1. Introduction
During the operation of wind turbines, the output power is in a constantly changing state due to the randomness and intermittency of the wind resource, which brings unpredictable influences to the operation state of the power system and may lead to system oscillation. Exploring a wind power prediction method which can relieve the peak load regulation and frequency modulation pressure of the power system and predict the possible oscillation of the system with a certain accuracy is very important [
1]. The real-time operation data of wind turbines records the actual operation status of wind turbines, and inevitably contains information on the interaction between wind turbines and power grids. Therefore, it is necessary to analyze them in depth and apply big data analysis to extract valuable information.
At present, there are three kinds of forecasting methods that are commonly used: physical methods, statistical methods, and combinations of the two methods [
2]. The purpose of the physical method is to describe the physical process of converting wind into electricity, and to simulate all the steps involved, according to the wind turbine background data, such as wind turbine position and fan parameters, to build the model and estimate the wind speed at the hub height of each wind turbine, and finally to obtain the output power through the wind power curve [
3]. This method involves a large number of meteorological theories and geomorphological parameters and is very difficult to solve. The statistical method aims to establish a nonlinear relationship between wind power and input variables directly by analyzing the statistical laws of time series, including sequential extrapolation and artificial intelligence prediction methods. Sequential extrapolation includes time series method, regression analysis method and Kalman filtering method [
4], etc. Artificial intelligence method includes artificial neural networks (ANN), support vector machines (SVM), deep learning [
5] and so on. A method using Least Squares Support Vector Machine (LSSVM) to predict wind speed and indirectly predict wind power output is proposed in [
6]. In reference [
7], an artificial neural network for wind power prediction is constructed based on Numerical Weather Prediction (NWP) data.
However, wind power data series is a kind of time series with dynamic characteristics, and the output of the system is not only related to the current time input, but also related to the past input. Recursive neural networks (RNN) [
8,
9] can not only use current input information but also historical information, so RNN has great advantages in processing timing information. As a special RNN model, LSTM network effectively avoids the problem of gradient disappearance and gradient explosion in the conventional RNN training process due to its special structural design [
10]. LSTM has many nonlinear transport layers and can be used in complex situations. With enough training data, LSTM model can explore the information contained in massive data.
Since the large-scale integration of wind power, the interaction between wind turbines and power grids [
11,
12] has become one of the topics of widespread concern. Many researches are carried to handle the process of wind integration with the grid. Reference [
13] investigates a renewable power system by jointly optimizing the expansion of renewable generation facilities and the transmission grid. It is proved that transmission can reduce cost of electricity when wind capacities and solar photovoltaics are installed separately. Reference [
14] presents a Two-layer nested model considering the uncertainty in forecasting photovoltaic power. Reference [
15] proposes a Mixed-Integer Nonlinear Programming MINLP model for grid connected solar–wind–pumped-hydroelectricity (PV-WT-PSH), which combines mixed integer modeling with an ANN model to predict energy flow between a local balancing area using PV-WT-PSH and the national power system.
At present, the complicated oscillation phenomenon caused by wind power integration includes sub-synchronous interaction (SSI) and low frequency oscillation [
16,
17,
18]. SSI mostly shows the exchange of energy between generator and alternating current at a frequency lower than the rated frequency of the system. The frequency value of low frequency oscillation is usually between 0.1 and 2.5 Hz, which is caused by the negative damping effect caused by the rapid excitation of the generator. According to the difference of internal mechanism, SSI can be divided into subsynchronous control interaction (SSCI) [
19] and subsynchronous torque interaction (SSTI) [
20]. SSCI is associated with the series capacitance of the control device and power electronic equipment, and may also occur in the case of low series compensation. SSTI [
21] is related to the mechanical power on the generator shaft system. Depending on the formation mechanism, this kind of oscillation problem can be subdivided into subsynchronous oscillation (SSO) [
22] and subsynchronous resonance (SSR) at SSTI level. SSR [
23,
24] is caused by resonance caused by series compensation capacitance in the power grid, and SSO is caused by positive feedback caused by defects of the control system itself.
The main contributions of this paper are as follows: (1) The principal component analysis of wind turbine-grid interaction is studied, and simulations prove the rationality of the selected component in the prediction of interaction between wind turbine and grid; (2) A prediction model of wind turbine-grid interaction based on PCA–LSTM is proposed.
The first part of the article puts forward the related factors of wind turbine-grid interaction and introduces the PCA analysis. In the second part, the prediction model of wind turbine gird interaction is proposed, and the principle of LSTM network and the design scheme of prediction model are introduced. The third part introduce the data flow diagram of the model in TensorFlow. The fourth part is experimental verification and result analysis, which verifies the accuracy of the proposed model.
Figure 1 shows the flowchart of the methodology used in this paper.
3. Prediction Model of Analysis Objects in Wind Turbine Grid Interaction
3.1. Long-Term and Short-Term Memory Network Structure
LSTM can be used as a complex nonlinear unit to construct a larger deep neural network, which can reflect the long-term memory effect. The LSTM network includes an input layer, an output layer, and multiple hidden layers. The hidden layer is composed of memory tuples, and its basic structure is shown in
Figure 2. The key to LSTM network is cell state. The state of the cells runs directly along the whole chain like a conveyor belt. In LSTM, cell state information is added or deleted through the gate structure, and whether information passes through can be selectively determined through the gate. It consists of a Sigmoid layer and a pair of multiplication operations. The output of gate structure is 0~1, which defines the degree of information passing through. The tanh layer in
Figure 2 is an activation function that can map a real number input into [−1, 1].
The LSTM tuple includes three gates, namely, an input gate, a forget gate and an output gate. The three gates control the flow of information between the tuple and the network. In the following formula, , , represent the state values of input gate, output gate and forgotten gate, respectively.
- (1)
Forget gate decides to forget information from the old cell state
, and the input is the input of the current layer
and the output of the previous layer
, the cell state output is:
- (2)
Generate information to be updated and store it in the cell needs two steps: (a) update the information by the result of the input gate passing through the sigmoid layer; (b)
will be added to the new candidate information by multiplying the old cell state with
to forget unnecessary information:
- (3)
The output information is determined by the output gate. First, the initial output is obtained through the Sigmoid layer, the cell state value is scaled between [−1, 1] with the tanh layer, and the output
can be easily obtained:
From Equations (7) to (11), , , , respectively represent the weight matrix of input gate, forget gate, output gate and tuple input, respectively represent the weight matrix of input gate, forgetting gate, output gate and tuple input to connect , and respectively represent the bias vectors of input gate, forget gate, output gate and tuple input. represents sigmoid activation function.
The LSTM model has the same structure as RNN model. It can be seen as multiple replications of the same neural network, and each neural network module will pass the message to the next one. After unfolding the loop, the structure is shown in
Figure 3.
The observation objects of wind turbine network interaction and wind speed data is the input to the LSTM model, and the expression of the prediction model can be derived from the network structure of
Figure 3:
In Equation (13), is the historical data, is the input parameter selected by PCA, in this case, it is wind speed.
The topological structure of LSTM model selected in this paper is shown in
Figure 4. After the principal component analysis of the original data, the analysis objects of wind turbine grid interaction and the selected principal component are chosen as inputs of the prediction model. We have two hidden layers. And the output layer gives the prediction of wind power, voltage and current in wind turbine grid interaction.
3.2. LSTM Prediction Model Design
3.2.1. Data Normalization
When predicting multi-variable time series, due to the different dimensions and numerical differences among different variables, considering the input and output range of nonlinear activation function in the model, and in order to equally handle the influence of various variables on wind power, voltage and current, it is necessary to normalize the raw data between [0, 1]. Normalization is carried out by MinMaxScaler, the formula is shown in Equation (14):
The predicted wind power, current and voltage data are subjected to inverse normalization processing to make them have physical significance. The formula is shown in Equation (15):
3.2.2. Model Parameter Selection
The establishment of LSTM prediction model requires five hyperparameters, namely, input dimension, input layer timesteps, number of hidden layers, dimension of each hidden layer and output dimension.
In an actual neural network, the number of hidden layers and neurons will directly affect the accuracy of network training and prediction so the number of hidden layers and neurons should be carefully selected. The network starts from a complex structure, which has many hidden layers and several hundred of neurons in each layer, then the over fitting problem happens, so that the number of layers should be reduced and some of the neurons should be dropped off until the generalization ability of the network is good enough, The best parameters for our model is found after many experiments, the following hyperparameters can obtain better prediction results: the input shape is 2, 5 time steps, the number of hidden layers is 2, 50 neurons are defined in the first hidden layer, 100 neurons are defined in the second hidden layer, and 1 neuron is defined in the output layer to predict the output. Adam function with random gradient descent is used as the optimization algorithm of the neural network.
3.2.3. Evaluation of Forecast Results
The mean absolute percentage error (MAPE) and root mean square error (RMSE) are used for evaluation the prediction results, and the error functions are shown in Equations (16) and (17), respectively:
In Equations (16) and (17), PN(i) and (i = 1, 2, 3, …, n) are the actual value and predicted value of the i th data, n represents the length of the data used for verification.