Short-term wind power forecast based on back-propagation neural network corrected by Markov chain

Along with the rapid development of the world economy, the corresponding energy demand has also increased greatly and the traditional fossil energy is facing the threat of energy exhaustion. At the same time, climate warming and increasingly serious environmental pollution caused by large-scale consumption of traditional fossil energy are becoming more and more serious, which poses serious threat to ecosystem, social economy and human health. In order to deal with the shortage of traditional fossil energy and environmental pollution brought by traditional fossil energy, green energy has become the development direction of governments all around the world. In China’s “13th Five-year Plan”, the requirements for energy security and green production have also been put forward. As a green and renewable energy, wind power has been widely applied and developed in the world. With the exhaustion of non-renewable fossil fuels such as coal and the increasing pollution to the environment, the technology of clean energy generation represented by wind power has attracted more and more attention. However, wind power is featured with natural volatility, randomness and intermittence, which makes it very difficult to dispatch the power grid. Therefore, it is necessary to have accurate wind power forecast means to solve the above problems. The accuracy of wind power forecast is very vital to the electric power dispatching department and will directly affect the amount of power supply to the wind power plant and the reasonable dispatch of wind power by the electric power dispatching department, which is of great significance to both the enterprises and the electric power department.

Wind power generation has volatility and intermittence because of the instability of wind, which will make it difficult for the power grid to dispatch wind power. At present, the important direction to solve this problem is to forecast the wind power output during a period of time in the future. The results of the short-term forecast can help the power grid to carry out reasonable economic dispatch, unit commitment operation and select appropriate opportunity to maintain the draught fan. At present, the methods of short-term wind power forecast mainly include random time series method, artificial neural network method, Kalman filtering method, support vector machine method, and different combinations of these methods. Literature (Fan et al., 2008) is short-term load forecast method based on wavelet decomposition, fuzzy grey clustering and BP neural network. Literature (Xiao et al., 2014) proposes a new power prediction model based on discrete time Markov chain theory. In the literature (Liu and Huang, 2012), the prediction accuracy of short-term wind power is further improved by comparing the first-order and second-order Markov chain models with different number of state space and modeling data. Literature (Peng et al., 2011) proposes a model based on grey-Markov chain for short-term forecast of wind power, analyzes the error transition sequence of grey fitting value and establishes the Markov state transition probability matrix. Literature (Shi et al., 2010) proposes a new short-term wind speed prediction method which utilizes the signal analysis characteristics of wavelet packets and the unsteady data prediction characteristics of the peak Markov chain.

The above research has played a positive role in eliminating the adverse effect of random output of wind power plant on the power grid, and has also provided a good reference for further improving and optimizing the wind power forecast methods (Pang, 2010; Zhang et al., 2012; Zhou et al., 2012). However, the time series method requires less historical data, the prediction period is short and the single data can’t form a reasonable error estimate so that the abrupt-changed information can’t be recognized. The Kalman filtering method can capture the change law of wind power well and can update the state information continuously, and can obtain more accurate prediction result. However, it is not suitable for the volatility and the violent situation. The support vector machine method needs less data, has strong nonlinear learning ability, short training time, strong generalization ability, and can effectively overcome the curse of dimensionality and local minimal problem, but the accuracy is greatly influenced by the selected kernel function structure. Thus, it raises high requirements on the accuracy and completeness of kernel function. In view of the existing problems of short-term wind power methods, this study proposes a wind power combined prediction model based on BP neural network (Zhou et al., 2012). The experimental results show that the proposed method can effectively improve the accuracy and reliability of wind power forecast, and the prediction accuracy is higher than that of single BP neural network.

Markov chain prediction is a prediction method to analyze the future development trend and possibility of random events according to the system state transition law discovered by Markov, a Russian mathematician. Its essence is to predict the probability of occurrence of time and predict the future change of time according to the present situation. The prediction of Markov chain mainly contains two processes: one is to determine the state space of Markov chain; the other one is to determine the state transition probability and the state transition matrix by calculation. The Markov chain prediction model can be expressed as:

$X ( n ) = X ( 0 ) P ^ { ( n ) }$   (1)

Where, X(n) is state probability vector at the moment of n; X(0) is state probability vector at the initial moment; P is state transition probability matrix.

The Formula (1) has the meaning of predicting the nth step according to P and X(0), and the key of the prediction is the determination of the state transition probability matrix P. According to the sample data, the number of occurrences of state i

$P _ { i j } \approx \frac { N _ { i j } } { N _ { i } }$ (2)

Then the kth state transition probability matrix is:

$P ^ { ( k ) } = \left( \begin{array} { c c c } { P _ { 11 } ( k ) { P _ { 12 } } ( k ) } & { \dots . . . } & { P _ { 1 n } ( k ) } \\ { P _ { 21 } ( k ) { P _ { 22 } } ( k ) } & { \dots . . . } & { P _ { 2 n } ( k ) } \\ { \cdots . . . } & { \ldots . . . } & { \ldots . . . } \\ { P _ { n 1 } ^ { ( k ) } P _ { n 2 } ^ { ( k ) } } & { \ldots . . } & { P _ { n n } ^ { ( k ) } } \end{array} \right)$        (3)

In the solution of state probability, the classification of state is very important. The common methods are mean value-mean square error classification, cluster analysis and optimal segmentation.

5.1. Prediction simulation of BP neural network

The trained BP neutral network model is used to predict the power of wind turbine generator in the next 6 hours. The prediction result is shown in Table 1.

5.2. Corrected prediction result based on Markov chain

The prediction accuracy of Markov chain is mainly determined by the transition matrix. In order to construct the transition matrix, it is necessary to reasonably divide the error state interval which is generally determined by mean value-mean square error classification method and centered on the mean value x of samples. The standard deviation is s $= \sqrt { \frac { 1 } { n - 1 } \sum _ { i = 1 } ^ { n } \left( x _ { i } - x \right) ^ { 2 } }$. In general, a data sequence can be divided into: $( \overline { x } - s , \overline { x } ) , \left( \overline { x } , ( \overline { x } + s\right)$ and $( \overline { x } + s , \overline { x } + 2 s )$.

As can be seen from Table 1, the error between the simulated value and the actual value is between -15% and 15%, the average error is $\overline { x }$=-1.546, and the standard deviation is s=10.41. According to mean value-standard deviation classification method, the Markov states are divided into E₁=[-15%,-5%), E₂=[-5%,5%), E₃=[5%,15%] through the mean error and standard deviation of BP neural network simulation results. According to the above state division, the error state result of BP neural network can be obtained as shown in Table 2.

Table 1. Prediction result BP neural network

Table 2. State division of Markov chain

Then a Markov chain state transition table is obtained, as shown in Table 3. From Table 3, the state transition probability matrix is obtained as follows:

$P ^ { ( 1 ) } = \left[ \begin{array} { c c c } { 0.5 } & { 0.1 } & { 0.4 } \\ { 0.25 } & { 0 } & { 0.75 } \\ { 0.4 } & { 0.3 } & { 0.3 } \end{array} \right]$      (7)

The prediction result of the BP neural network is corrected by the Markov state transition probability matrix, and the correction result is shown in Table 4.

Table 4. Error correction result of Markov Chain

According to the data in Table 4, the actual generated power-BP neural network predicted power-Markov corrected predicted power changing curve and relative error curve chart are drawn, as shown in Figure 2 and Figure 3 below.

2.png

Figure 2. Comparison of actual power with predicted power and corrected power

By observing the curve of Figure 2, we find that the prediction curve of the two methods has basically the same trend with the actual power curve, and the prediction curve of Markov chain-BP neural network combined model has more coincidence with the actual power curve, which shows that the combined prediction method has higher accuracy than the BP neural network.

3.png

Figure 3. Contrast diagram of relative error before and after correction of Markov chain

It can be seen from Figure 3 that the changing trend of the relative error curve predicted by BP neural network is basically the same as that corrected by Markov chain, but the relative error data corrected by Markov chain is closer to zero and the fluctuation amplitude is smaller, indicating that the corrected data is closer to the measured value and the prediction stability is higher. Therefore, that prediction result of the BP neural network-Markov chain combined prediction model is closer to the actual value than that of the single BP neural network model, the prediction accuracy is higher, and the relative error ε is smaller than that of the BP neural network.

5.4. Error analysis

5.4.1. Selection of error formula

In order to standardize the evaluation of predicted performance, this study adopts RMSE (root-mean-square) error expression.

The predicted absolute error δ_t is the difference between the measured predicted value P'(t) and the true value P(t) at the moment t, namely

$\delta _ { t } = P ^ { \prime } ( t ) - P ( t )$    (8)

Predicted relative error:

$\varepsilon _ { t } = \frac { \delta _ { t } } { P ( t ) }$       (9)

Finally, the prediction error is defined as:

$E _ { \mathrm { RMSE } } = \sqrt { \frac { 1 } { N _ { \mathrm { T } } } \sum _ { h = 1 } ^ { \mathrm { N } _ { \mathrm { T } } } \varepsilon _ { t } ^ { 2 } }$  (10)

Where, N_T is the number of data used to evaluate the prediction error during the training period.

5.4.2. Error analysis

24 sets of relative error data are analyzed, and the results are shown in Table 5 and Table 6 below.

Table 5. Prediction results of BP neural network

Table 6. Prediction results of BP neural network-Markov chain combined model

It can be seen from Table 4 and Table 5 that the BP neural network model and the combined prediction model have superior performance. There are 25 sets of data with relative error less than 15% in the BP neural network, accounting for 100%, and 25 sets of data with relative error less than 5% in the combined prediction model. The network coincidence rate is as high as 100%. After calculation, the RMSE predicted by BP neural network is 13.54%, and the RMSE corrected by Markov chain is 3.51%.

According to the Interim Measures for Power Prediction Management of Wind Power Plant issued by the National Energy Administration, it is stipulated that the maximum error of daily prediction curve provided by the power prediction system of wind power plant shall not exceed 25%, the real-time prediction error shall not exceed 15%, and the root-mean-square error of all-day prediction result shall be less than 20%. The wind power forecast can be divided into daily forecast and real-time forecast. The daily forecast is the forecast of the next 00:00 to 24:00 and the real-time forecast refers to the forecast of future 15 minutes to 4 hours and the time resolution is 15 minutes. The forecast time in this study is the wind power value in the next 6 hours, which belongs to real-time forecast.

After analyzing the power prediction error data, the prediction result of the combined prediction model established in this study are in full compliance with the relevant requirements of the interim measures for power prediction management of wind power plant, and the prediction accuracy is higher than that of BP neural network.