An active power distribution network multi-type distributed power source cluster hierarchical optimization regulation method

Abstract

The application discloses a kind of active power distribution network multi-type distributed power cluster hierarchical optimization regulation methods, method includes: for the distributed power cluster of several preset, construct the mathematical model suitable for power distribution network time-varying response;Based on distributed model predictive control, the state quantity mathematical model of distributed power cluster is constructed;Considering the economy of power distribution network operation, based on the mathematical model of distributed power cluster, establish cluster upper regulation model, obtain cluster day-ahead overall power target by solving;Select the time scale of day as the regulation period of distributed resource cluster lower regulation system, establish cluster lower regulation model based on distributed model predictive control, correct each distributed power cluster output, ensure that each distributed power cluster tracks economic output plan.The method of the application solves the control target issued by the complementary collaborative regulation layer between upper cluster, optimizes the operating state in cluster, and locally suppresses the voltage out-of-limit caused by renewable energy change and load fluctuation.

Description

Technical Field

[0001] This invention relates to the field of power system control technology, and in particular to a hierarchical optimization control method for multi-type distributed power generation clusters in active distribution networks. Background Technology

[0002] Currently, cities are vigorously developing various types of distributed power sources, including solar photovoltaic, solar thermal, and wind power. Distributed power sources will form a comprehensive power supply system of diversified distributed new energy sources together with traditional energy sources. However, as the distributed energy industry continues to grow, the contradiction of insufficient development of distributed power sources will become increasingly prominent. In particular, the absorption problem caused by the intermittency and volatility of distributed power sources is prominent, leading to a series of problems such as power quality, power flow backflow, and node voltage exceeding limits, which seriously restrict the healthy and sustainable development of the clean energy industry. Therefore, in order to address the challenges brought by large-scale distributed power source access to grid operation and user power supply, it is of great significance to design a hierarchical optimization and control architecture for multi-type distributed power source clusters adapted to active distribution networks from the perspective of distributed power source group control and dispatch, and to study distributed power source cluster resilience enhancement and control technologies that consider grid-friendly coordination. Summary of the Invention

[0003] Technical Objective: To address the shortcomings of existing technologies, this invention discloses a hierarchical optimization and control method for multi-type distributed power generation clusters in active power distribution networks. This method addresses the control objectives issued by the complementary and coordinated control layer between upper-level clusters while optimizing the internal operating status of the clusters. It also locally mitigates voltage overruns caused by renewable energy changes and load fluctuations, facilitating the provision of frequency regulation and dynamic voltage regulation services when necessary.

[0004] Technical solution: To achieve the above technical objectives, the present invention adopts the following technical solution.

[0005] A hierarchical optimization control method for multi-type distributed power generation clusters in an active power distribution network, the method comprising:

[0006] S1. For several pre-defined distributed power generation clusters, construct a mathematical model that adapts to the time-varying response of the distribution network.

[0007] S2. Construct a mathematical model of the state variables of a distributed power supply cluster based on distributed model predictive control;

[0008] S3. Considering the economic efficiency of distribution network operation, based on the mathematical model of distributed power generation cluster, establish a cluster upper-level control model and solve to obtain the cluster's day-ahead overall power target.

[0009] S4. Select the intraday time scale as the control cycle of the distributed resource cluster lower-level control system, establish a cluster lower-level control model based on distributed model predictive control, correct the output of each distributed power cluster, and ensure that each distributed power cluster tracks the economic output plan.

[0010] Beneficial effects: This invention transforms the large-scale distributed power distribution network optimization and control into the optimization control of each distributed power cluster subsystem. Under the premise of ensuring the reliability of cluster operation, it performs real-time rolling power optimization control on the cluster output, alleviates problems such as node voltage exceeding limits under traditional control methods, and provides technical means for optimized scheduling. Attached Figure Description

[0011] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0012] Figure 2 This is a method block diagram according to an embodiment of the present invention. Detailed Implementation

[0013] To enable those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present application, and not all embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present application.

[0014] Example

[0015] As attached Figure 1 and attached Figure 2 As shown in this embodiment, a hierarchical optimization and control method for multi-type distributed power generation clusters in an active power distribution network includes the following steps:

[0016] S1. For a number of pre-defined distributed power generation clusters, construct a mathematical model that adapts to the time-varying response of the distribution network.

[0017] In this invention, the number of distributed power generation clusters and the number of nodes in each cluster are pre-defined. For a fixed number of clusters, a mathematical model adapted to the time-varying response of the distribution network is adopted. The node voltage amplitude is represented by a linear combination of the active power and reactive power injected into the node. The mathematical model is constructed as follows:

[0018] (1)

[0019] (2)

[0020] (3)

[0021] (4)

[0022] ,

[0023] In the formula, For each node in the distribution network system; The number of nodes refers to the number of centralized nodes in the distribution network system. , They are nodes at time t respectively The real part and the imaginary part of the voltage; , They are nodes at time t respectively The real part and the imaginary part of the voltage; Let be the power at time t; The active power injected into the distribution network system at time t. The reactive power injected into the distribution network system at time t. The node at time t The injected active power, The node at time t Injected reactive power, Let be the current in the power distribution network system at time t; , , They are nodes With nodes Resistance, reactance, and admittance matrices between lines; , They are nodes The equivalent coefficients of injected active and reactive power at time t to the corresponding tie lines;

[0024] Node With nodes The admittance matrix is ​​divided into four parts, namely Calculate the equivalent coefficient between the tie line and the power distribution system at time t. , The formula is as follows:

[0025] (5)

[0026] (6)

[0027] In the formula, It is the identity matrix; These are the conjugate parameters of the node voltage. Port voltage; is the admittance conjugate parameter.

[0028] node The expressions for the active power and reactive power injected at time t are as follows:

[0029] (7)

[0030] In the formula, , , , , , , , These represent the following at time t: distributed gas turbine (GT), distributed photovoltaic (PV), distributed wind turbine (WP), distributed energy storage (ES) discharge, distributed energy storage charging, load (L), electric vehicle charging station (EV) charging, and electric vehicle charging station discharge to the node. Injected active power; , , , These represent the distributed gas turbine (GT), distributed photovoltaic (PV), distributed wind turbine (WP), and load-to-node systems at time t. Injected reactive power.

[0031] To address the uncertainties in the combination of power, ramp rate, and energy factors during distributed generation (DG) aggregation, and considering the time-varying nature of these factors, multiple DG cluster aggregation models are constructed, taking into account the time coupling characteristics. Considering the time coupling characteristics and mutual constraints among the various influencing factors, the constraints for DG integration into the distribution network are as follows:

[0032] (8)

[0033] (9)

[0034] (10)

[0035] (11)

[0036] In the formula, The set of distributed power generation nodes connected to the distribution network; , , , , , , These represent the upper and lower limits of active power, reactive power, ramp rate, and energy, respectively, for node n. , Let be the active power and reactive power of node n at time t, respectively. , These are the active power of node n at time t+1 and time t-1, respectively. Let n be the energy of node n at time t-1.

[0037] S2. Construct a mathematical model of the state variables of a distributed power supply cluster based on distributed model predictive control (DMPC).

[0038] No. The state variables of a distributed power cluster are: This includes the power, voltage, and energy storage state of the distributed power cluster, as well as the state variables of the distributed power cluster. The constraints are shown in the following equation:

[0039] (12)

[0040] (13)

[0041] in, For distributed power supply clusters; , , The first Power, voltage, and energy storage state of charge of a distributed power cluster; , The first The upper and lower power limits of a distributed power cluster at various times; , The first The upper and lower voltage limits of a distributed power supply cluster at various times; and The first Upper and lower limits of the state of charge of each energy storage unit in a distributed power cluster; , Representing the first The upper and lower bound constraints of the state variables of a distributed power supply cluster. For the first The weight matrix of a distributed power cluster.

[0042] To ensure the consistency of information exchange among distributed power supply clusters, a consistency variable is introduced. The consensus algorithm is used to obtain the state of any cluster. The state update formula includes:

[0043] (14)

[0044] in, For the first The distributed power cluster in the ... The state variables in the next iteration; For the first The distributed power cluster in the first... The state variables in the next iteration; For the j-th distributed power cluster in the th... The state variables in the next iteration; This is the iteration step size; For an undirected graph, the topology indicator value of the information network between distributed power supply clusters is given when performing the (k+1)th iteration. There is power transfer between the j-th distributed power cluster and the j-th distributed power cluster, then ,on the contrary, ; For the first The weight matrix of each distributed power cluster is a preset value; For the first The distributed power cluster in the first... The set of adjacent distributed power source clusters in the next iteration.

[0045] Assuming all consistent variables satisfy:

[0046] (15)

[0047] Then let:

[0048] , (16)

[0049] in, For the k-th iteration of the consistent distributed power cluster And the network topology indication value between cluster j; For the k-th iteration of the consistent distributed power cluster The value indicating the network topology itself.

[0050] Equation (14) can be simplified to:

[0051] (17)

[0052] From equation (16), we can see that:

[0053] (18)

[0054] In this invention, As a cluster constraint factor, it is crucial for implementing cluster state constraints. With the continuous iterative updates of the cluster state variables... It will approach the weighted average of the initial states of all units in the system. .

[0055] (19)

[0056] in, This indicates the number of distributed generation clusters in the distribution network.

[0057] Constraints of distributed power clusters, i.e., consistency variables The calculation steps are as follows:

[0058] 1) Let , These represent the distances between the cluster state and the upper and lower bounds of the state constraints, respectively, and their expressions are as follows:

[0059] (20)

[0060] To ensure that the cluster state variables remain stable within the constraints during the iteration process, an adjustment factor is introduced. The upper and lower limits of the state are tracked and adjusted in real time. The update expressions for the upper and lower limits of the state are as follows:

[0061] (twenty one)

[0062] In the formula, , These are the upper and lower bounds of the updated cluster state constraints, respectively. For adjustment factors;

[0063] 2) Update cluster state variables Distance from state constraints:

[0064] (twenty two)

[0065] In the formula, , These represent the distances from the cluster state variables to the upper and lower limits of the updated cluster state constraints, respectively.

[0066] 3) Calculate consistency variables :

[0067] Distributed power cluster Send its own state variables to neighboring cluster j The distance between the cluster state variables and the updated cluster state constraint upper and lower bounds. and It receives the state variables of the neighboring cluster j and their upper and lower bounds, and calculates the consistency variables. As shown in the following formula:

[0068] (twenty three)

[0069] In the formula, consistency variables intermediate quantity Introducing cluster constraint factors may affect the convergence speed of equation (14), but will not affect its convergence.

[0070] make:

[0071] (twenty four)

[0072] in, For cluster There is a power transfer indication value between cluster j and cluster j. For cluster It has its own power transmission indication value.

[0073] but:

[0074] (25)

[0075] Represent the consensus control law of distributed power sources in matrix form:

[0076] (26)

[0077] (27)

[0078] In the formula, ; The main diagonal elements are The remaining elements are If a cluster exists within a given interval If there is power transfer with cluster j, then And satisfy ,otherwise .

[0079] Based on equation (26), a virtual decoupling control quantity is introduced. With the weight matrix W, the update equation (26) is as follows:

[0080] (28)

[0081] In the formula, This is the matrix of all cluster state variables in the (k+1)th iteration; is the state matrix of all clusters in the k-th iteration; W is the diagonal formed by the weight coefficients of each cluster.

[0082] The iteration time of the current distributed power cluster state variables is k. A distributed model predictive control method is used to control the power balance and energy transfer of each distributed power cluster. The predictive control time domain is... Cluster Decoupling control quantity It only applies to itself; therefore, its state variables are updated as follows:

[0083] (29)

[0084] With the current distributed power cluster Starting with the number of iterations k, the cluster In the predictive control time domain Internal state variables As shown in the following formula:

[0085] (30)

[0086] in: It is an intermediate variable.

[0087] ,

[0088] ,

[0089] ,

[0090] in, for of Power of 1.

[0091] S3. Considering the economic efficiency of distribution network operation, based on the mathematical model of distributed power generation cluster, establish a cluster upper-level control model and solve for the cluster's day-ahead overall power target.

[0092] The day-ahead control system uses the dynamic aggregation information of distributed power sources and the overall day-ahead operating plan of each cluster as the decision-making object. The objective function of the upper-level model is to minimize the overall global operating cost.

[0093] (31)

[0094] Where F represents the overall operating cost under the day-ahead control scheme of the distribution network; Indicates the number of periods of regulation in the previous day. ; Indicates the number of distributed generation clusters in the distribution network; , , They represent the clusters in time period t. The aggregated operating cost coefficient is a preset value. Indicates time-of-use electricity pricing; Represents a cluster Efforts plan; Represents a cluster Purchase and sale power; This indicates the current regulatory cycle. .

[0095] The constraints of the upper-level regulation model are as follows:

[0096] 1) Power balance constraints

[0097] (32)

[0098] in, Represents a cluster China Photovoltaic contributes its efforts; Represents a cluster Wind power output; Represents a cluster Medium energy storage capacity; Represents a cluster Medium energy storage charging power; Represents a cluster Medium energy storage discharge power.

[0099] 2) Equipment constraints

[0100] (33)

[0101] in, , Represents a cluster Upper and lower limits of wind power output; , Represents a cluster Upper and lower limits of China's photovoltaic power output; , Represents a cluster Upper and lower limits of medium-capacity energy storage; , Represents a cluster Upper and lower limits of medium-capacity energy storage; For cluster Medium-sized energy storage.

[0102] 3) Power interaction constraints

[0103] (34)

[0104] in, , This indicates the upper and lower limits of the power available for sale or purchase.

[0105] S4. Select the intraday time scale as the control cycle of the distributed resource cluster lower-level control system, establish a cluster lower-level control model based on distributed model predictive control, correct the output of each distributed power cluster, and ensure that each distributed power cluster tracks the economic output plan.

[0106] The objective function needs to ensure that the output of each distributed power cluster deviates from the intraday scheduling reference value within the intraday optimization scheduling period. The intraday quadratic optimization objective function is constructed as follows:

[0107] (35)

[0108] (36)

[0109] in, The minimum error between the predicted output and the actual reference output of each unit under distributed model predictive control; t is the current time value, T is the optimization period, and T is 15 min; Q and H are coefficient matrices, which are preset values; For distributed power clusters In the predictive control time domain Internal state variables, including distributed power clusters Power, voltage, and state of charge of energy storage devices; Distributed power clusters to be scheduled within the day Reference values ​​for power, voltage, and state of charge of reserve equipment. For distributed power clusters The increment relative to the previous moment, For distributed power clusters In the predictive control time domain Internal control quantity, For distributed power clusters In the predictive control time domain The control quantity within.

[0110] Distributed power cluster The state variables include the power, voltage, and energy storage state of charge of each distributed resource before / during the day, as shown in equations (37) and (38):

[0111] (37)

[0112] (38)

[0113] In the formula, and Distributed power clusters Actual and reference values ​​of wind and solar power output within the prediction time domain; and Distributed power clusters Actual and reference values ​​of load output within the prediction time domain; and Distributed power clusters Actual and reference values ​​of electric vehicle charging station output within the prediction time domain; and Distributed power clusters The actual and reference values ​​of gas turbine output in the prediction time domain; , , Distributed power clusters The actual charging and discharging power and reference value of the charging and discharging power of the energy storage device in the prediction time domain; and Distributed power clusters The actual and reference values ​​of voltage in the predicted time domain; and Distributed power clusters The actual state of charge and reference value of the energy storage device in the prediction time domain.

[0114] During the optimization process, each distributed power cluster uses the current actual operating state as a reference, sets constraints, and solves for the optimized correction control command. Therefore, its output power state variable can be determined by the current actual operating state and power increment.

[0115] 1) Ramp-up rate constraints for each unit within the distributed power cluster:

[0116] (40)

[0117] in, and These are the upper and lower limits of the ramp rate for each unit within the distributed power cluster. Each unit within the distributed power cluster includes distributed gas turbines (GT), distributed photovoltaics (PV), distributed wind turbines (WP), distributed energy storage (ES), loads (L), and electric vehicle charging stations (EV). The ramp rate of each unit within the predicted time domain;

[0118] 2) Power limits for each unit within the distributed power cluster:

[0119] (41)

[0120] in, and These are the upper and lower power limits for each unit within the distributed power cluster; The initial power values ​​of each unit at time t; For each unit in the prediction time domain Power increment within;

[0121] 3) Voltage constraints of each node within the distributed power supply cluster:

[0122] (42)

[0123] in, The voltage value of the node in the prediction time domain; and These are the lower voltage limit and the upper voltage limit, respectively.

[0124] 4) Constraints of distributed energy storage units:

[0125] ,

[0126] in, and These represent the charging and discharging power of the distributed energy storage unit in the prediction time domain; and These represent the maximum charging and discharging power of the distributed energy storage unit, respectively. For distributed energy storage units, the state of charge in the prediction time domain, and These represent the minimum and maximum states of charge, respectively. and These represent the initial and predicted states of charge of the distributed energy storage unit, respectively. The initial and final states of charge are always equal to ensure that the distributed energy storage unit has no capacity loss.

[0127] 5) Sampling feedback constraints:

[0128] ,

[0129] in, The power of each unit in the distributed power cluster during time period t is the sampled value at the current moment; This represents the actual operating power of each unit at the current moment; This is for the sampling error during operation.

[0130] This invention first constructs a mathematical model adapted to the time-varying response of the distribution network and solves the aggregation model of multiple distributed power generation clusters. Secondly, based on distributed model predictive control, it constructs a mathematical model of the state variables of the distributed power generation clusters. Then, considering the economic efficiency of distribution network operation, based on the cluster's dynamic aggregation information, it establishes a cluster upper-level control model and solves to obtain the cluster's day-ahead overall power target. Finally, it selects the intraday time scale as the control cycle of the distributed resource cluster lower-level control system and establishes a cluster lower-level control model based on distributed model predictive control. When there is a deviation between the predicted and actual output of new energy sources, distributed model predictive control is used to correct the output of each distributed power generation cluster, ensuring that each cluster tracks the economic output plan. This invention transforms the optimization and control of a large-scale distributed power distribution network into the optimization control of each distributed power generation cluster. It performs real-time rolling power optimization control of the cluster output while ensuring the reliability of cluster operation, alleviating problems such as node voltage exceeding limits under traditional control methods and providing a technical means for optimized scheduling.

[0131] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for hierarchical optimization control of multi-type distributed power clusters in an active power distribution network, characterized in that, The method comprises: S1, for a plurality of preset distributed power clusters, a mathematical model suitable for the time-varying response of the power distribution network is constructed; S2, a state quantity mathematical model of the distributed power cluster is constructed based on distributed model predictive control; S3, considering the operation economy of the power distribution network, a cluster upper regulation model is established based on the mathematical model of the distributed power cluster, and a cluster day-ahead overall power target is obtained by solving; in the cluster upper regulation model, the minimum global comprehensive operation cost is taken as an objective function, and constraint conditions include power balance constraints, equipment constraints, and power interaction constraints; the objective function formula includes: ， F represents the comprehensive operation cost under the day-ahead regulation scheme of the power distribution network; represents the number of time periods of day-ahead regulation; represents the number of distributed power clusters in the power distribution network; , , respectively represent the cluster aggregated operation cost coefficient; represents the time-of-use electricity price; represents the cluster output plan; represents the cluster purchased and sold power; represents the period of day-ahead regulation; S4, an inner-day time scale is selected as a regulation cycle of a distributed resource cluster lower regulation system, a cluster lower regulation model based on distributed model predictive control is established, the output of each distributed power cluster is corrected, and economic output plans of each distributed power cluster are ensured to be tracked; in the cluster lower regulation model, an inner-day quadratic optimization objective function is constructed, each distributed power cluster sets constraint conditions in the optimization process with reference to the actual operation state at the current time, and optimization correction control instructions are solved, the constraint conditions include distributed power cluster internal unit ramp rate constraints, distributed power cluster internal unit power upper and lower limit constraints, distributed power cluster internal node voltage constraints, distributed energy storage unit constraints, and sampling feedback constraints; the inner-day quadratic optimization objective function includes: ， ， wherein, is the minimum error between predicted output and actual reference output of each unit under distributed model predictive control; t is the current time value, T is the optimization period; Q and H are coefficient matrices; is the distributed power cluster The state variables within the prediction control time domain include the distributed power cluster power, voltage and state of charge of energy storage devices; is the distributed power cluster power, voltage and state of charge of energy storage devices reference value, is the distributed power cluster relative to the increment of the last time, is the distributed power cluster The control variable within the prediction control time domain , is the distributed power cluster The control variable within the prediction control time domain , 2. The hierarchical optimization and control method for multi-type distributed power generation clusters in an active distribution network according to claim 1, characterized in that: In the state quantity mathematical model of S2, the state quantity of the first distributed power cluster is , including the distributed power cluster power, voltage, and energy storage state of charge, the constraint condition formula of the state quantity of the distributed power cluster includes: ， ， ， in, For distributed power supply clusters; , , The first Power, voltage, and energy storage state of charge of a distributed power cluster; , The first The upper and lower power limits of a distributed power cluster at various times; , The first The upper and lower voltage limits of a distributed power supply cluster at various times; and The first Upper and lower limits of the state of charge of each energy storage unit in a distributed power cluster; , Representing the first The upper and lower bound constraints of the state variables of a distributed power supply cluster. For the first The weight matrix of a distributed power cluster.

3. The hierarchical optimization and control method for multi-type distributed power generation clusters in an active distribution network according to claim 2, characterized in that: In the state quantity mathematical model of S2, a consistency variable is introduced , and a state update formula of any cluster state quantity is obtained by using a consistency algorithm, which includes: ， ， ， in, For the first The distributed power cluster in the first... State variables in the next iteration; For the first The distributed power cluster in the first... State variables in the next iteration; For the j-th distributed power cluster in the th... State variables in the next iteration; This is the iteration step size; This is a topology indicator value for the information network between distributed power supply clusters; For the first The distributed power cluster in the first... The set of adjacent distributed power source clusters in the next iteration.

4. The method of claim 3, wherein the method further comprises: Consistent variables The computing process includes: The distance between the cluster state and the upper and lower limits of the state constraint is set; an adjustment factor is introduced to track and adjust the upper and lower limits of the state in real time; the cluster state quantity and the distance between the state constraint are updated; the distributed power cluster sends its state variable and the distance between the cluster state quantity and the updated cluster state constraint upper and lower limits to the adjacent cluster, and receives the state variable of the adjacent cluster and the upper and lower limits of the state variable, and finally calculates the consistency variable.

5. The method of claim 4, wherein the method further comprises: Consistent variables Computational formula Comprise: ， ， ， wherein, , are the distances of the cluster state quantity to the updated cluster state constraint upper and lower bounds, respectively, , are the updated cluster state constraint upper and lower bounds, respectively; is the adjustment factor.

6. The method of claim 1, wherein the method further comprises: In the state variable mathematical model of S2, the distributed model predictive control method is used to control the power balance and energy transmission of each distributed power cluster, and the prediction control time domain is , the cluster The calculation formula of the state variable in the prediction control time domain ​ Comprise: ， ， ， ， in, For cluster There is a power transfer indication value between cluster j and cluster j. For cluster It has its own power transmission indication value. For the first The second iteration The weight matrix of a distributed power cluster.

7. The hierarchical optimization and control method for multi-type distributed power generation clusters in an active distribution network according to claim 1, characterized in that: The power balance constraint formula includes: ， wherein, represents the cluster of photovoltaic power; represents the cluster of wind power; represents the cluster of energy storage power; represents the cluster of energy storage charging power; represents the cluster of energy storage discharging power; The equipment constraint formula includes: ， wherein , denotes the upper limit of the wind power output in the cluster ; , denotes the upper limit of the photovoltaic power output in the cluster ; , denotes the upper limit of the energy storage power in the cluster ; , denotes the upper limit of the energy storage energy in the cluster ; is the energy storage energy in the cluster ; The power interaction constraint formula includes: ， wherein , represent the upper and lower limits of the electricity purchase and sale power.

8. The hierarchical optimization and control method for multi-type distributed power generation clusters in an active distribution network according to claim 1, characterized in that: The distributed power cluster internal unit ramp rate constraint formula includes: ， ， wherein, and are the upper and lower limits of the ramp rate of each unit in the distributed power cluster, respectively; is the ramp rate of each unit in the prediction time domain. The distributed power cluster internal unit power upper and lower limit constraint formula includes: ， ， wherein, and are the upper and lower limits of power of each unit in the distributed power cluster, respectively; is the initial value of power of each unit at time t; is the power increment of each unit in the predicted time domain . The distributed power cluster internal node voltage constraint formula includes: ， wherein, is the voltage value of the node at the prediction time horizon; and are the lower and upper voltage values, respectively; The distributed energy storage unit constraint formula includes: ， ， wherein, and are the charging and discharging power of the distributed energy storage unit in the prediction time horizon, respectively; and are the maximum charging and discharging power of the distributed energy storage unit, respectively; is the state of charge of the distributed energy storage unit in the prediction time horizon, and are the minimum and maximum state of charge, respectively; and are the initial and final state of charge of the distributed energy storage unit, respectively. The sampling feedback constraint formula includes: ， wherein, is the sampling value of the power of each unit in the distributed power cluster at the current time t; is the actual operating power of each unit at the current time; is the operating sampling error.

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