Optical storage constant volume site selection optimal configuration method and device based on second-order cone convex relaxation

Abstract

The invention relates to a second-order cone-convex relaxation-based optical storage constant-volume site selection optimization configuration method and device, and the method comprises the steps: constructing a multi-target double-layer optimization model on the basis of the operation constraint conditions of a photovoltaic system and an energy storage system; constraining the multi-target double-layer optimization model by using a safe operation constraint condition; utilizing a second-order cone-convex relaxation technology to relax the constraint conditions of the power flow equation of the power distribution network in the safe operation constraint conditions, and converting the multi-objective double-layer optimization model into a distributed optical storage collaborative optimization configuration model; and performing iterative calculation on the distributed optical storage collaborative optimization configuration model by using a commercial solver to determine the optimal position and the optimal capacity configuration of the target power distribution network accessed to the distributed power supply. According to the method, the electric energy quality when the distributed power supply is connected to the power distribution network can be improved, and the consumption capability of distributed photovoltaic power is improved under the condition of economy.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, and in particular to a method and device for optimizing the location selection of photovoltaic power storage based on second-order cone convex relaxation. Background Art

[0002] In recent years, environmental pollution and energy crisis have been aggravated, and the drawbacks of traditional power generation methods have gradually emerged. Distributed power generation and grid-connected operation represented by photovoltaic (PV) have received widespread attention. Photovoltaic power generation has high economic and social benefits, and small and medium-sized distributed power sources (DGs) can be consumed locally, and have the advantages of cleanliness and efficiency. Renewable DGs power generation technology based on wind power generation and photovoltaic power generation has received worldwide attention, and distributed photovoltaic (DPV) has been widely used in countries around the world due to its low investment cost, flexible power generation methods and zero pollution.

[0003] Large-scale distributed photovoltaics are decentralized and connected to the distribution network. The volatility and randomness of their output have brought great challenges to the safe and stable operation of the distribution network. Energy storage systems (ES) have fast power throughput capabilities, that is, fast response speed and flexible charging and discharging power regulation. They can play an important role in promoting large-scale distributed photovoltaic grid-connected planning, and the reasonable configuration of energy storage is the prerequisite for its effective application. Therefore, it is necessary to study the coordinated optimization operation of distributed photovoltaics and distributed energy storage.

[0004] In recent years, domestic and foreign scholars have conducted a lot of research on the site selection and capacity determination of DGs and DES. At present, there are many planning research results for distributed photovoltaics and distributed energy storage in distribution networks, which are mainly reflected in two aspects: single planning and joint planning. Single planning was the focus of early research, which focused on the study of DG and ESS site selection and capacity determination considering the total planning cost and power quality of the power grid, or the study of the impact of DG and ESS access on traditional distribution network planning. As a research hotspot in recent years, joint planning mainly studies the complementary advantages and resource reorganization between multiple planning objects to achieve the goal of joint optimization and realize the coordinated optimization configuration of resources. Summary of the invention

[0005] The present invention provides a method and device for optimizing the location selection of photovoltaic power storage based on second-order cone convex relaxation, so as to improve the power quality when the distributed power source is connected to the distribution network, and to improve the absorption capacity of distributed photovoltaic power under economic conditions.

[0006] The technical solution adopted by the present invention to solve the technical problem is: to provide a method for optimizing the location and configuration of a fixed-capacity optical storage system based on second-order cone convex relaxation, comprising the following steps:

[0007] A multi-objective two-layer optimization model is constructed based on the constraints of the operation of the photovoltaic system and the energy storage system. The multi-objective two-layer optimization model includes an upper model and a lower model, wherein the output result of the upper model is the input of the lower model. The upper model is established with the goal of minimizing the reverse load rate and voltage deviation of the distribution transformer, and is used to select the grid-connected location. The lower model is established with the goal of minimizing the sum of the daily comprehensive cost of energy storage and photovoltaics and the net load change of nodes at adjacent times, and is used to determine the energy storage and photovoltaic configuration capacity.

[0008] Using safe operation constraints to constrain the multi-objective two-level optimization model;

[0009] The second-order cone convex relaxation technology is used to relax the distribution network power flow equation constraint in the safe operation constraint, and the multi-objective two-layer optimization model is converted into a distributed photovoltaic storage collaborative optimization configuration model;

[0010] The distributed photovoltaic and energy storage collaborative optimization configuration model is iteratively calculated using a commercial solver to determine the optimal location and optimal capacity configuration for the target distribution network to access the distributed power source.

[0011] The upper model is: Among them, f 上1 is the reverse load rate of the distribution transformer, f 上2 is the voltage deviation, P PV,i is the active output power of the photovoltaic node i, P load is the active power of the load, S e Indicates the rated capacity of the distribution transformer, U k is the voltage of node k, expressed as: U0 is the voltage at the power supply point, R i and X i are the line resistance and reactance between node i-1 and node i, respectively, P L,k and Q L,k are the active load and reactive load of node k respectively, P PV,k and Q PV,k are the active output power and reactive output power of the photovoltaic node k, U N is the rated voltage.

[0012] The underlying model is: Among them, f 下1 is the daily comprehensive cost of energy storage and photovoltaics, f 下2 is the sum of the changes in the net load of the nodes at adjacent moments, f inv is the investment cost of the energy storage system, expressed as: f ope is the operation and maintenance cost of the energy storage system, expressed as: f loss is the active network loss cost, expressed as: f pun is the penalty cost for abandoning light, expressed as: f pva is the peak-to-valley arbitrage profit, expressed as: F cr is the capital recovery coefficient, Ω s is a set of typical scenarios, λ s is the probability of occurrence of scenario s, c p and c e are the unit power cost and unit capacity cost of the energy storage system respectively, and are the rated power and rated capacity of the nth energy storage system under scenario s, N e is the number of energy storage systems connected, T represents the charge and discharge operation time of the energy storage system, c o is the unit electricity operation and maintenance cost of the energy storage system, and are the charging power and discharging power of the nth energy storage system at time t under scenario s, Δt is the unit scheduling duration, c pri,t is the time-of-use electricity price at time t, I s,ij,t is the current of branch ij at time t under scenario s, r ij is the resistance of branch ij, N PV is the number of distributed photovoltaic connections, c pun is the penalty cost of abandoned light per unit power, and are the predicted output and actual dispatched output of the mth distributed photovoltaic unit at time t under scenario s, is the grid power at time t under scenario s, expressed as: is the load at time t, is the output of distributed photovoltaic power at time t under scenario s.

[0013] The constraints for the operation of the photovoltaic system and the energy storage system include:

[0014] The operating constraints of the energy storage system are expressed as: Where S(t) represents the SOC of the energy storage system at time t, P ch (t) and P dis (t) respectively represent the charging power and discharging power of the energy storage system at time t, η ch and η dis They represent the charging efficiency and discharging efficiency of the energy storage system, E essIt represents the capacity of the energy storage system when it is fully charged, and Δt is the unit dispatching time;

[0015] The energy storage system constraints are expressed as: Where S is the SOC of the energy storage system, S min and S max is the minimum SOC and maximum SOC allowed by the energy storage system, p ch is the charging power of the energy storage system, is the maximum charging power allowed by the energy storage system, p dis is the discharge power of the energy storage system, is the maximum discharge power allowed by the energy storage system, S(0) represents the SOC of the energy storage system at the initial moment, and S(T) represents the SOC of the energy storage system at time T;

[0016] The operating constraints of the photovoltaic system are expressed as: Where E is a given sample set D = {x1, x2, ..., x m} and the photovoltaic data clusters C={C1,C2,...,C K}, μ i is the mean vector of the i-th photovoltaic data cluster.

[0017] The safety operation constraints include:

[0018] The constraints of the distribution network power flow equation are expressed as: Among them, U i,t and U j,t are the voltages of nodes i and j at time t, respectively, j,t and q j,t are the active injection power and reactive injection power of node j at time t, r ij and x ij are the resistance and reactance of branch ij, respectively, P ij,t and Q ij,t are the active power and reactive power of the first end of branch ij at time t, I ij,t is the current of branch ij at time t, P jk,t and Q jk,t are the active power and reactive power of the head end of branch jk at time t, respectively. k:j→k represents the set of child nodes with node j as the parent node.

[0019] The constraints for safe operation of distribution network are expressed as: Among them, U i is the voltage at node i, V i min and V i max is the voltage lower and upper limits of node i; Iij is the current in branch ij, is the upper limit of the current of branch ij;

[0020] The access distributed generation penetration level constraint is expressed as: Where ρ is the distribution network penetration rate, P PV is the distributed photovoltaic active power output, P L is the active load of the system;

[0021] Voltage deviation constraint, expressed as: U N (1-ε1)≤U i ≤U N (1-ε2), where U N Rated voltage, ε1 and ε2 are both voltage deviation rates;

[0022] The reverse load rate constraint is expressed as: i ≤λ imax , where λ i represents the reverse load rate of the distribution transformer at node i, λ imax is the upper limit of the reverse load rate of the distribution transformer at node i.

[0023] The second-order cone convex relaxation technique is used to relax the power distribution network flow equation constraint condition in the safe operation constraint condition, specifically including:

[0024] Introducing new matrix variables and in, and They are respectively the square of the voltage at node i and the square of the current at branch ij at time t;

[0025] Using Matrix Variables and By optimizing the constraints of the power flow equation of the distribution network, we can obtain:

[0026] Use SOCP to optimize the constraints of the power flow equation of the distribution network. Relax and convert to standard second-order cone form:

[0027] The technical solution adopted by the present invention to solve the technical problem is: to provide a device for optimizing the location and configuration of a light storage constant volume based on second-order cone convex relaxation, comprising:

[0028] A construction module is used to construct a multi-objective two-layer optimization model based on the constraints of the operation of the photovoltaic system and the energy storage system. The multi-objective two-layer optimization model includes an upper model and a lower model, wherein the output result of the upper model is the input of the lower model, the upper model is established with the goal of minimizing the reverse load rate and voltage deviation of the distribution transformer, and is used to select the grid-connected location, and the lower model is established with the goal of minimizing the sum of the daily comprehensive cost of energy storage and photovoltaics and the net load change of nodes at adjacent times, and is used to determine the energy storage and photovoltaic configuration capacity;

[0029] A constraint module, used to constrain the multi-objective two-level optimization model using safe operation constraints;

[0030] A relaxation module, used for relaxing the distribution network power flow equation constraint in the safety operation constraint by using the second-order cone convex relaxation technology, and converting the multi-objective two-layer optimization model into a distributed photovoltaic storage collaborative optimization configuration model;

[0031] The solution module is used to use a commercial solver to iteratively calculate the distributed photovoltaic storage collaborative optimization configuration model to determine the optimal location and optimal capacity configuration for the target distribution network to access the distributed power source.

[0032] The upper model constructed by the building block is: Among them, f 上1 is the reverse load rate of the distribution transformer, f 上2 is the voltage deviation, P PV,i is the active output power of the photovoltaic node i, P load is the active power of the load, S e Indicates the rated capacity of the distribution transformer, U k is the voltage of node k, expressed as: U0 is the voltage at the power supply point, R i and X i are the line resistance and reactance between node i-1 and node i, respectively, P L,k and Q L,k are the active load and reactive load of node k respectively, P PV,k and Q PV,k are the active output power and reactive output power of the photovoltaic node k, U N is the rated voltage.

[0033] The lower model constructed by the building block is: Among them, f 下1 is the daily comprehensive cost of energy storage and photovoltaics, f 下2 is the sum of the changes in the net load of the nodes at adjacent moments, f inv is the investment cost of the energy storage system, expressed as: fope is the operation and maintenance cost of the energy storage system, expressed as: f loss is the active network loss cost, expressed as: f pun is the penalty cost for abandoning light, expressed as: f pva is the peak-to-valley arbitrage profit, expressed as: F cr is the capital recovery coefficient, Ω s is a set of typical scenarios, λ s is the probability of occurrence of scenario s, c p and c e are the unit power cost and unit capacity cost of the energy storage system respectively, and are the rated power and rated capacity of the nth energy storage system under scenario s, N e is the number of energy storage systems connected, T represents the charge and discharge operation time of the energy storage system, c o is the unit electricity operation and maintenance cost of the energy storage system, and are the charging power and discharging power of the nth energy storage system at time t under scenario s, Δt is the unit scheduling duration, c pri,t is the time-of-use electricity price at time t, I s,ij,t is the current of branch ij at time t under scenario s, r ij is the resistance of branch ij, N PV is the number of distributed photovoltaic connections, c pun is the penalty cost of abandoned light per unit power, and are the predicted output and actual dispatched output of the mth distributed photovoltaic unit at time t under scenario s, is the grid power at time t under scenario s, expressed as: is the load at time t, is the output of distributed photovoltaic power at time t under scenario s.

[0034] The constraints for the operation of the photovoltaic system and the energy storage system include:

[0035] The operating constraints of the energy storage system are expressed as: Where S(t) represents the SOC of the energy storage system at time t, P ch (t) and P dis (t) respectively represent the charging power and discharging power of the energy storage system at time t, η ch and η dis They represent the charging efficiency and discharging efficiency of the energy storage system, E essIt represents the capacity of the energy storage system when it is fully charged, and Δt is the unit dispatching time;

[0036] The energy storage system constraints are expressed as: Where S is the SOC of the energy storage system, S min and S max is the minimum SOC and maximum SOC allowed by the energy storage system, p ch is the charging power of the energy storage system, is the maximum charging power allowed by the energy storage system, p dis is the discharge power of the energy storage system, is the maximum discharge power allowed by the energy storage system, S(0) represents the SOC of the energy storage system at the initial moment, and S(T) represents the SOC of the energy storage system at time T;

[0037] The operating constraints of the photovoltaic system are expressed as: Where E is a given sample set D = {x1, x2, ..., x m} and the photovoltaic data clusters C={C1,C2,...,C K}, μ i is the mean vector of the i-th photovoltaic data cluster.

[0038] The safety operation constraints include:

[0039] The constraints of the distribution network power flow equation are expressed as: Among them, U i,t and U j,t are the voltages of nodes i and j at time t, respectively, j,t and q j,t are the active injection power and reactive injection power of node j at time t, r ij and x ij are the resistance and reactance of branch ij, respectively, P ij,t and Q ij,t are the active power and reactive power of the first end of branch ij at time t, I ij,t is the current of branch ij at time t, P jk,t and Q jk,t are the active power and reactive power of the head end of branch jk at time t, respectively. k:j→k represents the set of child nodes with node j as the parent node.

[0040] The constraints for safe operation of distribution network are expressed as: Among them, U i is the voltage at node i, and V i max is the voltage lower and upper limits of node i; I ij is the current in branch ij, is the upper limit of the current of branch ij;

[0041] The access distributed generation penetration level constraint is expressed as: Where ρ is the distribution network penetration rate, P PV is the distributed photovoltaic active power output, P L is the active load of the system;

[0042] Voltage deviation constraint, expressed as: U N (1-ε1)≤U i ≤U N (1-ε2), where U N Rated voltage, ε1 and ε2 are both voltage deviation rates;

[0043] The reverse load rate constraint is expressed as: i ≤λ imax , where λ i represents the reverse load rate of the distribution transformer at node i, λ imax is the upper limit of the reverse load rate of the distribution transformer at node i.

[0044] The relaxation module comprises:

[0045] Introduce unit, used to introduce new matrix variables and in, and They are respectively the square of the voltage at node i and the square of the current at branch ij at time t;

[0046] Optimization unit for using matrix variables and By optimizing the constraints of the power flow equation of the distribution network, we can obtain:

[0047] The relaxation processing unit is used to use SOCP to adjust the constraints of the optimized distribution network power flow equation. Relax and convert to standard second-order cone form:

[0048] The technical solution adopted by the present invention to solve its technical problem is: to provide an electronic device, including a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the steps of the above-mentioned method for optimizing the location and configuration of a light storage constant capacity based on second-order cone convex relaxation are implemented.

[0049] The technical solution adopted by the present invention to solve its technical problem is: providing a computer-readable storage medium on which a computer program is stored, and when the computer program is executed by a processor, the steps of the above-mentioned method for optimizing the location and configuration of optical storage constant capacity based on second-order cone convex relaxation are implemented.

[0050] Beneficial Effects

[0051] Due to the adoption of the above-mentioned technical solution, the present invention has the following advantages and positive effects compared with the prior art: the photovoltaic storage capacity location optimization configuration method based on second-order cone convex relaxation provided by the present invention significantly improves the operating efficiency and economic benefits of the photovoltaic storage system in a high-penetration distribution network. By adopting the second-order cone relaxation technology, the present invention can convert a non-convex optimization problem into a convex optimization problem, so that the optimization process can ensure the global optimal solution. Compared with traditional heuristic methods and local optimization methods, the present invention comprehensively considers factors such as investment cost and voltage deviation during the optimization process, so that the final configuration scheme has significant advantages in terms of economy. By optimizing the location and capacity of the photovoltaic storage system, the present invention effectively improves the utilization rate of renewable energy, reduces dependence on traditional fossil energy, and is beneficial to environmental protection and energy conservation. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 It is a flow chart of the method for optimizing the location and configuration of a fixed-capacity optical storage system based on second-order cone convex relaxation according to the first embodiment of the present invention. DETAILED DESCRIPTION

[0053] The present invention will be further described below in conjunction with specific embodiments. It should be understood that these embodiments are only used to illustrate the present invention and are not intended to limit the scope of the present invention. In addition, it should be understood that after reading the content taught by the present invention, those skilled in the art can make various changes or modifications to the present invention, and these equivalent forms fall within the scope limited by the appended claims of the application equally.

[0054] The first embodiment of the present invention relates to a method for optimizing the location and configuration of photovoltaic and storage capacity based on second-order cone convex relaxation. This method aims at the problems of power quality degradation, voltage over-limit and reverse overload of distribution transformers when traditional substations need to be upgraded and equipped with photovoltaic and storage equipment, or when the penetration rate of distributed power sources in substations is increased. A multi-objective two-layer optimization configuration model is established. The optimal location and capacity configuration scheme for the target distribution network to access the distributed power sources is obtained by optimizing and solving the multi-objective two-layer optimization configuration model. This method can improve the power quality when the distributed power sources are connected to the distribution network and improve the absorption capacity of distributed photovoltaics while being economical. Figure 1 As shown, the specific steps include:

[0055] Step 1, construct a multi-objective two-layer optimization model based on the constraints of the operation of the photovoltaic system and the energy storage system. The multi-objective two-layer optimization model constructed in this embodiment includes an upper model and a lower model, wherein the output result of the upper model is the input of the lower model, the upper model is established with the goal of minimizing the reverse load rate and voltage deviation of the distribution transformer, and is used to select the grid-connected location, and the lower model is established with the goal of minimizing the daily comprehensive cost of energy storage and photovoltaics and the sum of the net load changes of nodes at adjacent times (i.e., energy storage participates in peak shaving and valley filling), and is used to determine the energy storage and photovoltaic configuration capacity.

[0056] In this step, the operating constraints of the photovoltaic system and the energy storage system include the operating constraints of the energy storage system, the energy storage system constraints and the operating constraints of the photovoltaic system.

[0057] The energy storage system in this embodiment can both provide active support to the distribution network and absorb power from the distribution network. Therefore, the operating constraints of the energy storage system can be expressed as:

[0058]

[0059] Where S(t) represents the SOC of the energy storage system at time t, P ch (t) and P dis (t) respectively represent the charging power and discharging power of the energy storage system at time t, η ch and η dis They represent the charging efficiency and discharging efficiency of the energy storage system, E ess It represents the capacity of the energy storage system when it is fully charged, and Δt is the unit scheduling time.

[0060] In this implementation, the energy storage system constraints can be expressed as:

[0061] S min ≤S≤S max

[0062]

[0063] S(0)=S(T)

[0064] Where S is the SOC of the energy storage system, S min and S max is the minimum SOC and maximum SOC allowed by the energy storage system, p ch is the charging power of the energy storage system, is the maximum charging power allowed by the energy storage system, p dis is the discharge power of the energy storage system, is the maximum discharge power allowed by the energy storage system, S(0) represents the SOC of the energy storage system at the initial moment, and S(T) represents the SOC of the energy storage system at time T.

[0065] In this implementation, K-means clustering is used to cluster photovoltaic data. Given a sample set D = {x1, x2, ..., x m}, measure the photovoltaic data clusters C = {C1, C2, ..., C K}, which can be measured by minimizing the average error. Therefore, the operating constraints of the photovoltaic system in this embodiment are expressed as:

[0066]

[0067] Among them, μ i is the mean vector of the i-th photovoltaic data cluster.

[0068] In this embodiment, when constructing the upper model, the reverse load rate and voltage deviation of the distribution transformer are minimized, so the upper model can be expressed as:

[0069]

[0070] Among them, f 上1 is the reverse load rate of the distribution transformer, f 上2 is the voltage deviation, P PV,i is the active output power of the photovoltaic node i, P load is the active power of the load, S e Indicates the rated capacity of the distribution transformer, U k is the voltage of node k, expressed as: U0 is the voltage at the power supply point, R i and X i are the line resistance and reactance between node i-1 and node i, respectively, P L,k and Q L,k are the active load and reactive load of node k respectively, P PV,k and Q PV,k are the active output power and reactive output power of the photovoltaic node k, U N is the rated voltage.

[0071] After the photovoltaic and storage grid-connected locations are determined through the upper model, the lower model is established with the daily comprehensive cost of energy storage and photovoltaics and the sum of the net load changes of nodes at adjacent times as the target. The lower model can be expressed as:

[0072] minf 下1 =f inv +f ope +f loss +f pun -f pva

[0073]

[0074] Among them, f 下1 is the daily comprehensive cost of energy storage and photovoltaics, f 下2 It is the sum of the changes in the net load of the nodes at adjacent moments.

[0075] f inv is the investment cost of the energy storage system, expressed as:

[0076]

[0077] Among them, F cr is the capital recovery coefficient, r is the discount rate, y is the service life of the energy storage system, Ω s is a set of typical scenarios, λ s is the probability of occurrence of scenario s, c p and c e are the unit power cost and unit capacity cost of the energy storage system respectively, and are the rated power and rated capacity of the nth energy storage system under scenario s, N e is the number of energy storage systems connected. ope is the operation and maintenance cost of the energy storage system, expressed as:

[0078]

[0079] Where T represents the charge and discharge operation time of the energy storage system, c o is the unit electricity operation and maintenance cost of the energy storage system, and They are respectively the charging power and discharging power of the nth energy storage system at time t under scenario s, and Δt is the unit scheduling duration.

[0080] f loss is the active network loss cost, expressed as:

[0081]

[0082] Among them, c pri,t is the time-of-use electricity price at time t, I s,ij,t is the current of branch ij at time t under scenario s, r ij is the resistance of branch ij.

[0083] f pun is the penalty cost for abandoning light, expressed as:

[0084]

[0085] Among them, N PV is the number of distributed photovoltaic connections, c punis the penalty cost of abandoned light per unit power, and They are respectively the predicted output and actual dispatched output of the mth distributed photovoltaic unit at time t under scenario s.

[0086] f pva is the peak-to-valley arbitrage profit, expressed as:

[0087]

[0088] is the grid power at time t under scenario s, expressed as:

[0089]

[0090] Among them, P t l is the load at time t, is the output of distributed photovoltaic power at time t under scenario s.

[0091] Step 2: Constrain the multi-objective two-level optimization model using safe operation constraints. The safe operation constraints in this step include distribution network power flow equation constraints, distribution network safe operation constraints, distributed generation penetration level constraints, voltage deviation constraints, and reverse load rate constraints.

[0092] The power flow equation constraint condition of the distribution network in this embodiment is based on the DistFlow power flow equation, which regards the distribution network as a network composed of multiple branches, and finally obtains the power flow distribution of the entire network by recursively calculating the branch current and node voltage. The power flow equation constraint condition of the distribution network can be expressed as:

[0093]

[0094] Among them, U i,t and U j,t are the voltages of nodes i and j at time t, respectively, j,t and q j,t are the active injection power and reactive injection power of node j at time t, r ij and x ij are the resistance and reactance of branch ij, respectively, P ij,t and Q ij,t are the active power and reactive power of the first end of branch ij at time t, I ij,t is the current of branch ij at time t, P jk,t and Q jk,t are the active power and reactive power of the head end of branch jk at time t, respectively. k:j→k represents the set of child nodes with node j as the parent node.

[0095] The constraints for safe operation of distribution network can be expressed as:

[0096]

[0097] Among them, U i is the voltage at node i, V i min and V i max is the voltage lower and upper limits of node i; I ij is the current in branch ij, is the upper limit of the current in branch ij.

[0098] The access distributed generation penetration level constraint can be expressed as:

[0099]

[0100] Where ρ is the distribution network penetration rate, P PV is the distributed photovoltaic active power output, P L is the active load of the system.

[0101] The voltage deviation constraint can be expressed as:

[0102] U N (1-ε1)≤U i ≤U N (1-ε2)

[0103] Among them, U N Rated voltage, ε1 and ε2 are both voltage deviation rates. Normally, the voltage deviation of a 10kV power supply line is ±7% of the reference voltage.

[0104] The reverse load rate constraint can be expressed as:

[0105] λ i ≤λ imax

[0106] Among them, λ i represents the reverse load rate of the distribution transformer at node i, λ imax is the upper limit of the reverse load rate of the distribution transformer at node i. Normally, according to the “Guidelines for Assessment of the Carrying Capacity of Distributed Generation Access to the Grid”, the reverse load rate shall not exceed 80%.

[0107] Step 3: Use the second-order cone convex relaxation technology to relax the distribution network power flow equation constraints in the safe operation constraints, and convert the multi-objective two-layer optimization model into a distributed photovoltaic storage collaborative optimization configuration model.

[0108] In this step, the second-order cone convex relaxation technology is used to relax the distribution network power flow equation constraints in the safe operation constraints, specifically:

[0109] Introducing new matrix variables and in, and They are respectively the square of the voltage at node i and the square of the current at branch ij at time t;

[0110] Using Matrix Variables and By optimizing the constraints of the power flow equation of the distribution network, we can obtain:

[0111] Use SOCP to optimize the constraints of the power flow equation of the distribution network. Relax and convert to standard second-order cone form:

[0112] After being processed by the above-mentioned second-order cone relaxation technology, the originally non-convex optimization problem can be converted into a convex optimization problem, so that the optimization process can ensure the acquisition of the global optimal solution.

[0113] Step 4, use a commercial solver to iteratively calculate the distributed photovoltaic storage collaborative optimization configuration model to determine the optimal location and optimal capacity configuration of the target distribution network to access the distributed power source. The commercial solver used in this step can be YALMIP or CPLEX. Solving with a mature commercial solver can greatly improve the efficiency of solving the optimization problem. Experimental data show that the application of the method of this embodiment in a large-scale distribution network significantly reduces the optimization solution time and can obtain the optimal configuration solution within a reasonable computing time.

[0114] It is not difficult to find that the photovoltaic storage capacity location optimization configuration method based on second-order cone convex relaxation provided by the present invention significantly improves the operating efficiency and economic benefits of the photovoltaic storage system in a high-penetration distribution network. Compared with traditional heuristic methods and local optimization methods, the present invention comprehensively considers factors such as investment cost and voltage deviation during the optimization process, so that the final configuration scheme has significant advantages in terms of economy. By optimizing the location and capacity of the photovoltaic storage system, the present invention effectively improves the utilization rate of renewable energy, reduces dependence on traditional fossil energy, and is beneficial to environmental protection and energy conservation.

[0115] The second embodiment of the present invention relates to a device for optimizing the location and configuration of a light storage constant volume based on second-order cone convex relaxation, comprising:

[0116] A construction module is used to construct a multi-objective two-layer optimization model based on the constraints of the operation of the photovoltaic system and the energy storage system. The multi-objective two-layer optimization model includes an upper model and a lower model, wherein the output result of the upper model is the input of the lower model, the upper model is established with the goal of minimizing the reverse load rate and voltage deviation of the distribution transformer, and is used to select the grid-connected location, and the lower model is established with the goal of minimizing the sum of the daily comprehensive cost of energy storage and photovoltaics and the net load change of nodes at adjacent times, and is used to determine the energy storage and photovoltaic configuration capacity;

[0117] A constraint module, used to constrain the multi-objective two-level optimization model using safe operation constraints;

[0118] A relaxation module, used for relaxing the distribution network power flow equation constraint in the safety operation constraint by using the second-order cone convex relaxation technology, and converting the multi-objective two-layer optimization model into a distributed photovoltaic storage collaborative optimization configuration model;

[0119] The solution module is used to use a commercial solver to iteratively calculate the distributed photovoltaic storage collaborative optimization configuration model to determine the optimal location and optimal capacity configuration for the target distribution network to access the distributed power source.

[0120] The upper model constructed by the building block is: Among them, f 上1 is the reverse load rate of the distribution transformer, f 上2 is the voltage deviation, P PV,i is the active output power of the photovoltaic node i, P load is the active power of the load, S e Indicates the rated capacity of the distribution transformer, U k is the voltage of node k, expressed as: U0 is the voltage at the power supply point, R i and X i are the line resistance and reactance between node i-1 and node i, respectively, P L,k and Q L,k are the active load and reactive load of node k respectively, P PV,k and Q PV,k are the active output power and reactive output power of the photovoltaic node k, U N is the rated voltage.

[0121] The lower model constructed by the building block is: Among them, f 下1 is the daily comprehensive cost of energy storage and photovoltaics, f 下2 is the sum of the changes in the net load of the nodes at adjacent moments, f inv is the investment cost of the energy storage system, expressed as: fope is the operation and maintenance cost of the energy storage system, expressed as: f loss is the active network loss cost, expressed as: f pun is the penalty cost for abandoning light, expressed as: f pva is the peak-to-valley arbitrage profit, expressed as: F cr is the capital recovery coefficient, Ω s is a set of typical scenarios, λ s is the probability of occurrence of scenario s, c p and c e are the unit power cost and unit capacity cost of the energy storage system respectively, and are the rated power and rated capacity of the nth energy storage system under scenario s, N e is the number of energy storage systems connected, T represents the charge and discharge operation time of the energy storage system, c o is the unit electricity operation and maintenance cost of the energy storage system, and are the charging power and discharging power of the nth energy storage system at time t under scenario s, Δt is the unit scheduling duration, c pri,t is the time-of-use electricity price at time t, I s,ij,t is the current of branch ij at time t under scenario s, r ij is the resistance of branch ij, N PV is the number of distributed photovoltaic connections, c pun is the penalty cost of abandoned light per unit power, and are the predicted output and actual dispatched output of the mth distributed photovoltaic unit at time t under scenario s, is the grid power at time t under scenario s, expressed as: is the load at time t, is the output of distributed photovoltaic power at time t under scenario s.

[0122] The constraints for the operation of the photovoltaic system and the energy storage system include:

[0123] The operating constraints of the energy storage system are expressed as: Where S(t) represents the SOC of the energy storage system at time t, P ch (t) and P dis (t) respectively represent the charging power and discharging power of the energy storage system at time t, η ch and η dis They represent the charging efficiency and discharging efficiency of the energy storage system, E essIt represents the capacity of the energy storage system when it is fully charged, and Δt is the unit dispatching time;

[0124] The energy storage system constraints are expressed as: Where S is the SOC of the energy storage system, S min and S max is the minimum SOC and maximum SOC allowed by the energy storage system, p ch is the charging power of the energy storage system, is the maximum charging power allowed by the energy storage system, p dis is the discharge power of the energy storage system, is the maximum discharge power allowed by the energy storage system, S(0) represents the SOC of the energy storage system at the initial moment, and S(T) represents the SOC of the energy storage system at time T;

[0125] The operating constraints of the photovoltaic system are expressed as: Where E is a given sample set D = {x1, x2, ..., x m} and the photovoltaic data clusters C={C1,C2,...,C K}, μ i is the mean vector of the i-th photovoltaic data cluster.

[0126] The safety operation constraints include:

[0127] The constraints of the distribution network power flow equation are expressed as: Among them, U i,t and U j,t are the voltages of nodes i and j at time t, respectively, j,t and q j,t are the active injection power and reactive injection power of node j at time t, r ij and x ij are the resistance and reactance of branch ij, respectively, P ij,t and Q ij,t are the active power and reactive power of the first end of branch ij at time t, I ij,t is the current of branch ij at time t, P jk,t and Q jk,t are the active power and reactive power of the head end of branch jk at time t, respectively. k:j→k represents the set of child nodes with node j as the parent node.

[0128] The constraints for safe operation of distribution network are expressed as: Among them, U i is the voltage at node i, V i min and V i max is the voltage lower and upper limits of node i; Iij is the current in branch ij, is the upper limit of the current of branch ij;

[0129] The access distributed generation penetration level constraint is expressed as: Where ρ is the distribution network penetration rate, P PV is the distributed photovoltaic active power output, P L is the active load of the system;

[0130] Voltage deviation constraint, expressed as: U N (1-ε1)≤U i ≤U N (1-ε2), where U N Rated voltage, ε1 and ε2 are both voltage deviation rates;

[0131] The reverse load rate constraint is expressed as: i ≤λ imax , where λ i represents the reverse load rate of the distribution transformer at node i, λ imax is the upper limit of the reverse load rate of the distribution transformer at node i.

[0132] The relaxation module comprises:

[0133] Introduce unit, used to introduce new matrix variables and in, and They are respectively the square of the voltage at node i and the square of the current at branch ij at time t;

[0134] Optimization unit for using matrix variables and By optimizing the constraints of the power flow equation of the distribution network, we can obtain:

[0135] The relaxation processing unit is used to use SOCP to adjust the constraints of the optimized distribution network power flow equation. Relax and convert to standard second-order cone form:

[0136] The third embodiment of the present invention relates to an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the steps of the optical storage constant capacity site selection optimization configuration method based on second-order cone convex relaxation of the first embodiment are implemented.

[0137] The fourth embodiment of the present invention relates to a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the steps of the method for optimizing the location of a light storage constant capacity based on second-order cone-convex relaxation of the first embodiment.

[0138] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment in combination with software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage and optical storage, etc.) that contain computer-usable program code.

[0139] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0140] These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory produce a manufactured product including an instruction method, which is implemented in the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0141] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

Claims

1. A method for optimizing the location and configuration of a fixed-capacity solar energy storage system based on second-order cone convex relaxation, characterized in that: The following steps are involved: A multi-objective two-layer optimization model is constructed based on the constraints of the operation of the photovoltaic system and the energy storage system. The multi-objective two-layer optimization model includes an upper model and a lower model, wherein the output result of the upper model is the input of the lower model. The upper model is established with the goal of minimizing the reverse load rate and voltage deviation of the distribution transformer, and is used to select the grid-connected location. The lower model is established with the goal of minimizing the sum of the daily comprehensive cost of energy storage and photovoltaics and the net load change of nodes at adjacent times, and is used to determine the energy storage and photovoltaic configuration capacity. Using safe operation constraints to constrain the multi-objective two-level optimization model; The second-order cone convex relaxation technology is used to relax the distribution network power flow equation constraint in the safe operation constraint, and the multi-objective two-layer optimization model is converted into a distributed photovoltaic storage collaborative optimization configuration model; The distributed photovoltaic and energy storage collaborative optimization configuration model is iteratively calculated using a commercial solver to determine the optimal location and optimal capacity configuration for the target distribution network to access the distributed power source.

2. The method for optimizing the location and configuration of a photovoltaic storage system based on second-order cone convex relaxation according to claim 1 is characterized in that: The upper model is: Among them, f 上1 is the reverse load rate of the distribution transformer, f 上2 is the voltage deviation, P PV,i is the active output power of the photovoltaic node i, P load is the active power of the load, S e Indicates the rated capacity of the distribution transformer, U k is the voltage of node k, expressed as: U0 is the voltage at the power supply point, R i and X i are the line resistance and reactance between node i-1 and node i, respectively, P L,k and Q L,k are the active load and reactive load of node k respectively, P PV,k and Q PV,k are the active output power and reactive output power of the photovoltaic node k, U N is the rated voltage.

3. The method for optimizing the location and configuration of a photovoltaic storage system based on second-order cone convex relaxation according to claim 1 is characterized in that: The underlying model is: Among them, f 下1 is the daily comprehensive cost of energy storage and photovoltaics, f 下2 is the sum of the changes in the net load of the nodes at adjacent moments, f inv is the investment cost of the energy storage system, expressed as: f ope is the operation and maintenance cost of the energy storage system, expressed as: f loss is the active network loss cost, expressed as: f pun is the penalty cost for abandoning light, expressed as: f pva is the peak-to-valley arbitrage profit, expressed as: F cr is the capital recovery coefficient, Ω s is a set of typical scenarios, λ s is the probability of occurrence of scenario s, c p and c e are the unit power cost and unit capacity cost of the energy storage system respectively, and are the rated power and rated capacity of the nth energy storage system under scenario s, N e is the number of energy storage systems connected, T represents the charge and discharge operation time of the energy storage system, c o is the unit electricity operation and maintenance cost of the energy storage system, and are the charging power and discharging power of the nth energy storage system at time t under scenario s, Δt is the unit scheduling duration, c pri,t is the time-of-use electricity price at time t, I s,ij,t is the current of branch ij at time t under scenario s, r ij is the resistance of branch ij, N PV is the number of distributed photovoltaic connections, c pun is the penalty cost of abandoned light per unit power, and are the predicted output and actual dispatched output of the mth distributed photovoltaic unit at time t under scenario s, is the grid power at time t under scenario s, expressed as: is the load at time t, is the output of distributed photovoltaic power at time t under scenario s.

4. The method for optimizing the location and configuration of a photovoltaic storage system based on second-order cone convex relaxation according to claim 1 is characterized in that: The constraints for the operation of the photovoltaic system and the energy storage system include: The operating constraints of the energy storage system are expressed as: Where S(t) represents the SOC of the energy storage system at time t, P ch (t) and P dis (t) respectively represent the charging power and discharging power of the energy storage system at time t, η ch and η dis They represent the charging efficiency and discharging efficiency of the energy storage system, E ess Indicates the capacity of the energy storage system when it is fully charged. Δt is the unit scheduling duration; The energy storage system constraints are expressed as: Where S is the SOC of the energy storage system, S min and S max is the minimum SOC and maximum SOC allowed by the energy storage system, p ch is the charging power of the energy storage system, is the maximum charging power allowed by the energy storage system, p dis is the discharge power of the energy storage system, is the maximum discharge power allowed by the energy storage system, S(0) represents the SOC of the energy storage system at the initial moment, and S(T) represents the SOC of the energy storage system at time T; The operating constraints of the photovoltaic system are expressed as: Where E is a given sample set D = {x1, x2, ..., x m } and the photovoltaic data clusters C={C1,C2,...,C K }, μ i is the mean vector of the i-th photovoltaic data cluster.

5. The method for optimizing the location and configuration of a photovoltaic storage system based on second-order cone convex relaxation according to claim 1 is characterized in that: The safety operation constraints include: The constraints of the distribution network power flow equation are expressed as: Among them, U i,t and U j,t are the voltages of nodes i and j at time t, respectively, j,t and q j,t are the active injection power and reactive injection power of node j at time t, r ij and x ij are the resistance and reactance of branch ij, respectively, P ij,t and Q ij,t are the active power and reactive power of the first end of branch ij at time t, I ij,t is the current of branch ij at time t, P jk,t and Q jk,t are the active power and reactive power of the first end of branch jk at time t, respectively. k:j→k represents the set of child nodes with node j as the parent node. The constraints for safe operation of the distribution network are expressed as: Among them, U i is the voltage at node i, and is the voltage lower and upper limits of node i; I ij is the current in branch ij, is the upper limit of the current of branch ij; The access distributed generation penetration level constraint is expressed as: Where ρ is the distribution network penetration rate, P PV is the distributed photovoltaic active power output, P L is the active load of the system; Voltage deviation constraint, expressed as: U N (1-ε1)≤U i ≤U N (1-ε2), where U N Rated voltage, ε1 and ε2 are both voltage deviation rates; The reverse load rate constraint is expressed as: i ≤λ imax , where λ i represents the reverse load rate of the distribution transformer at node i, λ imax is the upper limit of the reverse load rate of the distribution transformer at node i.

6. The method for optimizing the location and configuration of a photovoltaic storage system based on second-order cone convex relaxation according to claim 5 is characterized in that: The second-order cone convex relaxation technique is used to relax the power distribution network flow equation constraint condition in the safe operation constraint condition, specifically including: Introducing new matrix variables and in, and They are respectively the square of the voltage at node i and the square of the current at branch ij at time t; Using Matrix Variables and By optimizing the constraints of the power flow equation of the distribution network, we can obtain: Use SOCP to optimize the constraints of the power flow equation of the distribution network. Relax and convert to standard second-order cone form:

7. A device for optimizing the location and configuration of a light storage constant volume based on second-order cone convex relaxation, characterized in that: include: A construction module is used to construct a multi-objective two-layer optimization model based on the constraints of the operation of the photovoltaic system and the energy storage system. The multi-objective two-layer optimization model includes an upper model and a lower model, wherein the output result of the upper model is the input of the lower model, the upper model is established with the goal of minimizing the reverse load rate and voltage deviation of the distribution transformer, and is used to select the grid-connected location, and the lower model is established with the goal of minimizing the sum of the daily comprehensive cost of energy storage and photovoltaics and the net load change of nodes at adjacent times, and is used to determine the energy storage and photovoltaic configuration capacity; A constraint module, used to constrain the multi-objective two-level optimization model using safe operation constraints; A relaxation module is used to relax the distribution network power flow equation constraints in the safe operation constraints using the second-order cone convex relaxation technology, and convert the multi-objective two-layer optimization model into a distributed photovoltaic and storage collaborative optimization configuration model; a solution module is used to iteratively calculate the distributed photovoltaic and storage collaborative optimization configuration model using a commercial solver to determine the optimal location and optimal capacity configuration for the target distribution network to connect to the distributed power source.

8. The device for optimizing the location and configuration of a light storage constant volume based on second-order cone convex relaxation according to claim 7 is characterized in that: The upper model constructed by the building block is: Among them, f 上1 is the reverse load rate of the distribution transformer, f 上2 is the voltage deviation, P PV,i is the active output power of the photovoltaic node i, P load is the active power of the load, S e Indicates the rated capacity of the distribution transformer, U k is the voltage of node k, expressed as: U0 is the voltage at the power supply point, R i and X i are the line resistance and reactance between node i-1 and node i, respectively, P L,k and Q L,k are the active load and reactive load of node k respectively, P PV,k and Q PV,k are the active output power and reactive output power of the photovoltaic node k, U N is the rated voltage.

9. The device for optimizing the location and configuration of a light storage constant volume based on second-order cone convex relaxation according to claim 7, characterized in that: The lower model constructed by the building block is: Among them, f 下1 is the daily comprehensive cost of energy storage and photovoltaics, f 下2 is the sum of the changes in the net load of the nodes at adjacent moments, f inv is the investment cost of the energy storage system, expressed as: f ope is the operation and maintenance cost of the energy storage system, expressed as: f loss is the active network loss cost, expressed as: f pun is the penalty cost for abandoning light, expressed as: f pva is the peak-to-valley arbitrage profit, expressed as: F cr is the capital recovery coefficient, Ω s is a set of typical scenarios, λ s is the probability of occurrence of scenario s, c p and c e are the unit power cost and unit capacity cost of the energy storage system respectively, and are the rated power and rated capacity of the nth energy storage system under scenario s, N e is the number of energy storage systems connected, T represents the charge and discharge operation time of the energy storage system, c o is the unit electricity operation and maintenance cost of the energy storage system, and are the charging power and discharging power of the nth energy storage system at time t under scenario s, Δt is the unit scheduling duration, c pri,t is the time-of-use electricity price at time t, I s,ij,t is the current of branch ij at time t under scenario s, r ij is the resistance of branch ij, N PV is the number of distributed photovoltaic connections, c pun is the penalty cost of abandoned light per unit power, and are the predicted output and actual dispatched output of the mth distributed photovoltaic unit at time t under scenario s, is the grid power at time t under scenario s, expressed as: is the load at time t, is the output of distributed photovoltaic power at time t under scenario s.

10. The device for optimizing the location and configuration of a light storage constant volume based on second-order cone convex relaxation according to claim 7, characterized in that: The constraints for the operation of the photovoltaic system and the energy storage system include: The operating constraints of the energy storage system are expressed as: Where S(t) represents the SOC of the energy storage system at time t, P ch (t) and P dis (t) respectively represent the charging power and discharging power of the energy storage system at time t, η ch and η dis They represent the charging efficiency and discharging efficiency of the energy storage system, E ess Indicates the capacity of the energy storage system when it is fully charged. Δt is the unit scheduling duration; The energy storage system constraints are expressed as: Where S is the SOC of the energy storage system, S min and S max is the minimum SOC and maximum SOC allowed by the energy storage system, p ch is the charging power of the energy storage system, is the maximum charging power allowed by the energy storage system, p dis is the discharge power of the energy storage system, is the maximum discharge power allowed by the energy storage system, S(0) represents the SOC of the energy storage system at the initial moment, and S(T) represents the SOC of the energy storage system at time T; The operating constraints of the photovoltaic system are expressed as: Where E is a given sample set D = {x1, x2, ..., x m } and the photovoltaic data clusters C={C1,C2,...,C K }, μ i is the mean vector of the i-th photovoltaic data cluster.

11. The device for optimizing the location and configuration of a light storage constant volume based on second-order cone convex relaxation according to claim 7, characterized in that: The safety operation constraints include: The constraints of the distribution network power flow equation are expressed as: Among them, U i,t and U j,t are the voltages of nodes i and j at time t, respectively, j,t and q j,t are the active injection power and reactive injection power of node j at time t, r ij and x ij are the resistance and reactance of branch ij, respectively, P ij,t and Q ij,t are the active power and reactive power of the first end of branch ij at time t, I ij,t is the current of branch ij at time t, P jk,t and Q jk,t are the active power and reactive power of the first end of branch jk at time t, respectively. k:j→k represents the set of child nodes with node j as the parent node. The constraints for safe operation of the distribution network are expressed as: Among them, U i is the voltage at node i, and is the voltage lower limit and upper limit of node i; I ij is the current in branch ij, is the upper limit of the current of branch ij; The access distributed generation penetration level constraint is expressed as: Where ρ is the distribution network penetration rate, P PV is the distributed photovoltaic active power output, P L is the active load of the system; Voltage deviation constraint, expressed as: U N (1-ε1)≤U i ≤U N (1-ε2), where U N Rated voltage, ε1 and ε2 are both voltage deviation rates; The reverse load rate constraint is expressed as: i ≤λ imax , where λ i represents the reverse load rate of the distribution transformer at node i, λ imax is the upper limit of the reverse load rate of the distribution transformer at node i.

12. The device for optimizing the location and configuration of a light storage constant volume based on second-order cone convex relaxation according to claim 11, characterized in that: The relaxation module comprises: Introduce unit, used to introduce new matrix variables and in, and They are respectively the square of the voltage at node i and the square of the current at branch ij at time t; Optimization unit for using matrix variables and By optimizing the constraints of the power flow equation of the distribution network, we can obtain: The relaxation processing unit is used to use SOCP to adjust the constraints of the optimized distribution network power flow equation. Relax and convert to standard second-order cone form:

13. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the computer program, the steps of the method for optimizing the location and configuration of a light storage constant capacity based on second-order cone convex relaxation as described in any one of claims 1 to 6 are implemented.

14. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of the method for optimizing the location and configuration of a light storage constant capacity based on second-order cone convex relaxation as described in any one of claims 1 to 6 are implemented.

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