CN111798037B

CN111798037B - Data-driven optimal power flow calculation method based on stacked extreme learning machine framework

Info

Publication number: CN111798037B
Application number: CN202010528642.4A
Authority: CN
Inventors: 余娟; 雷星雨; 杨知方; 高倩; 李�杰; 余红欣
Original assignee: Chongqing University; Electric Power Research Institute of State Grid Chongqing Electric Power Co Ltd; State Grid Corp of China SGCC
Current assignee: Chongqing University; Electric Power Research Institute of State Grid Chongqing Electric Power Co Ltd; State Grid Corp of China SGCC
Priority date: 2020-06-10
Filing date: 2020-06-10
Publication date: 2024-08-06
Anticipated expiration: 2040-06-10
Also published as: CN111798037A

Abstract

The invention discloses a data-driven optimal power flow calculation method based on a stacked extreme learning machine frame, which mainly comprises the following steps: 1) Establishing an extreme learning machine model; 2) Stacking a plurality of extreme learning machine models layer by layer to establish a stacked extreme learning machine; 3) Optimizing the stacking type extreme learning machine to obtain an optimized stacking type extreme learning machine; 4) Establishing a data-driven optimal power flow learning frame; 5) And (5) calculating the data-driven optimal power flow learning framework by using the optimized stacked extreme learning machine. The invention can be widely applied to the problem of improving the calculation efficiency of the neural network algorithm in the analysis of the power system.

Description

Data-driven optimal power flow calculation method based on stacked extreme learning machine framework

Technical Field

The invention relates to the field of power system analysis and artificial intelligent machine learning, in particular to a data-driven optimal power flow calculation method based on a stacked extreme learning machine frame.

Background

Optimal Power Flow (OPF) of a power system is one of the most important tools in power system analysis, and is commonly used in key fields such as market clearing, network optimization, voltage control, power generation scheduling and the like. However, the nonlinearity and non-convexity of the OPF model results in excessive OPF computation burden, which makes it difficult to meet the demand of on-line computation of the power system. Although the power flow linearization method can improve the calculation efficiency to a certain extent, the method ignores key information such as voltage amplitude, reactive power and the like, and is difficult to ensure the global optimum of the optimization result. The existing OPF method mainly improves the calculation efficiency at the cost of reducing the calculation accuracy, so that a large number of samples need to be iterated in probability analysis, and the high uncertainty has a great hidden risk in a power system.

In recent years, data-driven methods have been widely used in power system analysis, including estimation of transfer distribution factors, jacobian matrices, admittance matrices, suppression of uncertainty, regression, and the like. Therefore, the neural network is widely applied, the performance of the neural network algorithm mainly depends on the selection of the super-parameters, and no effective algorithm is available at present to solve the problem of overlarge manual parameter adjustment cost caused by a large amount of super-parameters. Compared with the traditional neural network algorithm based on Back-Propagation (BP), the Stacked Extreme Learning Machine (SELM) is a new machine learning method based on a data-driven optimal power flow calculation method of a stacked extreme learning machine framework, can randomly generate input weights of hidden layer neurons, and can determine the output weights through simple matrix calculation. The method can obviously improve the training speed of the neural network and reduce the number of super parameters needing to be adjusted. Meanwhile, the method divides a larger-scale neural network into a plurality of small-scale neural networks which are calculated in series, so as to obtain less memory occupation and higher feature extraction capability. However, due to the randomness of the input weights and the analytical solution process of the output weights, SELM has limited learning ability, and a learning framework of SELM needs to be further designed to be suitable for complex OPF calculation.

The OPF is a data-driven optimal power flow calculation method based on a stacked extreme learning machine framework, which is a common method for an electric power system and obtains an optimal solution according to the running state of the system under the condition of considering various constraint conditions. By means of the machine learning technology, the complex relation between the running state of the system and the OPF optimization result is learned, and the calculation efficiency can be greatly improved. An efficient data-driven OPF calculation method requires not only high accuracy and speed, but also good generalization capability. Therefore, the SELM training is fast and the parameter adjustment is less, so that the requirement of OPF calculation can be met. However, the complexity of the relationship between OPF input (system operating state) and output (optimal power flow solution) makes it difficult for the original SELM to learn it effectively.

In view of the foregoing, there is a need to develop a SELM algorithm framework for combining high training speed and less parameter adjustment capability to overcome the above problems in a data-driven optimal power flow calculation method based on a stacked extreme learning machine framework.

Disclosure of Invention

The invention aims to provide a data-driven optimal power flow calculation method based on a stacked extreme learning machine frame, which mainly comprises the following steps:

1) Establishing an extreme learning machine model, which mainly comprises the following steps:

1.1 A) an input data set X is acquired.

1.2 An output matrix H of a model hiding layer of the extreme learning machine is established, namely:

H＝g(WX+b) (1)

where H is the hidden layer output matrix. g (·) is the activation function. W is a randomly generated input weight matrix. b is a randomly generated bias vector.

1.3 Calculating an output weight matrix beta between the hidden layer and the output layer, namely:

β＝(H^TH)^-1T (2)

In the formula, T represents a target matrix for learning of the extreme learning machine model.

2) Stacking a plurality of extreme learning machine models layer by layer to establish a stacked extreme learning machine (S extreme learning machine model).

Stacking a plurality of extreme learning machine models layer by layer, and mainly comprising the following steps of:

2.1 Dividing the stacked extreme learning machine into a plurality of sub-ELM neural networks stacked layer by using a PCA dimension reduction method, and randomly generating hidden layer neuron parameters of the first sub-ELM neural network. The number of hidden layer neurons generated at random is denoted as L _m. The initial value of m is 1.

2.2 Using L2 regularization to optimize the hidden layer output matrix H _m of the mth sub-ELM neural network, namely:

Where β _m is the output weight matrix for the mth iteration and satisfies F _m denotes an optimization function.

2.3 Calculating an output weight matrix beta _m of the mth iteration, namely:

Where C is a penalty factor. H _m is the hidden layer output matrix for the mth iteration.

2.4 The principal component analysis method is utilized to reduce the dimension of the output weight matrix beta _m, and a feature vector matrix V _m∈R^L ^×L is generated. The number of original hidden neurons is denoted as L _m, and the number of hidden neurons after dimension reduction is denoted as L _m. The feature vectors of the first l _m columns are marked as

Reduced hidden layer output matrix after dimension reductionThe following is shown:

2.5 Randomly generating L _m-l_m hidden neurons and calculating a hidden layer output matrix H _new with L _m-l_m hidden neurons.

2.6 Iteratively updating the hidden layer output matrix H _m+1, namely:

2.7 Based on the hidden layer output matrix H _m+1 updated by iteration, optimizing the feature vector matrix V _m+1 to obtain an optimized feature vector And returns to step 3.2) until the iteration ends.

3) And establishing a data-driven optimal power flow learning framework based on the stacking type extreme learning machine.

The objective function F of the data-driven optimal power flow learning framework is as follows:

the constraints are shown in the formulas (8) to (12), respectively, that is:

Where PD _i、QD_i represents the load active and reactive power requirements, respectively. PF _k、QF_k、V_i、θ_i represents the state variables of the branch active power, branch reactive power, voltage amplitude and voltage phase angle, respectively. PG _i、QG_i represents control variables of the generator active power and reactive power output, respectively. F is an objective function of the system running cost at the best steady state. S _G、S_B、S_K represents a system generator set, a node and a branch, respectively. i. j represents the node number. k represents the branch index. a _2i、a_1i、a_0i are the power generation cost coefficients, respectively. θ _ij＝θ_i-θ_j is the phase angle difference between the i-th and j-th nodes. G _ij、B_ij represents the conductance and susceptance between the i-th and j-th nodes, respectively. PF _ij represents the active power state variables of the branches where node i and node j are located. * Representing a lower limit; The upper limit is indicated.

4) Setting a reinforcement layer in the stacking type extreme learning machine to strengthen the learning ability of the stacking type extreme learning machine frame; the reinforcement layer is a multi-supervision layer and is used for correcting errors of the stacked extreme learning machine.

5) And (3) calculating the data-driven optimal power flow learning framework by using the optimized stacked extreme learning machine, wherein the main steps are as follows:

5.1 Active power demand PD _i and reactive power demand QD _i into the stacked extreme learning machine, outputting branch active power PF _k, branch reactive power QF _k.

5.2 Branch active power PF _k, branch reactive power QF _k into the stacked extreme learning machine, output voltage magnitude state variable V _i and voltage phase angle state variable θ _i.

5.3 Active power demand PD _i, reactive power demand QD _i, branch active power PF _k, branch reactive power QF _k, voltage magnitude state variable V _i, and voltage phase angle state variable θ _i are input into the stacked extreme learning machine, outputting the generator active power output control variable PG _i, reactive power output control variable QG _i, and the objective function F of system running cost at optimum steady state.

It should be noted that the invention firstly builds a SELM algorithm framework through a stacked extreme learning mechanism with a multi-layer neural network structure. On the basis, the invention provides a data-driven optimal power flow learning framework based on OPF feature decomposition and error correction. Based on the model, a three-stage SELM neural network structure is built for improving learning accuracy. The learning targets are separated through the three-stage input-output layer design, so that the purposes of correcting learning errors and improving the SELM learning ability are achieved. The invention develops a data-driven OPF learning framework, and decomposes the characteristics of an OPF mathematical model into three stages so as to reduce the learning complexity and the learning error. The method particularly relates to contents such as feature decomposition, multi-parameter planning (MPP), network structure, optimal power flow, sample classification, stacked extreme learning machine and the like.

The technical effects of the invention are undoubtedly that the invention achieves the following technical effects:

1) The SELM mapping is directly used, so that time consumption caused by a large number of iterations in OPF calculation is avoided;

2) No system topology and parameters are required;

3) A high-quality solution can be obtained in a short time, and guide information is provided for improving the OPF calculation speed.

4) The invention constructs a data-driven OPF learning framework, thereby achieving the purposes of improving training speed and reducing super-parameter adjustment.

In conclusion, the method can be widely applied to the problem of improving the calculation efficiency of the neural network algorithm in the analysis of the power system.

Drawings

FIG. 1 is a data driven OPF learning framework of the method of the invention;

FIG. 2 is a schematic diagram of a three-stage SELM network structure and its reinforcement layer design according to the present invention;

FIG. 3 is a schematic diagram of a first stage enhancement mode of the present invention;

FIG. 4 is a comparison of IEEE 39 node system voltage magnitudes;

FIG. 5 is an IEEE 39 node system active power output error comparison;

Detailed Description

The present invention is further described below with reference to examples, but it should not be construed that the scope of the above subject matter of the present invention is limited to the following examples. Various substitutions and alterations are made according to the ordinary skill and familiar means of the art without departing from the technical spirit of the invention, and all such substitutions and alterations are intended to be included in the scope of the invention.

Example 1:

Referring to fig. 1 to 3, a data-driven optimal power flow (optimal power flow, OPF) calculation method based on a Stacked Extreme Learning Machine (SELM) framework mainly includes the following steps:

1) An Extreme Learning Machine (ELM) model is built, and the main steps are as follows:

1.1 A) an input data set X is acquired.

H＝g(WX+b) (1)

β＝(H^TH)^-1T (2)

2) Stacking a plurality of extreme learning machine models layer by layer to establish a stacked extreme learning machine.

Stacking a plurality of extreme learning machine models layer by layer, and establishing a stacked extreme learning machine mainly comprises the following steps:

2.1 Dividing the stacked extreme learning machine into a plurality of sub-ELM neural networks stacked layer by using a PCA dimension reduction method (principal component analysis method, PRINCIPAL COMPONENT ANALYSIS), and randomly generating hidden layer neuron parameters of the first sub-ELM neural network. The number of hidden layer neurons generated at random is denoted as L _m. The initial value of m is 1.

2.2 Since some parameters are obtained from the last layer after the dimension reduction, only some parameters are randomly generated. Information of input data is transferred from the first layer to the last layer, so that the hidden layer output matrix H _m of the mth sub ELM neural network can be optimized by using L2 regularization, namely:

2.3 Calculating an output weight matrix beta _m of the mth iteration, namely:

Where C is a penalty factor for making a trade-off between training error and output weight norm. H _m is the hidden layer output matrix for the mth iteration. And m is the iteration number, namely the number of sub ELM neural networks.

2.4 The principal component analysis method is utilized to reduce the dimension of the output weight matrix beta _m, and a feature vector matrix V _m∈R^L ^×L is generated. The number of original hidden neurons is denoted as L _m, and the number of hidden neurons after dimension reduction is denoted as L _m. The feature vectors of the first l _m columns are marked asR is a real number. L× L, L ×l represents the dimension.

2.6 Iteratively updating the hidden layer output matrix H _m+1, namely:

the constraints are shown in the formulas (8) to (12), respectively, that is:

Where PD _i、QD_i represents the load active and reactive power requirements, respectively. PF _k、QF_k、V_i、θ_i represents the state variables of the branch active power, branch reactive power, voltage amplitude and voltage phase angle, respectively. PG _i、QG_i represents control variables of the generator active power and reactive power output, respectively. F is an objective function of the system running cost at the best steady state. S _G、S_B、S_K represents a system generator set, a node and a branch, respectively. i. j represents the node number. k represents the branch index. a _2i、a_1i、a_0i are the power generation cost coefficients, respectively. θ _ij＝θ_i-θ_j is the phase angle difference between the i-th and j-th nodes. G _ij、B_ij represents the conductance and susceptance between the i-th and j-th nodes, respectively. PF _ij represents the active power state variables of the branches where node i and node j are located. * Representing a lower limit; The upper limit is indicated. PG _i, Lower and upper limits of control variables representing generator active power output.QG _i represents the upper and lower limits of the control variable of the generator reactive power output.V _i represents the upper and lower voltage amplitude limits.Representing the upper limit of the branch active power state variable.

The OPF model contains the physical information of the power system, including the power grid topology, line parameters and corresponding physical laws, etc. But the non-linearity and non-convexity of the OPF model result in the computation process requiring multiple iterations, consuming a lot of time. From a data-driven perspective, the calculation of OPF can be seen as a non-linear mapping: the system power requirement PD _i,QD_i is taken as input and the OPF calculation PG _i,QG_i,V_i,θ_i,PF_k,QF_k, F is taken as output. The mapping relation between the input and the output can be subjected to offline learning through historical data or analog data.

4) A reinforcement layer is provided in the stacked extreme learning machine to enhance learning ability of the stacked extreme learning machine frame. The reinforcement layer is a multi-supervision layer and is used for correcting errors of the stacked extreme learning machine. The multi-supervision layer is used for correcting errors of the single supervision layer. The model is used for separating learning targets, so that learning errors of the OPF model are corrected, learning accuracy is improved, as shown in fig. 2, each stage is provided with a hidden layer with a similar structure, and the model is provided with an enhancement mode with a multi-supervision layer structure, so that learning capacity of SELM is improved. Taking the first phase of the subnet as an example, as shown in fig. 3. The hidden layer of SELM includes two components:

a) SLEM regressions of single supervision layer;

b) SLEM regressions.

In actual case, the output generated by the input PD _i,QD_i May deviate from the true value PF _k,QF_k, so multiple supervisory layers are used to reduce PF _k,QF_k and PF in single layer SLEM learningErrors between them.

5) Referring to fig. 1, the optimized stacked extreme learning machine is utilized to calculate a learning framework of data driving optimal power flow ((optimal power flow, OPF)), and the main steps are as follows:

5.1 First stage (f: PD _i,QD_i→PF_k,QF_k): the branch active power and reactive branch power are learned, the branch power is separated from a complex OPF model and used for SELM learning, namely, the active power requirement PD _i and the reactive power requirement QD _i are input into a stacked extreme learning machine, and the branch active power PF _k and the branch reactive power QF _k are output. In fig. 1, P _i、Q_i represents the active power and the reactive power of the node i, respectively. P _ij、Q_ij represents the active power and the reactive power of the branch where node i and node j are located, respectively.

5.2 A second stage (f: PF _k,QF_k→V_i,θ_i): the voltage amplitude and the voltage phase angle are learned, wherein physical information in a tide model is covered, including line parameter information, corresponding physical laws and the like, namely, the branch active power PF _k and the branch reactive power QF _k are input into a stacked extreme learning machine provided with a strengthening layer, and a voltage amplitude state variable V _i and a voltage phase angle state variable theta _i are output.

5.3 The third stage (f：PD_i,QD_i,PF_k,QF_k,V_i,θ_i→PG_i,QG_i,F)： learns the control variables and objective function values, further improving learning performance, namely, inputting the active power demand PD _i, the reactive power demand QD _i, the branch active power PF _k, the branch reactive power QF _k, the voltage amplitude state variable V _i and the voltage phase angle state variable θ _i into a stacked extreme learning machine provided with a reinforcement layer, outputting the control variable PG _i of the active power output of the generator, the control variable QG _i of the reactive power output and the objective function F of the system running cost in the optimal steady state.

The core idea of the solution process is to reduce the learning difficulty of the OPF. The whole resolving process is based on ResNet design concept, and a path for directly connecting input and output is provided in the middle layer. The second stage and the third stage are an error correction process in the whole resolving process, and according to the state variable obtained from the first stage, the learning target of the model can be directly calculated through the tide model. The optimal S-extreme learning machine model is combined through three stages, learning errors are gradually reduced, and finally the precision requirement is met.

Example 2:

Referring to fig. 4 and 5, an experiment for verifying a data-driven optimal power flow calculation method based on a stacked extreme learning machine framework mainly comprises the following steps:

1) Building an experiment system: IEEE 39, 57, 118 node and polish 2383 node systems. When wind power generation and photovoltaic power generation are connected to different nodes, the wind power generation is compliant with the Weber distribution, and the photovoltaic power generation is compliant with the Beta distribution. The renewable energy permeability and the load fluctuation rate are shown in table 1, and the comparison results of various schemes are shown in table 2. The hardware and software used in the simulation is: intel i7-8700K CPU, 32G RAM, WINDOWS 10 and MATLAB2018b.

2) The accuracy index p is introduced to measure the accuracy of learning performance, i.e., the probability that the learning error is less than the threshold thr.

Wherein: And T is a predicted value and an actual value, respectively; for V and θ, the parameters for the threshold thr are 0.001p.u and 0.5 ⁰; for PF, QF, PG and QG, the threshold thr is 1% of the mean value of itself in the training data; for the objective function value F, the threshold thr is 0.1% of the mean value of itself in the training data.

Table 1 uncertainty in the case

Table 2 results of various protocol comparisons

O represents considered x represents not considered

Table 3 improvements in IEEE 39 node systems

3) Evaluation analysis

To demonstrate the benefits achieved by the proposed method, we compared the learning effect of M3, M4, M5 in an IEEE 39 node system, as shown in table 3. The number of training samples and the number of test samples were 30000 and 10000, respectively. The number of hidden neurons L is 1000 and 100. The number of hidden neurons L is reduced to 100, which is 10% of the hidden neurons L. The number of iterations of single layer SELM was 10. The number of layers of the enhancement mode is 2. Penalty factor C is set to 230. From the comparison, the following conclusions can be drawn:

a) For M3 and M4, the original SELM direct learning is difficult to achieve better effect because of the complex OPF model. In order to solve the problem, the invention provides an OPF regression framework, which decomposes a learning task into three stages, reduces the learning complexity of the OPF model and obviously improves the learning effect of each variable.

B) For M4 and M5, the learning effect is improved due to the enhancement mode. In the enhanced mode, two supervision layers balance accuracy and network complexity, and learning accuracy is greatly improved.

The invention also discusses the error correction problem of the three-stage SELM network. The voltage amplitude of the generator (learning target of the second stage) and the active power output (learning target of the third stage) can be calculated by the physical power flow model using the output of the first stage (i.e., PF _k,QF_k) and the output of the second stage (i.e., V _i,θ_i), respectively. For the voltage, the values obtained in the first stage and the second stage are compared with the actual values, as shown in fig. 4. The active power output errors obtained in the second and third phases are compared as shown in fig. 5. The voltage amplitude error has been corrected in the second stage, and the third stage is mainly used for correcting the errors of the control variables and the objective function values. The three stages improve the learning precision and meet the precision requirement.

4) Compared with the existing algorithm

The performance of M0, M1, M2 and M5 was compared in the present invention, and the results are shown in tables 4 and 5. The class parameter m is set to2 in the sample pre-classification and the voltage magnitude constraint is selected to identify the critical region. The super parameter settings are the same as for the V-B node for IEEE 39, 57, and 118 systems. The deep learning based network has 4 hidden layers with 400 nodes per layer. The pre-training and fine tuning were set to 200 and 500 iterations, respectively. For the Poland 2383 node system, the deep learning based network has 4 hidden layers, with 700 nodes per layer. In the algorithm provided by the invention, the training sample number and the test sample number are respectively set to 100000 and 10000. The hidden neurons L and the reduced hidden neurons L were set to 7000 and 700, respectively. The number of iterations of the single layer SELM is set to 30.

Table 4 learning effect comparison

Table 5 training versus test time

From the experimental results the following conclusions can be drawn:

a) In all OPF calculation cases, the method provided by the invention has the highest precision.

B) The neural network test time trained in M1, M2, and M5 is acceptable and much less than M0.

C) Due to the existence of the BP process, the training cost of the deep learning method is far higher than that of the algorithm of the invention. Meanwhile, the deep learning method requires adjustment of a large number of super parameters. In contrast, the present invention can be easily migrated to a different system with similar accuracy as long as the super parameters are slightly adjusted.

In summary, according to the data driving OPF method based on the SELM framework and the physical information provided by the present invention, the learning task is decomposed into three stages, so that the learning ability is improved, and the learning complexity is significantly reduced. Thus, the present invention may provide technical support for power system analysis.

Claims

1. The data-driven optimal power flow calculation method based on the stacked extreme learning machine framework is characterized by mainly comprising the following steps of:

1) Establishing an extreme learning machine model;

2) Stacking a plurality of extreme learning machine models layer by layer to establish a stacked extreme learning machine;

3) Establishing a data driving optimal power flow learning framework based on a stacking type extreme learning machine;

4) Setting a reinforcement layer in the stacking type extreme learning machine to strengthen the learning ability of the stacking type extreme learning machine frame;

5) The stacked extreme learning machine is utilized to calculate the data driving optimal power flow learning frame;

the main steps of establishing the extreme learning machine model are as follows:

1.1 Acquiring an input data set X;

H＝g(WX+b) (1)

wherein H is a hidden layer output matrix; g (·) is the activation function; w is a randomly generated input weight matrix; b is a randomly generated bias vector;

β＝(H^TH)^-1T (2)

Wherein T represents a target matrix for learning of the extreme learning machine model;

2.1 Dividing the stacked extreme learning machine into a plurality of sub-ELM neural networks stacked layer by using a PCA dimension reduction method, and randomly generating hidden layer neuron parameters of a first sub-ELM neural network; the number of hidden layer neurons generated randomly is recorded as L _m; the initial value of m is 1;

Where β _m is the output weight matrix for the mth iteration and satisfies F _m denotes an optimization function; c is a penalty factor; h _m is the hidden layer output matrix for the mth iteration;

2.3 Calculating an output weight matrix beta _m of the mth iteration, namely:

wherein, C is a penalty factor;

2.4 Using principal component analysis to reduce the dimension of the output weight matrix beta _m and generating a feature vector matrix V _m∈R^L×L; the number of the original hidden neurons is marked as L _m, and the number of the hidden neurons after dimension reduction is marked as L _m; the feature vectors of the first l _m columns are marked as

2.5 Randomly generating L _m-l_m hidden neurons, and calculating to obtain a hidden layer output matrix H _new with L _m-l_m hidden neurons;

2.6 Iteratively updating the hidden layer output matrix H _m+1, namely:

2.7 Based on the hidden layer output matrix H _m+1 updated by iteration, optimizing the feature vector matrix V _m+1 to obtain an optimized feature vector And returning to the step 2) until the iteration is finished;

Wherein a _2i、a_1i、a_0i is a power generation cost coefficient; PG _i represents a control variable of active power output of the generator; f is an objective function of the system running cost;

the constraints are shown in the formulas (8) to (12), respectively, that is:

PF_k＝PF_ij＝V_iV_j(G_ijcosθ_ij+B_ijsinθ_ij)-V_i ²G_ij (9)

wherein PD _i、QD_i represents the load active and reactive power requirements, respectively; PF _k、QF_k、V_i、θ_i represents the state variables of the branch active power, branch reactive power, voltage amplitude and voltage phase angle, respectively; PG _i、QG_i represents control variables of active power and reactive power output of the generator respectively; s _G、S_B、S_K respectively represents a system generator set, a node and a branch; i. j represents a node number; k represents a branch index; θ _ij＝θ_i-θ_j is the phase angle difference between the i-th and j-th nodes; g _ij、B_ij represents the conductance and susceptance between the ith and jth nodes, respectively; PF _ij represents the active power state variables of the branches where node i and node j are located; * Representing a lower limit; Representing an upper limit;

the reinforcement layer is a multi-supervision layer and is used for correcting errors of the stacked extreme learning machine;

the main steps of the method for calculating the data driving optimal power flow learning framework by using the stacking type extreme learning machine are as follows:

5.1 Active power demand PD _i and reactive power demand QD _i into the stacked extreme learning machine, outputting branch active power PF _k, branch reactive power QF _k;

5.2 Inputting the branch active power PF _k and the branch reactive power QF _k into a stacked extreme learning machine, and outputting a voltage amplitude state variable V _i and a voltage phase angle state variable theta _i;