Fixed demand-based preset time distributed power system economic dispatching method

Abstract

The invention discloses an economic dispatching method for a preset time distributed power system based on a fixed demand. The method comprises the steps of 1, describing an economic dispatching problem as a convex optimization problem with fixed constraints, and constructing a model of a power system; 2, based on the model of the power system, designing a preset time distributed economic dispatching algorithm under fixed constraints, and converging to an optimal solution before time Tc; and step 3, applying the algorithm to a model of the power system, and solving a convex optimization problem under a fixed demand in the power system, that is, optimizing the output power of each generator, and minimizing the sum of the costs of all generators under the condition of ensuring that the output of all generators meets the demand. According to the method, a central processing unit is not needed, each node in the network only needs to exchange own state information with the neighbor node, the optimal value of the economic dispatching problem can be solved, the communication cost is reduced, and the system energy is saved. Meanwhile, the system can accurately converge to the optimal solution before the predefined time.

Description

Technical Field

[0001] The present invention belongs to the technical field of power system dispatching, and in particular relates to an economic dispatching method for a preset time distributed power system based on fixed demand. Background Art

[0002] At present, the commonly used existing technology in the industry is that distributed optimization algorithms play a vital role in the application of power systems, especially in the field of economic dispatch. Its core goal is to reduce the overall power generation cost as much as possible on the basis of ensuring the balance between power supply and demand. Traditional economic dispatch is usually carried out in a centralized system, which relies on a central data processing center to complete the collection, processing and transmission of data. The center uses a centralized optimization algorithm to determine the optimal solution and pass the results to each power generation unit. However, there are some obvious shortcomings in the centralized system.

[0003] First, once a data processing center fails, it may cause the entire system to be interrupted. Second, in the centralized processing process, a large amount of data needs to be processed, which not only increases the computing burden but also increases the cost.

[0004] In order to solve these problems, distributed economic dispatch methods have gradually received attention and developed.

[0005] In a distributed framework, each generator only communicates and interacts with neighboring nodes, and performs local calculations according to the designed distributed algorithm, which greatly reduces the cost of communication network construction and improves fault tolerance. Compared with the traditional centralized framework, when solving economic scheduling problems under a distributed framework, due to the dispersion of tasks, on the one hand, expensive data processing centers are no longer required, and on the other hand, the system fault tolerance is enhanced. At the same time, since nodes only communicate with their neighboring nodes, the communication cost is greatly reduced and the system energy is saved. In addition, most of the existing distributed methods are asymptotically convergent, finite time convergent, or fixed time convergent. Such methods cannot know whether the network has reached convergence, or require complex calculations, which is extremely inconvenient and costly in actual engineering use. The preset time algorithm solves this problem well, but in existing research, the preset time algorithm makes the convergence value of the system have a certain error and cannot converge accurately.

[0006] To sum up, how to solve the economic scheduling problem while artificially setting the convergence time of the network so that the system can converge accurately is a very important issue. Summary of the invention

[0007] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the present invention is to provide a method for economic dispatch of a distributed power system with a preset time based on fixed demand. This method does not require a central processor, and each node in the network only needs to communicate its own state information with neighboring nodes to achieve the solution of the optimal value of the economic dispatch problem, thereby reducing communication costs and saving system energy. At the same time, the system can accurately converge to the optimal solution before the predefined time.

[0008] In order to achieve the above object, the technical solution adopted by the present invention is:

[0009] A method for economic dispatching of a distributed power system with preset time based on fixed demand, comprising the following steps;

[0010] Step 1: Describe the economic dispatch problem as a convex optimization problem with fixed constraints and build a model of the power system;

[0011] Step 2: Based on the power system model described in step 1, a preset time distributed economic dispatch algorithm under fixed constraints is designed. The algorithm is c Converged to the optimal solution before;

[0012] Step 3: Apply the algorithm designed in step 2 to the model of the power system described in step 1 to solve the convex optimization problem under fixed demand in the power system. By optimizing the output power of each generator, the sum of the costs of all generators is minimized while ensuring that the output of all generators meets the demand.

[0013] The step 1 is specifically as follows:

[0014] The total power demand D at the current moment is sent to any node in the power system, each generator set in the power system is regarded as a node, and an upper limit T of the acceptable convergence time is set c , the model of the power system is expressed as:

[0015]

[0016]

[0017] Where P(t)=[P1(t),P2(t),…,P N (t)] T ∈R N The output power of the generator is used as the decision vector, and the total required power D is used as the global constraint variable; i (P i (t)) is the cost of the i-th node at the current moment, α i ,β i ,γ iis the cost coefficient of the ith node, and f(P(t)) is the total cost of the power system at the current moment.

[0018] Furthermore, each generator set in the power system model described in step 1 only knows its own local objective function f i (P i (t)), the global objective function f(P(t)) is the sum of all local objective functions, that is N is the number of nodes. The generator sets calculate the global optimal solution through interactive sharing of local information. Information is shared through communication links between nodes, so that nodes with communication links can obtain information sent by each other.

[0019] In step 2, based on the model of the power system in step 1, according to the preset time distributed economic dispatch algorithm under fixed constraints, through mutual communication between nodes and neighboring nodes, the node with a direct communication link connection to a node is the neighboring node of the node, and the auxiliary variable q at the current moment is obtained. i The value of (t), the auxiliary variable is the information of the interaction between nodes, which does not contain any real physical information. Therefore, it has the ability to protect privacy;

[0020] Based on the calculated values ​​of auxiliary variables, the optimization variable P is optimized by using the preset time distributed economic dispatch algorithm under fixed constraints. i (t) is updated, and finally the i-th (i=1,2,…,N) generation node of the power system is dispatched according to the optimal value P i * Under this scheduling method, the power generation cost of the power system can be guaranteed to be c before reaching the minimum.

[0021] The preset time distributed economic dispatch algorithm under fixed constraints in step 2 is as follows:

[0022]

[0023] Among them, P i (t) is the dynamic optimization value of the i-th generator set at time t, and the initial value must meet the condition D is the target total power demand; q i (t) is an auxiliary variable, which represents the updated Lagrangian value of the i-th generator set at time t, i = 1, 2, ..., N; α i and β i is the cost coefficient of the ith generator set; s(t) is a custom function defined as c is a normal number, T c is a predefined time.

[0024] Since the auxiliary variable information q in the node interaction algorithm i (t), avoiding the transmission of original information in the network and improving privacy and security.

[0025] The step 3 is specifically as follows:

[0026] Select the Lyapunov function as prove It further proves that V can c Before it converges to 0 exactly, that is, the auxiliary variables q of all generators i , i=1,2,...,N are all within the preset time T c Converge to their weighted average within That is q i Converges to the Lagrangian optimal value λ * , prove the convergence time Substitute into the power update function The optimal solution of the original convex optimization problem with dynamic constraints is in, represents the weight of the i-th generator group, ω=[ω1,ω2,...,ω N ] T ; q=[q1,q2,...,q N ] T , m is a fixed constant, α i ,β i is the cost coefficient of the generator, q * for q i The final consistent value.

[0027] Through the above process, the preset time distributed economic dispatch algorithm under the fixed constraints in step 2 can make the output power of all generators meet the demand, and the sum of the costs of each generator reaches the global minimum. Each generator only exchanges information with some generators, and does not require fully connected communication conditions, which greatly reduces the communication cost.

[0028] The preset time T c It is only the upper bound of the time it takes for the system to converge to the optimal solution. The convergence time of the system is t<T c , after the system reaches convergence, the state of the system will maintain the optimal solution operation.

[0029] Beneficial effects of the present invention:

[0030] The present invention transforms the economic dispatch problem into a convex optimization problem with fixed constraints. Due to the use of a distributed algorithm, the entire network does not require a central processor, and each generator node only needs to communicate its own state information with its neighboring nodes. That is, in the preset time distributed economic dispatch algorithm under the fixed constraints, q i (t) is the auxiliary variable information q of the i-th node i ,q j (t) is the auxiliary variable information q of the neighbor node j of the i-th node i By designing a preset time distributed economic scheduling algorithm under fixed constraints, all nodes will be guaranteed to be at the optimal solution before the preset time.

[0031] In step 3 of the present invention, it is only necessary to set a preset time T c , then the convergence time of the system is t <T c Moreover, the cost of the system can accurately reach the global minimum without error, which improves the accuracy and convergence speed of the preset time economic scheduling method and reduces the cost of using the algorithm for users. The present invention lays a theoretical foundation for solving problems such as economic scheduling and demand invariance that can be transformed into convex optimization problems with fixed constraints. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a flow chart of a method for economic dispatching of a distributed power system at a preset time based on fixed demand provided by an embodiment of the present invention.

[0033] Figure 2 It is a schematic diagram of a four-node communication topology provided by an embodiment of the present invention.

[0034] Figure 3 is the auxiliary variable q provided in the embodiment of the present invention i (t) change curve.

[0035] Figure 4 is the power P output by the generator i provided in the embodiment of the present invention i (t) change curve.

[0036] Figure 5 is the cost C of running the generator i provided by the embodiment of the present invention i (t) change curve.

[0037] Figure 6 It is a curve diagram of the change of the total cost C(t) of the microgrid operation provided by the embodiment of the present invention. DETAILED DESCRIPTION

[0038] The present invention will be further described in detail below in conjunction with the accompanying drawings.

[0039] like Figure 1As shown, the preset time distributed economic scheduling problem under fixed constraints provided by an embodiment of the present invention includes the following steps:

[0040] S101: The economic dispatch problem is described as a convex optimization problem with fixed constraints as follows: It is used to transform the practical problem into a mathematical optimization problem, which facilitates the development of relevant algorithms to solve the problem;

[0041]

[0042]

[0043] Where P(t)=[P1(t),P2(t),…,P N (t)] T ∈R N is the decision vector, D is the global constraint variable, i.e., the total required power, f i (P i (t)) is the cost of the ith node at the current moment, and f(P(t)) is the total cost of the power system at the current moment.

[0044] S102: Design a preset time distributed economic scheduling algorithm under fixed constraints: used to enable each node to iterate the optimal value at the current moment through distributed communication, so as to keep the total cost of the system to the minimum;

[0045]

[0046] Among them, P i (t) is the dynamic optimization value of the i-th node at time t, and the initial value must meet the condition D is the target total power demand; q i (t) is an auxiliary variable, which represents the Lagrangian value updated by the i-th node at time t, i = 1, 2, ..., N; α i and β i is the cost coefficient of the ith node; s(t) is a custom function defined as c is a normal number, T c is a predefined time.

[0047] In the above distributed algorithm, network node i monitors its own state variable q i (t), and transmit it to neighboring nodes. Since the nodes interact with each other to avoid the transmission of original information in the network, privacy and security are improved.

[0048] S103: When the network topology is an undirected connected graph, the convex optimization problem under fixed constraints can be solved by selecting appropriate adjustable parameters. prove It further proves that V can c Previously, it converged to 0 exactly, that is, the auxiliary variables q of all nodes i , i=1,2,...,N are all within the preset time T c Converge to their weighted average within That is q i Converges to the Lagrangian optimal value λ * , it can be proved that the convergence time Substitute into the power update function The optimal solution of the original convex optimization problem with dynamic constraints is The preset time T c It is only the upper bound of the time it takes for the system to converge to the optimal solution. The convergence time of the system is t<T c , after the system reaches convergence, the state of the system will maintain the optimal solution operation.

[0049] where q * is the optimal value of the variable q(t) in the algorithm described in S102, P i * is the variable P in the algorithm described in S102 i The other parameters are the same as those described in S102.

[0050] The effects of the application embodiments of the present invention are further described below in conjunction with simulation.

[0051] Taking the economic dispatch problem of microgrid system as an example, numerical simulation is carried out. Assume that there are four generator nodes in the microgrid system, and its communication topology is as follows: Figure 2 The figure shows an undirected connected graph. The economic dispatch problem of this microgrid system is:

[0052]

[0053]

[0054] Among them, α i ,β i ,γ i is the cost coefficient, and the specific parameter values ​​are shown in Table 1; P i is the active power of the ith generator set; C is the total cost function; D is the total load demand.

[0055] In this microgrid system, each generator only needs to establish a communication link with some of the generators. Figure 2In the communication topology, each node represents a generator set. Each generator set has the ability to run the algorithm independently. When the system is working, it is necessary to set the total demand of the entire system for one of the generator sets, and set a unified preset time (the maximum acceptable convergence time) for all the generator sets. The generator sets in the system can continuously optimize their output power through the distribution used to achieve the global minimum cost.

[0056] Table 1 Cost coefficient

[0057]

[0058]

[0059] Total load demand D = 870MW, preset time is set to T c =1s, and the other parameters are c=60.

[0060] Figure 3 are the four generator auxiliary variables q i (t) shows the convergence curve diagram. The auxiliary variables of all the generator nodes converge to the same before the preset time. The consistency of the auxiliary variables indicates that the auxiliary variables have reached the optimal state.

[0061] Figure 4 The output power of the four generators reaches its optimum when the auxiliary variables reach their optimum, and the total power always meets the demand conditions.

[0062] Figure 5 for the cost of four generators.

[0063] Figure 6 is the total cost of the entire microgrid system, and the total cost reaches the minimum after the auxiliary variables are consistent.

[0064] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for economic dispatching of a distributed power system with preset time based on fixed demand, characterized in that: The steps include: Step 1: Describe the economic dispatch problem as a convex optimization problem with fixed constraints and construct a model of the power system; Step 2: Based on the power system model described in step 1, a preset time distributed economic dispatch algorithm under fixed constraints is designed. The algorithm is c Converged to the optimal solution before; Step 3: Apply the algorithm designed in step 2 to the model of the power system described in step 1 to solve the convex optimization problem under fixed demand in the power system, that is, by optimizing the output power of each generator, minimize the sum of the costs of all generators while ensuring that the output of all generators meets the demand.

2. The method for economic dispatching of a distributed power system with preset time based on fixed demand according to claim 1, characterized in that: The step 1 is specifically as follows: The total power demand D at the current moment is sent to any node in the power system, each generator set in the power system is regarded as a node, and an upper limit T of the acceptable convergence time is set c , the model of the power system is expressed as: Where P(t)=[P1(t),P2(t),…,P N (t)] T ∈R N The output power of the generator is used as the decision vector, and the total required power D is used as the global constraint variable; i (P i (t)) is the cost of the i-th node at the current moment, f i (P i (t)) = α i P i 2 (t)+β i P i (t)+γ i , α i ,β i ,γ i is the cost coefficient of the ith node, and f(P(t)) is the total cost of the power system at the current moment.

3. The method for economic dispatching of a distributed power system with preset time based on fixed demand according to claim 2, characterized in that: In the power system model described in step 1, each generator set only knows its own local objective function f i (P i (t)), the global objective function f(P(t)) is the sum of all local objective functions, that is N is the number of nodes. The generator sets calculate the global optimal solution through interactive sharing of local information. Information is shared through communication links between nodes, so that nodes with communication links can obtain information sent by each other.

4. The method for economic dispatching of a distributed power system with preset time based on fixed demand according to claim 3, characterized in that: In step 2, based on the model of the power system in step 1, according to the preset time distributed economic dispatch algorithm under fixed constraints, through mutual communication between nodes and neighboring nodes, the node with a direct communication link connection to a node is the neighboring node of the node, and the auxiliary variable q at the current moment is obtained. i The auxiliary variables are the information of the interaction between nodes, which do not contain any real physical information.

5. The method for economic dispatching of a distributed power system with preset time based on fixed demand according to claim 4, characterized in that: Based on the calculated values ​​of auxiliary variables, the optimization variable P is optimized by using the preset time distributed economic dispatch algorithm under fixed constraints. i (t) is updated, and finally the i-th (i=1,2,…,N) generation node of the power system is dispatched according to the optimal value P i * Under this scheduling method, the power generation cost of the power system can be guaranteed to be c before reaching the minimum.

6. The method for economic dispatching of a distributed power system with preset time based on fixed demand according to claim 5, characterized in that: The preset time distributed economic dispatch algorithm under fixed constraints in step 2 is as follows: Among them, P i (t) is the dynamic optimization value of the i-th generator set at time t, and the initial value must meet the condition D is the target total power demand; q i (t) is an auxiliary variable, which represents the updated Lagrangian value of the i-th generator set at time t, i = 1, 2, ..., N; α i and β i is the cost coefficient of the ith generator set; s(t) is a custom function defined as c is a normal number, T c A predefined time.

7. The method for economic dispatching of a distributed power system with preset time based on fixed demand according to claim 1, characterized in that: The step 3 is specifically as follows: Select the Lyapunov function as prove Prove that V can c Before it converges to 0 exactly, that is, the auxiliary variables q of all generators i , i=1,2,...,N are all within the preset time T c Converge to their weighted average within That is q i Converges to the Lagrangian optimal value λ * , prove the convergence time Substitute into the power update function The optimal solution of the original convex optimization problem with dynamic constraints is in, represents the weight of the i-th generator group, ω=[ω1,ω2,...,ω N ] T ; q=[q1,q2,...,q N ] T , m is a fixed constant, α i ,β i is the cost coefficient of the generator, q * for q i The final consistent value.

8. The method for economic dispatching of a distributed power system with preset time based on fixed demand according to claim 7, characterized in that: The preset time T c It is only the upper bound of the time it takes for the system to converge to the optimal solution. The convergence time of the system is t<T c , after the system reaches convergence, the state of the system will maintain the optimal solution operation.

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