CN112865109A - Load flow calculation method of data-driven electric power system - Google Patents

Load flow calculation method of data-driven electric power system Download PDF

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CN112865109A
CN112865109A CN202110054583.6A CN202110054583A CN112865109A CN 112865109 A CN112865109 A CN 112865109A CN 202110054583 A CN202110054583 A CN 202110054583A CN 112865109 A CN112865109 A CN 112865109A
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刘一欣
郭力
李霞林
张宇轩
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Tianjin University
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    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J3/00—Circuit arrangements for ac mains or ac distribution networks
    • H02J3/04—Circuit arrangements for ac mains or ac distribution networks for connecting networks of the same frequency but supplied from different sources
    • H02J3/06—Controlling transfer of power between connected networks; Controlling sharing of load between connected networks
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/10—Power transmission or distribution systems management focussing at grid-level, e.g. load flow analysis, node profile computation, meshed network optimisation, active network management or spinning reserve management
    • H—ELECTRICITY
    • H02—GENERATION; CONVERSION OR DISTRIBUTION OF ELECTRIC POWER
    • H02J—CIRCUIT ARRANGEMENTS OR SYSTEMS FOR SUPPLYING OR DISTRIBUTING ELECTRIC POWER; SYSTEMS FOR STORING ELECTRIC ENERGY
    • H02J2203/00—Indexing scheme relating to details of circuit arrangements for AC mains or AC distribution networks
    • H02J2203/20—Simulating, e g planning, reliability check, modelling or computer assisted design [CAD]

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Abstract

The invention discloses a load flow calculation method of a data-driven power system, which comprises the steps of collecting historical operating data of the power system, which is detected by a measuring instrument, taking part of parameter data in the historical operating data as input variables of load flow calculation, and taking parameter data related to the input variables in the rest data as output variables of the load flow calculation; increasing dimensionality of input variables and output variables of the power flow by adopting a Koopman operator theory, mapping the input variables and the output variables into a linear relation, and fitting according to collected historical operation data to obtain a linear transfer matrix between the input variables and the output variables; and obtaining the output value of any input variable corresponding to the load flow by the fitted linear transfer matrix, and finishing the load flow calculation. The invention realizes the linearization of the power flow nonlinear equation in a high-dimensional space and improves the linearization degree. Due to the high linearization level, the basic characteristics of the system can be obtained by only one calculation without adjustment along with the change of the running state.

Description

Load flow calculation method of data-driven electric power system
Technical Field
The invention relates to a power system load flow calculation method, in particular to a data-driven power system load flow calculation method.
Background
At present, the traditional linearization power flow calculation method is difficult to accurately calculate the network state under the large-range power fluctuation due to the low linearization degree of the model. The network topology structure and the network parameters in the power distribution network are difficult to obtain, and certain difficulty is brought to analysis. The model-based method needs to estimate a large amount of actual parameters, and the advantages of the data driving method are more prominent along with popularization and application of high-precision measuring equipment.
In data-driven power flow calculation, parameters are usually calculated by using a linear regression method to determine the implicit relationship between power flow input and output. The current methods for writing flow linearization are mainly classified into 4 categories: 1) the method for linearizing the trend at the operation reference point by using the mode of a Jacobian matrix and the like is simple and easy to use, but has a limited linearization range, and has weak adaptability in a scene with high proportion of renewable energy sources and large load fluctuation; 2) the linear method for simplifying the traditional power flow equation represented by the direct current power flow has a large number of assumptions in simplification, so the calculation accuracy is limited; 3) the method can represent a power flow equation into a linear form without difference and is applied to the estimation of the optimal power flow and the power flow state to a certain extent, but the decomposition method is difficult to be popularized to the corresponding relation of other power flows, such as the difficulty of representing the state space of voltage by using injected power and the like, in addition, when the method relates to nodes with a voltage control type, such as PV type nodes, the injected power of the nodes cannot be represented into the quadratic form of the voltage, so the method is difficult to realize the linearization in a system relating to the nodes; 4) the linear relation between the node voltage and the node injection current is established by utilizing a circuit theory, and the linear relation between the linear node injection power and the node injection current is combined to realize the linearization of the power flow equation, but the nonlinear characteristic between the injection power and the injection current is strong, so the accuracy of a linearization model is influenced by the nonlinear characteristic.
In the existing data-driven power flow calculation method, some documents record that a linear mapping relation with node injection power is obtained through a state space form constructed in the method, and a Support Vector Regression (SVR) method is provided for obtaining the linear power flow relation through historical measurement data regression. In order to enhance the adaptability of the linear regression model to the nonlinear trend in the data driving method, some documents describe that the calculation accuracy is improved by adding a constant term matrix, and on the basis, some documents describe that the influence of the constant term matrix on the measurement data error is increased.
However, the existing power flow calculation method still has certain defects and shortcomings:
(1) due to the fact that a timely network topology structure cannot be obtained and the parameters of a network frame structure in the power distribution network are not accurate, a large error often exists in traditional model-based load flow calculation.
(2) The existing data-driven load flow calculation linearization model is low in linearity degree and cannot adapt to network load flow calculation with large-amplitude power fluctuation, such as a network with a high-permeability distributed power supply, and the calculation accuracy is low.
(3) For the lack of a general mathematical model among different variables in the load flow calculation, the ideal calculation accuracy can be obtained only by establishing mathematical relations for different variable relations respectively.
Disclosure of Invention
The invention provides a method for calculating a power flow of a data-driven power system, which aims to solve the technical problems in the prior art.
The technical scheme adopted by the invention for solving the technical problems in the prior art is as follows: a power flow calculation method of a data-driven power system collects historical operating data of the power system, which is obtained by detection of a measuring instrument, a part of parameter data in the historical operating data is used as an input variable of power flow calculation, and parameter data related to the input variable in the rest data is used as an output variable of the power flow calculation; increasing dimensionality of input variables and output variables of the power flow by adopting a Koopman operator theory, mapping the input variables and the output variables into a linear relation, and fitting according to collected historical operation data to obtain a linear transfer matrix between the input variables and the output variables; and obtaining the output value of any input variable corresponding to the load flow by the fitted linear transfer matrix, and finishing the load flow calculation.
Further, the method comprises the steps of:
determining an input variable x and an output variable y used for load flow calculation in historical operating data of a power system;
step two, setting psi (x) as a rising-dimension operation function of the input variable x, and rising the dimension of the input variable x to obtain rising-dimension data x of the xLift，
Figure BDA0002900445890000021
Step three, setting y as MxliftObtaining a transfer matrix M by using a least square method;
step four, any group of input variables xrAfter increasing dimension, x is obtainedLift,rAnd obtaining the output variable value y from Mr。
Further, when the network has NnA node and NlWhen the line is one, the input variable satisfies:
Figure BDA0002900445890000022
the output variables satisfy:
Figure BDA0002900445890000023
further, let the output variables be: y ═ y1 y2 y3 ... ym]TIs provided with
Figure BDA0002900445890000031
Then the transition matrix M1、M2…MmAre independent of each other.
Further, the input variables x include: active power P of PQ nodePQAnd reactive power QPQ(ii) a Active power P of PV nodePVAnd a voltage amplitude VPV(ii) a Voltage amplitude V of the balanced noderefAnd phase angle thetaref。
Further, the output variable y includes: voltage amplitude V of PQ nodePQAnd phase angle thetaPQ(ii) a Voltage phase angle theta of PV nodePVAnd reactive power QPV(ii) a Active power P of balance noderefAnd reactive power Qref。
Further, the output variable y further includes: active power P at head and tail ends of network lineLAnd reactive power QL。
The invention has the advantages and positive effects that:
1) compared with the traditional data driving mode, the distribution line at the tail end of the power system is often adjusted along with the requirements of users, parameters used in actual use of the model-based method can be difficult to update in time, and calculation errors are caused.
2) The invention realizes the linearization of the power flow nonlinear equation in a high-dimensional space, and improves the linearization degree compared with the traditional linearization method. Due to the high linearization level, the basic characteristics of the system can be obtained by only one calculation without adjustment along with the change of the running state.
3) The invention establishes a general mathematical structure to reflect the high-dimensional linear implicit relation among different tidal current variables, including node voltage amplitude, active power, reactive power and the like of a voltage phase angle line, and realizes high-precision calculation.
Drawings
FIG. 1 is a flow chart of the operation of the present invention.
FIG. 2 is a graph of the mean absolute error of the voltage amplitude of the power flow node of the system in the standard IEEE118 node calculation by the method and the comparison method of the invention.
FIG. 3 is a graph of the mean absolute error of the voltage phase angle of the power flow node of the system in the standard IEEE118 node calculation by the method and the comparison method of the invention.
FIG. 4 is a graph comparing the mean absolute error of the active power of the power flow line of the standard IEEE118 node system calculated by the method and the comparison method.
FIG. 5 is a graph of the mean absolute error of the reactive power of the flow line of the system in the standard IEEE118 node system calculated by the method and the comparison method.
Detailed Description
For further understanding of the contents, features and effects of the present invention, the following embodiments are enumerated in conjunction with the accompanying drawings, and the following detailed description is given:
referring to fig. 1, a method for calculating a power flow of a data-driven power system collects historical operating data of the power system, which is obtained by detection of a measuring instrument, uses a part of parameter data in the historical operating data as input variables of power flow calculation, and uses parameter data related to the input variables in the rest of data as output variables of the power flow calculation; increasing dimensionality of input variables and output variables of the power flow by adopting a Koopman operator theory, mapping the input variables and the output variables into a linear relation, and fitting according to collected historical operation data to obtain a linear transfer matrix between the input variables and the output variables; and obtaining the output value of any input variable corresponding to the load flow by the fitted linear transfer matrix, and finishing the load flow calculation.
The core of the Koopman operator theory is: a non-linear system in a low dimensional space can be converted to a linear system after the dimensions are raised. The power flow equation in the power system is a nonlinear equation set, and after the dimensionality of input and output variables in power flow calculation is increased, the linear relation between the input and output variables can be obtained. In actual calculation, the original low-dimensional space is increased by tens to hundreds of dimensions for calculation.
Further, the method may comprise the steps of:
determining an input variable x and an output variable y which can be used for load flow calculation in historical operating data of a power system;
step two, psi (x) can be set as a rising-dimension operation function of the input variable x, and rising-dimension data x of x can be obtained after rising dimension of the input variable xLift，
Figure BDA0002900445890000041
Step three, y ═ Mx can be setliftObtaining a transfer matrix M by using a least square method;
step four, any group of input variables xrAfter increasing dimension, x is obtainedLift,rAnd obtaining the output variable value y from Mr。
Further, when the network has NnA node and NlFor a line, the input variables may satisfy:
Figure BDA0002900445890000042
the output variables can satisfy:
Figure BDA0002900445890000043
further, the output variables may be set to: y ═ y1 y2 y3 ... ym]TIs provided with
Figure BDA0002900445890000044
Then the transition matrix M1、M2…MmAre independent of each other.
Further, the input variable x may include: active power P of PQ nodePQAnd reactive power QPQ(ii) a Active power P of PV nodePVAnd a voltage amplitude VPV(ii) a Voltage amplitude V of the balanced noderefAnd phase angle thetaref。
Further, the output variable y may include: voltage amplitude V of PQ nodePQAnd phase angle thetaPQ(ii) a Voltage phase angle theta of PV nodePVAnd reactive power QPV(ii) a Active power P of balance noderefAnd reactive power Qref。
Further, the output variable y may further include: active power P at head and tail ends of network lineLAnd reactive power QL。
The working principle of the invention is further explained below in connection with a preferred embodiment of the invention:
the core of the Koopman operator theory is: a non-linear system in a low-dimensional space may be converted into a linear system in a high-dimensional space. The power flow equation in the power system is a nonlinear equation set, and the linear relation of input and output variables can be obtained after the dimensionality of the input and output variables in the power flow calculation is increased.
1) High-dimensional linear relationship:
if a non-linear system of equations y ═ f (x) exists, where x and y are column vectors,x∈R1×k，y∈R1×l(ii) a And performing ascending-dimension transformation on x as shown in formula (1), wherein psi (x) is an ascending-dimension operation function of the input vector x.
Figure BDA0002900445890000051
According to Koopman operator theory, then the existence operator M satisfies the linear mapping relation as shown in equation (2):
y＝Mxlift (2)
2) a dimension-raising function:
when the rising dimension function is used to raise the N dimension, the basic structure is as the following formula (3).
Figure BDA0002900445890000052
The formation of the ascending-dimension function contains various types, the common types are divided into two types, one is the selection of a new state space, and the other is the use of a function which contains the original variable and has stronger nonlinearity as the ascending-dimension element.
In the raising dimension element based on the nonlinear function, raising different dimensions requires selecting different basis vectors c:
ψi(x)＝flift(x-ci) (4)
in the formula, ciIs an elevated i-dimensional basis vector, ci∈R1×kThe base can select any value within the value of the variable.
A log function-based upscaling function is given as shown in the formulas (5) and (6):
Figure BDA0002900445890000053
Figure BDA0002900445890000061
the core of the Koopman operator theory is: a low-dimensional nonlinear system can be represented as a linear system in a high-dimensional space. The load flow calculation equation in the power system is a nonlinear equation system and can also be mapped to a linear equation in a high-dimensional space. The following is a preferred embodiment of the invention:
1) basic form of load flow calculation
In load flow calculation, selecting input variables and output variables:
1) input variables, including active power P of PQ nodePQReactive power QPQ(ii) a Active power P of PV nodePVAmplitude of voltage VPV(ii) a Voltage amplitude V of the balanced noderefAnd phase angle thetaref。
2) Output variables are: voltage amplitude V of PQ nodePQPhase angle thetaPQ(ii) a Voltage phase angle theta of PV nodePVAnd reactive power QPV(ii) a Active power P of balance noderefAnd reactive power Qref. In addition, the output result according to the demand trend also comprises the active power P of the head end and the tail end of the network lineLAnd reactive power QL。
After the power flow input variable is determined, the output variable has a unique solution, for example, the traditional power flow equation is a nonlinear equation set of the node voltage and the node injection power. The invention adopts a high-dimensional linearization method to map the input and output variables of the power flow into a linear relation in a high-dimensional space. Please see the following formula:
x＝[Vref θref PPQ QPQ PPV VPV]T (7)
y＝[VPQ θPQ θPV QPV Pref Qref PL QL]T (8)
when the network under study has NnA node and NlWhen the line is one, the input variable satisfies:
Figure BDA0002900445890000062
output variable fullFoot
Figure BDA0002900445890000063
2) Calculating output data
Variables in the output variables y can be selected as required in the calculation, and different output variables have the same data regression structure. With PLAnd QLFor example, equation (2) expands the output parameter to yield equation (9):
Figure BDA0002900445890000064
in the formula (9), the reaction mixture is,
Figure BDA0002900445890000065
to obtain PLF＝M1xli，QLF＝M2xliftIn the visible, M1、M2The matrices are independent of each other. Based on a data driving method, different types of output variables have no logic association in calculation, so that the output variables can be selected according to requirements, the calculated amount is greatly reduced, and the calculation speed is improved.
3) Least squares estimation
Collecting historical operation data of the power system, which is detected by a measuring instrument, taking part of parameter data in the historical operation data as input variables of load flow calculation, and taking parameter data related to the input variables in the rest data as output variables of the load flow calculation; training sets of input variables and output variables are made separately.
After the training data is obtained, the M matrix can be determined by a least square estimation method without depending on the parameter information of the grid structure.
1.3 data-driven load flow calculation step based on Koopman theory
The method comprises the following steps:
a large amount of random input data and corresponding output data X and Y can be obtained by the existing more accurate load flow calculation method. The existing power flow calculation method is used as a comparison method.
After the dimension of X is increased, X is obtainedLift。
For equation (2), the transfer matrix M is obtained using the least squares method.
Then any set of input variables xrAfter increasing dimension, x is obtainedLift,rAnd then obtaining a calculation result yr。
The verification is carried out by adopting grid standard examples with different structures, including IEEE33, IEEE123 node radial distribution network, and a grid system comprising IEEE24, IEEE30, IEEE57 and IEEE118 nodes.
The following calculation methods written by Liu Lu Xiao Campsis, Zhang Ning, kang Chong Qing and the like are used as comparison methods: in the Data-drive Power Flow Linear A Regression analysis Approach (IEEE Trans on Smart Grid), randomly generated training Data and detection Data are adopted in the calculation example to carry out calculation accuracy verification, calculation errors of a comparison method and the calculation method of the invention are compared within 3 different ranges of a Power Flow input parameter, the specific range is shown in table 1, and comparison indexes comprise a system PQ node voltage amplitude value, all node voltage phase angles, and active Power and reactive Power at one end of a line. In order to avoid that the relative error can not reflect the error level well when the calculated value is close to the 0 value, the following comparison errors all adopt average absolute errors. Fig. 1 to 4 are comparison graphs of calculation accuracy of the comparison index and the like.
As can be seen from tables 2 and 3, when random samples in the same interval are selected, the calculation accuracy of the method of the present invention is completely superior to that of the comparison method, and in the looped network structure network (IEEE5, IEEE30, IEEE57, IEEE118, NREL118), the errors of the voltage amplitude and the phase angle are substantially smaller by one order of magnitude than those of the comparison method, and the radial network (IEEE33) is also superior to that of the comparison method. The method of the present invention has greater advantages than table 2 in table 3, which shows that the method of the present invention performs better in terms of calculation error in the process from range 1 to range 2, which means that the method of the present invention can better reflect the nonlinear characteristics of the power flow equation when the network operation has larger fluctuation.
Taking the IEEE118 node case containing complex ring network as an example, the calculation results of IEEE standard calculation using data obtained by range 1 training are shown in fig. 2 to 5. In most nodes and lines, the calculation error of the method is lower than that of the comparison method in different nodes and different lines, and the maximum error is obviously lower than that of the comparison method.
In a power distribution network containing a high-proportion distributed power supply, the load fluctuation of the power distribution network can be further enhanced by the distributed power supply, a range 3 is adopted in an example to reflect the possible power reverse situation of the whole power distribution network, the fluctuation range of active power is selected to be between-50% and 200% of that of a standard example, and reactive power is also set to be between-30% and 35% of the active power due to the fact that an inverter of the distributed power supply participates in a self voltage control strategy. Since the object of the analysis is the distribution network, it is assumed that such a network does not include nodes that provide a reference voltage, and therefore the effects of the PV nodes are not considered. IEEE33 and IEEE123 nodes were selected for the example analysis. The training data used were 500 sets and 1000 sets, respectively, and the calculation results are shown in table 4, using a raised dimension function to raise the dimension by 200. Therefore, in the radial network with larger backward power, the method provided by the invention has higher calculation precision.
TABLE 1
Figure BDA0002900445890000081
Table 2: error range 1
Figure BDA0002900445890000082
Table 3: error range 2
Figure BDA0002900445890000091
Table 4: error range 3
Figure BDA0002900445890000092
The main reason for the difference in accuracy is that the comparison method uses a linear numerical regression model, only a constant term matrix is introduced to enhance the regression characteristic of the nonlinear relation, the capability of reflecting the nonlinear relation is relatively weak, and the defects are more prominent when the load fluctuation range is large. The method reflects the linear relation of a low-dimensional space through the high-dimensional linear relation, essentially uses a nonlinear ascending function to fit an original nonlinear equation, and has stronger adaptability to the nonlinear equation. When the fluctuation range of the load is enlarged, the advantage of the improved dimension linearization power flow method to the nonlinear adaptability is more obvious.
The above-mentioned embodiments are only for illustrating the technical ideas and features of the present invention, and the purpose thereof is to enable those skilled in the art to understand the contents of the present invention and to carry out the same, and the present invention shall not be limited to the embodiments, i.e. the equivalent changes or modifications made within the spirit of the present invention shall fall within the scope of the present invention.

Claims (7)

1. A power flow calculation method of a data-driven power system is characterized by collecting historical operating data of the power system, which is detected by a measuring instrument, taking part of parameter data in the historical operating data as input variables of power flow calculation, and taking parameter data related to the input variables in the rest data as output variables of the power flow calculation; increasing dimensionality of input variables and output variables of the power flow by adopting a Koopman operator theory, mapping the input variables and the output variables into a linear relation, and fitting according to collected historical operation data to obtain a linear transfer matrix between the input variables and the output variables; and obtaining the output value of any input variable corresponding to the load flow by the fitted linear transfer matrix, and finishing the load flow calculation.
2. The data driven power system load flow calculation method of claim 1, comprising the steps of:
determining an input variable x and an output variable y used for load flow calculation in historical operating data of a power system;
step two, setting psi (x) as a rising-dimension operation function of the input variable x, and rising the dimension of the input variable x to obtain rising-dimension data x of the xLift，
Figure FDA0002900445880000011
Step three, setting y as MxliftObtaining a transfer matrix M by using a least square method;
step four, any group of input variables xrAfter increasing dimension, x is obtainedLift,rAnd obtaining the output variable value y from Mr。
3. The data driven power system flow calculation method of claim 2, wherein when a network has NnA node and NlWhen the line is one, the input variable satisfies:
Figure FDA0002900445880000012
the output variables satisfy:
Figure FDA0002900445880000013
4. the data driven power flow calculation method according to claim 2, wherein the output variables are: y ═ y1 y2 y3 ... ym]TIs provided with
Figure FDA0002900445880000014
Then the transition matrix M1、M2…MmAre independent of each other.
5. The data driven power system flow calculation method of claim 2, wherein inputting the variable x comprises: active power P of PQ nodePQAnd reactive power QPQ(ii) a Active power P of PV nodePVAnd a voltage amplitude VPV(ii) a Voltage amplitude V of the balanced noderefAnd phase angleθref。
6. The data driven power system flow calculation method of claim 2, wherein the output variable y comprises: voltage amplitude V of PQ nodePQAnd phase angle thetaPQ(ii) a Voltage phase angle theta of PV nodePVAnd reactive power QPV(ii) a Active power P of balance noderefAnd reactive power Qref。
7. The data driven power system flow calculation method of claim 6, wherein outputting the variable y further comprises: active power P at head and tail ends of network lineLAnd reactive power QL。
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WO2023159813A1 (en) * 2022-02-24 2023-08-31 云南电网有限责任公司电力科学研究院 Incomplete dimension raising-based method for optimizing data-driven power system, and application thereof

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