Line overload correction method for multi-regional power system based on DC optimal power flow

Abstract

The present invention relates to a power system overload regulation technology, and specifically to a multi-regional power system line overload correction method based on DC optimal power flow. First, the dimension of the power grid is reduced by partitioning the large-scale power system using a decomposition method, and the global problem is decomposed into each sub-problem associated with a specific control area, while adding the risk cost of line overload. It includes: using a decomposition method to decompose the global problem into multiple regional sub-problems; introducing the risk cost of line overload; iterating the sub-problem once to update the variables, and if the convergence condition is met, the global optimal solution is obtained; if the convergence condition is not met, it returns to iterating the sub-problem once. By exchanging boundary variables and Lagrange multipliers associated with coupling constraints, coordination between sub-problems can be achieved through an iterative process, thereby converging to the global optimum. The method proposed by the correction method can quickly alleviate line overload while ensuring system safety during the mitigation period.

Description

Technical Field

[0001] The invention belongs to the technical field of power system overload regulation, and in particular relates to a multi-region power system line overload correction method based on direct current optimal power flow. Background Art

[0002] We have entered the era of large power grids, high voltages and large units. The interconnection of power systems can bring significant economic benefits. At the same time, the interconnection of power grids makes the scale of power systems larger, which increases the possibility of accidents. Due to the relatively weak grid structure, the geographical distance between the load and the power generation center, and the heavy load of the connecting line, the occurrence of local faults may cause safety and stability problems of the entire system. Therefore, how to ensure the safe, stable and economic operation of such a super-large-scale power system has become a huge problem before us. With the continuous advancement of power marketization and regional networking, the operation status of the power grid has become more and more complex and changeable and close to its limit level. During operation, due to some destructive reasons, the power system sometimes collapses. With the progress of society and the development of science and technology, some large power systems have emerged around the world in recent years. These systems are usually characterized by wide range and strong nonlinearity.

[0003] Alleviating transmission line overload is an important task in power system operation. After accidents or disturbances such as power generation losses and unexpected load fluctuations, the operating point of the power grid may change. If the system survives the outage or disturbance, it will operate in a new stable state, in which one or more transmission lines may be overloaded. Once this happens, appropriate corrective measures must be taken immediately to alleviate line overload and avoid line outages. In the operation of large interconnected power systems, the demand for economic efficiency is increasing. One of the fundamental issues is how to effectively solve the large-scale security-constrained economic dispatch of super-large systems. It is crucial to develop distributed algorithms for such large-scale multi-regional economic dispatch. Compared with centralized control, distributed control has significant advantages in protecting privacy, saving communication resources, and avoiding single node failures. Distributed optimization and control will also improve the reliability and resilience of future power systems.

[0004] In the past few decades, decomposition techniques based on Lagrangian, enhanced Lagrangian, curved decomposition and optimal condition decomposition have enabled optimization problems to be decomposed and solved in a distributed manner. Therefore, decomposition techniques are also an important tool for distributed optimization of power systems and have been proposed for various applications such as distributed optimal power flow, power outage prevention, and automatic generation control. Among them, the optimal condition decomposition technique only requires the exchange of a small amount of boundary information and does not require any central coordination. Therefore, the optimal condition decomposition technique is simple, efficient and practical. Most importantly, the optimal condition decomposition technique can ensure data privacy in the decision-making process and provide a fully distributed solution to the coordinated optimization problem. The optimal condition decomposition technique allows the related control sub-problems to be solved in parallel in an iterative manner until the required accuracy is achieved.

[0005] However, centralized control frameworks may suffer from some performance limitations, such as huge communication and computational burdens, single points of failure, and privacy issues. Meanwhile, distributed control frameworks are flexible, easy to compute, and can adapt to changes in network topology.

[0006] In some cases, the Lagrangian procedure may have difficulty converging to the optimal solution of the global system (in the absence of convexity assumptions), and the convergence rate depends on the correct choice of several parameters and requires the intervention of a central agent to update this information. Summary of the invention

[0007] The purpose of the present invention is to solve the line overload problem of large-scale multi-regional power systems. The dimensionality of the power grid is reduced by partitioning the large-scale power system using a decomposition method, while adding the risk cost of line overload, and then solving the sub-problems corresponding to each sub-region, so as to obtain the global optimal solution of the entire system, and quickly alleviate the line overload while ensuring the system safety during the mitigation period.

[0008] In order to solve the above technical problems, the present invention adopts the following technical solution: a multi-regional power system line overload correction method based on DC optimal power flow, comprising:

[0009] Step 1: Use the decomposition method to decompose the global problem into multiple regional sub-problems;

[0010] Step 2: Introduce the risk cost of line overload;

[0011] Step 3: Iterate the sub-problem once and update the variables. If the convergence condition is met, the global optimal solution is obtained; if the convergence condition is not met, return to iterating the sub-problem once.

[0012] In the above-mentioned multi-regional power system line overload correction method based on DC optimal power flow, the global problem is decomposed into multiple regional sub-problems using a decomposition method, which specifically includes the following steps:

[0013] Step 1.1, a N B Busbar, N G Generator and N L The DC-OPF problem of the transmission grid composed of transmission lines is formulated as a mathematical optimization problem:

[0014]

[0015] stB·θ=PD (2)

[0016] θ ref =0 (3)

[0017]

[0018]

[0019] Where B represents the global network admittance matrix, θ represents the phase angle vector of the bus voltage, P represents the generator power output vector, D represents the bus active power demand vector, and θ ref represents the voltage phase angle of the reference bus, θ i ,θ j represents the voltage phase angle of busbar i, j, x ij The reactance of internal wiring or connecting wires, The transmission capacity of the internal line or connecting line, P i min Minimum output power of the generator, P i max Maximum output power of the generator;

[0020] Step 1.2: Use the optimal condition decomposition in the decomposition technique to decompose the original problem into regional sub-problems by region; add a new variable T representing the flow at both ends of each connecting line to the sub-problem ij , the power balance equation on the connecting line is identified as a coupling constraint, and Lagrangian relaxation is performed on this constraint; OPF decoupling is performed on the connecting line connecting adjacent areas;

[0021] The regional sub-problem is formulated as follows:

[0022]

[0023]

[0024] If region A contains the reference bus:

[0025] For all connecting lines in region A:

[0026] For all connecting lines in region A:

[0027] For all internal connections in region A:

[0028] For all generators in region A: P i min ≤P i ≤P i max (12)

[0029] The Lagrange multiplier associated with equation (9) is Interpreted as the export price of electricity on the connecting line, T A Represents the set of all connected lines in region A. Variables with a '-' on top indicate that their values ​​are assigned fixed values ​​obtained from the previous iteration in the neighboring region;

[0030] The compact form is:

[0031]

[0032]

[0033] s A (x A )≤0 (15)

[0034] Where N is the total number of subproblems or regions, x A represents the variables contained in region A; constraint c A is a complex constraint that contains variables from multiple regions. A is a non-complex constraint, containing variables from one region; c A and A Both equality and inequality constraints are included, among which inequality constraints are handled by the interior point method; variables with a '-' on top indicate that their values ​​are assigned fixed values ​​from the previous iteration obtained from neighboring regions; in the OPF problem, complex constraints include power flow equilibrium equations on buses placed on region boundaries, while other constraints are considered non-complex constraints.

[0035] In the above-mentioned multi-regional power system line overload correction method based on DC optimal power flow, introducing the risk cost of line overload specifically includes the following steps:

[0036] The risk cost of line overload is defined as the square of excess power flow, and the set of all overloaded transmission lines is OL, then l ij The risk cost of ∈OL is:

[0037]

[0038] Among them, O ijis the risk cost coefficient, P ij It is line l ij The active power on

[0039] Security constraints: For all conform to;

[0040] Introducing variables The compact form of the above subproblem can be written as:

[0041]

[0042]

[0043] s A (x A )≤0 (19).

[0044] In the above-mentioned multi-regional power system line overload correction method based on DC optimal power flow, performing an iterative update of variables for a sub-problem includes the following steps:

[0045] Step 3.1: Use the interior point method to process the above inequality constraints and transform them into equality constraints. Then define the Lagrangian function of the global problem equations (1) to (5) as:

[0046]

[0047] Among them, α A and γ A denote the Lagrange multipliers of complex constraints and non-complex constraints respectively; the Newton-Raphson method is used to find the solution of the relevant KKT conditions; c in formula (20) A (x1,...,x N ) and s A (x A ) are all equality constraints, and the objective function contains the potential barrier term related to the interior point method; z represents all variables that need to be determined, including the Lagrange multiplier. The above process is equivalent to solving the following linear equations to obtain the update of the variable Δz:

[0048] H sys Δz=-r (21)

[0049] in

[0050]

[0051] Among them, r represents the KKT conditions, which must be zero in the optimal state for the algorithm to stop; H sys The Jacobian matrix representing the KKT condition; H sysis a symmetric matrix. By rearranging the variables according to the regions to which they are assigned, equation (21) is transformed into:

[0052]

[0053] in:

[0054]

[0055]

[0056]

[0057] The off-diagonal blocks are H AB , A≠B contains non-zero terms for updating variables in the coupled subproblems, which does not allow independent solutions to the coupled subproblems; the optimal condition is decomposed by separating the off-diagonal blocks, i.e., H AB , the elements in A≠B are set to zero to decouple the subproblems; in equation (23), H is given by Replaced by:

[0058]

[0059] The subproblems are decoupled and the following Newton-Raphson method is performed in each region:

[0060]

[0061] And update its variable z A ←z A +Δz A ; After this update, the updated values ​​of the bus-related variables on the boundary are exchanged between the subproblems to calculate H AA and r A ;

[0062] The search direction Δx of subproblems (17) to (19) A , Δα A Compute independently of each other, allowing parallel implementation in a distributed computing environment;

[0063] Step 3.2: If the variable does not change significantly in two consecutive iterations, the algorithm stops; otherwise, it continues in step 3.1.

[0064] Compared with the prior art, the present invention proposes that there is no need to solve the optimal solution of the sub-problem in one iteration, thereby saving computing time and improving computing efficiency. The present invention can also be implemented in a distributed computing environment, and the coordinator does not need to update information, but collects and distributes this information. The present invention does not need to estimate the Lagrange multipliers (like most common Lagrange relaxation methods). At the same time, the method requires very few parameters and clearly specifies their update process. The method of the present invention exchanges boundary variables and Lagrange multipliers related to coupling constraints, and the coordination between sub-problems can be achieved through an iterative process, thereby converging to the global optimum. The method of the present invention can quickly alleviate line overload while ensuring system safety during the relief period. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 A flow chart of a multi-regional power system line overload correction control strategy based on DC optimal power flow provided by an embodiment of the present invention;

[0066] Figure 2 A schematic diagram of a power system model provided by an embodiment of the present invention;

[0067] FIG. 3 (a) The outlet price α of the connection line 102-305 when there is no line overload in the embodiment of the present invention ij evolution;

[0068] FIG. 3( b ) The outlet price α of the connection line 105-202 when there is no line overload in the embodiment of the present invention ij evolution;

[0069] FIG. 3(c) The outlet price α of the connection line 205-302 when there is no line overload in the embodiment of the present invention ij evolution;

[0070] Figure 4 The evolution of the active power output of the generator when there is no line overload provided by the embodiment of the present invention;

[0071] FIG. 5( a ) The export price of the connection line 102-305 when the internal connection lines 101-102, 201-202, 301-302 are overloaded in the embodiment of the present invention ij evolution;

[0072] FIG. 5( b ) The outlet price α of the connection line 105-202 when the internal connection lines 101-102, 201-202, 301-302 are overloaded in the embodiment of the present invention ij evolution;

[0073] FIG. 5( c ) The outlet price α of the connection line 205-302 when the internal connection lines 101-102, 201-202, 301-302 are overloaded in the embodiment of the present invention ij evolution;

[0074] Figure 6 The evolution of the active power output of the generator when the internal connecting lines 101-102, 201-202, 301-302 provided in the embodiment of the present invention are overloaded;

[0075] FIG. 7 (a) The outlet price α of the connection line 102-305 when the internal connection lines 101-102, 201-202, 301-302, 304-305 are overloaded in the embodiment of the present invention ij evolution;

[0076] FIG. 7( b ) The outlet price α of the connection line 102-305 when the internal connection lines 101-102, 201-202, 301-302, 304-305 are overloaded in the embodiment of the present invention ij evolution;

[0077] FIG. 7( c ) The outlet price α of the connection line 102-305 when the internal connection lines 101-102, 201-202, 301-302, 304-305 are overloaded in the embodiment of the present invention ij evolution;

[0078] Figure 8 The evolution of the active power output of the generator when the internal connecting lines 101-102, 201-202, 301-302, 304-305 provided in the embodiment of the present invention are overloaded. DETAILED DESCRIPTION

[0079] The technical solutions in the embodiments of the present invention will be described clearly and completely below in combination with the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0080] It should be noted that, in the absence of conflict, the embodiments of the present invention and the features in the embodiments may be combined with each other.

[0081] The present invention will be further described below in conjunction with specific embodiments, but the present invention is not limited thereto.

[0082] Most common Lagrangian procedures require solving subproblems until optimality to obtain multiplier updates, and the coordinator needs to update information. This embodiment proposes an agent-based distributed method for alleviating line overload after an emergency occurs in a multi-regional transmission power system, which can solve the line overload problem of large-scale or multi-regional power systems. Considering the nature of the thermal overload problem and the focus of the distributed control strategy, only the overload of active power and the control of power generation re-dispatch are considered. First, the dimension of the power grid is reduced by partitioning the large-scale power system using a decomposition method, and the global problem is decomposed into each subproblem associated with a specific control area, while adding the risk cost of line overload. By exchanging boundary variables and Lagrangian multipliers associated with coupling constraints, coordination between subproblems can be achieved through an iterative process, thereby converging to the global optimum. The method proposed in this embodiment can quickly alleviate line overload while ensuring system safety during mitigation.

[0083] This embodiment provides a multi-regional power system line overload correction method based on DC optimal power flow, including: using a decomposition method to decompose the global problem into multiple regional sub-problems; introducing the risk cost of line overload; and iterating the sub-problems once.

[0084] In addition, the global problem is decomposed into multiple regional sub-problems using the decomposition method, and a new variable T for the flow at both ends of each connecting line is introduced. ij and Lagrange multipliers associated with complex constraints And use the optimal condition decomposition in the decomposition method. The specific method is as follows:

[0085] Add a new variable T to the subproblem to represent the flow at both ends of each link. ij , the power balance equations on the connecting lines are identified as coupled constraints, on which Lagrangian relaxation is performed. The Lagrangian multipliers associated with the complex constraints are It can be interpreted as the export price of electricity on the connection line. The method proposed in this embodiment is to perform OPF decoupling on the connection lines connecting adjacent areas. OPF decoupling is performed around the connection lines rather than the boundary nodes.

[0086] Using the optimal condition decomposition in the decomposition method, this algorithm is an extension of the Lagrangian relaxation method. This algorithm has better convergence than the Lagrangian method and the enhanced Lagrangian method. This algorithm divides a large-scale power system into several regions, and achieves the global optimal solution by solving the optimal solution of each sub-region. It can be well applied to multi-region power system problems.

[0087] Introduce the risk cost of line overload, the risk cost is given by the function (x) +=max(0,x), which means that once the overload is eliminated, the cost is zero. Compared with the basic DC-OPF, the objective function consists of two parts: the power generation cost of the generator output and the risk cost of the line overload. The weights of the two cost components can be expressed by the coefficient o ij Adjustment is made, introducing variable Z ij .

[0088] Introducing variable Z ij , due to the coupling risk cost between adjacent buses and the non-smooth function |·|, (·) + , it is difficult to find a distributed algorithm to solve the corrective control problem in the subproblem. To solve this problem, we introduce the variable Z ij ,in With variable Z ij and Z ji The power flow constraints associated with overloaded lines have been redefined, where a larger Z ij or Z ji There is a penalty term with higher risk cost in the objective function.

[0089] An iteration of the subproblem includes the following four steps:

[0090] Use the interior point method to handle inequality constraints, solve the KKT conditions of the subproblems, solve the Jacobian matrix, and calculate the iterative value.

[0091] Solve the KKT conditions of the subproblems and decouple the subproblems by assigning the values ​​of the variables from the neighbor regions to fixed values ​​(constants) obtained from the previous iteration from the neighbor regions.

[0092] When implementing: Figure 1 As shown, a multi-regional power system line overload correction method based on DC optimal power flow includes:

[0093] S1: A B Busbar, N G Generator and N L The DC-OPF (direct current optimal power flow) problem of the transmission grid composed of transmission lines is expressed as a mathematical optimization problem as follows:

[0094]

[0095] st B·θ=PD (2)

[0096] θ ref =0 (3)

[0097]

[0098]

[0099] Where B represents the global network admittance matrix, θ represents the phase angle vector of the bus voltage, P represents the generator power output vector, D represents the bus active power demand vector, and θ ref represents the voltage phase angle of the reference bus, θ i ,θ j represents the voltage phase angle of busbar i, j, x ij The reactance of the internal circuit (or connecting wire), The transmission capacity of the internal line (or connecting line), P i min Minimum output power of the generator, P i max The maximum output power of the generator.

[0100] S2: Using the optimal condition decomposition in the decomposition technique, the original problem can be decomposed into regional sub-problems by region. In the sub-problems, a new variable T representing the flow at both ends of each connecting line is added ij , the power balance equations on the connecting lines are identified as coupling constraints, on which Lagrangian relaxation is performed. The decomposition is complete when the combination of KKT conditions for all subproblems is the same as the KKT conditions for the original problem. The coordination between subproblems can be achieved through an iterative process by exchanging boundary variables and Lagrangian multipliers associated with the coupling constraints, thereby converging to the global optimum. The KKT-based decomposition technique is optimal as long as the termination condition is met at the end of the iteration.

[0101] The regional subproblem is formulated as follows:

[0102]

[0103]

[0104] (If region A contains the reference bus) (8)

[0105] For all the connecting lines in area A (9)

[0106] For all the connecting lines in region A (10)

[0107] For all internal connections in region A (11)

[0108] P i min ≤P i ≤P i max, for all generators in region A (12)

[0109] The Lagrange multipliers associated with constraint (9) are can be interpreted as the export price of electricity on the connecting line. A Represents the set of all connected lines in region A. Variables with a '-' on top indicate that their values ​​are assigned fixed values ​​obtained from the previous iteration in the neighboring region.

[0110] can be written in compact form:

[0111]

[0112]

[0113] s A (x A )≤0 (15)

[0114] Where N is the total number of subproblems or regions, x A represents the variables contained in region A. Constraint c A is defined as a complex constraint because it contains variables from multiple regions, and the constraint s A is defined as a non-complex constraint because it contains variables from only one region. Note that c A and A Both equality and inequality constraints are included, where inequality constraints can be handled using interior point methods. Variables with a '-' on top indicate that their values ​​are assigned fixed values ​​from the previous iteration obtained from neighboring regions. In the considered OPF problem, complex constraints include power flow equilibrium equations on buses placed on the region boundaries, while other constraints are considered non-complex constraints.

[0115] S3: The goal of the decomposition algorithm proposed in this embodiment is to immediately start adjusting the generation to alleviate the line overload once the line overload is detected. Inspired by the Joule heat formula, the risk cost of line overload is first defined as the square of the excess power flow. Denote the set of all overloaded transmission lines as OL, then l ij The risk cost of ∈OL is (the risk cost coefficient is o ij ):

[0116]

[0117] Among them, P ij It is line l ij The active power on

[0118] To ensure system safety during the implementation of corrective measures, it is necessary to avoid new line overloads while alleviating existing line overloads. This requires that safety constraints For all conform to.

[0119] At the same time, the variable Therefore, the compact form of the above subproblem can be written as:

[0120]

[0121]

[0122] s A (x A )≤0 (19)

[0123] S4: Each subproblem (17)-(19) is solved by deriving the KKT condition and then applying the Newton-Raphson method, while calculating the search direction Δx A , Δα A .

[0124] First, we can use the interior point method to process the above inequality constraints and transform them into equality constraints. Then, the Lagrangian function of the global problem (1)-(5) is defined as:

[0125]

[0126] Among them, α A and γ A denote the Lagrange multipliers of complex constraints and non-complex constraints respectively. Then the Newton-Raphson method is used to find the solution of the relevant KKT conditions. Note that c in (20) A (x1,...,x N ) and s A (x A ) are all equality constraints, and the objective function contains the potential barrier term related to the interior point method. Let z represent all the variables that need to be determined, including the Lagrange multipliers. The above process is equivalent to solving the following linear equations to obtain the update of the variable Δz:

[0127] H sys Δz=-r (21)

[0128] in

[0129]

[0130] Here, r represents the KKT conditions, which must be zero in the optimal state for the algorithm to stop. sysrepresents the Jacobian matrix of the KKT condition. Note that H sys is a symmetric matrix, and by rearranging the variables according to the regions to which they are assigned, (21) is transformed into:

[0131]

[0132] here:

[0133]

[0134]

[0135]

[0136] The off-diagonal blocks are H AB , A≠B contains non-zero terms for the variable updates in the coupled subproblems, which does not allow independent solutions to the coupled subproblems. The optimality condition is decomposed by separating the off-diagonal blocks, i.e., H AB , the elements in A≠B are set to zero to decouple the subproblems. Therefore, in (23), H is Instead, here:

[0137]

[0138] Therefore, the subproblems are decoupled and each region can perform the following Newton-Raphson method:

[0139]

[0140] And update its variable z A ←z A +Δz A After this update, the updated values ​​of the bus-related variables on the boundary are exchanged between the subproblems to compute H AA and r A , because H AA and r A Some of the terms in contain variables from other subproblems.

[0141] The search direction (Δx A , Δα A ) can be computed independently of each other, allowing parallel implementation in a distributed computing environment.

[0142] S5: If the variable does not change significantly in two consecutive iterations, the algorithm will stop. Otherwise, it will continue in S4.

[0143] Example 1

[0144] This example consists of three IEEE14 nodes, and each area is connected by three connection lines: 105-202, 205-302, and 305-102. Figure 2 As shown, there are 42 busbars, 15 generating units, 60 internal connecting lines and 3 connecting lines. Bus 101 is used as a reference bus. The determination method includes the following steps:

[0145] S11: Initial operation state: We assume that the normal operation point of the test system is determined by the DCOPF problem. Since the IEEE14 bus system does not provide the power flow capacity of the line, it is estimated based on its initial power flow, which is set here as Let α=1.

[0146] S12: Line overload: In order to cause line overload, a hypothetical disturbance is used in the system, thereby reducing the power flow capacity. For the bus system used in this example, the initial power flows of all branches are sorted in descending order and then divided into three cases:

[0147] When there is no line overload;

[0148] The flow capacity of the internal connections 101-102, 201-202, 301-302 Down to

[0149] The flow capacity of the internal connections 101-102, 201-202, 301-302, 304-305 Down to

[0150] S13: Optimize model parameters: Here, o=10 and T0=10 are selected.

[0151] S14: Calculate using the above method, the results are as follows:

[0152] No line overload connection line 102-305 export price α ij The evolution of is shown in Figure 3(a). When there is no line overload, the outlet price of the connecting line 105-202 is α ij The evolution of is shown in Figure 3(b). When there is no line overload, the outlet price of the connecting line 205-302 is α ij The evolution of is shown in Figure 3(c).

[0153] The evolution of the active power output of the generator when there is no line overload is as follows Figure 4 shown.

[0154] Internal connection line 101-102, 201-202, 301-302 overload connection line 102-305 export price α ij The evolution of is shown in Figure 5(a).

[0155] Internal connection line 101-102, 201-202, 301-302 overload connection line 105-202 export price α ij The evolution of is shown in Figure 5(b).

[0156] Internal connection line 101-102, 201-202, 301-302 overload connection line 205-302 export price α ij The evolution of is shown in Figure 5(c).

[0157] When the internal connecting lines 101-102, 201-202, 301-302 provided in Example 1 are overloaded, the evolution of the active power output of the generator is as follows: Figure 6 shown.

[0158] Internal connection line 101-102, 201-202, 301-302, 304-305 overload connection line 102-305 export price α ij The evolution of is shown in Figure 7(a).

[0159] Internal connection line 101-102, 201-202, 301-302, 304-305 overload connection line 102-305 export price α ij The evolution of is shown in Figure 7(b).

[0160] Internal connection line 101-102, 201-202, 301-302, 304-305 overload connection line 102-305 export price α ij The evolution of is shown in Figure 7(c).

[0161] When the internal connecting lines 101-102, 201-202, 301-302, 304-305 provided in Example 1 are overloaded, the evolution of the active power output of the generator is as follows: Figure 8 shown.

[0162] It can be seen that during the algorithm implementation process, after a short initial oscillation, all values ​​converge to the optimal value. Therefore, the proposed algorithm can well cope with the line overload problem of multi-regional power systems.

[0163] The above are only preferred embodiments of the present invention, and are not intended to limit the implementation methods and protection scope of the present invention. Those skilled in the art should be aware that all solutions obtained by equivalent substitutions and obvious changes made using the contents of the specification of the present invention should be included in the protection scope of the present invention.

Claims

1. A multi-regional power system line overload correction method based on DC optimal power flow, characterized by: include: Step 1: Use the decomposition method to decompose the global problem into multiple regional sub-problems; Step 2: Introduce the risk cost of line overload; Introduction The risk cost of line overload specifically includes the following steps: The risk cost of line overload is defined as the square of excess power flow, and the set of all overloaded transmission lines is OL, then l ij The risk cost of ∈OL is: Among them, O ij is the risk cost coefficient, P ij It is line l ij The active power on Security constraints: For all conform to; Introducing variables The compact form of the above subproblem can be written as: s A (x A )≤0 (19); Step 3: Iterate the sub-problem once and update the variables. If the convergence condition is met, the global optimal solution is obtained; if the convergence condition is not met, return to iterate the sub-problem once. Iterating the sub-problem once and updating the variables includes the following steps: Step 3.1: Use the interior point method to process the above inequality constraints and transform them into equality constraints. Define the Lagrangian function of the global problem as: Among them, α A and γ A denote the Lagrange multipliers of complex constraints and non-complex constraints respectively; the Newton-Raphson method is used to find the solution of the relevant KKT conditions; c in formula (20) A (x1,...,x N ) and s A (x A ) are all equality constraints, and the objective function contains the potential barrier term related to the interior point method; z represents all variables that need to be determined, including the Lagrange multiplier. The above process is equivalent to solving the following linear equations to obtain the update of the variable Δz: H sys Δz=-r (21) in Among them, r represents the KKT conditions, which must be zero in the optimal state for the algorithm to stop; H sys The Jacobian matrix representing the KKT condition; H sys is a symmetric matrix. By rearranging the variables according to the regions to which they are assigned, equation (21) is transformed into: in: The off-diagonal blocks are H AB , A≠B contains non-zero terms for updating variables in the coupled subproblems, which does not allow independent solutions to the coupled subproblems; the optimal condition is decomposed by separating the off-diagonal blocks, i.e., H AB , the elements in A≠B are set to zero to decouple the subproblems; in equation (23), H is given by Replaced by: The subproblems are decoupled and the following Newton-Raphson method is performed in each region: And update its variable z A ←z A +Δz A ; After this update, the updated values ​​of the bus-related variables on the boundary are exchanged between the subproblems to calculate H AA and r A ; The search direction Δx of subproblems (17) to (19) A , Δα A Compute independently of each other, allowing parallel implementation in a distributed computing environment; Step 3.2: If the variable does not change significantly in two consecutive iterations, the algorithm stops; otherwise, it continues in step 3.

1.

2. The multi-regional power system line overload correction method based on DC optimal power flow according to claim 1 is characterized in that: Using the decomposition method to decompose the global problem into multiple regional sub-problems specifically includes the following steps: Step 1.1, a N B Busbar, N G Generator and N L The DC-OPF problem of the transmission grid composed of transmission lines is expressed as a mathematical optimization problem: st B·θ=PD (2) i ref =0 (3) Where B represents the global network admittance matrix, θ represents the phase angle vector of the bus voltage, P represents the generator power output vector, D represents the bus active power demand vector, and θ ref represents the voltage phase angle of the reference bus, θ i ,θ j represents the voltage phase angle of busbar i, j, x ij The reactance of internal wiring or connecting wires, The transmission capacity of the internal line or connecting line, P i min Minimum output power of the generator, P i max Maximum output power of the generator; Step 1.2: Use the optimal condition decomposition in the decomposition technique to decompose the original problem into regional sub-problems by region; add a new variable T representing the flow at both ends of each connecting line to the sub-problem ij , the power balance equation on the connecting line is identified as a coupling constraint, and Lagrangian relaxation is performed on this constraint; OPF decoupling is performed on the connecting line connecting adjacent areas; The regional sub-problem is formulated as follows: If region A contains the reference bus: For all connecting lines in region A: For all connecting lines in region A: For all internal connections in region A: For all generators in region A: P i min ≤P i ≤P i max (12) The Lagrange multiplier associated with equation (9) is Interpreted as the export price of electricity on the connecting line, T A Represents the set of all connected lines in region A. Variables with a '-' on top indicate that their values ​​are assigned fixed values ​​obtained from the previous iteration in the neighboring region; The compact form is: s A (x A )≤0 (15) Where N is the total number of subproblems or regions, x A represents the variables contained in region A; constraint c A is a complex constraint that contains variables from multiple regions. A is a non-complex constraint, containing variables from one region; c A and A Both equality and inequality constraints are included, among which inequality constraints are handled by the interior point method; variables with a '-' on top indicate that their values ​​are assigned fixed values ​​from the previous iteration obtained from neighboring regions; in the OPF problem, complex constraints include power flow equilibrium equations on buses placed on region boundaries, while other constraints are considered non-complex constraints.

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