / wind power) at a rate of 0.78 kg CO2 / kWh, and then selling these reductions to the carbon market.
[0073] Deep reinforcement learning response, specifically:
[0074] The state is updated using a GRU network, and the equation is:
[0075] z t =σ(W z ·[h t-1 ,x t ])
[0076] r t =σ(W r ·[h t-1 ,x t ])
[0077]
[0078] The Dueling DQN architecture is adopted, where Q(s,a)=V(s)+(A(s,a)-mean(A(s,:))), combined with priority experience replay P(i=(|δ i |+ε) α / ∑(|δ j |+ε) α train;
[0079] Where V(s) is the state value function, and A(s,a) is the action advantage function; δ i The TD error is α = 0.6.
[0080] It should be noted that the parameters of the formula in this invention are determined in the following way: equipment nameplate data (such as η) pv Emax, etc.), historical data analysis (such as Σ matrix), field testing (such as K... u T u ) and standards and specifications (such as communication latency requirements).
[0081] The above embodiments describe the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are only illustrative of the principles of the present invention. Various changes and modifications can be made to the present invention without departing from the scope of the principles of the present invention, and all such changes and modifications fall within the protection scope of the present invention.
Claims
1. A virtual power plant control method for aggregating distributed energy resources and flexible loads, characterized in that, Includes the following steps: Construct a collaborative control architecture that includes a resource layer, aggregation layer, optimization layer, control layer, and market layer; The resource layer enables standardized access and multi-frequency data acquisition for distributed energy and flexible loads, and establishes an LSTM wind and solar forecasting model, energy storage efficiency constraints, and flexible load elasticity matrix. The aggregation layer uses an improved K-means++ algorithm to cluster resources, generating equivalent virtual machine groups and equivalent adjustable loads, and ensures communication and security through 5G+TSN low-latency network and blockchain evidence storage; The optimization layer constructs a multi-objective optimization model, sets constraints, handles uncertainties, and uses MIQP to solve deterministic scenarios, while for uncertain scenarios, it achieves distributed optimization by improving the ADMM algorithm. The control layer utilizes MPC to perform rolling optimization every 15 minutes and executes closed-loop control based on priority strategies; it also uses edge computing agents to execute PID control, enabling dynamic adjustment of energy storage charging and discharging power and load temperature setpoint. The market tier participates in the 24-hour curve of the day-ahead market declaration, and the real-time market handles deviations of ±5%; 30% of the demand response revenue is returned to users, and commercial operation is achieved by combining carbon trading.
2. The virtual power plant control method according to claim 1, characterized in that, It also includes load responses based on deep reinforcement learning, specifically: The state is updated using a GRU network, with the equation z. t =σ(W z ·[h t-1 x t ]), r t =σ(W r ·[h t-1 x t ]) The Dueling DQN architecture is adopted, where Q(s, a) = V(s) + (A(s, a) - mean(A(s, :))), combined with priority experience replay P(i) = (|δ i |+ε) α / ∑(|δ j |+ε) α train; Where V(s) is the state value function, and A(s, a) is the action advantage function; δ i The TD error is α = 0.
6.
3. The virtual power plant control method according to claim 1 or 2, characterized in that, The multi-frequency data acquisition includes: acquiring photovoltaic / wind power output, energy storage SOC, and micro gas turbine status on the power generation side; and acquiring power demand, adjustable range, and response time on the load side.
4. The virtual power plant control method according to claim 3, characterized in that, The LSTM-based wind and solar prediction model is P pv,t =G t ×η pv ×A pv ×FF, where G t For the irradiance of the inclined plane, A pv Where is the area of the photovoltaic panel, and FF is the ratio of the actual maximum power to the theoretical power. The dynamic equation for the SOC constraint is SOC t+1 =SOC t +(P ch,t η-P dis,t / η)Δt / E max Where SOC is the state of charge, P ch,t Let P be the charging power at time t. dis,t Let t be the discharge power at time t.
5. The virtual power plant control method according to claim 1 or 2, characterized in that, The improved K-means++ algorithm selects the initial cluster centers through a distance-weighted sampling strategy. The resource clustering is based on geographical region, resource type, and flexibility characteristics.
6. The virtual power plant control method according to claim 5, characterized in that: The communication protocol parameters of the 5G+TSN low-latency communication network include latency constraints t proc +t trans ≤150ms and SM9 signature encryption e(P1, P2) s = e(Q1, Q2).
7. The virtual power plant control method according to claim 1 or 2, characterized in that, The objective function of the multi-objective optimization model is Constraints include power balance ∑P gen +∑(P ch -P dis )=∑P load +P grid With the continuity of energy storage SOC 8. The virtual power plant control method according to claim 7, characterized in that, The uncertainty handling includes: Multiple sets of wind and solar power output scenarios are randomly generated. After retaining typical scenarios using a scenario reduction method, robust optimization is applied. The robust optimization process sets an uncertainty interval and constructs a nonparametric kernel density estimate K(u) = 0.75(1-u). 2 I(|u|≤1), Opportunity Constraint Transformation P w +P v +Φ -1 (1-ε)σ≥P min and the ellipsoidal uncertainty set 9. The virtual power plant control method according to claim 8, characterized in that, The steps of the improved ADMM algorithm for distributed optimization are as follows: Objective function decomposition: f i (x i ) = C i (x i )+λ T (A ixi -b); Penalty factor adaptive adjustment: ρ k+1 =ρ k ×(1+sign(r T s)δ); Convergence criterion: ||r k ||2≤ε pri And ||s k ||2≤ε dual .
10. The virtual power plant control method according to claim 1 or 2, characterized in that, The priority strategy described is millisecond-level response for energy storage and second-level response for interruptible loads; the parameter for PID control is K. p =0.6K u K i =2K p / T u K d =K p T u / 8.
