A multi-objective inter-domain collaborative distributed optimization control method for distribution network

Abstract

The invention discloses a multi-objective inter-domain collaborative distributed optimization control method for a distribution network, which mainly comprises the following steps: step 1, for a distribution network connected to multiple microgrids, dynamically partitioning the distribution network according to node voltage sensitivity; step 2, establishing an upper optimization model based on the partitioning, taking active network loss and voltage quality in each region as objective functions, and taking power flow equation constraints, safe operation constraints, photovoltaic output constraints in the distribution network, and power constraints of a public interconnection line between the distribution network and the microgrid as constraint conditions; step 3, solving the upper optimization model by adopting a fully distributed ADMM algorithm based on improved penalty factor modulation to obtain the power of the public interconnection line between the distribution network and the microgrid; step 4, constructing a lower optimization model, taking the operation cost of the microgrid as the objective function, taking the power balance constraints of the internal power of the microgrid and the power of the public interconnection line between the distribution network and the microgrid, MT operation constraints, DE operation constraints, and BESS charging / discharging constraints as constraint conditions, and solving the lower optimization model.

Description

Technical Field

[0001] The invention relates to a multi-objective inter-domain coordinated distributed optimization control method for a distribution network. Background Art

[0002] In recent years, distributed energy resources (DER) have been highly penetrated in the distribution system, such as photovoltaics (PV), electric vehicles (EV), and battery energy storage systems (BESS). [1] The operation and dispatching methods of traditional distribution networks can no longer meet the new requirements. [2] . Distribution network voltage optimization control methods are mainly divided into the following three types: local optimization control, centralized optimization control and distributed optimization control. Among them, distributed control can achieve centralized control effects only through the collection of local information and weak communication between neighbors. Compared with global optimization, it is more real-time and can well cope with the randomness of distributed energy and the uncertainty of load output. [3] As an effective unit for integrating distributed power sources, microgrid (MG) has developed rapidly in recent years, and access to active distribution networks in the form of microgrid groups has broad application prospects. [4] , but the access of MGs increases the requirements for system planning, management and control [5] .

[0003] Domestic and foreign scholars have conducted extensive research on microgrids and microgrid clusters. Reference [6] studied the hierarchical control strategies and methods of multi-microgrids. Reference [7] established different distributed power models in the microgrid and proposed an optimal scheduling method for the microgrid cluster from the perspective of centralized control. Reference [8] studied the energy management method of the microgrid cluster from the perspective of distributed control. Reference [5] proposed a two-level optimal control scheme for renewable energy and traditional power production, bidirectional power flow, dynamic storage system and random modeling problems. Reference [9] proposed a two-level planning model for the power and reserve capacity planning problem of coupled microgrids under the jurisdiction of the distribution system operator (DSO). The upper layer of the model represents the microgrid planner, whose goal is to minimize its planning and operating costs, while the lower layer represents the DSO, whose main goal is to ensure reliable power supply.

[0004] The voltage partition distributed optimization control method of the distribution network can achieve global optimal control of voltage through coordination among multiple regions of the distribution network. At the same time, it can also reduce the computational complexity, improve the optimization calculation efficiency, and have good optimization effect. In recent years, the alternating direction multiplier method ADMM (Alternating Direction Method of Multipliers) has become an important method for solving the distributed optimization control problem of power system partitions. References [10-11] all constructed distributed photovoltaic reactive power optimization control methods based on ADMM with nodes as units. Reference

[12] proposed an active distribution network partition distributed voltage control method based on ADMM on the basis of establishing a linearized power flow model of a three-phase unbalanced distribution network. Since the feedback-based scheme can effectively reduce the impact of modeling mismatch introduced by the linearized power flow model, in actual implementation, this method can be implemented online. Reference

[13] After dividing the distribution network into regions based on cluster performance indicators of electrical distance and cluster voltage regulation capability, a two-layer voltage control strategy combining cluster autonomous optimization (CAO) and distributed cluster coordinated optimization (DICCO) is adopted to achieve joint optimization control of active and reactive power of photovoltaic units. However, in the solution process, the ADMM used in the above literature is prone to problems such as too many iterations and slow calculation speed. Therefore, it is of great significance to study the acceleration method of ADMM to improve the computational efficiency of the distributed optimization control algorithm of active distribution network voltage.

[0005] [References]

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[0015]

[10] .Wang Y,Zhao T,Ju C,et al.Two-level distributed voltage / varcontrol using aggregated PV inverters in distribution networks[J].IEEETransactions on Power Delivery,2020,35(4):1844-1855.

[0016]

[11] . P,Backhaus S,Chertkov M.Optimal distributed control ofreactive power via the alternating direction method of multiplier[J].IEEETransactions on Energy Conversion,2014,29(4):968-977.

[0017]

[12] .Hao JL,Wei S,Hao Z.Distributed voltage control in distributionnetworks:online and robust implementations[J].IEEE Transactions on SmartGrid,2018,9(6),6106-6117.

[0018] Chai YY, Guo L, Wang CS, et al.Network partition and voltagecoordination control for distribution networks with high penetration of distributed PV units[J]. IEEE Transactions on Power Systems, 2018, 33(3):3396-3407. Summary of the invention

[0019] In view of the above-mentioned prior art, the technical problem to be solved by the present invention is to provide an inter-domain collaborative distributed optimization control method that can solve the multi-objective optimization problem of a multi-microgrid distribution system.

[0020] In order to solve the above technical problems, the present invention proposes a distribution network multi-objective inter-domain collaborative distributed optimization control method, which mainly includes:

[0021] Step 1: For a distribution network connected to multiple microgrids, dynamically partition the distribution system according to the voltage sensitivity of each node in the distribution network;

[0022] Step 2: Establish an upper optimization model based on the partitions. The upper optimization model takes active network loss and voltage quality in each region as the objective function, and takes power flow equation constraints, safe operation constraints, photovoltaic active and reactive output constraints in the distribution network, and public tie line power constraints between the distribution network and the microgrid as constraints;

[0023] Step 3: Use the fully distributed ADMM algorithm to solve the upper optimization model to optimize the active network loss and voltage quality of the distribution network, and obtain the public tie line power between the distribution network and the microgrid;

[0024] Step 4: construct and solve the lower-level optimization model, which takes the microgrid operating cost as the objective function, and takes the power balance constraint between the microgrid internal power and the power of the public interconnection line between the distribution network and the microgrid, the micro gas turbine operating constraint, the diesel generator operating constraint, and the battery energy storage system charging / discharging constraint as the constraint conditions, and solves them to minimize the microgrid operating cost.

[0025] Furthermore, the multi-objective inter-domain coordinated distributed optimization control method for distribution network of the present invention comprises:

[0026] The specific steps of step 1 are as follows:

[0027] 1-1) According to the operating status of the distribution network connected to multiple microgrids at this moment, the Jacobian matrix J and its inverse matrix J of the system are obtained: -1, we can get J from formula (1) -1 Relationship with voltage-active power sensitivity;

[0028]

[0029] Where ΔP and ΔQ are the changes in active power and reactive power injected into the PQ node, respectively; Δδ and ΔV are the changes in the voltage phase angle and voltage amplitude of the PQ node, respectively; J is the Jacobian matrix of the system; the voltage sensitivity of the relaxed node in the distribution network is defined as 0;

[0030] 1-2) According to J -1 Obtain the voltage-active power sensitivity matrix of each PQ node to each microgrid node;

[0031] 1-3) Partition all PQ nodes; compare the sensitivity values ​​of each PQ node to the active power injected into each microgrid, set the partition mark of the PQ node to the microgrid number corresponding to the maximum sensitivity value, and divide the nodes with the same partition mark into the same area;

[0032] 1-4) Partition the slack nodes; after obtaining the partition results of the PQ nodes, finally divide the slack nodes directly into the area where the PQ nodes connected to them are located;

[0033] 1-5) Adjacent region coupling: For each region, add the nodes in the adjacent regions that are connected to this region to this region, so that the adjacent regions have a common coupling branch.

[0034] In step 2, area a is set, and the active network loss and voltage quality of area a are taken as the objective function, and its expression is as follows:

[0035]

[0036] In formula (2), n a Indicates the number of nodes in area a; I ij Represents the current flowing through line ij; r ij represents the resistance and reactance of line ij; P ij , Q ij Respectively represent the active and reactive power transmitted on line ij; V i is the voltage of node i; V i spec V i Reference value of

[0037] For area a, the membership function expression corresponding to each target in the area is as follows:

[0038]

[0039] In formula (3), μ asrepresents the membership of the sth objective function in region a; f as min and f as max They represent the minimum and maximum values ​​of the sth objective function in region a respectively;

[0040] Suppose the satisfaction variable of region a is is the minimum value of all target memberships, indicating the satisfaction degree of multi-target decision-making in region a; maximizing the satisfaction variable The regional fuzzy optimization model is as follows:

[0041]

[0042] The objective function of the proposed distributed multi-objective fuzzy optimization is to maximize the sum of satisfaction of all regions:

[0043]

[0044] In formula (5), r is the number of regions obtained by the proposed partitioning method.

[0045] In step 2, the constraints include:

[0046] 2-1) Flow equation constraint: For radial distribution network, a simplified flow equation (DistFlow) described in branch form is used, which is expressed as follows:

[0047]

[0048] In formula (6): V 1 is the equilibrium node voltage; V ref V 1 Reference value; V j is the voltage amplitude at node j, U j =V j 2 , U i =V i 2 ;P jk , Q jk is the transmission power of the head end of line jk, k:j→k represents the set of end nodes k of all lines pointed to by node j as the head end; r ij 、x ij are the resistance and reactance of line ij respectively; are the active and reactive power of node j load respectively; p g j ,q g j are the active and reactive power transmitted from the microgrid at node j to the main grid respectively;

[0049] 2-2) Safety operation constraints are expressed as follows:

[0050] 1-ε≤V j ≤1+ε (7)

[0051] In formula (7), ε represents the allowable voltage deviation, which is set to 0.05 pu;

[0052] 2-3) The constraints on photovoltaic active and reactive output in the distribution network are expressed as follows:

[0053]

[0054] In formula (8): P PV,j , Q PV,j P is the photovoltaic active and reactive power injected into node j; MPPT PV,j The active power injected into the node at the MPPT point for the photovoltaic operation of node j; S PV,j is the photovoltaic installed capacity of node j;

[0055] 2-4) The power constraint of the public tie line between the distribution network and the microgrid is expressed as follows:

[0056]

[0057] In formula (9), P min pcc,w and P max pcc,w MG w The minimum and maximum values ​​of the power transmitted by the public tie line between the active distribution network and ...

[0058] In step 3, the fully distributed ADMM algorithm is a fully distributed ADMM algorithm based on improved penalty factor modulation, which is as follows:

[0059] 3-1) Decompose the optimization problem of the whole system into coordinated calculation of r regional sub-optimization problems, and the upper-level optimization problem is equivalently transformed into formula (10):

[0060]

[0061] In formula (10), h a (x a ) represents the equality constraint of the subproblem in region a; g a (x a ) represents the inequality constraint of the subproblem in region a; x a Represents the set of all variables in region a Region b represents the region adjacent to region a; X a,ij = {P a,ij ,Q a,ij ,Ua,i ,U a,j} represents the state variable of the coupling branch in region a;

[0062] 3-2) The standard ADMM algorithm expression is as follows:

[0063]

[0064] In formula (11), m is the number of iterations; λ is the augmented Lagrange multiplier vector, ρ m is the penalty parameter at the mth iteration;

[0065] From the first and second terms of the first two equations of equation (11), we can get:

[0066]

[0067]

[0068] Let u m =λ m / ρ m , constant ||λ m || 2 2 / 2ρ m can be omitted, then formula (11) can be transformed into:

[0069]

[0070] In formula (14), ω m is the correction factor, whose value is ρ m / ρ m+1 ;

[0071] The average value of the last calculation result of this area and the calculation result of the last iteration of the adjacent area is selected as the reference value of the next iteration calculation to replace the boundary variable value of the adjacent area, that is:

[0072]

[0073] The iterative solution formula for area a is as follows:

[0074]

[0075] The algorithm iteration convergence criterion is that the original residual and dual residual of each region tend to zero. The convergence criterion of region a is shown in formula (17), where ε is the convergence accuracy;

[0076]

[0077] 3-3) During the penalty factor modulation process, set the counting factor τ 1 , τ 2And the starting threshold σ, the counting factor is updated according to formula (18) in each iteration:

[0078]

[0079] Then the penalty factor is updated according to formula (19);

[0080]

[0081] In step 4, the microgrid operation cost objective function is expressed as follows:

[0082] minf MGw =C MT,w +C DE,w +C BESS,w (20)

[0083] In formula (20), C MT,w For MG w Operating cost of microturbine (MT); C DE,w For MG w Operating cost of internal diesel generator (DE); C BESS,w For MG w The depreciation cost generated during the charging / discharging process of the energy storage battery (BESS) in the battery.

[0084] In step 4, the constraints include:

[0085] 4-1) The power balance constraint between the internal power of the microgrid and the power of the public tie line between the distribution network and the microgrid is expressed as follows:

[0086] P MT,w +P DE,w +P BESS,w +P pcc,w =P load,w -P PV,w -P WT,w (twenty one)

[0087] In formula (21), P MT,w , P DE,w , P BESS,w , P pcc,w , P load,w , P PV,w and P WT,w They are the MT output, DE output, BESS charging and discharging power, tie line power between the microgrid and the distribution network, load power, PV unit output and wind turbine unit output in the microgrid w; the tie line power is defined as follows: pcc,w When it is positive, it means that the microgrid w absorbs equivalent power from the distribution network, otherwise it means that the microgrid outputs equivalent power to the distribution network;

[0088] 4-2) Micro gas turbine operation constraints are expressed as follows:

[0089]

[0090] In formula (22), P MT,min,w , P MT,max,w are the minimum active power and maximum active power of MT in microgrid w respectively; P MT,w,t , P MT,w,t-1 are the active output of MT in microgrid w at time t and time t-1 respectively; R MT,up,w , R MT,down,w are the maximum ramp-up rate and ramp-down rate of MT in microgrid w, respectively;

[0091] 4-3) Diesel generator operation constraints are expressed as follows:

[0092]

[0093] In formula (23), Δt is the difference between adjacent time periods; P DE,min,w , P DE,max,w are the minimum active power and maximum active power of DE in microgrid w respectively; P DE,w,t , P DE,w,t-1 are the active output of DE in microgrid w at time t and time t-1 respectively; R DE,up,w , R DE,down,w are the maximum ramp-up rate and ramp-down rate of DE in microgrid w, respectively;

[0094] 4-4) Battery energy storage system charge / discharge constraints are expressed as follows:

[0095]

[0096] In formula (24), Δt is the difference between adjacent time periods; SOC w,t , SOC w,t-1 are the charges of BESS in microgrid w at time t and time t-1 respectively; E BESS,w is the capacity of BESS in microgrid w; SOC min,w , SOC max,w They are the minimum and maximum charge of BESS in microgrid w respectively.

[0097] Compared with the prior art, the present invention has the following beneficial effects:

[0098] The optimization control method described in the present invention is based on the reasonable partitioning of the distribution network according to the voltage sensitivity, and the network loss and voltage in the distribution network are optimized simultaneously by using the fully distributed ADMM method. The proposed improved penalty factor modulation strategy improves the convergence performance of the ADMM algorithm. The two-layer optimization method gives full play to the regulating role of the microgrid on the distribution system, improves the safety and economy of the distribution network operation, and can reasonably dispatch the equipment in the microgrid to minimize the operation cost of the microgrid. The simulation results of the improved IEEE 33-node example show that the method proposed in the present invention can effectively improve the voltage quality and reduce the system network loss. The proposed improved penalty factor modulation strategy can avoid the problems of residual oscillation and slow convergence speed caused by the traditional penalty factor modulation strategy, so that the algorithm has stable convergence performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0099] Figure 1 It is a schematic diagram of regional division;

[0100] Figure 2 is a flow chart of the improved penalty factor modulation method;

[0101] Figure 3 It is a two-layer control framework diagram of a zoned distribution network system containing multiple microgrids;

[0102] Figure 4 It is a flowchart for solving the hierarchical partition optimization scheduling model;

[0103] Figure 5 It is a schematic diagram of the active distribution network structure containing multiple microgrids;

[0104] Figure 6 It is the daily active output prediction curve of photovoltaic in the distribution network;

[0105] Figure 7 It is the daily active and reactive output prediction curve of the distribution network load;

[0106] Figure 8a It is the daily output curve of MG1 internal load, photovoltaic and wind power generation;

[0107] Figure 8b It is the daily output curve of MG2 internal load, photovoltaic and wind power generation;

[0108] Figure 8c It is the daily output curve of MG3 internal load, photovoltaic and wind power generation;

[0109] Figure 9a It is the voltage-active power sensitivity side view;

[0110] Figure 9b It is the top view of voltage-active power sensitivity;

[0111] Fig.10aIt is a schematic diagram of the partition situation when t=1-8 and 19-24;

[0112] Fig.10b This is a schematic diagram of the partition situation when t=9~10 and 17~18

[0113] Fig.10c It is a schematic diagram of the partition situation when t=11~16;

[0114] Fig.11a This is a comparison chart of system network loss before and after optimization;

[0115] Fig.11b It is a comparison chart of the average voltage offset of the system nodes before and after optimization;

[0116] Fig.12 It is the reactive power output strategy curve of the photovoltaic inverter in the distribution network;

[0117] Fig.13 is the output power curve of the tie line in the distribution network system;

[0118] Fig.14a This is the diagram of the scheduling results of each device in MG1;

[0119] Fig.14b It is the diagram of the scheduling results of each device in MG2;

[0120] Fig.14c It is the diagram of the scheduling results of each device in MG3;

[0121] Fig.15 It is a comparison of the number of ADMM iterations under three modulation strategies. DETAILED DESCRIPTION

[0122] The design idea of ​​the present invention is to solve the voltage fluctuation problem caused by the integration of renewable energy through the optimization management of microgrids. First, the distribution system is rationally partitioned using voltage sensitivity, and then the grid loss and voltage quality are taken as the optimization targets. The ADMM method with the proposed improved penalty factor modulation strategy is adopted to achieve the distributed optimization of the distribution system and improve the convergence speed of the algorithm.

[0123] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but the following embodiments are by no means intended to limit the present invention in any way.

[0124] A distribution network multi-objective inter-domain collaborative distributed optimization control method of the present invention comprises the following steps:

[0125] Step 1: For a distribution network connected to multiple microgrids, dynamically partition the distribution system containing multiple microgrids according to the voltage sensitivity of each node in the distribution network:

[0126] If the distribution network system is divided into r connected physical areas, the set of all areas is represented by R; for a certain area a, N a represents the node set of area a, E a represents the branch set of area a, e ij ∈E a Represents a branch in region a. The connection between adjacent regions is coupled through the branches on the region boundaries, that is, adjacent regions share a branch. Figure 1 Taking the 10-node distribution system shown in the figure as an example, the node set of area 1 is {1,2,3,4}, the node set of area 2 is {3,4,5,6,7}, and the node set of area 3 is {6,7,8,9,10}. Area 1 and area 2 are connected by branch e 34 To couple, area 2 and area 3 are connected through branch e 67 The coupling branches are combined with Indicates. Figure 1 System, the set of coupled branches O: = {e 45 ,e 78}. Coupling branch e ij The state variables include the power P transmitted by the branch ij , Q ij , the voltage square of the nodes at both ends of the branch U i , U j The state variables of the coupling branch in region a are represented by vector X a,ij :={P a,ij ,Q a,ij ,U a,i ,U a,j}express.

[0127] The partitioning process is as follows:

[0128] Step 1: According to the operating status of the distribution network at this moment, obtain the system Jacobian matrix J and its inverse matrix J -1 , J can be obtained by the following formula -1 Relationship with voltage-active power sensitivity;

[0129]

[0130] Where ΔP and ΔQ are the changes in active power and reactive power injected into the PQ node, respectively; Δδ and ΔV are the changes in the voltage phase angle and voltage amplitude of the PQ node, respectively; J is the Jacobian matrix of the system. The voltage sensitivity of the relaxed node in the distribution network is defined as 0.

[0131] Step 2: According to J -1 Obtain the voltage-active power sensitivity matrix of each PQ node to each microgrid node;

[0132] Step 3: Partition all PQ nodes; compare the sensitivity values ​​of each PQ node to the active power injected into each microgrid, set the partition mark of the PQ node to the microgrid number corresponding to the maximum sensitivity value, and divide the nodes with the same partition mark into the same area;

[0133] Step 4: Partition the slack nodes. After obtaining the partition results of the PQ nodes, finally partition the slack nodes directly to the area where the PQ nodes connected to them are located.

[0134] Step 5: Adjacent region coupling: For each region, add the nodes in the adjacent regions that are connected to this region to this region so that the adjacent regions have common coupling branches.

[0135] Step 2: Establish an upper optimization model based on the partitions. The upper optimization model takes active network loss and voltage quality in each region as the objective function, and takes power flow equation constraints, safe operation constraints, photovoltaic active and reactive output constraints in the distribution network, and public tie line power constraints between the distribution network and the microgrid as constraints; wherein,

[0136] (2-1) takes active network loss and voltage quality as the objective function, taking the objective function in a certain area a as an example, its expression is as follows:

[0137]

[0138] Among them, n a Indicates the number of nodes in area a. ij Represents the current flowing through line ij; r ij represents the resistance and reactance of line ij; P ij , Q ij Respectively represent the active and reactive power transmitted on line ij; V i is the voltage of node i; V i spec V i Reference value of

[0139] For a certain area a, the membership function expression corresponding to each target in the area is as follows:

[0140]

[0141] Among them, μ as represents the membership of the sth objective function in region a; f as min and f as max They represent the minimum and maximum values ​​of the sth objective function in region a respectively.

[0142] Suppose the satisfaction variable of region a is is the minimum value of all target memberships, indicating the satisfaction of the multi-target decision in region a. The regional fuzzy optimization model is as follows:

[0143]

[0144] Based on the defined regional satisfaction variables, the objective function of distributed multi-objective fuzzy optimization can be obtained. For the entire distribution system, it is hoped that the satisfaction of each region is as large as possible. Therefore, the objective function of the proposed distributed multi-objective fuzzy optimization is to maximize the sum of the satisfaction of all regions:

[0145]

[0146] Where r is the number of regions obtained by the proposed partitioning method.

[0147] (2-2) Among the constraints:

[0148] 1) Flow equation constraint: For radial distribution network, the simplified flow equation (DistFlow) described in branch form is as follows:

[0149]

[0150] Where: V 1 is the equilibrium node voltage; V ref V 1 Reference value; V j is the voltage amplitude at node j, U j =V j 2 , U i =V i 2 ;P jk , Q jk is the transmission power of the head end of line jk, k:j→k represents the set of end nodes k of all lines pointed to by node j as the head end; r ij 、x ij are the resistance and reactance of line ij respectively; are the active and reactive power of the load at node j respectively; are the active and reactive power transmitted from the microgrid at node j to the main grid respectively.

[0151] 2) Safe operation constraints, expressed as follows:

[0152] 1-ε≤V j ≤1+ε

[0153] In the formula, ε represents the allowable voltage deviation, which is set to 0.05pu;

[0154] 3) The constraints on photovoltaic active and reactive output in the distribution network are expressed as follows:

[0155]

[0156] Where: P PV,j , Q PV,j P is the photovoltaic active and reactive power injected into node j; MPPT PV,j The active power injected into the node at the MPPT point for the photovoltaic operation of node j; S PV,j is the photovoltaic installed capacity of node j.

[0157] 4) The power constraint of the public tie line between the distribution network and the microgrid is expressed as follows:

[0158]

[0159] Where P min pcc,w and P max pcc,w MG w The minimum and maximum values ​​of the power transmitted by the public tie line between the active distribution network and ...

[0160] The distribution network multi-objective fuzzy optimization model of the present invention is inspired by the multi-objective fuzzy optimization method and constructs a distributed multi-objective fuzzy optimization model based on the concept of regional satisfaction, thereby obtaining a compromise solution for the distributed multi-objective optimization of system voltage quality and active network loss.

[0161] Step 3: Use the fully distributed ADMM algorithm to solve the upper optimization model to optimize the active network loss and voltage quality of the distribution network, and obtain the public tie line power between the distribution network and the microgrid, including the following steps:

[0162] (3-1) The optimization problem of the whole system is decomposed into the coordinated calculation of r regional sub-optimization problems. The upper-level optimization problem can be equivalently transformed into the following formula:

[0163]

[0164] In the formula, h a (x a ) represents the equality constraint of the subproblem in region a; g a (x a ) represents the inequality constraint of the subproblem in region a; x a Represents the set of all variables in region a Region b indicates a region adjacent to region a.

[0165] (3-2) The standard ADMM algorithm expression is as follows:

[0166]

[0167] Where: m is the number of iterations; λ is the augmented Lagrange multiplier vector, ρ m is the penalty parameter at the mth iteration.

[0168] Using the standard ADMM algorithm expression, the first two equations of the first and second terms can be obtained:

[0169]

[0170]

[0171] Let u m =λ m / ρ m , constant ||λ m || 2 2 / 2ρ m can be omitted, then the standard ADMM algorithm expression can be transformed into:

[0172]

[0173] Among them, ω m is the correction factor, whose value is ρ m / ρ m+1 .

[0174] In order to make u m The update does not require the participation of the central coordinator. The algorithm is converted into synchronous calculation. The average value of the last calculation result of this area and the calculation result of the last iteration of the adjacent area is selected as the reference value of the next iteration calculation to replace the boundary variable value of the adjacent area, that is:

[0175]

[0176] The iterative solution formula for a certain area a is obtained as follows:

[0177]

[0178] The algorithm iteration convergence criterion is that the original residual and dual residual in each region tend to zero. The convergence criterion of region a is shown in the following formula, where ε is the convergence accuracy.

[0179]

[0180] (3-3) Based on the ADMM algorithm, an improved penalty factor modulation method is introduced to correct the penalty factor, thereby improving the convergence efficiency of the algorithm. The existing methods usually use the following iterative algorithm to correct the penalty parameter of the ADMM algorithm to promote r m and dm Synchronous convergence of:

[0181]

[0182] The present invention proposes an improved penalty parameter modulation scheme based on the traditional penalty factor modulation method:

[0183] In the penalty factor modulation process, the counting factor τ is set 1 , τ 2 And the starting threshold σ, the counting factor is updated in each iteration as follows:

[0184]

[0185] Then the penalty factor is updated as follows;

[0186]

[0187] The flowchart of the improved penalty factor modulation method is as follows: Figure 2 The proposed improved penalty factor modulation strategy can avoid the problems of residual oscillation and slow convergence caused by the traditional penalty factor modulation strategy, and make the algorithm have stable convergence performance.

[0188] Step 4: Construct and solve the lower-level optimization model. The lower-level optimization model takes the microgrid operating cost as the objective function, and takes the power balance constraint between the microgrid's internal power and the power of the public interconnection line between the distribution network and the microgrid, the micro gas turbine operating constraints, the diesel generator operating constraints, and the battery energy storage system charging / discharging constraints as constraints, and solves them to minimize the microgrid operating cost.

[0189] (4-1) The microgrid operation cost objective function is expressed as follows:

[0190] minf MGw =C MT,w +C DE,w +C BESS,w

[0191] In the formula, C MT,w For MG w Operating cost of microturbine (MT); C DE,w For MG w Operating cost of internal diesel generator (DE); C BESS,w For MG w The depreciation cost generated during the charging / discharging process of the energy storage battery (BESS) in the battery.

[0192] Among them, C MT,w and C DE,w The cost function expression is as follows:

[0193] C MT,w =C op,MT,w +C fu,MT,w

[0194] C DE,w =C op,DE,w +C fu,DE,w

[0195] Among them C op,MT,w and C fu,MT,w MG w The operation and maintenance cost and fuel cost of the internal MT, C op,DE,w and C fu,DE,w MG w The operation and maintenance cost and fuel cost of DE are expressed as follows:

[0196]

[0197]

[0198] Where: P MT,w and P DE,w MG w Output power of MT and DE; K op,MT,w and K op,DE,w MG w Cost coefficient for internal MT and DE operation and maintenance; K fu,MT,w and K fu,DE,w MG w Fuel price coefficient for MT and DE; V fu,MT (P MT,w ) and V fu,DE (P DE,w ) are MG w The fuel consumption of MT and DE; assuming that the exhaust temperature of the micro-turbine and bromide refrigeration machine of MT remains unchanged, the mathematical model of its fuel consumption characteristics is:

[0199] V fu,MT =∑P MT Δt / (η MT ·L g )

[0200] Where V fu,MT is the natural gas consumption; Δt is the time interval; P MT The output of MT; L g is the lower calorific value of natural gas; η MT is the power generation efficiency of MT.

[0201] As an important power generation unit in microgrid, the power generation characteristics of diesel generator (DE) can be expressed by quadratic function model.

[0202] V fu,DE =α(P DE ) 2 +βP DE +γ

[0203] Where: V fu,DE is the fuel consumption of DE; P DE is the output power of DE; α, β, and γ are 2.6667, 0.1637, and 0.00015 respectively.

[0204] C BESS,w The cost function expression is as follows:

[0205] C BESS,w =P BESS,w ·ζ(P BESS,w )

[0206] Where: P BESS,w For MG w The charging and discharging power of the BESS; ζ(P BESS,w ) is MG w Depreciation coefficient of BESS charging and discharging.

[0207] (4-2) Among the constraints:

[0208] 1) The power balance constraint between the internal power of the microgrid and the power of the public tie line between the distribution network and the microgrid is expressed as follows:

[0209] P MT,w +P DE,w +P BESS,w +P pcc,w =P load,w -P PV,w -P WT,w

[0210] Where: P MT,w , P DE,w , P BESS,w , P pcc,w , P load,w , P PV,w and P WT,w They are the MT output, DE output, BESS charging and discharging power, tie line power between the microgrid and the distribution network, load power, PV unit output and wind turbine unit output in the microgrid w; the tie line power is defined as follows: pcc,w When it is positive, it means that the microgrid w absorbs equivalent power from the distribution network, otherwise it means that the microgrid outputs equivalent power to the distribution network;

[0211] 2) Micro gas turbine operation constraints, expressed as follows:

[0212]

[0213] Where P MT,min,w , P MT,max,w are the minimum active power and maximum active power of MT in microgrid w respectively; P MT,w,t , P MT,w,t-1 are the active output of MT in microgrid w at time t and time t-1 respectively; R MT,up,w , R MT,down,w are the maximum ramp-up rate and ramp-down rate of MT in microgrid w, respectively;

[0214] 3) Diesel generator operation constraints are expressed as follows:

[0215]

[0216] Where Δt is the difference between adjacent time periods; P DE,min,w , P DE,max,w are the minimum active power and maximum active power of DE in microgrid w respectively; P DE,w,t , P DE,w,t-1 are the active output of DE in microgrid w at time t and time t-1 respectively; R DE,up,w , R DE,down,w are the maximum ramp-up rate and ramp-down rate of DE in microgrid w, respectively;

[0217] 4) Battery energy storage system charge / discharge constraints, expressed as follows:

[0218]

[0219] In the formula, Δt is the difference between adjacent time periods; SOC w,t , SOC w,t-1 are the charges of BESS in microgrid w at time t and time t-1 respectively; E BESS,w is the capacity of BESS in microgrid w; SOC min,w , SOC max,w They are the minimum and maximum charge of BESS in microgrid w, and their values ​​are 0.2 and 0.9 respectively.

[0220] In summary, the two-layer control framework of the zoned distribution network system containing multiple microgrids is as follows: Figure 3 The solution flow chart of the hierarchical partition optimization scheduling model is shown in Figure 4As shown in the figure. Based on the sensitivity zoning, the upper optimization model takes the active network loss and voltage quality of each region as the objective function, and takes the power flow equation constraint, safe operation constraint, photovoltaic active and reactive output constraint in the distribution network and the power constraint of the public interconnection line between the distribution network and the microgrid as the constraint conditions. The fully distributed ADMM algorithm is used for solution, and the improved penalty factor modulation method is used to accelerate the convergence speed of the algorithm. The lower optimization model takes the microgrid operation cost as the objective function, and takes the power balance constraint of the microgrid internal power and the power of the public interconnection line between the distribution network and the microgrid, MT operation constraint, DE operation constraint, and BESS charge / discharge constraint as the constraint conditions to achieve the optimization of the microgrid operation cost.

[0221] Research Materials:

[0222] The improved IEEE33 node distribution network is used to verify the method of the present invention. The improved IEEE33 node network topology containing multiple microgrids is as follows: Figure 5 The photovoltaic inverter capacities at nodes 13, 18, 27, and 32 are 500kW, 700kW, 600kW, and 800kW, respectively. The output forecast of each photovoltaic power generation for 24 hours is shown in Figure 6 The distribution network load forecast curve is shown in Figure 7 . Assume that the output power of MT in each MG is between 10 and 300kW, the initial power is 10kW, and the maximum climbing rate and descent rate are 120kW and 180kW respectively. The output power range of DE is 5 to 300kW, the initial power is 10kW, and the maximum climbing rate and descent rate are 160kW and 180kW respectively. The BESS capacity and maximum charge and discharge power in MG1 are 500 kWh and 100 kW respectively, and the BESS capacity and maximum charge and discharge power in MG2 and MG3 are 800 kWh and 120 kW respectively. Assume that the initial SOC of BESS is 0.5. Figure 8a , Figure 8b , Figure 8c The daily output curves of load, photovoltaic and wind power generation in the three microgrids are given respectively. The network loss and internal loss of the incorporated microgrid on the interconnection line are not considered, and the wind / photovoltaic output power is fully absorbed. The time-of-use gas price of natural gas is shown in Table 1. The voltage threshold is 0.05pu, and the initial value of the ADMM penalty factor ρ 0 =250, convergence accuracy ε=10 -6 .

[0223] Table 1

[0224]

[0225] The sensitivity of the PQ node to the voltage-active power of each microgrid node is as follows: Figure 9a As shown in b, due to the change of voltage sensitivity, there are 3 different results within 24 hours. The results of the partitions at each time are shown in Fig.10a , Fig.10b , Fig.10c In order to verify the effectiveness of the method proposed in the present invention, the system network loss and node average voltage deviation before and after optimization are compared. Fig.11a and Fig.11b As shown. It can be seen that the network loss and voltage optimization effects obtained by the proposed method are not much different from those of the centralized optimization method. When the multi-microgrid is not incorporated, the system network loss and node voltage deviation are large, especially when t=20, the system network loss and voltage deviation both reach the maximum value. After optimization, the system network loss and voltage deviation are significantly improved, the system network loss is reduced by 42.69%, and the system voltage deviation is reduced by 74.83%, which proves the effectiveness of the method proposed in the present invention.

[0226] The output power of the tie line in the system and the reactive power output of each photovoltaic inverter are shown in Fig.12 and Fig.13 It can be seen from the dispatching results that PV inverters can provide reactive power compensation, and the MGs connected to the distribution network can optimize the power flow by balancing the supply and demand relationship of the system.

[0227] The dispatch result of MG1-MG3 is as follows: Fig.14a , Fig.14b , Fig.14c As shown. In order to meet the power constraints of the tie line, the microgrid dispatches the controllable power supply and BESS output to minimize the microgrid operation cost. When the output of the power supply device in the microgrid cannot meet the load and tie line power constraints, the BESS needs to be called for power supply to maintain the reliable operation of the system; on the contrary, if the output is excessive, the excess power will be stored in the BESS.

[0228] In order to illustrate the effectiveness of the improved penalty factor modulation strategy proposed in the present invention, the number of iterations required for the improved penalty factor modulation strategy, the traditional penalty factor modulation strategy and the fixed penalty factor strategy are compared. Fig.15 It can be seen that compared with the fixed penalty factor strategy, the convergence performance of the traditional penalty factor modulation strategy has been greatly improved, but the number of iterations required is still relatively high at some points, and the modulation strategy proposed in the present invention has obvious improvements at these points, and the total number of iterations is reduced by about 60% compared with the traditional method, which proves that the proposed method has stable convergence performance.

[0229] Although the present invention has been described above in conjunction with the accompanying drawings, the present invention is not limited to the above-mentioned specific embodiments, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can make many modifications without departing from the purpose of the present invention, all of which are within the protection of the present invention.

Claims

1. A multi-objective inter-domain collaborative distributed optimization control method for a distribution network, characterized by: The following steps are involved: Step 1: For a distribution network connected to multiple microgrids, dynamically partition the distribution system according to the voltage sensitivity of each node in the distribution network; Step 2: Establish an upper optimization model based on the partitions. The upper optimization model takes active network loss and voltage quality in each region as the objective function, and takes power flow equation constraints, safe operation constraints, photovoltaic active and reactive output constraints in the distribution network, and public tie line power constraints between the distribution network and the microgrid as constraints; Step 3: Use the fully distributed ADMM algorithm to solve the upper optimization model to optimize the active network loss and voltage quality of the distribution network, and obtain the public tie line power between the distribution network and the microgrid; Step 4: construct and solve the lower-level optimization model, which takes the microgrid operating cost as the objective function, and takes the power balance constraint between the microgrid internal power and the power of the public interconnection line between the distribution network and the microgrid, the micro gas turbine operating constraint, the diesel generator operating constraint, and the battery energy storage system charging / discharging constraint as the constraint conditions, and solves them to minimize the microgrid operating cost.

2. A distribution network multi-objective inter-domain collaborative distributed optimization control method according to claim 1, characterized in that: The specific steps of step 1 are as follows: 1-1) According to the operating status of the distribution network connected to multiple microgrids at this moment, the Jacobian matrix J and its inverse matrix J of the system are obtained: -1 , we can get J from formula (1) -1 Relationship with voltage-active power sensitivity; Where ΔP and ΔQ are the changes in active power and reactive power injected into the PQ node, respectively; Δδ and ΔV are the changes in the voltage phase angle and voltage amplitude of the PQ node, respectively; J is the Jacobian matrix of the system; the voltage sensitivity of the relaxed node in the distribution network is defined as 0; 1-2) According to J -1 Obtain the voltage-active power sensitivity matrix of each PQ node to each microgrid node; 1-3) Partition all PQ nodes; compare the sensitivity values ​​of each PQ node to the active power injected into each microgrid, set the partition mark of the PQ node to the microgrid number corresponding to the maximum sensitivity value, and divide the nodes with the same partition mark into the same area; 1-4) Partition the relaxed nodes; After obtaining the partition results of the PQ nodes, finally the slack nodes are directly assigned to the area where the PQ nodes connected to them are located; 1-5) Adjacent region coupling: For each region, add the nodes in the adjacent regions that are connected to this region to this region, so that the adjacent regions have a common coupling branch.

3. A distribution network multi-objective inter-domain collaborative distributed optimization control method according to claim 1, characterized in that: In step 2, area a is set, and the active network loss and voltage quality of area a are taken as the objective function, and its expression is as follows: In formula (2), n a Indicates the number of nodes in area a; I ij Represents the current flowing through line ij; r ij represents the resistance and reactance of line ij; P ij , Q ij Respectively represent the active and reactive power transmitted on line ij; V i is the voltage of node i; V i spec V i Reference value of For area a, the membership function expression corresponding to each target in the area is as follows: In formula (3), μ as represents the membership of the sth objective function in region a; f as min and f as max They represent the minimum and maximum values ​​of the sth objective function in region a respectively; Suppose the satisfaction variable of region a is is the minimum value of all target memberships, indicating the satisfaction degree of multi-target decision-making in region a; maximizing the satisfaction variable The regional fuzzy optimization model is as follows: The objective function of the proposed distributed multi-objective fuzzy optimization is to maximize the sum of satisfaction of all regions: In formula (5), r is the number of regions obtained by the proposed partitioning method.

4. A distribution network multi-objective inter-domain collaborative distributed optimization control method according to claim 1, characterized in that: In step 2, the constraints include: 2-1) Flow equation constraint: For radial distribution network, a simplified flow equation (DistFlow) described in branch form is used, which is expressed as follows: In formula (6): V1 is the equilibrium node voltage; V ref is the reference value of V1; V j is the voltage amplitude at node j, U j =V j 2 , U i =V i 2 ;P jk , Q jk is the transmission power of the head end of line jk, k:j→k represents the set of end nodes k of all lines pointed to by node j as the head end; r ij 、x ij are the resistance and reactance of line ij respectively; p c j ,q c j are the active and reactive power of node j load respectively; p g j ,q g j are the active and reactive power transmitted from the microgrid at node j to the main grid respectively; 2-2) Safety operation constraints are expressed as follows: 1-ε≤V j ≤1+ε (7) In formula (7), ε represents the allowable voltage deviation, which is set to 0.05 pu; 2-3) The constraints on photovoltaic active and reactive output in the distribution network are expressed as follows: In formula (8): P PV,j , Q PV,j P is the photovoltaic active and reactive power injected into node j; MPPT PV,j The active power injected into the node at the MPPT point for the photovoltaic operation of node j; S PV,j is the photovoltaic installed capacity of node j; 2-4) The power constraint of the public tie line between the distribution network and the microgrid is expressed as follows: In formula (9), P min pcc,w and P max pcc,w MG w The minimum and maximum values ​​of the power transmitted by the public tie line between the active distribution network and ...

5. A distribution network multi-objective inter-domain collaborative distributed optimization control method according to claim 1, characterized in that: In step 3, the fully distributed ADMM algorithm is a fully distributed ADMM algorithm based on improved penalty factor modulation, including: 3-1) Decompose the upper optimization problem into coordinated calculations of r regional sub-optimization problems, as shown below: In formula (10), h a (x a ) represents the equality constraint of the subproblem in region a; g a (x a ) represents the inequality constraint of the subproblem in region a; x a Represents the set of all variables in region a Region b represents the region adjacent to region a; X a,ij = {P a,ij ,Q a,ij ,U a,i ,U a,j } represents the state variable of the coupling branch in region a; 3-2) The standard ADMM algorithm expression is as follows: In formula (11), m is the number of iterations; λ is the augmented Lagrange multiplier vector, ρ m is the penalty parameter at the mth iteration; From the first two terms and quadratic terms of formula (11), we can get: Let u m =λ m / ρ m , constant ||λ m ||2 2 / 2ρ m If omitted, equation (11) is transformed into: In formula (14), ω m is the correction factor, whose value is ρ m / ρ m+1 ; The average value of the last calculation result of this area and the calculation result of the last iteration of the adjacent area is selected as the reference value of the next iteration calculation to replace the boundary variable value of the adjacent area, that is: The iterative solution formula for area a is as follows: The algorithm iteration convergence criterion is that the original residual and dual residual of each region tend to zero. The convergence criterion of region a is shown in formula (17), where ε is the convergence accuracy; 3-3) In the penalty factor modulation process, the counting factors τ1, τ2 and the start threshold σ are set, and the counting factors are updated according to formula (18) in each iteration: Then the penalty factor is updated according to formula (19); 6. A distribution network multi-objective inter-domain collaborative distributed optimization control method according to claim 1, characterized in that: In step 4, the microgrid operation cost objective function is expressed as follows: In formula (20), C MT,w For MG w Operating cost of microturbine (MT); C DE,w For MG w Operating cost of internal diesel generator (DE); C BESS,w For MG w The depreciation cost generated during the charging / discharging process of the energy storage battery (BESS) in the battery.

7. A distribution network multi-objective inter-domain collaborative distributed optimization control method according to claim 1, characterized in that: In step 4, the constraints include: 4-1) The power balance constraint between the internal power of the microgrid and the power of the public tie line between the distribution network and the microgrid is expressed as follows: P MT,w +P DE,w +P BESS,w +P pcc,w =P load,w -P PV,w -P WT,w (21) In formula (21), P MT,w , P DE,w , P BESS,w , P pcc,w , P load,w , P PV,w and P WT,w They are the MT output, DE output, BESS charging and discharging power, tie line power between the microgrid and the distribution network, load power, PV unit output and wind turbine unit output in the microgrid w; the tie line power is defined as follows: pcc,w When it is positive, it means that the microgrid w absorbs equivalent power from the distribution network, otherwise it means that the microgrid outputs equivalent power to the distribution network; 4-2) Micro gas turbine operation constraints are expressed as follows: In formula (22), P MT,min,w , P MT,max,w are the minimum active power and maximum active power of MT in microgrid w respectively; P MT,w,t , P MT,w,t-1 are the active output of MT in microgrid w at time t and time t-1 respectively; R MT,up,w , R MT,down,w are the maximum ramp-up rate and ramp-down rate of MT in microgrid w, respectively; 4-3) Diesel generator operation constraints are expressed as follows: In formula (23), Δt is the difference between adjacent time periods; P DE,min,w , P DE,max,w are the minimum active power and maximum active power of DE in microgrid w respectively; P DE,w,t , P DE,w,t-1 are the active output of DE in microgrid w at time t and time t-1 respectively; R DE,up,w , R DE,down,w are the maximum ramp-up rate and ramp-down rate of DE in microgrid w, respectively; 4-4) Battery energy storage system charge / discharge constraints are expressed as follows: In formula (24), Δt is the difference between adjacent time periods; SOC w,t , SOC w,t-1 are the charges of BESS in microgrid w at time t and time t-1 respectively; E BESS,w is the capacity of BESS in microgrid w; SOC min,w , SOC max,w They are the minimum and maximum charge of BESS in microgrid w respectively.

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