CN106845705A - The Echo State Networks load forecasting model of subway power supply load prediction system - Google Patents

Abstract

A short-term load forecasting system for a subway power supply system, including a load statistics module, a load data call module, a load data forecast module, a forecast error statistics module, a graph output module, and a data output module; wherein the load statistics module is used to count historical load data, load The data call module calls the historical load data in the load statistics module and sends it to the load data prediction module. The load data prediction module predicts the future load according to the historical load data and outputs the forecast data. The forecast error statistics module calibrates the output forecast data. Afterwards, output the corrected forecast data through the graphic output module and the data output module; wherein the load data forecast module is constructed by using the short-term load forecast model of the subway power supply system based on the echo state neural network. The prediction model based on echo state neural network has good prediction accuracy and prediction stability.

Description

Echo State Neural Network Load Forecasting Model of Subway Power Supply Load Forecasting System

technical field

The invention relates to the field of short-term load forecasting of a subway power supply system, in particular to a short-term load forecasting system for a subway power supply system based on an echo state neural network load forecasting model.

Background technique

Urban subway transportation is a symbol of urban modernization, and it is an ideal public transportation tool in a modern city that can meet the travel needs of citizens. While it brings us quickness and convenience, it will also bring negative impacts to the power grid. As a high-power nonlinear load, the characteristics of the operation of the subway and the impact on the regional power grid after it is put into operation should be the focus of the power sector. . For the estimated serious problems, appropriate preventive measures should be taken to control the negative impact within the allowable range. The load of the subway power supply system has the characteristics of randomness, volatility and instability. These characteristics cause the load of the subway power supply system to have an impact on the power grid and interfere with the safety, stability and economic operation of the power grid. By predicting the load of the subway power supply system, the adverse impact on the power grid can be effectively reduced to ensure the safe and stable operation of the power system.

The echo state neural network consists of an input layer, a reserve pool, and an output layer. The reserve pool is a dynamic network consisting of a large number of randomly connected neurons. The application of the reserve pool overcomes the problems of slow convergence speed and easy to fall into local minimum of the traditional neural network. The echo state neural network has been applied in many research fields such as photovoltaic power prediction. However, the research on load forecasting of subway power supply system is a research blank at present, especially the use of echo state neural network to forecast the load of subway power supply system is in a research vacuum.

Contents of the invention

In order to fill the gaps in the prior art, the present invention proposes a short-term load forecasting system for a subway power supply system, including a load statistics module, a load data call module, a load data forecast module, a forecast error statistics module, a graphic output module and a data output module; The load statistics module is used to count historical load data, the load data call module calls the historical load data in the load statistics module and sends it to the load data prediction module, and the load data prediction module predicts the future load according to the historical load data and outputs the forecast data After the forecast error statistics module calibrates the output forecast data, the revised forecast data is output through the graphic output module and the data output module; wherein the load data forecast module adopts the short-term load of the subway power supply system based on the echo state neural network built predictive models.

Further, the short-term load forecasting model of the subway power supply system based on the echo state neural network is obtained using the following algorithm: construct the echo state neural network, including an input layer, a reserve pool, and an output layer; the input layer in the network model has k input nodes , the reserve pool has n internal nodes, and the output layer has l output nodes;

At time t, the input vector of the network is u(t)=[u ₁ (t),u ₂ (t),···,u _k (t)] ^T , and the internal state vector is x(t)=[ x ₁ (t),x ₂ (t),···,x _n (t)] ^T , the output vector is y(t)=[y ₁ (t),y ₂ (t),···,y _l (t)] ^T , then the state equation and output equation of the ESN prediction model are:

x(t+1)＝f(w ⁱⁿ u(t+1)+wx(t)+w ^back y(t)) (1)

y(t+1)＝f ^out (w ^out (u(t+1),x(t+1),y(t+1))) (2)

^In the formula, win represents the input connection weight matrix from the input layer to the reserve pool, w represents the internal connection weight matrix of the reserve pool, w ^back represents the feedback connection weight matrix from the output layer to the reserve pool, and w ^out represents the connection weight matrix from the reserve pool to the output The output connection weight matrix of the layer, f represents the excitation function of the reserve pool unit, which takes the hyperbolic tangent function; f ^out represents the excitation function of the output unit, which takes the identity function;

The output connection weight matrix w ^out is determined by the given training samples (u(t),y(t),(t=1,2,···,q)), and its training process can be divided into two stage:

(1) Sampling stage

First, assign a value to the initial state of the network, usually the initial state of the network is 0, that is, x(t)=0. Then the training samples (u(t), t= ^1,2 ,...,q) are input into the dynamic reserve pool through win, and the network state vector x(t ) and the calculation of the output vector y(t);

From a certain moment h, the internal state variables and corresponding sample data of the echo state neural network system are recorded, and then the phasor ([u ₁ (j),u ₂ (j),···,u _k (j)] ^T ;[x ₁ (j),x ₂ (j),···,x _n (j)] ^T ) to form the matrix B(q-h+1), and use the phasor ([y ₁ (j),y ₂ (j),···,y ₃ (j)] ^T ) to form a matrix T(q-h+1,l). Where j=h, h+1,...,q;

(2) Weight calculation stage

According to the internal state data and sample data recorded by the echo state neural network system in the sampling process, the output connection weight matrix w ^out is obtained through least square linear regression calculation. Due to the internal state variable x(t) of the network and the actual output of the network There is a linear relationship between them, so the actual output of the network is used To approximate the ideal output y(t) of the network:

In the process of calculating the weight w _i ^out , it is necessary to ensure that the root mean square error of the above formula is the smallest, so the problem can be transformed into an optimization problem for solving the following formula:

From a mathematical point of view, this is a linear regression problem, which can be transformed into the problem of finding the inverse matrix of matrix B, that is, w ^out = B ^-1 T, and the training of the echo state neural network is over.

The present invention designs a short-term load forecasting system for a subway power supply system integrating statistics and prediction, and proposes a short-term load forecasting model and a construction method for the subway power supply system based on an echo state neural network. The echo state neural network consists of an input layer, a reserve pool, and an output layer. The reserve pool is a dynamic network consisting of a large number of randomly connected neurons. The application of the reserve pool overcomes the problems of slow convergence speed and easy to fall into local minimum of the traditional neural network. The historical data of the actual subway power supply system is used for simulation verification. The simulation results show that the prediction model based on the echo state neural network has good prediction accuracy and prediction stability.

Description of drawings

Fig. 1 is the schematic diagram of short-term load forecasting system of subway power supply system of the present invention;

Fig. 2 is the schematic diagram of the echo state neural network prediction model of the subway power supply system short-term load forecasting system of the present invention;

Fig. 3 is a graph showing the comparison between the short-term load forecasting system of the subway power supply system of the present invention and the BP-NN forecasting model.

detailed description

Based on the comprehensive and in-depth analysis of the load characteristics of the subway power supply system and the research on the precise and advanced load forecasting model, a short-term load forecasting system for the subway power supply system integrating statistics and forecasting is designed. As shown in Figure 1, the short-term load forecasting system of the subway power supply system of the present invention includes a load statistics module, a load data call module, a load data forecast module, a forecast error statistics module, a graphic output module and a data output module. The load statistics module is used to count historical load data, the load data calling module calls the statistical data in the load statistics module and sends it to the load data prediction module, and the load data prediction module predicts the future load according to the historical load data and outputs the forecast data, After the prediction error statistics module calibrates the output prediction data, the corrected prediction data is output through the graphic output module and the data output module.

In the short-term load forecasting system of the subway power supply system, the load forecasting module is a core module, and the short-term load forecasting model of the subway power supply system based on the echo state neural network is a core algorithm of the module.

The echo state neural network is a new type of recurrent neural network, and its network structure consists of an input layer, a reserve pool, and an output layer. The reserve pool is a dynamic network, which is composed of a large number of randomly connected neurons. When the input signal enters the reserve pool, it will excite the complex nonlinear state space inside, and then output the network signal through the output layer. The traditional recursive neural network training algorithm is complex and the amount of calculation is large. In the echo state neural network prediction model, the establishment of the reserve pool and the completion of network training are carried out separately. During network training, only the weights from the reserve pool to the output layer need to be adjusted, and other The weight value will not change after the network is initialized. The training algorithm is simple and the calculation amount is small, which can effectively solve the local optimal problem. The echo state neural network prediction model is shown in Figure 2.

In Fig. 2, the solid line connection represents the necessary connection weight of the prediction model, and the dotted line connection is not necessary for forming the prediction model, but is a connection weight selected according to different situations. It can be seen from Figure 2 that the input layer in the network model has k input nodes, the reserve pool has n internal nodes, and the output layer has l output nodes. At time t, the input vector of the network is u(t)=[u ₁ (t),u ₂ (t),···,u _k (t)] ^T , and the internal state vector is x(t)=[ x ₁ (t),x ₂ (t),···,x _n (t)] ^T , the output vector is y(t)=[y ₁ (t),y ₂ (t),···,y _l (t)] ^T . Then the state equation and output equation of the ESN prediction model are:

x(t+1)＝f(w ⁱⁿ u(t+1)+wx(t)+w ^back y(t)) (1)

y(t+1)＝f ^out (w ^out (u(t+1),x(t+1),y(t+1))) (2)

^In the formula, win represents the input connection weight matrix from the input layer to the reserve pool, w represents the internal connection weight matrix of the reserve pool, w ^back represents the feedback connection weight matrix from the output layer to the reserve pool, and w ^out represents the connection weight matrix from the reserve pool to the output The output connection weight matrix of the layer. f represents the excitation function of the reserve pool unit, and generally takes the hyperbolic tangent function; f ^out represents the excitation function of the output unit, and generally takes the identity function.

The echo state neural network prediction model only needs to determine the network output connection weight matrix w ^out through the given training samples (u(t), y(t), (t=1,2,···,q)), namely Yes, the training process can be divided into two stages: the sampling stage and the weight calculation stage.

(1) Sampling stage

First, assign a value to the initial state of the network, usually the initial state of the network is 0, that is, x(t)=0. Then the training samples (u(t), t= ^1,2 ,...,q) are input into the dynamic reserve pool through win, and the network state vector x(t ) and the calculation of the output vector y(t).

By calculating the output connection weight matrix w ^out , the echo state neural network system needs to record its internal state variables and corresponding sample data from a certain moment h, and then use the phasor ([u ₁ (j),u ₂ (j ),···,u _k (j)] ^T ; [x ₁ (j),x ₂ (j),···,x _n (j)] ^T ) to form matrix B(q-h+1) , and use the phasor ([y ₁ (j),y ₂ (j),···,y ₃ (j)] ^T ) to form the matrix T(q-h+1,l). Where j=h, h+1, . . . , q.

(2) Weight calculation stage

According to the internal state data and sample data recorded by the echo state neural network system in the sampling process, the output connection weight matrix w ^out is obtained through least square linear regression calculation. Due to the internal state variable x(t) of the network and the actual output of the network There is a linear relationship between them, so the actual output of the network is used To approximate the ideal output y(t) of the network:

In the process of calculating the weight w _i ^out , it is necessary to ensure that the root mean square error of the above formula is the smallest, so the problem can be transformed into an optimization problem for solving the following formula:

From a mathematical point of view, this is a linear regression problem, which can be transformed into the problem of finding the inverse matrix of matrix B, that is, w ^out = B ^-1 T, and the training of the echo state neural network is over.

Taking a city's subway power supply system as the research object, the historical load data of the subway power supply system is simulated and analyzed. Through the analysis of the load characteristics of the subway power supply system, it can be known that the day type factor has a greater impact on the load of the subway power supply system. Therefore, the input quantity used in the forecast model of this patent includes the day type of the forecast day, the load at the same time of the day before the forecast day, the load of the first three hours and the next three hours, and the load at the same time of the week before the forecast day. The output of the forecast model is the load value at the forecast time of the forecast day.

Due to the existence of singular values in the sample data, the dimensions of the variables are also different, which will affect the prediction accuracy of the prediction model. Therefore, the original data needs to be normalized before network training. Day type data is divided into three categories, 1 is used for Monday, 0.2 is used for Tuesday to Friday, and 0.1 is used for Saturday and Sunday.

Construct the echo state neural network prediction model and the BP prediction model to simulate and predict the load of the subway power supply system on a certain day, the simulation results are shown in Figure 3, and compare the predicted value and actual value with the predicted value of the BP prediction model. The error comparison results are shown in Table 1.

Table 1 Comparison of prediction errors of two models

It can be seen from Figure 1 and Table 1 that the average prediction error of the echo state neural network prediction model is 2.65% higher than that of the BP-NN prediction model, and the maximum prediction error of the echo state neural network prediction model is higher than that of the BP-NN prediction model. The maximum prediction error of the model is increased by 2.90%, indicating that the prediction accuracy of the ESN prediction model is significantly higher than that of the BP-NN prediction model.

Although the present invention has been described in detail in conjunction with the embodiments, those skilled in the art should understand that various modifications and variations are allowed without departing from the spirit and essence of the present invention, and they all fall into the rights of the present invention. within the scope of protection requested.

Claims (2)

1. A short-term load forecasting system for a subway power supply system is characterized in that it includes a load statistics module, a load data call module, a load data forecast module, a forecast error statistics module, a graphic output module and a data output module; wherein the load statistics module is used for statistics Historical load data, the load data call module calls the historical load data in the load statistics module and sends it to the load data prediction module, the load data prediction module predicts the future load according to the historical load data and outputs the forecast data, and the forecast error statistics module outputs After the forecast data is calibrated, the revised forecast data is output through the graphic output module and the data output module; wherein the load data forecast module is constructed by using the short-term load forecast model of the subway power supply system based on the echo state neural network. 2. subway power supply system short-term load forecasting system according to claim 1, is characterized in that, described subway power supply system short-term load forecasting model based on echo state neural network adopts following algorithm to obtain: Construct an echo state neural network, including an input layer, a reserve pool, and an output layer; in the network model, the input layer has k input nodes, the reserve pool has n internal nodes, and the output layer has l output nodes; At time t, the input vector of the network is u(t)=[u ₁ (t),u ₂ (t),···,u _k (t)] ^T , and the internal state vector is x(t)=[ x ₁ (t),x ₂ (t),···,x _n (t)] ^T , the output vector is y(t)=[y ₁ (t),y ₂ (t),···,y _l (t)] ^T , then the state equation and output equation of the prediction model are respectively: x(t+1)＝f(w ⁱⁿ u(t+1)+wx(t)+w ^back y(t)) (1) y(t+1)＝f ^out (w ^out (u(t+1),x(t+1),y(t+1))) (2) ^In the formula, win represents the input connection weight matrix from the input layer to the reserve pool, w represents the internal connection weight matrix of the reserve pool, w ^back represents the feedback connection weight matrix from the output layer to the reserve pool, and w ^out represents the connection weight matrix from the reserve pool to the output The output connection weight matrix of the layer, f represents the excitation function of the reserve pool unit, which takes the hyperbolic tangent function; f ^out represents the excitation function of the output unit, which takes the identity function; The output connection weight matrix w ^out is determined by the given training samples (u(t),y(t),(t=1,2,···,q)), and its training process can be divided into two stage: (1) Sampling stage First, assign a value to the initial state of the network, usually the initial state of the network is 0, that is, x(t)=0. Then the training samples (u(t), t= ^1,2 ,...,q) are input into the dynamic reserve pool through win, and the network state vector x(t ) and the calculation of the output vector y(t); From a certain moment h, the internal state variables and corresponding sample data of the echo state neural network system are recorded, and then the phasor ([u ₁ (j),u ₂ (j),···,u _k (j)] ^T ;[x ₁ (j),x ₂ (j),···,x _n (j)] ^T ) to form the matrix B(q-h+1), and use the phasor ([y ₁ (j),y ₂ (j),···,y ₃ (j)] ^T ) to form a matrix T(q-h+1,l). Where j=h, h+1,...,q; (2) Weight calculation stage According to the internal state data and sample data recorded by the echo state neural network system during the sampling process, the output connection weight matrix w ^out is obtained through the linear regression calculation of the least square method, because the internal state variable x(t) of the network is different from the actual output of the network There is a linear relationship between them, so the actual output of the network is used To approximate the ideal output y(t) of the network: $\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; k</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; u</span>}\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; u</span>}\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$ In the process of calculating the weight w _i ^out , it is necessary to ensure that the root mean square error of the above formula is the smallest, so the problem can be transformed into an optimization problem for solving the following formula: $\mathrm{<span\; class="notranslate">\; min</span>}\frac{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; q</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; h</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}\underset{\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; h</span>}}{\overset{\mathrm{<span\; class="notranslate">\; q</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; the\; y</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; k</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; u</span>}\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; k</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; no</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}}{{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}}^{\mathrm{<span\; class="notranslate">\; o</span>}\mathrm{<span\; class="notranslate">\; u</span>}\mathrm{<span\; class="notranslate">\; t</span>}}{\mathrm{<span\; class="notranslate">\; x</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; k</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$ From a mathematical point of view, this is a linear regression problem, which can be converted to the inverse matrix problem of matrix B, namely: w ^out = B ^-1 T (5) Calculate w ^out by formula (5); The echo state neural network training is over.