Optimization method and application of data-driven power system based on incomplete dimensionality increase

Abstract

The present invention discloses an optimization method for a data-driven power system based on incomplete dimensionality increase, and further divides the power flow independent variables into control variables and disturbance variables. Among them, the control variables, as the optimization variables in the optimization problem, can select controllable devices in the power grid, such as the output active and reactive power of the controllable power supply and the operating status of other controlled devices; and the disturbance variables are uncontrolled independent variables, such as the voltage amplitude of the balancing node, the node injected with reactive power PV node, the node injected with active power and voltage amplitude. In the present invention, only the disturbance variables are dimensionally increased, and the nonlinear characteristics of the power flow are adapted by the nonlinear function in the dimension increase function; while the control variables are not dimensionally increased, so as to keep the power flow constraint as a linear expression about the control variable, to simplify the form of the power flow constraint and simplify the solution, and at the same time, a higher precision optimization effect can be achieved. The optimization method of the present invention can be used to achieve distributed photovoltaic power optimization scheduling.

Description

Technical Field

[0001] The present invention relates to a data-driven power system optimization calculation method, and in particular to a data-driven power system optimization calculation method based on incomplete dimensionality-raising linear regression. Background Art

[0002] As a basic condition that needs to be met for system operation, power flow constraints are widely used in power system optimization calculations. However, due to the non-convex nonlinear characteristics of the classical power flow equation [1] , it is difficult to achieve fast and global optimal solution when directly used as constraint conditions in optimization calculations. In addition, the existing various linearized and simplified power flow models rely on power grid topology information and line parameters, but it is difficult to obtain the above accurate parameters in actual medium and low voltage distribution networks, resulting in low accuracy of power flow constraints in actual projects and difficulty in practical application. [2] .

[0003] In response to the above problems, various types of power flow equations have been developed in existing research to meet the needs of optimization calculations. Currently, power flow models can be divided into five types according to their mathematical structure and parameter sources:

[0004] 1) Simplified power flow equation and equivalent approximation [3][4][5] This type of method represents the original variables of the system in a linear form, but it is difficult to adapt to the nonlinear characteristics of the system in scenarios such as heavy loads and large-scale distributed power access, resulting in a decrease in power flow accuracy and failure to meet the system's optimal operation and regulation.

[0005] 2) Nonlinear power flow. The Distflow model, which is widely used in distribution network optimization, establishes a nonlinear relationship between the square of the voltage amplitude, the square of the branch current, and the branch power. However, it still belongs to a non-convex nonlinear equation system and needs to be convexly relaxed for solution. [6] However, the optimization objective of convex relaxation optimization needs to match the convexification method so that the optimization result satisfies the power flow constraint, which limits the selection of optimization objectives.

[0006] 3) Power flow based on new state space. A large number of studies have established various types of linear power flow calculations based on different state spaces and simplified models. [7][8] By selecting the state space of different kernel functions, the linear mathematical structure under the new state space can be obtained, and accurate power flow calculation results can be obtained to meet the nonlinear calculation requirements of the distribution network under large-scale power fluctuations. However, the reselected transition space is restricted by the kernel function, and threshold matching is required in the selection of the objective function, which greatly limits the application of this method in optimization calculations.

[0007] 4) Data-driven linear power flow [2]Compared with the model-based linear power flow, it has the advantage of not relying on grid topology and line parameter information and has higher engineering application value. However, this method is based on a linear mathematical model and therefore is also not adaptable to the nonlinear characteristics of the system.

[0008] 5) Data-driven trends based on increased dimensionality [9] , by using the dimensionality-raising method to describe the nonlinear system in the low-dimensional space with the linear model in the high-dimensional space, it has higher power flow calculation accuracy for the system with strong nonlinearity. However, the dimensionality-raising function usually has a complex mathematical structure, which limits its application in optimization solutions.

[0009] In summary, the existing power flow constraints still have certain defects and shortcomings:

[0010] (1) In actual projects, it is often difficult to obtain the timely network topology of medium and low voltage distribution networks, and the line parameters are inaccurate. The power flow model derived from the classical power flow equation has large errors in the calculation results due to its reliance on accurate network parameters, which makes it difficult to meet the needs of actual projects.

[0011] (2) In a heavy-load, high-distributed-generation-permeability power grid, the system will exhibit a higher degree of nonlinear characteristics. The linear power flow model is difficult to fit the nonlinear characteristics of the system, and the nonlinear power flow equation as a constraint has poor adaptability in solving optimization problems. Existing methods are difficult to achieve both easy solution and high accuracy.

[0012] (3) In the linear power flow model based on the reselection of state space, the higher-precision state space has a poor fit with the objective function selection of the optimization model, and high-precision power flow constraints can only be established for a very small number of specific objective functions. Therefore, it has poor adaptability in power system optimization.

[0013] [References]

[0014] [1] Yang Z,

[0015] [2][Liu Y,Zhang N,Wang Y,et al.Data-Driven Power Flow Linearization:ARegression Approach[J].IEEE Transactions on Smart Grid,2017,10(3):2569-2580

[0016] [3]Sulc P,Backhaus S,Chertkov M.Optimal Distributed Control ofReactive Power Via the Alternating Direction Method of Multipliers[J].IEEETransactions on Energy Conversion,2013,29(4):968-977.

[0017] [4]Yang J,Zhang N,Kang C,et al.A State-Independent Linear Power FlowModel With Accurate Estimation of Voltage Magnitude[J].IEEE Transactions onPower Systems,2017,32(5):3607-3617.

[0018] [5]T.Akbari and M.T.Bina,“Linear approximated formulation of acoptimalpower flow using binary discretisation,”IET Gener.Transmiss.Distrib.,vol.10,no.5,pp.1117–1123,2016.

[0019] [6]Baran,M,Wu,et al.Optimal sizing of capacitors placed on a radialdistribution system[J].Power Delivery IEEE Transactions on,1989.

[0020] [7]Baran,M,Wu,et al.Optimal sizing of capacitors placed on a radialdistribution system[J].Power Delivery IEEE Transactions on,1989.

[0021] [8]Yang Z, Zhong H, Xia Q, et al. A novel network model for optimal powerflow with reactive power and network losses[J]. Electric Power Systems Research, 2017.

[0022] [9]Guo L, Zhang Y, Li X, et al. Data-driven Power Flow CalculationMethod: A Lifting Dimension Linear Regression Approach [J]. IEEE Transactions on Power Systems. Early Access. Summary of the invention

[0023] In view of the above-mentioned prior art, the present invention proposes a data-driven power system optimization method based on incomplete dimensionality-upgraded linear regression. Since a low-dimensional nonlinear system can be represented as a linear system in a high-dimensional space, an appropriate kernel function can be selected to upscale the power flow variables in the low-dimensional space, and realize the mapping relationship of the power flow calculation in the high-dimensional space to adapt to the nonlinear characteristics of heavy-load and high-penetration distributed power systems. The independent variables of the system are divided into control variables and disturbance variables. The proposed method only upscales the disturbance variables to achieve the nonlinear fitting of the system; and does not upscale the control variables to ensure the linear characteristics of the control variables in the power flow constraints, so as to facilitate the optimization solution. Based on incomplete dimensionality-upgraded data-driven power flow constraint optimization, while satisfying the easy-to-solve characteristics, a higher-precision optimization effect can be achieved.

[0024] In order to solve the above technical problems, the present invention proposes an optimization method for a data-driven power system based on incomplete dimensionality increase. In the optimization method, the power flow independent variable is divided into a control variable u and a disturbance variable x; wherein the control variable u is used as the optimization variable in the optimization problem; the disturbance variable is an uncontrolled independent variable; the control variable u is not dimensionalized to keep the power flow constraint as a linear expression of the control variable u, and the disturbance variable x is dimensionalized to adapt to the nonlinear characteristics of the power flow through the nonlinear function in the dimensionality increase function. The optimization method includes the following steps:

[0025] Step 1) Classify the historical operation data of the power grid analysis object, including the control variable u in the independent variable of the power flow variable, the disturbance variable x to the state variable y; wherein: the control variable u selects the output active power P of the controllable power supply in the power grid DG and reactive power Q DG , u=[P DG Q DG ] T ; The disturbance variable x includes the equilibrium node voltage amplitude V ref , the injected active power P of the PQ node PQ and reactive power Q PQ , the injected active power P of the PV node PV With the voltage amplitude Q PV , x=[V ref , P PQ , Q PQ , P PV , V PV ] T ; The state variable y is selected according to the calculation requirements;

[0026] Step 2) Use the following formula to perform dimension-upgrading calculation on the disturbance variable x to obtain the disturbance variable x after dimension-upgrading: lift ;

[0027]

[0028] Among them, ψ(x) is the dimension-raising function of the input vector x;

[0029] Step 3) An incomplete dimensionality-enhanced power system data-driven power flow algorithm is established by the following formula, and the least squares method is used for parameter regression to determine the power flow mapping matrix M, so as to achieve high-precision power flow mapping of the control variable u and the disturbance variable x to the state variable y;

[0030]

[0031] In the formula, M0 and M1 are both block matrices of the M matrix; the disturbance variable x to the state variable y specifically includes:

[0032] x=[V ref , P PQ , Q PQ , P PV , V PV ] T

[0033] y=[V PQ , P L , Q L ,…] T

[0034] The least squares estimation is performed based on the linear structure of the following formula to determine the mapping relationship matrix M of the power flow;

[0035] y=Mx lift

[0036] Step 4) Through the M matrix obtained in step 3), establish the incomplete dimensionality-upgrading power flow constraints for the control variable u, the disturbance variable x to the state variable y; integrate it into the traditional optimization framework, establish the optimization objective function, and then obtain the optimization model of the data-driven power system based on incomplete dimensionality-upgrading, and use the optimization model as the basis for data-driven power system operation optimization.

[0037] Further, in step 2) of the optimization method,

[0038] When using the dimension raising function to raise N dimensions, the basic structure of the dimension raising operation function is as follows:

[0039]

[0040] In the dimension-raising elements based on nonlinear functions, different basis vectors c need to be selected to raise different dimensions:

[0041] ψ i (x) = f lift (xc i )

[0042] In the formula, c i is the i-th dimension basis vector raised, The basis can choose any random number within the variable value; a dimensionality-raising function based on the logarithmic function is given as follows:

[0043]

[0044] The optimization method of the present invention can realize the power optimization scheduling of distributed photovoltaics; including:

[0045] The established incomplete dimensional power flow mapping relationship of distributed photovoltaics is as follows:

[0046]

[0047] Where V PQ Indicates the voltage amplitude of the PQ node;

[0048] The distributed power generation optimization scheduling model with power flow constraints based on the above-mentioned incomplete dimensional power flow mapping relationship of distributed photovoltaics is as follows:

[0049] Min ∑|Q DG -Q′ DG |

[0050]

[0051] In the formula, Q′ DG is the reactive power output vector before distributed photovoltaic regulation; V min , V max Respectively represent the lower and upper limits of the voltage amplitude of the distribution network under analysis; S DG A vector representing the installed photovoltaic capacity; Respectively represent P DG , Q DG , S DG The square of each element in .

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] 1) Compared with the power flow constraint based on the physical model, the proposed method does not rely on the actual grid topology and line parameters, avoids the power flow constraint error caused by parameter errors, and has higher application value in actual engineering.

[0054] 2) The disturbance variables are upgraded in dimension to fit the nonlinear characteristics of the system in high-dimensional space, which has higher constraint accuracy than linear power flow constraints.

[0055] 3) Compared with the existing nonlinear power flow constraint equations, the proposed method has higher objective function adaptability because no new control variable state space is defined; and the power flow constraint is expressed as a linear equation of the control variable, which retains the characteristic of easy solution of the constraint. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a basic topology diagram of an embodiment of the present invention;

[0057] Figure 2 A comparison diagram of node voltage distribution between the method of the present invention and the control method when minimizing the average voltage deviation rate is the optimization target;

[0058] Figure 3 A comparison diagram of reactive power regulation amount between the method of the present invention and the control method when minimizing the average voltage deviation rate is the optimization target;

[0059] Figure 4 is a comparison diagram of average voltage deviation rate optimization results of the method of the present invention and the control method when minimizing the average voltage deviation rate is the optimization target;

[0060] Figure 5 A comparison diagram of node voltage distribution between the method of the present invention and the control method when minimizing the reactive power regulation amount of the distributed power source is the optimization target;

[0061] Figure 6 The figure is a comparison diagram of reactive power regulation amount between the method of the present invention and the control method when minimizing the reactive power regulation amount of distributed power sources is the optimization goal. DETAILED DESCRIPTION

[0062] The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, but the following embodiments are by no means intended to limit the present invention in any way.

[0063] The design idea of ​​the optimization method of the data-driven power system based on incomplete dimensionality increase proposed in the present invention is to further divide the power flow independent variable into the control variable u and the disturbance variable x. Among them, the control variable u is used as the optimization variable in the optimization problem, and the controllable equipment in the power grid, such as the output active and reactive power P of the controllable power supply, can be selected. DG , Q DG and the operating status of other controlled devices, etc., u=[P DG Q DG ] T ; The disturbance variable is an uncontrolled independent variable, such as the voltage amplitude V of the equilibrium node ref , PQ node injects reactive power P PQ , Q PQ , the node injected active power and voltage amplitude P of the PV node PV , Q PV etc., x=[V ref , P PQ , Q PQ , P PV , V PV ] T In the present invention, only the disturbance variable x is dimensionally upgraded, and the nonlinear characteristics of the power flow are adapted through the nonlinear function in the dimension-upgrading function; while the control variable u is not dimensionally upgraded to keep the power flow constraint as a linear expression about u, so as to simplify the power flow constraint form and simplify the solution.

[0064] 1. The main contents of the optimization method proposed in the present invention are as follows:

[0065] 1-1. Data-driven power flow calculation based on dimensionality increase

[0066] The power flow equation in the power system in low-dimensional space is a nonlinear equation system. By increasing the dimensions of the input and output variables in the power flow calculation, the linear relationship between the input and output variables can be obtained.

[10]

[0067] 1) High-dimensional linear relationship. If there is a nonlinear equation system y = f(x), where x and y are column vectors, Perform a dimensionality-raising transformation on x as shown in formula (1), where ψ(x) is the dimensionality-raising function of the input vector x.

[0068]

[0069] Then there exists an operator M that satisfies the linear mapping relationship as shown in formula (2):

[0070] y=Mx lift (2)

[0071] 2) Dimensionality-raising function: When the dimension-raising function is used to raise the N-dimensionality, the basic structure of the dimension-raising operation function is as follows (3).

[0072]

[0073] In the dimension-raising elements based on nonlinear functions, different basis vectors c need to be selected to raise different dimensions:

[0074] ψ i (x) = f lift (xc i ) (4)

[0075] In the formula, c i is the i-th dimension basis vector raised, The basis can be any random number within the variable value. A dimensionality-raising function based on the logarithmic function is given as shown in formula (5):

[0076]

[0077] 1-2. Data-driven power flow calculation based on dimensionality increase

[0078] 1) Basic form of power flow calculation

[0079]

[0080] In the power flow calculation, the independent variables include: voltage amplitude of the balancing node, reactive power injected into the PQ node, active power injected into the PV node and voltage amplitude, which correspond to: V ref , P PQ , Q PQ , P PV , Q PV; Since the dependent variable only describes the specific state of the system under the dependent variable, each dependent variable is independent of each other in the calculation, so it can be selected according to the calculation needs, such as the voltage amplitude V of the PQ node PQ , branch active and reactive power P L , Q L wait.

[0081] 2) Least Squares Estimation

[0082] According to the needs of power flow calculation, the historical operation data of the power grid analysis phase is corresponding to the independent variable X and the dependent variable Y of the power flow, and the least squares estimation is performed based on the linear structure of formula (2) to determine the mapping relationship matrix M of the power flow.

[0083] 1-3. Data-driven tide optimization method based on incomplete dimensionality increase

[0084] Since complete dimensionality increase introduces all independent variables of power flow into the calculation of the dimensionality increase function, the power flow equation is expressed as a nonlinear equation of all independent variables, and the complex dimensionality increase function makes it difficult to solve the power flow as a constraint condition, which limits the application of data-driven power flow models based on dimensionality increase in optimization problems.

[0085] To this end, the present invention further divides the power flow independent variable into a control variable u and a disturbance variable x. Among them, the control variable u is used as the optimization variable in the optimization problem, and the controllable device in the power grid, such as the output active and reactive power P of the controllable power supply, can be selected. DG , Q DG and the operating status of other controlled devices, etc., u=[P DG Q DG ] T ; The disturbance variable is an uncontrolled independent variable, such as the voltage amplitude V of the equilibrium node ref , PQ node injects reactive power P PQ , Q PQ , the node injected active power and voltage amplitude P of the PV node PV , Q PV etc., x=[V ref , P PQ , Q PQ , P PV , V PV ] T .

[0086] In the present invention, only the disturbance variable x is dimensionally upgraded, and the nonlinear characteristics of the power flow are adapted through the nonlinear function in the dimension-upgrading function; while the control variable u is not dimensionally upgraded, so as to keep the power flow constraint as a linear expression about u, so as to simplify the form of the power flow constraint and simplify the solution. Based on the idea, the incomplete dimension-upgrading expression is shown as (7).

[0087]

[0088] Where M0 and M1 are block matrices of the M matrix.

[0089] 1-4. The optimization steps of the data-driven power system based on incomplete dimensionality increase proposed by the present invention are summarized as follows:

[0090] Step 1) Classify and correspond the historical operation data of the power grid analysis object, including the control variable u in the independent variable of the power flow variable, the disturbance variable x to the state variable y. Among them, the control variable u is used as the optimization variable in the optimization problem, and the controllable devices in the power grid, such as the output power of the controllable power supply and the operating status of other controlled devices, etc., the output active power P of the controllable power supply DG and reactive power Q DG , u=[P DG Q DG ] T ; The disturbance variable x is an uncontrolled independent variable, such as uncontrollable load and power supply variables, which can include the voltage amplitude V of the equilibrium node ref , the injected active power P of the PQ node PQ and reactive power Q PQ , the injected active power P of the PV node PV With the voltage amplitude Q PV , x=[V ref , P PQ , Q PQ , P PV , V PV ] T ; The dependent variable y can be selected according to the calculation requirements, such as the node voltage amplitude.

[0091] Step 2) Use formula (1) to perform dimension-upgrading calculation on the disturbance variable x to obtain the disturbance variable x after dimension-upgrading. lift .

[0092] Step 3) The incomplete dimensionality-enhanced power system data-driven power flow algorithm is established through formula (7), and the least squares method is used for parameter regression to determine the power flow mapping matrix M, thereby realizing high-precision power flow mapping from the control variable u and the disturbance variable x to y.

[0093] Step 4) Through the M matrix obtained in step 3), establish the incomplete dimensionality increase flow constraints for the control variable u, the disturbance variable x to the state variable y, integrate it into the traditional optimization framework, establish the optimization objective function, and then obtain the optimization model of the data-driven power system based on incomplete dimensionality increase, and use the optimization model as the basis for data-driven power system operation optimization.

[0094] Taking the power optimization scheduling of distributed photovoltaic as an example, the incomplete dimensional power flow mapping relationship established by distributed photovoltaic is shown in formula (8):

[0095]

[0096] In the formula, V PQ represents the voltage amplitude of the PQ node; x is the disturbance variable (all other independent variables except the control variable, such as the active and reactive power of the load node, the voltage amplitude of the balance node, etc.).

[0097] The power optimization dispatching model of distributed generation with power flow constraints is constructed based on formula (8). In the overvoltage scenario, taking the objective function of the minimum reactive power regulation of distributed generation as an example, the optimization model is as follows:

[0098]

[0099] In the formula, Q′ DG is the reactive power output vector before distributed photovoltaic regulation; V min , V max Respectively represent the lower and upper limits of the voltage amplitude of the analyzed distribution network; S DG A vector representing the installed PV capacity. Respectively represent P DG , Q DG , S DG The square of each element in .

[0100] 2. Research Materials

[0101] The IEEE 33 node system is used for verification, which includes 11 distributed power access points. The specific topology is as follows: Figure 1 shown.

[0102] An overvoltage scenario was selected to verify the effectiveness of the invention. The maximum voltage was 1.077 (pu), the line always had 3.34MW of reverse active power, and the reactive power was not reversed, which was 1.36MVar. This scenario has a strong nonlinear characteristic due to the presence of large reverse power and non-reverse reactive power.

[0103] When the output power of distributed power sources is large, the distribution network will have certain overvoltage problems. The adjustable reactive power of distributed power sources can be adjusted to make the grid operation meet the voltage constraints.

[0104] Two examples are established to illustrate that the incomplete dimensionality-upgraded power flow constraint of the present invention has higher calculation accuracy than the linear power flow model while not relying on the precise topological information and line parameters of the power grid. Example 1 and Example 2 take minimizing the voltage deviation rate and minimizing the reactive power regulation of distributed power sources as optimization objectives, respectively, and establish an optimization model based on the distribution network voltage constraint and the distributed power source operation constraint. The example uses the optimization model based on the DLPF (Decoupled Linearized Power Flow) type linear power flow in the literature [4] as a control method for comparison.

[0105] Example 1

[0106] Figure 2 The method proposed in this invention and the power flow optimization model based on DLPF [4] The node voltage distribution comparison chart shows that the theoretical adjustment results of the two methods are very close after adjustment, and the voltage is maintained around 1. The Newton-Raphson precise power flow calculation results are used as a benchmark to verify the adjustment power results of the two optimization methods to evaluate the adjustment accuracy. Among them, the control method cannot adapt to the strong nonlinear characteristics of high-penetration distributed power sources after access to the distribution network due to the use of a simple linear model, and the error level is relatively large. The average voltage error of the control method is 0.009173, and the maximum voltage error is 0.017370, while the average voltage error and maximum voltage error of the method proposed in the present invention are 0.000612 and 0.002434, respectively, which are 25.14% and 14.01% of the control method, respectively, and have higher adjustment accuracy. Figure 3 The figure is a comparison chart of the reactive power regulation of distributed power sources between the method proposed by the present invention and the control method.

[0107] Figure 4 The optimization target of the method proposed in the present invention and the control method is the average voltage deviation rate of the power grid. The theoretical adjustment result of the control method is 0.000878. However, since the linear model cannot match the nonlinear characteristics of the system when the system is in high-power reverse transmission, the actual adjustment result is 0.00949, and the relative error reaches 90.75%. The optimization result of the method proposed in the present invention is 0.000798, the actual adjustment result is 0.000897, and the relative error is 11.04%. Compared with the control method, the method proposed in the present invention does not rely on any network topology information and line parameters, and can obtain higher control accuracy.

[0108] Example 2

[0109] Figure 5The node voltage distribution comparison diagram of the method proposed in the present invention and the control method, the maximum overvoltage before adjustment exceeds 1.07 (per unit value), and the upper limit of the normal operating voltage is set to 1.05 (per unit value); after optimization, it can be seen that the method proposed in the present invention and the control method both achieve effective voltage control, and the voltage constraint is satisfied after adjustment, but the actual adjustment value of the proposed method and the control method differs from the theoretical optimization value due to the existence of power flow error, wherein the voltage after adjustment of the method proposed in the present invention is higher, while the voltage of the control method is lower. Comparing the adjustment results of the two, the average voltage error and the maximum voltage error of the control method are 0.004643 and 0.009381 respectively, while the average voltage error of the adjustment result of the method proposed in the present invention is, and the maximum voltage error is 0.002273 and 0.003944, which are 48.96% and 42.04% of the control method respectively, and have a smaller voltage adjustment error. Figure 6 For Figure 5 The corresponding reactive power regulation amount of distributed power sources, the proposed method has a smaller regulation voltage error and a smaller reactive power regulation amount of distributed power sources.

[0110] Although the present invention has been described above in conjunction with the accompanying drawings, the present invention is not limited to the above-mentioned specific embodiments, which are merely illustrative rather than restrictive. Under the guidance of the present invention, ordinary technicians in this field can make many modifications without departing from the purpose of the present invention, all of which are within the protection of the present invention.

Claims

1. A data-driven power system optimization method based on incomplete dimensionality increase, characterized by: In the optimization method, the power flow independent variable is divided into a control variable u and a disturbance variable x; wherein the control variable u is used as the optimization variable in the optimization problem; the disturbance variable is an uncontrolled independent variable; the control variable u is not dimensionally increased to keep the power flow constraint as a linear expression about the control variable u, and the disturbance variable x is dimensionally increased to adapt to the nonlinear characteristics of the power flow through a nonlinear function in the dimension-up function; the optimization method comprises the following steps: Step 1) Classify the historical operation data of the power grid analysis object, including the control variable u in the independent variable of the power flow variable, the disturbance variable x to the state variable y; wherein: the control variable u selects the output active power P of the controllable power supply in the power grid DG and reactive power Q DG , u=[P DG Q DG ] T ; The disturbance variable x includes the equilibrium node voltage amplitude V ref , the injected active power P of the PQ node PQ and reactive power Q PQ , the injected active power P of the PV node PV With the voltage amplitude Q PV , x=[V ref , P PQ , Q PQ , P PV , V PV ] T ; The state variable y is selected according to the calculation requirements; Step 2) Use the following formula to perform dimension-upgrading calculation on the disturbance variable x to obtain the disturbance variable x after dimension-upgrading: lift ; Among them, ψ(x) is the dimension-raising function of the input vector x; When using the dimension raising function to raise N dimensions, the basic structure of the dimension raising operation function is as follows: In the dimension-raising elements based on nonlinear functions, different basis vectors c need to be selected to raise different dimensions: ψ i (x)=f lift (x-c i ) In the formula, c i is the i-th dimension basis vector raised, The basis can choose any random number within the variable value; a dimensionality-raising function based on the logarithmic function is given as follows: Step 3) An incomplete dimensionality-enhanced power system data-driven power flow algorithm is established by the following formula, and the least squares method is used for parameter regression to determine the power flow mapping matrix M, so as to achieve high-precision power flow mapping of the control variable u and the disturbance variable x to the state variable y; In the formula, M0 and M1 are both block matrices of the M matrix; the disturbance variable x to the state variable y specifically includes: x=[V ref ,P PQ ,Q PQ ,P PV ,V PV ] T y=[V PQ ,P L ,Q L ,…] T The least squares estimation is performed based on the linear structure of the following formula to determine the mapping relationship matrix M of the power flow; y=Mx lift Step 4) Using the M matrix obtained in step 3), establish an incomplete dimensional power flow constraint for the control variable u, the disturbance variable x to the state variable y; integrate it into the traditional optimization framework, establish an optimization objective function, and then obtain an optimization model of the data-driven power system based on incomplete dimensionality increase, and perform data-driven power system operation optimization based on the optimization model; The optimization method realizes the power optimization scheduling of distributed photovoltaic, including: The established incomplete dimensional power flow mapping relationship of distributed photovoltaics is as follows: Where V PQ Indicates the voltage amplitude of the PQ node; The distributed power generation optimization scheduling model with power flow constraints based on the above-mentioned incomplete dimensional power flow mapping relationship of distributed photovoltaics is as follows: Min ∑|Q DG -Q′ DG | In the formula, Q′ DG is the reactive power output vector before distributed photovoltaic regulation; V min , V max Respectively represent the lower and upper limits of the voltage amplitude of the analyzed distribution network; S DG A vector representing the installed photovoltaic capacity; Respectively represent P DG , Q DG , S DG The square of each element in .

Images