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Ultra-short-term power forecast of photovoltaic power station based on VMD–LSTM model optimised by SSA

Publicado en línea: 05 Sep 2022
Volumen & Edición: AHEAD OF PRINT
Páginas: -
Recibido: 25 Apr 2022
Aceptado: 15 Jun 2022
Detalles de la revista
License
Formato
Revista
eISSN
2444-8656
Primera edición
01 Jan 2016
Calendario de la edición
2 veces al año
Idiomas
Inglés
Introduction

Nowadays, traditional fossil fuels are being exhausted. Meanwhile, the excessive use of fossil fuels has caused serious environmental pollution. Developing renewable energy is one of the important ways to solve environmental problems and the energy crisis [1]. Solar energy is a clean, low-carbon and inexhaustible energy source. As one of the important ways to utilise solar energy, photovoltaic power generation has developed rapidly in recent years [2, 3]. Photovoltaic power generation is affected by sun's radiation, temperature, clouds, weather and other factors [4]. These factors cause frequent fluctuation of photovoltaic power, affect the safe and stable operation of the power system and restrict the further application of the photovoltaic system [5, 6]. Accurate prediction of photovoltaic power is of great significance to ensure the stability of the power grid and promote the large-scale utilisation of photovoltaic power.

At present, photovoltaic power forecasting methods are mainly divided into two categories: methods based on physical modelling and statistical methods based on historical data. The method based on physical modelling relies on the dynamic relationship between solar radiation and physical laws, but there is a general problem of low levels of accuracy and robustness [7, 8, 9]. Compared with physical modelling, the statistical method based on historical data only depends on historical data and uses data-driven feature extraction to predict the trend of photovoltaic power generation, without much physical knowledge. Therefore, the statistical method based on historical data is becoming one of the most popular photovoltaic power forecasting methods. Wang et al. [10] have put forward a short-term forecasting method of photovoltaic power based on a gradient boosting tree. This model uses historical weather data and photovoltaic power generation data to train the model. Simulation results show that this method is superior to the support vector machine and the autoregressive moving average model. Another work [11] uses the stepwise regression method to obtain important features as input and then uses multiple linear regression to predict the power. The simulation results show that this method can achieve high prediction accuracy when the number of features is small. The above method is a machine learning algorithm in the field of photovoltaic power generation prediction. Machine learning algorithm is more suitable for small batches of data; it is difficult to process a large number of input data, and there is the problem of disappearing or exploding gradient, which limits the accuracy of photovoltaic power prediction [12, 13].

Compared with the traditional machine learning model, the deep learning model has better feature learning ability and big data learning ability; moreover, it can deliver more accurate prediction results. Gao et al. [14] have established a long short-term memory (LSTM) network model, based on daily average solar irradiance, minimum temperature, maximum temperature, air temperature, relative humidity and other meteorological information, and predicted the daily power generation of large photovoltaic power plants by weather classification. Haixiang et al. [15] put forward a photovoltaic power forecasting method based on the deep convolution neural network, which uses solar radiation temperature, wind speed and historical power data to forecast short-term photovoltaic power generation. Mao and Kaixuan [16] use the complementary set empirical mode decomposition method to decompose historical power data and send it to the deep belief network optimised by the quenching algorithm. The example shows that this method is not affected by the geographical location of the photovoltaic power station [17]. Taking irradiance, temperature, wind speed, relative humidity and historical power data as input, particle swarm optimisation (PSO) is used to optimise the LSTM model and predict photo-voltaic power. Experiments prove the accuracy of this method, and the prediction accuracy is higher than that of the traditional LSTM model.

Compared with machine learning models, the above-mentioned deep learning models have achieved certain results in prediction accuracy and prediction efficiency. However, in the actual prediction process, the deep learning models also have some problems, such as difficulty in convergence and poor robustness, and most models take little account of sudden weather changes, while the weather conditions have great influence on photovoltaic prediction. In order to further improve the accuracy of the ultra-short-term forecast of photovoltaic power stations, this paper divides the weather conditions into two categories according to whether there is a sudden change in the weather. The sparrow search algorithm (SSA) is introduced to optimise the parameters of the variational mode decomposition (VMD) method, and the optimised VMD method is used to decompose the photovoltaic sequence and send it to an LSTM network. The final forecast result is obtained by superimposing the forecast results of each modal component. The errors of back propagation (BP), artificial neural network (ANN), LSTM and the VMD–LSTM models are compared with that of the proposed model, and the results show the accuracy of the proposed model.

Influence of weather type on photovoltaic output

Photovoltaic output is affected by many factors, such as location, environment and meteorology. In this paper, the historical power data and meteorological data of a 50 MW photovoltaic power generation system for the year 2020 are selected as the samples, and the photovoltaic output period in a day is predicted and analysed. The sampling period of this power station is 15 minutes, and there are 52 sampling points. Figure 1 shows the photovoltaic output in different weather conditions. It can be clearly observed from the figure that the photovoltaic output in stable weather is relatively stable, and the curve is similar to a parabola. When the weather suddenly changes, the photovoltaic output fluctuates greatly, which affects the stable operation of the power grid. The output of a photovoltaic power station is quite different under stable and abrupt weather conditions, so it is necessary to separately forecast abrupt weather (abrupt weather) and smooth weather (non-abrupt weather).

Fig. 1

Influence of weather types on photovoltaic power

Model and mechanism
VMD based on SSA optimisation
VMD approach

VMD adopts a completely non-recursive modal decomposition method, which decomposes data sequence f into multiple modal sub-functions uk and solves the problem of loss of high-frequency signal and aliasing in traditional modal decomposition. The formula for calculating uk bandwidth is as follows: {min{uk},{wk}kt[(δ(t)+jπt)×uk(t)]ejωkt2s.t.kuk(t)=f(t), \left\{{\matrix{{\mathop {\min}\limits_{\{{u_k}\},\{{w_k}\}} \sum\limits_k {{\left\| {{\partial _t}\left[{\left({\delta (t) + {j \over {\pi t}}} \right) \times {u_k}(t)} \right]{e^{- j{\omega _k}t}}} \right\|}^2}} \hfill \cr {s.t.\;\sum\limits_k {u_k}(t) = f(t),} \hfill \cr}} \right. where {uk} represents the modal component and {ωk} is the centre frequency of the modal component.

The formula in Eq. (1) is solved by using the augmented Lagrange function to obtain the following expression: L({uk},{ωk},λ)=αk=1Kt[(δ(t)+jπt)×uk(t)]ejωkt2+f(t)k=1Kuk(t)2+λ(t),f(t)k=1Kuk(t) \matrix{{L\left({\{{u_k}\},\{{\omega _k}\},\lambda} \right)} \hfill & {= \alpha \sum\limits_{k = 1}^K {{\left\| {{\partial _t}\left[{\left({\delta (t) + {j \over {\pi t}}} \right) \times {u_k}(t)} \right]{e^{- j{\omega _k}t}}} \right\|}^2} + {{\left\| {f(t) - \sum\limits_{k = 1}^K {u_k}(t)} \right\|}^2}} \hfill \cr {} \hfill & {+ \left\langle {\lambda (t),f(t) - \sum\limits_{k = 1}^K {u_k}(t)} \right\rangle} \hfill \cr} The alternating direction method of multipliers (ADMM) algorithm is used to further solve Eq. (2) to obtain Eqs (3) and (4): u^kn+1(ω)=f^(ω)iku^i(ω)+λ^(ω)/21+2α(ωωk)2; \hat u_k^{n + 1}(\omega) = {{\hat f(\omega) - \sum\limits_{i \ne k} {{\hat u}_i}(\omega) + \hat \lambda (\omega)/2} \over {1 + 2\alpha {{(\omega - {\omega _k})}^2}}}; ωkn+1=0ω|u^k(ω)|dω0|u^k(ω)|2dω; \omega _k^{n + 1} = {{\int_0^\infty \omega \left| {{{\hat u}_k}(\omega)} \right|d\omega} \over {\int_0^\infty {{\left| {{{\hat u}_k}(\omega)} \right|}^2}d\omega}}; where u^kn+1 \hat u_k^{n + 1} and ωkn+1 \omega _k^{n + 1} are the Wiener filter and frequency centre of each component, respectively.

SSA optimisation

The SSA is a bionic intelligent algorithm, and its behaviour characteristics are modelled after sparrows’ foraging and anti-predation behaviours. The sparrow population is composed of two sub-populations: joiner and discoverer. The search and foraging activities of the whole sparrow population is based on the change in the discoverer's position. In order to increase the predation rate, participants follow the discoverer to get food while constantly monitoring the discoverer. Sparrows in different positions will choose different escape strategies after realising that the population is in danger. The comprehensive performance of common algorithms, such as moth–flame optimisation algorithm, grey wolf optimisation algorithm and PSO algorithm, is inferior to hat of the SSA in terms of accuracy and stability; so, SSA with better searching ability is used to optimise VMD.

Optimising VMD based on SSA

The VMD decomposition method decomposes data series by setting variables, such as decomposition number, fidelity coefficient and convergence conditions. The decomposition quantity K and penalty factor α control the accuracy of the VMD decomposition method. The setting of the decomposition quantity K should be reasonable. When the K setting is large, decomposition is excessive, while data are lost when the K setting is small. It is determined by the bandwidth penalty variable α, and the bandwidth scale affects the extraction effect of the sequence. When the VMD method is used to decompose non-stationary and non-linear sequences, the subjective settings of the decomposition number K and the penalty factor α affect the accuracy of decomposition. Therefore, the SSA algorithm is proposed in this paper to optimise VMD parameters.

The aim of optimising VMD using the SSA algorithm is to decompose sequence f (t) into K eigenmode functions ui, and the decomposition process is shown in Eq. (5). f(t)=u1(t)+u2(t)++uk(t)=i=1kui(t). f(t) = {u_1}(t) + {u_2}(t) + \cdots + {u_k}(t) = \sum\limits_{i = 1}^k {u_i}(t).

When the actual decomposition components of the signal are all orthogonal, the energy of the original data sequence f (t) is equal to the sum of the energy of the K decomposition sequences, as shown in Eq. (6). Ef1=f2(t)dt {E_{f1}} = \int\limits_{- \infty}^\infty {f^2}(t)dt EBIMF=u1(t)dt++uk(t)dt {E_{BIMF}} = \int\limits_{- \infty}^\infty {u_1}(t)dt + \ldots + \int\limits_{- \infty}^\infty {u_k}(t)dt Ef1=EBIMF {E_{f1}} = {E_{BIMF}}

When the BIMF is not completely orthogonal, then Ef1 and EBIMF have energy error Eerr. Eerr=|Ef1EBIMF|. {E_{err}} = \left| {{E_{f1}} - {E_{BIMF}}} \right|.

The orthogonality of the BIMF component is determined by the value of Eerr. The smaller the Eerr is, the better is the orthogonality effect and the better is the representation effect of the sub-components on the sequence f (t).

To sum up, the solution process of [K,α] by the VMD decomposition method is as follows:

Setting the initial population and related parameters of the SSA and selecting Eerr as fitness function.

After decomposing the data sequence by the VMD method, the fitness value of the sparrows is obtained using Eq. (8).

Updating the position of sparrows through the optimisation mechanism of the SSA and comparing the energy differences in different positions to constantly find the minimum fitness value.

The minimum fitness value is obtained through cyclic iteration of Steps (2)–(4), at which time point, the sparrow position is the best position and [K,α] is the output.

VMD decomposition is carried out on the data sequence by using the optimal component number K and penalty variable α.

Decomposition result

For selecting a photovoltaic power sequence to optimise the VMD decomposition method by SSA, the population number of SSA is set to 20; the number of iterations is set to 30; the search range of the decomposition quantity K is [2, 16] and the optimisation range of the penalty factor α is [0,3000]. According to the change in the optimal fitness value, the optimal [K,α] combination is [6,1578], and the minimum energy error is 0.551. The VMD decomposition results of SSA optimisation of a photovoltaic power sequence are shown in Figure 2.

Fig. 2

VMD decomposition results

LSTM neural network
Neurological principles of long-term and short-term memories

When a recurrent neural network (RNN) processes long-time series data, the gradient is easy to explode, resulting in poor processing effect. The LSTM network solves the gradient problem when an RNN network processes long sequence data by setting the cell state and three-door structure in the hidden layer, so that the memory information can be saved for a long time. The internal structure of an LSTM network is shown in Figure 3.

Fig. 3

LSTM network structure.LSTM, long short-term memory

The inputs of the LSTM network are the sequence xt, hidden layer state ht−1 and the memory cell state ct−1 at the previous moment, and the outputs are the hidden layer state ht, candidate state ct, forgetting gate t time result ft, input gate t time result and output gate t time result ot. In the LSTM network, the forgetting gate is used to determine whether information is retained, the input gate determines the data input, and the output gate determines the data output. The LSTM calculation formula is as follows: {it=σ(Wxixt+Whiht1+Wcict1+bi)ft=σ(Wxfxt+Whfht1+Wcfct1+bf)ct=ftht1+ittanh(Wxcxt+Whcht1+bc)ot=σ(Wxoxt+Whoht1+Wcoct1+bc)ht=ottanh(ct), \left\{{\matrix{{{{\boldsymbol{i}}_t} = \sigma \left({{{\boldsymbol{W}}_{{\rm{xi}}}}{{\boldsymbol{x}}_t} + {{\boldsymbol{W}}_{{\rm{hi}}}}{{\boldsymbol{h}}_{t - 1}} + {{\boldsymbol{W}}_{{\rm{ci}}}}{{\boldsymbol{c}}_{t - 1}} + {{\boldsymbol{b}}_i}} \right)} \hfill \cr {{{\boldsymbol{f}}_t} = \sigma \left({{{\boldsymbol{W}}_{{\rm{xf}}}}{{\boldsymbol{x}}_t} + {{\boldsymbol{W}}_{{\rm{hf}}}}{{\boldsymbol{h}}_{t - 1}} + {{\boldsymbol{W}}_{{\rm{cf}}}}{{\boldsymbol{c}}_{t - 1}} + {{\boldsymbol{b}}_f}} \right)} \hfill \cr {{{\boldsymbol{c}}_t} = {{\boldsymbol{f}}_t}{{\boldsymbol{h}}_{t - 1}} + {{\boldsymbol{i}}_t}\tanh \left({{{\boldsymbol{W}}_{{\rm{xc}}}}{{\boldsymbol{x}}_t} + {{\boldsymbol{W}}_{{\rm{hc}}}}{{\boldsymbol{h}}_{t - 1}} + {{\boldsymbol{b}}_c}} \right)} \hfill \cr {{{\boldsymbol{o}}_t} = \sigma \left({{{\boldsymbol{W}}_{{\rm{xo}}}}{{\boldsymbol{x}}_t} + {{\boldsymbol{W}}_{{\rm{ho}}}}{{\boldsymbol{h}}_{t - 1}} + {{\boldsymbol{W}}_{{\rm{co}}}}{c_{t - 1}} + {{\boldsymbol{b}}_c}} \right)} \hfill \cr {{{\boldsymbol{h}}_t} = {{\boldsymbol{o}}_t}\tanh \left({{{\boldsymbol{c}}_t}} \right),} \hfill \cr}} \right. where Wx, Wh and Wc are different weight matrices; bi, bc, bf and bo represent the offset vectors; σ and tanh are the activation functions.

Both LSTM network and BP neural network use gradient optimisation algorithm to transform weights. In order to solve the problem of large parameter dimension, Adam algorithm is used to optimise the random objective function.

Structure of long-term and short-term memory neural networks

The parameters of the LSTM network model of the first and second layers are as follows: dropout value is 0.2; the function is optimised to Adam; the activation function takes tanh; the number of nodes is 50; training times are 1,000; batch size is 72; and the average absolute error function is selected as the loss function.

Power prediction model
Modelling classification

Because the weather type has a great influence on the photovoltaic output, in order to improve the prediction accuracy, this paper separately predicts abrupt weather (sunny, cloudy, rainy and snowy) and the non-abrupt weather (sunny to cloudy, sunny to cloudy, etc.). In order to test the accuracy of the VMD–LSTM model optimised by SSA, four models, namely BP, ANN, LSTM and VMD–LSTM, were established and compared with the proposed model. When evaluating the accuracy of the model, the average absolute percentage error eMAPE, the root mean square error eRMSE and the Hill inequality coefficient eTIC are selected, and the expressions are as follows: eMAPE=1Zi=1Z|yiyiyi| {e_{MAPE}} = {1 \over Z}\sum\limits_{i = 1}^Z \left| {{{y_i^{'} - {y_i}} \over {{y_i}}}} \right| eRMSE=i=1Z(yiyi)2Z {e_{RMSE}} = \sqrt {{{\sum\limits_{i = 1}^Z {{\left({y_i^{'} - {y_i}} \right)}^2}} \over Z}} eTIC=i=1Z(yiyi)2i=1Z(yi)2+i=1Z(yi)2 {e_{TIC}} = {{\sqrt {\sum\limits_{i = 1}^Z {{\left({y_i^{'} - {y_i}} \right)}^2}}} \over {\sqrt {\sum\limits_{i = 1}^Z {{\left({y_i^{'}} \right)}^2}} + \sqrt {\sum\limits_{i = 1}^Z {{\left({{y_i}} \right)}^2}}}} where y is the true value of power; y is the predicted value of power; and Z is for sample purpose.

Weather prediction model

The photovoltaic output of different weather types is predicted separately, and the prediction process is shown in Figure 4. In non-abrupt weather, the historical PV power station output data in sunny, rainy, snowy, cloudy or cloudy weather is decomposed by SSA–VMD, and all sub-components are added to meteorological conditions and sent to the LSTM network for prediction. Photovoltaic output fluctuates greatly in abrupt weather, so in abrupt weather forecast, the time of maximum output power in a day (2:00 pm) is selected for decomposition, so that the original complex power sequence becomes a number of stable data sequences, and then meteorological factors are added and sent to the LSTM network.

Fig. 4

Forecast process

Example analysis
Source of examples

To prove the accuracy of the VMD–LSTM model optimised by SSA, the 366-day historical power data of a power station with an installed capacity of 50 MW for the period from 1 January 2020 to 31 December 2020 is selected as the experimental sample. Sunny, cloudy, rainy, snowy and abrupt weather in 2020 has been recorded for 142 days, 46 days, 37 days, 39 days and 102 days, respectively. Taking sunny weather, rain and snow weather in non-abrupt weather, and sunny-to-cloudy weather in abrupt weather as examples, the training sample days of cloudy weather, rain and snow weather and sunny to cloudy weather are 120 days, 32 days and 24 days, respectively, and the test sample days are 22 days, 7 days and 5 days, respectively.

Forecast results
Sunny weather forecast

The forecast results of each forecast model for sunny weather are shown in Figure 5. In sunny weather, the fluctuation of photovoltaic power is small. It can be clearly seen in the figure that there is a big deviation between the predicted value and the real value of the BP neural network. When the power value is larger, the error is more obvious. Statistical errors of the five models are plotted in Table 1. Comparing the prediction errors of BP, ANN and LSTM models, the eMAPE values of the LSTM model are 0.096 and 0.082 lower than those of BP and ANN, respectively, which indicates that the deep learning model has obvious precision advantages over the traditional neural network and can extract more detailed characteristics of the photovoltaic data series. On November 7, eMAPE, eRMSE and eTIC of the SSA–VMD–LSTM prediction model were 0.179, 56.833 and 0.076, respectively. Among the five models, the three error evaluation indices were the smallest, and when the photovoltaic power curve fluctuated at 11 am, the SSA–VMD–LSTM power prediction curve was still consistent with the actual power curve.

Fig. 5

Forecast results of photovoltaic power on a sunny day on November 7

Prediction error of photovoltaic power in clear weather

Date Model eMAPE eRMSE eTIC

7 November 2020 BP 0.411 192.574 0.191
ANN 0.397 125.084 0.147
LSTM 0.315 102.218 0.123
VMD–LSTM 0.239 75.886 0.096
SSA–VMD–LSTM 0.179 56.833 0.076
6 October 2020 BP 0.456 183.681 0.212
ANN 0.527 172.535 0.128
LSTM 0.327 90.399 0.125
VMD–LSTM 0.287 66.757 0.074
SSA–VMD–LSTM 0.222 72.644 0.073

ANN, artificial neural network; BP, back propagation; eMAPE, average absolute percentage error; eRMSE, root mean square error; eTIC, Hill inequality coefficient; LSTM, long short-term memory; SSA, sparrow search algorithm; VMD, variational mode decomposition

Forecast of rain and snow

Figure 6 shows the photovoltaic output forecast of each forecast model in rain and snow weather, and Table 2 shows the model errors. Compared with the photovoltaic power in cloudy weather, the photovoltaic power in rainy and snowy weather decreases and fluctuates obviously. At this time, the prediction accuracy of each model has decreased, and there are obvious errors between the predicted power and the actual power of the BP and ANN models, which are no longer suitable for the prediction of photovoltaic power. On June 5, compared with BP, ANN and LSTM, the eMAPE values of the VMD–LSTM and SSA–VMD–LSTM models decreased obviously. The main reason was that the complexity of data sequence was reduced by VMD, and redundant interference was avoided.

Fig. 6

Forecast results of photovoltaic power on a cloudy day of June 5

Forecast error of photovoltaic power in rain and snow

Date Model eMAPE eRMSE eTIC

5 June 2020 BP 0.694 305.577 0.335
ANN 0.745 209.348 0.238
LSTM 0.517 151.906 0.188
VMD–LSTM 0.369 109.707 0.148
SSA–VMD–LSTM 0.294 101.777 0.117
16 August 2020 BP 0.871 287.903 0.312
ANN 0.803 233.221 0.210
LSTM 0.632 140.579 0.186
VMD–LSTM 0.426 117.406 0.134
SSA–VMD–LSTM 0.317 105.887 0.124

ANN, artificial neural network; BP, back propagation; eMAPE, average absolute percentage error; eRMSE, root mean square error; eTIC, Hill inequality coefficient; LSTM, long short-term memory; SSA, sparrow search algorithm; VMD, variational mode decomposition

Weather forecast from sunny to cloudy

When the weather changes from sunny to cloudy, the photovoltaic power prediction results of each model are shown in Figure 7, and the errors are shown in Table 3. The complexity of photovoltaic power data series in abrupt weather is higher than that in non-abrupt weather, and the deviation between the predicted power of BP and ANN models and the actual power is greater, which obviously reduces the prediction accuracy. As can be seen from Table 3, on January 8, the eMAPE value of the SSA–VMD–LSTM prediction model decreased by 0.350, 0.318, 0.242 and 0.067, respectively compared with BP, ANN, LSTM and VMD–LSTM models, i.e. the prediction accuracy of the SSA–VMD–LSTM model is still the highest in sudden weather.

Fig. 7

Forecast results of sudden change weather on January 8

Prediction error of photovoltaic power in abrupt weather

Date Model eMAPE eRMSE eTIC

8 January 2020 BP 0.708 251.918 0.287
ANN 0.676 252.247 0.287
LSTM 0.600 218.179 0.268
VMD–LSTM 0.425 183.933 0.217
SSA–VMD–LSTM 0.358 154.512 0.200
13 September 2020 BP 0.700 268.636 0.339
ANN 0.728 276.354 0.254
LSTM 0.577 247.426 0.270
VMD–LSTM 0.473 229.952 0.239
SSA–VMD–LSTM 0.381 150.918 0.229

ANN, artificial neural network; BP, back propagation; eMAPE, average absolute percentage error; eRMSE, root mean square error; eTIC, Hill inequality coefficient; LSTM, long short-term memory; SSA, sparrow search algorithm; VMD, variational mode decomposition

Error comparison of the combined model

In order to further highlight the accuracy of the SSA optimisation method, this paper counts the test results of all test samples of the power generation system within 1 year and obtains the average errors of the VMD–LSTM and SSA–VMD–LSTM prediction models, as shown in Table 4.

Comparison of prediction errors between VMD–LSTM and SSA–VMD–LSTM

Model eMAPE eRMSE eTIC

VMD–LSTM 0.327 91.150 0.106
SSA–VMD–LSTM 0.207 85.673 0.058

eMAPE, average absolute percentage error; eRMSE, root mean square error; eTIC, Hill inequality coefficient; LSTM, long short-term memory; SSA, sparrow search algorithm; VMD, variational mode decomposition

Compared with the eRMSE, eMAPE and eTIC of the VMD–LSTM model optimised by SSA, the eRMSE, eMAPE and eTIC of the VMD–LSTM model decreased by 0.120, 5.477 and 0.048, respectively; in other words, the accuracy of optimising the decomposition quantity and the penalty factor of the VMD method by SSA was obviously improved compared with manually determining the parameters.

Conclusions

In order to improve the accuracy of photovoltaic power forecasting, this paper puts forward a combined forecasting model, which combines the VMD decomposition method optimised by the sparrow intelligent algorithm with the deep learning algorithm, builds four models (namely BP, ANN, LSTM and VMD–LSTM) and compares their errors with the proposed SSA–VMD–LSTM coupling model. The main conclusions are as follows.

In data processing, SSA-optimised VMD method combined with LSTM network can describe the long memory characteristics of a time series, which greatly improves the prediction accuracy compared with the traditional non-combination prediction model.

SSA can optimise the decomposition quantity and the penalty factor in VMD, which gives lower eRMSE, eMAPE and eTIC values for the SSA–VMD–LSTM model than the VMD–LSTM model by 0.120, 5.477 and 0.048, respectively. The prediction accuracy of the SSA–VMD–LSTM model is obviously higher than that of the VMD–LSTM model.

The model proposed in this paper can decompose high-complexity photovoltaic data into more regular sub-components, and its coupling model has obvious advantages, which renders it suitable for ultra-short-term power forecasting of photovoltaic power stations.

Fig. 1

Influence of weather types on photovoltaic power
Influence of weather types on photovoltaic power

Fig. 2

VMD decomposition results
VMD decomposition results

Fig. 3

LSTM network structure.LSTM, long short-term memory
LSTM network structure.LSTM, long short-term memory

Fig. 4

Forecast process
Forecast process

Fig. 5

Forecast results of photovoltaic power on a sunny day on November 7
Forecast results of photovoltaic power on a sunny day on November 7

Fig. 6

Forecast results of photovoltaic power on a cloudy day of June 5
Forecast results of photovoltaic power on a cloudy day of June 5

Fig. 7

Forecast results of sudden change weather on January 8
Forecast results of sudden change weather on January 8

Forecast error of photovoltaic power in rain and snow

Date Model eMAPE eRMSE eTIC

5 June 2020 BP 0.694 305.577 0.335
ANN 0.745 209.348 0.238
LSTM 0.517 151.906 0.188
VMD–LSTM 0.369 109.707 0.148
SSA–VMD–LSTM 0.294 101.777 0.117
16 August 2020 BP 0.871 287.903 0.312
ANN 0.803 233.221 0.210
LSTM 0.632 140.579 0.186
VMD–LSTM 0.426 117.406 0.134
SSA–VMD–LSTM 0.317 105.887 0.124

Prediction error of photovoltaic power in abrupt weather

Date Model eMAPE eRMSE eTIC

8 January 2020 BP 0.708 251.918 0.287
ANN 0.676 252.247 0.287
LSTM 0.600 218.179 0.268
VMD–LSTM 0.425 183.933 0.217
SSA–VMD–LSTM 0.358 154.512 0.200
13 September 2020 BP 0.700 268.636 0.339
ANN 0.728 276.354 0.254
LSTM 0.577 247.426 0.270
VMD–LSTM 0.473 229.952 0.239
SSA–VMD–LSTM 0.381 150.918 0.229

Prediction error of photovoltaic power in clear weather

Date Model eMAPE eRMSE eTIC

7 November 2020 BP 0.411 192.574 0.191
ANN 0.397 125.084 0.147
LSTM 0.315 102.218 0.123
VMD–LSTM 0.239 75.886 0.096
SSA–VMD–LSTM 0.179 56.833 0.076
6 October 2020 BP 0.456 183.681 0.212
ANN 0.527 172.535 0.128
LSTM 0.327 90.399 0.125
VMD–LSTM 0.287 66.757 0.074
SSA–VMD–LSTM 0.222 72.644 0.073

Comparison of prediction errors between VMD–LSTM and SSA–VMD–LSTM

Model eMAPE eRMSE eTIC

VMD–LSTM 0.327 91.150 0.106
SSA–VMD–LSTM 0.207 85.673 0.058

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