Data-mechanism driven linear power flow optimization method considering voltage amplitude and phase angle

Abstract

The invention provides a data-mechanism driven linear power flow optimization method considering voltage amplitude and phase angle. The model used in the method can calculate the optimal voltage amplitude and the phase angle control quantity of the power system, and the scheduling optimization precision is effectively improved. Different from existing linear power flow models such as direct current power flow, theta-v type linear power flow, theta-vk type linear power flow and theta-lnv type linear power flow, the model is based on a data-mechanism dual-drive method, and model errors are continuously reduced through Gaussian process regression prediction reference values and repeated iteration. And a linear active / reactive power network loss item based on Taylor expansion is introduced, so that the precision of the model is improved and nonlinearity of a solving model is avoided, thereby facilitating solving.

Description

Technical Field

[0001] The present invention relates to the field of power system dispatch optimization, and in particular to a data-mechanism driven linear power flow optimization method considering voltage amplitude and phase angle. Background Art

[0002] As a major contributor to carbon emissions, power system dispatch optimization is a key breakthrough. Power system dispatch optimization coordinates the power generation plans of conventional and renewable energy units to achieve efficient matching of power generation resources, load balancing, and cost minimization, thereby reducing reliance on fossil energy and promoting sustainable development. However, load forecast deviations, renewable energy output fluctuations, and dispatch model errors generated during the dispatch process constantly challenge the safe and stable operation of the power system. These factors reduce system stability and generate unnecessary carbon emissions. Therefore, reducing power system dispatch errors is particularly important for achieving the dual carbon goals and improving dispatch safety and economic efficiency.

[0003] The dispatch optimization model based on DC power flow is the current mainstream power system dispatch optimization solution, but this solution does not consider reactive power flow and voltage amplitude, and its accuracy is low. This patent proposes a new data-mechanism driven linear power flow optimization model that considers voltage amplitude and phase angle. The optimization results of this model can more accurately reflect the active / reactive power flow and voltage amplitude / phase angle values ​​of the power system. Compared with the existing DC power flow, θ-v linear power flow, θ-v k Different from linearized power flow models such as quasi-linear power flow and θ-lnv quasi-linear power flow, the proposed model is based on a data-mechanism dual-driven method. It continuously reduces the model error through Gaussian process regression prediction of reference values ​​and repeated iterations. It also introduces linear active / reactive network loss terms based on Taylor expansion, which improves the model accuracy while avoiding nonlinearity in the solution model, making it easier to solve. Summary of the Invention

[0004] This invention aims to provide a linear power flow optimization method. It derives a dispatch optimization model that considers voltage amplitude and phase angle. Furthermore, it proposes a quasi-hot start method based on Gaussian process regression and iteration. This method improves model accuracy while avoiding nonlinearities in the solution model, thereby facilitating the solution. Simulation examples demonstrate the effectiveness and practicality of the proposed method.

[0005] The technical solutions for implementing the present invention are as follows:

[0006] A data-mechanism driven linear power flow optimization method considering voltage amplitude and phase angle is characterized by the following steps:

[0007] Step 1: Take the voltage phase angle θ and the square of the amplitude v 2As variables, the AC power flow model of the power system is linearized with voltage phase angle and amplitude reference values;

[0008] Step 2: Based on Taylor expansion, derive the linear terms of active and reactive network losses and add them to the corresponding branch power flow equation constraints to form the final linearized power flow equation constraints;

[0009] Step 3: Read the system's new energy and load data, and use the Gaussian process regression model to give the system voltage amplitude and phase angle reference initial values;

[0010] Step 4: Based on the initial reference value or the reference value obtained from the previous round of linear power flow calculation, perform the current round of linear optimal power flow calculation to obtain the power flow scheduling result and the reference value required for the next round of iteration; determine whether the current round of iteration meets the termination condition of the iteration. If so, terminate the iteration and output the scheduling result of the linear optimal power flow. BRIEF DESCRIPTION OF THE DRAWINGS

[0011] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0012] Figure 1 Flowchart provided for the present invention;

[0013] Figure 2 Provide a schematic diagram of step three of the present invention; DETAILED DESCRIPTION

[0014] The following is a clear and complete description of the technical solutions in the embodiments of the present invention, in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in this field based on the embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0015] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings. The specific analysis process is as follows:

[0016] Figure 1 The flow chart of the present invention comprises the following steps:

[0017] Step 1: Use the voltage phase angle θ and the square of the amplitude v 2 As variables, the AC power flow model of the power system is linearized with voltage phase angle and amplitude reference values;

[0018] Assume that the active and reactive powers of line (i, j) are P ij and Q ij , then the line power flow equality constraint can be expressed as:

[0019]

[0020] Where, v i and v j are the voltage amplitudes at the beginning and end of the line, θ ij is the voltage phase difference between the first and the last two terminals, g ij and b ij are the conductance and susceptance of the circuit respectively.

[0021] The nonlinearity of the AC power flow model mainly comes from the line equation constraint (1). The nonlinearity mainly comes from the quadratic term of voltage and the trigonometric function term of phase angle. In addition, the voltage and phase angle are coupled with each other, making the model unable to be directly solved by the convex optimization solver.

[0022] This patent uses θ and v 2 As variables, the linear decoupling of voltage amplitude and phase angle is completed based on the following two assumptions:

[0023]

[0024] Where, v i,0 and v j,0 are the voltage amplitude reference values ​​of nodes i and j, θ ij,0 is the voltage phase angle difference reference value between node i and node j. The reference value can be obtained by referring to steps 3 and 4. After the reference value is introduced, the error of the second assumption can be achieved. Combining equations (1) and (2) yields the following linear power flow without considering grid losses:

[0025]

[0026] Formula (3) divides the line flow into variables: and θ ij Two linear terms, hereinafter referred to as amplitude decoupling term and phase angle decoupling term.

[0027] Step 2: Based on Taylor expansion, derive the linear terms of active and reactive network losses and add them to the corresponding branch power flow equation constraints to form the final linearized power flow equation constraints;

[0028] The source of error in the first assumption in step 1 is essentially the failure to consider the impact of active and reactive network losses on the power flow calculation. The derivation process of the linear term of network loss in this patent is as follows:

[0029] a. Amplitude and phase angle decoupling

[0030] Taylor expansion of the cosine function and ignoring Item, and take the voltage amplitude reference value v i,0 and v j,0 , we can get:

[0031]

[0032] b. Voltage phase angle-network loss linearization

[0033] Take the voltage phase angle difference reference value θ ij,0 , and Taylor expansion is performed at the reference value to obtain the corresponding affine reduction equation:

[0034]

[0035] c. Voltage amplitude-network loss linearization

[0036] Take the voltage amplitude reference value v i,0 and v j,0 , and the corresponding affine reduction equation is obtained:

[0037]

[0038] Observing the derivation process of network loss term, it can be found that the error of network loss term mainly depends on the reference value of voltage amplitude and phase angle. i,0 =v i ,v j,0 =v j ,θ ij,0 =θ ij When , equations (5)-(6) are accurate, while equation (4) The error can be ignored.

[0039] In summary, the new linear power flow line model is as follows:

[0040]

[0041] In the formula, active network loss and reactive network loss The values ​​are:

[0042]

[0043] Step 3: Read the system's new energy and load data, and use the Gaussian process regression model to give the system voltage amplitude and phase angle reference initial values;

[0044] The Gaussian process regression model is a nonparametric model that uses a Gaussian process (GP) prior to perform regression analysis on data. It is primarily used to construct approximate models of complex systems or functions and is widely used in fields such as engineering design optimization and machine learning. Using the Gaussian process regression model to predict system voltage conditions can provide the model with high-quality initial reference values ​​at a low time cost.

[0045] Gaussian process regression assumes that the target function y(x) is a linear combination of known functions plus a random process Z(x), that is:

[0046]

[0047] Among them, β i represents the linear regression coefficient, Z(x) represents the random process that provides local approximation, its mean is zero, and the spatial covariance function is:

[0048] cov[Z(x(i)),Z(x(j))]=σ 2 R(θ,x(i),x(j)) (10)

[0049] Among them, σ 2 is the process variance, R is the correlation function, and θ is the parameter of the correlation function. We can use multiple sets of known renewable energy generation data and system load data (input x) and opf calculation results (output y(x)) to use the maximum likelihood method to construct an approximate model of the opf voltage amplitude and phase angle initial value. The specific process is as follows: Figure 2 shown.

[0050] Step 4: Based on the initial reference value or the reference value obtained from the previous round of linear power flow calculation, perform the current round of linear optimal power flow calculation to obtain the power flow scheduling result and the reference value required for the next round of iteration; determine whether the current round of iteration meets the termination condition of the iteration. If so, terminate the iteration and output the scheduling result of the linear optimal power flow;

[0051] The reference value selection method for Gaussian process regression is still somewhat different from the solution value. This section introduces an iterative reference value update mechanism so that the reference value approaches the solution value during the iterative update process, and gives the termination conditions for two iterations.

[0052] Modify equations (7)-(8) into the iterative format (11)-(12):

[0053]

[0054] Where t=1, 2, 3, ... represents the number of iterations, and the reference value selected by the Gaussian process regression model is used as the initial value of the voltage amplitude reference value v i,0 and vj,0 Initial value of voltage phase angle reference θ ij,0 , until the termination condition is met, the voltage amplitude v obtained in each iteration i,t and v j,t , voltage phase angle θ ij,t They will serve as reference values ​​for the next round of iteration.

[0055] The reference value obtained in each iteration should be closer to the solution value than the reference value of the previous iteration. To this end, the following auxiliary objective function can be introduced into the objective function:

[0056]

[0057] Where ||·||1 represents the L-1 norm that can be solved in the solver, and θ t is the vector or matrix corresponding to the voltage amplitude and phase angle in the tth iteration, c v and c θ is the corresponding auxiliary objective function coefficient, which can be selected as a constant or adaptive value to control the speed of iterative convergence.

[0058] The iteration termination condition can be directly used as the iteration round number t. Generally, when t = 2, the linear power flow can achieve a higher accuracy. You can also use f aux ≤ε, where ε is the set convergence accuracy.

[0059] Application Examples

[0060] Taking the IEEE 30-bus standard calculation system, the IEEE 39-bus standard calculation system, the IEEE 69-bus standard calculation system and the highest voltage level system in a northwestern province as examples, the traditional θ-v 2 The method of the present invention is demonstrated by comparing it with a quasi-linear power flow model.

[0061] Taking the mean relative error MAPE and mean absolute error MAE of the voltage phase angle and amplitude corresponding to the system as indicators, the calculation error comparison of the two models is shown in the following table:

[0062]

[0063]

[0064] As can be seen from the table, the accuracy of this model is significantly better than the traditional θ-v 2 Quasi-linear power flow model with better accuracy and practicality.

[0065] It should be noted that the contents not described in detail in the embodiments of the present invention belong to the prior art known to those skilled in the art.

[0066] The above description is merely a preferred embodiment of the present invention, but the scope of protection of the invention is not limited thereto. Any changes or substitutions that can be easily conceived by a person skilled in the art within the technical scope disclosed in the present invention should be included in the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be based on the scope of protection of the claims.

Claims

1. A data-mechanism driven linear power flow optimization method considering voltage amplitude and phase angle, Its characteristics include the following steps: Step 1: Using the voltage phase angle θ and the squared amplitude v2 as variables, linearize the AC power flow model of the power system with the voltage phase angle and amplitude reference values; Step 2: Based on Taylor expansion, derive the linear terms of active and reactive network losses and add them to the corresponding branch power flow equation constraints to form the final linearized power flow equation constraints; Step 3: Read the system's new energy and load data, and use the Gaussian process regression model to give the system voltage amplitude and phase angle reference initial values; Step 4: Based on the initial reference value or the reference value obtained from the previous round of linear power flow calculation, perform the current round of linear optimal power flow calculation to obtain the power flow scheduling results and the reference value required for the next round of iteration; Determine whether this round of iteration meets the termination condition of the iteration. If so, terminate the iteration and output the scheduling result of the linear optimal power flow.

2. A data-mechanism driven linear power flow optimization method considering voltage amplitude and phase angle according to claim 1, characterized in that: In step 1, the linear decoupling of voltage amplitude and phase angle is completed based on the following two assumptions: Where, v i and v j are the voltage amplitudes of nodes i and j, θ ij is the voltage phase angle difference between node i and node j; v i,0 and v j,0 are the voltage amplitude reference values ​​of nodes i and j, θ ij,0 is the voltage phase angle difference reference value between node i and node j. This gives the linear power flow without considering network losses:

3. A data-mechanism driven linear power flow optimization method considering voltage amplitude and phase angle according to claim 1, characterized in that: In step 2, first, the active network loss after linearization is and reactive network loss The expression is as follows: The line power flow equation constraints considering active / reactive network losses are as follows:

4. A data-mechanism driven linear power flow optimization method considering voltage amplitude and phase angle according to claim 1, characterized in that: In step 3, the Gaussian regression model and the random process covariance expression are as follows: cov[Z(x(i)),Z(x(j))]=σ 2 R(θ,x(i),x(j)) (6) Among them, β i represents the linear regression coefficient, Z(x) represents the random process that provides local approximation, σ 2 is the process variance, R is the correlation function, and θ is the parameter of the correlation function.

5. A data-mechanism driven linear power flow optimization method considering voltage amplitude and phase angle according to claim 1, characterized in that: In step 4, an iterative update reference value mechanism is introduced so that the reference value approaches the solution value during the iterative update process. The iterative expression is as follows: Where t = 1, 2, 3, ... represents the number of iterations. The reference values ​​selected by the Gaussian process regression model are used as the initial reference values ​​of the voltage amplitude and the voltage phase angle. The voltage amplitude and phase angle obtained in each iteration will be used as the reference values ​​for the next iteration until the termination condition is met. During the iteration process, auxiliary functions need to be added to the objective function: Where ||·||1 represents the L-1 norm that can be solved in the solver, and θ t is the vector or matrix corresponding to the voltage amplitude and phase angle in the tth iteration, c v and c θ is the corresponding auxiliary objective function coefficient, which can be selected as a constant or adaptive value to control the speed of iterative convergence. The iteration termination condition can be directly used as the iteration round number t. Generally, when t = 2, the linear power flow can achieve a higher accuracy. You can also use f aux ≤ε, where ε is the set convergence accuracy.

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