Fast and robust solving method for power flow based on damping Newton-homotopy hot start

Abstract

The invention provides an electric power flow fast and steady solving method based on damping Newton-homotopy hot start. The method comprises the steps of obtaining electric power parameters of a target power grid, wherein the electric power parameters comprise the active power of a generator, the reactive power of the generator, the active power of a load and the reactive power of the load; constructing power flow residual errors for n buses, namely nodes, of a target power grid, and establishing a power flow steady-state solving model by taking minimization of the power flow residual errors as a target; based on an LM damping Newton method and backtracking line search, constructing a solver for solving the power flow steady-state solving model; after the resolver is deployed online, inputting the current power parameters of the power grid into the resolver, and then adopting homotopy hot start to obtain a power flow; according to the method, the voltage and the branch power flow of each node can be quickly and stably obtained under complex constraint and disturbance conditions, and the operation requirements in new normal states such as high-proportion access of new energy, load random fluctuation and frequent topology switching can be met.

Description

TECHNICAL FIELD

[0001] The present application relates to a kind of based on damping Newton-homotopy hot start power flow fast robust solution method, belong to power flow calculation field. BACKGROUND

[0002] In recent years, to adapt to high proportion access of new energy, rapid growth of electrification load and normalization of complex operating conditions, power system has higher requirements for the timeliness and robustness of power flow calculation. As the basic link of planning, operation and control, power flow calculation needs to give the voltage of each node and the branch power flow result under multi-source, multi-load and multi-constraint conditions, to support safety check, state estimation and dispatching decision. This trend requires power flow algorithm to have greater convergence domain and stronger anti-disturbance ability while ensuring accuracy.

[0003] Unlike the traditional scenario that assumes small perturbation and fixed initial value for fast convergence, modern power grids exhibit new characteristics of strong coupling, strong nonlinearity and strong uncertainty. Existing methods to improve robustness rely on empirical parameter tuning or separate processing of power flow solution and external prediction and control: for example, by predicting load and output in advance and then calling conventional NR or PQ decomposition for solution, or using heuristic and robust optimization to relax constraints and correct boundaries in the periphery. Although good results can be achieved in some conditions, they are highly sensitive to initial values, parameters and prediction errors, especially in large disturbance and topology switching scenarios, which still cannot avoid convergence failure or unacceptable calculation time.

[0004] With the development of high-performance computing and data-driven methods, researchers have tried to introduce line search, damped Newton, continuous homotopy and incremental sparse solution to enhance the globality and efficiency of power flow solution. However, in the face of PV limit switching, ill-conditioned Jacobian and combined challenges of multi-scenario continuous advancement, a single improvement method often cannot balance large convergence domain and calculation time delay; lack of systematic initial value construction, limit switching hysteresis and homotopy advancement coordination mechanism is still the main obstacle to engineering implementation.

[0005] Therefore, under the premise of poor initial value, limit switching and multi-scenario rolling calculation, there is an urgent need for a power flow solution strategy for engineering application: it can expand the convergence domain, improve numerical robustness and significantly reduce the overall calculation time under complex constraints and disturbance conditions, and can fully utilize the correlation of adjacent conditions to realize continuous advancement, providing reliable example support for dispatching and simulation. SUMMARY

[0006] The purpose of the present application is to provide a power flow fast robust solution method based on damping Newton-homotopy hot start to solve the problem of long calculation time under complex constraints and disturbance conditions in the prior art.

[0007] The technical solution of this invention is:

[0008] A fast and robust solution method for power flow based on damped Newton-homotope thermal start includes the following steps:

[0009] S1. Obtain the power parameters of the target power grid, including the active power of the generator, the reactive power of the generator, the active power of the load, and the reactive power of the load.

[0010] S2. For the n buses, i.e. nodes of the target power grid, construct the power flow residual vector, and establish a power flow steady-state solution model with the goal of minimizing the power flow residual vector.

[0011] S3. Based on the LM damped Newton method and backtracking search, a solver is constructed to solve the steady-state solution model of power flow.

[0012] S4. After deploying the solver online, input the current power parameters of the power grid into the solver and use homotopic hot start to obtain the power flow.

[0013] Furthermore, in step S1, the target power grid includes generators, loads, a solver, and a transmission network. The transmission network includes transformers, reactive power compensation devices, and transmission and distribution lines. The transformers are connected to the transmission and distribution lines through the reactive power compensation devices, and the solver is connected to the generators, loads, and reactive power compensation devices respectively.

[0014] Further, in step S2, the power flow residual vector r(x) = [r1(x), r2(x), ..., r i (x), ..., r n (x)] T Where T denotes transpose, r1(x), r2(x), ..., r i (x), ..., r n (x) represents the power flow residuals of n nodes, and at the same time:

[0015] When the i-th node is a PV node, the power flow residual r of the i-th node is... i (x)=[ΔP i ], where the active power imbalance of the i-th bus. , where P G,i P represents the active power of the generator corresponding to the i-th bus. L,i Let P be the active power of the load corresponding to the i-th bus. i For the active power injection of the i-th bus;

[0016] When the i-th node is a PQ node, the power flow residual r of the i-th node is... i (x)=[ΔP i ΔQ i ]T where, reactive power unbalance of the i-th bus where, Q G,i is the reactive power of the i-th bus corresponding to the generator, Q L,i is the reactive power of the i-th bus corresponding to the load, Q i is the reactive power injection of the i-th bus.

[0017] Further, in step S2, the objective function of the power flow steady-state solving model is:

[0018] (3)

[0019] where, r(x) is the power flow residual error, the state variable x includes the node voltage, phase and amplitude, and ║r(x)║2 is the 2-norm of r(x);

[0020] The constraint conditions include the node voltage amplitude constraint, branch power crossing line constraint and unit output constraint.

[0021] Further, in step S3, based on the LM damped Newton method and backtracking line search, and using homotopy warm start, a solver is constructed for solving the power flow steady-state solving model, specifically,

[0022] S31, initialization, given initial state variable x0 and initial damping factor μ0, wherein the initial state variable x0 includes initial node voltage, phase and amplitude; set the search step size α and the minimum step size αmin;

[0023] S32, when the current state variable x k , assemble the residual error r(x) and the Jacobian matrix J=[▽r1(x) T ,▽r2(x) T ,...,▽r i (x) T ,...,▽r n (x) T ] T ;

[0024] S33, solve , where I is the unit matrix, to obtain the correction amount Δx;

[0025] S34, calculate the new state variable x'=x+αΔx, and calculate the residual error at x' and the objective function value of x' ;

[0026] S35, when , where c is a constant, then the next state variable x k+1= x', go to next step S37; otherwise, go to next step S36;

[0027] S36, let a = ba, where step length adjustment coefficient b e (0, 1), return to step S34 until search step length a reaches minimum step length am;

[0028] S37, calculate gain ratio p: wherein, is the objective function value of new state variable x', is the objective function value of x', when gain ratio p is greater than first gain setting value p good , make , and g > 1; when gain ratio p is less than second gain setting value p bad , make ;

[0029] In step S37, the convergence condition is , and the physical feasibility conditions include node voltage, branch current, and reactive power of unit not exceeding limit, i.e. node voltage is between upper and lower voltage limits, branch current is not less than current threshold, and reactive power of unit is between upper and lower limits, wherein, is residual error threshold, is step length threshold.

[0030] S38, when reactive power of PV node does not exceed limit, go to next step S39; when reactive power of PV node exceeds upper limit threshold of reactive power, update reactive power of PV node to upper limit threshold of reactive power, and convert the PV node to PQ node, at the same time, take node voltage of the PV node as swing voltage, and go to next step S39; when reactive power of PV node exceeds lower limit threshold of reactive power, update reactive power of PV node to lower limit threshold of reactive power, and convert the PV node to PQ node, at the same time, take node voltage of the PV node as swing voltage, and go to next step S39;

[0031] S39, when reactive power of PQ node in step S38 is in set power interval for a set number of steps, the PQ node is converted to PV node again, and node voltage of the PQ node is updated to swing voltage; otherwise, the PQ node is still kept.

[0032] S310, repeat steps S32-S39 until maximum iteration number is reached and convergence condition is met, to obtain final state variable as power flow calculation result; when maximum iteration number is reached but convergence condition is not met, homotopy subsection promotion and failure bisection mechanism is used to obtain power flow calculation result.

[0033] Further, in step S37, the convergence condition is , and the physical feasibility condition includes that the node voltage, the branch current, and the reactive power of the unit are not out of limit, wherein is a residual threshold value, is a step threshold value.

[0034] The power flow fast and robust solving method based on the damping Newton-homotopy hot start has the advantages that the power flow fast and robust solving method based on the damping Newton-homotopy hot start can quickly and stably obtain the node voltage and the branch flow under the conditions of complex constraints and disturbances, can meet the operation requirements under the new normal state of high proportion of new energy access, random load fluctuation and frequent topology switching, and is suitable for power transmission and distribution networks, active distribution networks and multi-scenario power flow calculation of distributed power sources / energy storage. BRIEF DESCRIPTION OF DRAWINGS

[0035] Figure 1 is a flow schematic diagram of the power flow fast and robust solving method based on the damping Newton-homotopy hot start of the embodiment of the application;

[0036] Figure 2 is an explanatory diagram of the target power grid in the embodiment. DETAILED DESCRIPTION

[0037] The preferred embodiments of the application will be described in detail below with reference to the accompanying drawings.

[0038] The embodiment provides a power flow fast and robust solving method based on damping Newton-homotopy hot start, which comprises the following steps, Figure 1

[0039] S1, the power parameters of the target power grid, including the active power of the generator, the reactive power of the generator, the active power of the load and the reactive power of the load.

[0040] In step S1, the target power grid comprises a generator, a load, a solver and a power transmission network, the power transmission network comprises a transformer, a reactive power compensation device and a power transmission and distribution line, the transformer is connected to the power transmission and distribution line through the reactive power compensation device, and the solver is connected to the generator, the load and the reactive power compensation device, respectively. Figure 2

[0041] S2, a power flow residual error vector is constructed for n buses, i.e., nodes, of the target power grid, and a power flow steady-state solving model is established with the minimization of the power flow residual error vector as the target.

[0042] In step S2, the power flow residual error vector r(x) is constructed as [r1(x), r2(x),..., r i (x),..., r n (x)] T ​​Where T denotes transpose, r1(x), r2(x), ..., r i (x), ..., r n (x) represents the power flow residuals of n nodes, and at the same time:

[0043] When the i-th node is a PV node, the power flow residual r of the i-th node is... i (x)=[ΔP i ], where the active power imbalance of the i-th bus. , where P G,i P represents the active power of the generator corresponding to the i-th bus. L,i Let P be the active power of the load corresponding to the i-th bus. i For the active power injection of the i-th bus;

[0044] When the i-th node is a PQ node, the power flow residual r of the i-th node is... i (x)=[ΔP i ΔQ i ] T The reactive power imbalance of the i-th bus is... , where Q G,i Let Q be the reactive power of the generator corresponding to the i-th bus. L,i Q represents the reactive power of the load corresponding to the i-th bus. i For the reactive power injection of the i-th bus.

[0045] In step S2, the objective function of the power flow steady-state solution model is... for:

[0046] (3)

[0047] Where r(x) is the power flow residual, and the state variable x includes node voltage, phase and magnitude, where ║r(x)║2 is the 2 norm of r(x);

[0048] The constraints include node voltage amplitude constraints, branch power over-limit constraints, and unit output constraints.

[0049] S3. Based on the LM damped Newton method and backtracking search, a solver is constructed to solve the steady-state solution model of power flow.

[0050] In step S3, based on the LM damped Newton method and backtracking search, and using homotopy hot start, a solver is constructed to solve the steady-state power flow model. Specifically,

[0051] S31, initialization is performed, and initial state variable x0 and initial damping factor μ0 are given, wherein the initial state variable x0 includes initial node voltage, phase and amplitude; search step α and minimum step αmin are set;

[0052] S32, the current state variable x k is updated to x T = x T + Δx, wherein Δx is obtained by solving the following equation: i T n T T ;

[0053] S33, solving , wherein I is a unit matrix, to obtain the correction amount Δx;

[0054] S34, a new state variable x = x + αΔx is calculated, and the residual at x and the objective function value of x

[0055] are calculated ; k+1 ;

[0056] S36, let α = βα, wherein the step adjustment coefficient β ∈ (0, 1), return to step S34 until the search step α reaches the minimum step αmin;

[0057] S37, calculate the gain ratio ρ: , wherein is the objective function value of the new state variable x , is the objective function value of , when the gain ratio ρ is greater than the first gain setting value ρ good , make , γ > 1; when the gain ratio ρ is less than the second gain setting value ρ bad , make ;

[0058] In step S37, the convergence condition is , and the physical feasibility conditions include that the node voltage, branch current and reactive power of the unit are not out of limit, that is, the node voltage is between the upper limit and the lower limit of the voltage, the branch current is not less than the current threshold, and the reactive power of the unit is between the upper limit and the lower limit, wherein is the residual threshold, is the step threshold. ​​

[0059] S38, when the reactive power of the PV node is not out of bounds, entering next step S39; when the reactive power of the PV node exceeds the upper limit threshold of the reactive power, updating the reactive power of the PV node to the upper limit threshold of the reactive power, and converting the PV node into a PQ node, and taking the node voltage of the PV node as the swing voltage, and entering next step S39; when the reactive power of the PV node exceeds the lower limit threshold of the reactive power, updating the reactive power of the PV node to the lower limit threshold of the reactive power, and converting the PV node into a PQ node, and taking the node voltage of the PV node as the swing voltage, and entering next step S39;

[0060] S39, when the reactive power of the PQ node in step S38 is in the set power interval for a set number of steps, the PQ node is converted into a PV node again, and the node voltage of the PQ node is updated to the swing voltage; otherwise, the PQ node is still maintained.

[0061] In step S39, when the swing is triggered, the node voltage is restored to the swing voltage, and the Jacobian matrix is reconstructed according to the PV rule in the iteration, so that the PV / PQ frequent jitter near the boundary can be avoided.

[0062] S310, repeating steps S32-S39 until the maximum number of iterations is reached and the convergence condition is met, obtaining the final state variable as the power flow calculation result; when the maximum number of iterations is reached but the convergence condition is not met, using the homotopy subsection promotion and failure bisection mechanism to obtain the power flow calculation result.

[0063] S4, after deploying the solver online, inputting the current power parameters of the power grid into the solver, and using homotopy warm start to obtain the power flow.

[0064] In step S4, the homotopy warm start is used, and when the rolling scene is input into the solver, the current output of the solver is taken as the next input. The power flow includes the node voltage, the active and reactive power of the branch.

[0065] The power flow fast and robust solving method based on the damped Newton-homotopy warm start can quickly and stably obtain the node voltage and branch flow under complex constraint and disturbance conditions, can meet the operation requirements under the new normal state of high proportion of new energy access, random load fluctuation and frequent topology switching, and is suitable for power transmission and distribution network, active distribution network and multi-scene power flow calculation of distributed power / energy storage.

[0066] The power flow fast and robust solving method based on damping Newton-homotopy thermal start-up can model the power flow equation as a nonlinear equation, minimize the two norm residual of the objective function, and use Levenberg-Marquardt (LM) damping Newton and backtracking line search as the iteration kernel, so that the calculation and memory overhead can be reduced, the iteration number and CPU time are relatively optimal, numerical stability and efficiency are considered, boundary robustness is realized by using PV reactive power over-limit projection and hysteresis rotation to suppress boundary jitter, and numerical smoothness near the boundary is improved. In the adjacent scene or load amplification path, linear homotopy subsection promotion and automatic bisection refinement are introduced, and the power flow solution and statistics of each scene are output. Through the thermal start-up combined with homotopy subsection promotion, stable convergence can still be achieved after heavy load, low voltage and topology switching; single-step automatic bisection effectively reduces the divergence probability and significantly expands the convergence domain. The method has strong engineering adaptability and supports multiple types of systems including radial / nested, distributed power and ZIP load; the automatic reference node and virtual balancing unit mechanism guarantee the minimum solvability, and facilitate rapid landing on the dispatching and simulation platform.

[0067] The above only describes the embodiments of the present application and is not used to limit the present application. The present application can have various changes and variations for those skilled in the art. Any modification, equivalent replacement, improvement, etc. within the spirit and principle of the present application shall be included in the scope of claims of the present application.

Claims

1. A fast and robust solution method for power flow based on damped Newton-homotope hot start, characterized in that: Includes the following steps, S1. Obtain the power parameters of the target power grid, including the active power of the generator, the reactive power of the generator, the active power of the load, and the reactive power of the load. S2. For the n buses, i.e. nodes of the target power grid, construct the power flow residual vector, and establish a power flow steady-state solution model with the goal of minimizing the power flow residual vector. S3. Based on the LM damped Newton method and backtracking search, a solver is constructed to solve the steady-state solution model of power flow. S4. After deploying the solver online, input the current power parameters of the power grid into the solver and use homotopic hot start to obtain the power flow.

2. The fast and robust solution method for power flow based on damped Newton-homotope hot start as described in claim 1, characterized in that: In step S1, the target power grid includes generators, loads, a solver, and a transmission network. The transmission network includes transformers, reactive power compensation devices, and transmission and distribution lines. The transformers are connected to the transmission and distribution lines through the reactive power compensation devices. The solver is connected to the generators, loads, and reactive power compensation devices respectively.

3. The fast and robust solution method for power flow based on damped Newton-homotope hot start as described in claim 1 or 2, characterized in that: In step S2, the power flow residual vector r(x) = [r1(x), r2(x), ..., r i (x), ..., r n (x)] T Where T denotes transpose, r1(x), r2(x), ..., r i (x), ..., r n (x) represents the power flow residuals of n nodes, and at the same time: When the i-th node is a PV node, the power flow residual r of the i-th node is... i (x)=[ΔP i ], where the active power imbalance of the i-th bus. , where P G,i P represents the active power of the generator corresponding to the i-th bus. L,i Let P be the active power of the load corresponding to the i-th bus. i For the active power injection of the i-th bus; When the i-th node is a PQ node, the power flow residual r of the i-th node is... i (x)=[ΔP i ΔQ i ] T The reactive power imbalance of the i-th bus is... , where Q G,i Let Q be the reactive power of the generator corresponding to the i-th bus. L,i Q represents the reactive power of the load corresponding to the i-th bus. i For the reactive power injection of the i-th bus.

4. The fast and robust solution method for power flow based on damped Newton-homotope hot start as described in claim 3, characterized in that: In step S2, the objective function of the power flow steady-state solution model is... for: (3) Where r(x) is the power flow residual, and the state variable x includes node voltage, phase and magnitude, where ║r(x)║2 is the 2 norm of r(x); The constraints include node voltage amplitude constraints, branch power over-limit constraints, and unit output constraints.

5. The fast and robust solution method for power flow based on damped Newton-homotope hot start as described in claim 4, characterized in that: In step S3, based on the LM damped Newton method and backtracking search, and using homotopy hot start, a solver is constructed to solve the steady-state power flow model. Specifically, S31. Perform initialization, given initial state variable x0 and initial damping factor μ0, where initial state variable x0 includes initial node voltage, phase and amplitude; set search step size α and minimum step size αmin; S32, in the current state variable x k The assembly residual r(x) and the Jacobian matrix J = [▽r1(x)] T ,▽r2(x) T ,...,▽r i (x) T ,...,▽r n (x) T ] T ; S33, Solve Where I is the identity matrix, the correction amount Δx is obtained; S34. Calculate the new state variable x՛=x+αΔx, and calculate the residual at x՛ and the objective function value of x՛. ; S35, in When, where c is a constant, then the next state variable x k+1 If the value is equal to x, proceed to the next step S37; otherwise, proceed to the next step S36. S36. Let α = βα, where the step size adjustment coefficient β ∈ (0,1), return to step S34, until the search step size α reaches the minimum step size αmin; S37. Calculate the gain ratio ρ: ,in, Let x be the objective function value of the new state variable. for The objective function value is such that the gain ratio ρ is greater than the first gain setting value ρ. good At that time, γ > 1; when the gain ratio ρ is less than the second gain setting value ρ bad At that time, ; In step S37, the convergence condition is: , The physical feasibility conditions include node voltage, branch current, and the unit's reactive power not exceeding the limits, i.e., node voltage between the upper and lower voltage limits, branch current not less than the current threshold, and unit reactive power between the upper and lower limits. The residual threshold, This is the step size threshold; S38. If the reactive power of the PV node does not exceed the limit, proceed to the next step S39. If the reactive power of the PV node exceeds the upper limit threshold, update the reactive power of the PV node to the upper limit threshold, and convert the PV node to a PQ node. At the same time, use the node voltage of the PV node as the rotation voltage, and proceed to the next step S39. If the reactive power of the PV node exceeds the lower limit threshold, update the reactive power of the PV node to the lower limit threshold, and convert the PV node to a PQ node. At the same time, use the node voltage of the PV node as the rotation voltage, and proceed to the next step S39. S39. When the reactive power of the PQ node in step S38 remains within the set power range for a continuous period of time, the PQ node is converted back into a PV node, and the node voltage of the PQ node is updated to the slewing voltage; otherwise, the PQ node remains unchanged. S310. Repeat steps S32-S39 until the maximum number of iterations is reached and the convergence condition is met, and obtain the final state variables as the power flow calculation result; when the maximum number of iterations is reached but the convergence condition is not met, use the homotopy segmented advancement and failure binary search mechanism to obtain the power flow calculation result.

6. The fast and robust solution method for power flow based on damped Newton-homotope hot start as described in claim 5, characterized in that: In step S37, the convergence condition is: , And physical feasibility conditions include node voltage, branch current, and whether the reactive power of the unit exceeds the limit. The residual threshold, This is the step size threshold.

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