Medium–Long-Term PV Output Forecasting Based on the Graph Attention Network with Amplitude-Aware Permutation Entropy

Abstract

Medium–long-term photovoltaic (PV) output forecasting is of great significance to power grid planning, power market transactions, power dispatching operations, equipment maintenance and overhaul. However, PV output fluctuates greatly due to weather changes. Furthermore, it is frequently challenging to ensure the accuracy of forecasts for medium–long-term forecasting involving a long time span. In response to the above problems, this paper proposes a medium–long-term forecasting method for PV output based on amplitude-aware permutation entropy component reconstruction and the graph attention network. Firstly, the PV output sequence data are decomposed by ensemble empirical mode decomposition (EEMD), and the decomposed intrinsic mode function (IMF) subsequences are combined and reconstructed according to the amplitude-aware permutation entropy. Secondly, the graph node feature sequence is constructed from the reconstructed subsequences, and the mutual information of the node feature sequence is calculated to obtain the graph node adjacency matrix which is applied to generate a graph sequence. Thirdly, the graph attention network is utilized to forecast the graph sequence and separate the PV output forecasting results. Finally, an actual measurement system is used to experimentally verify the proposed method, and the outcomes indicate that the proposed method, which has certain promotion value, can improve the accuracy of medium–long-term forecasting of PV output.

1. Introduction

Solar energy, as a clean and renewable energy technology, has received widespread attention under the dual pressure of the global energy crisis and environmental pollution. However, the photovoltaic(PV) output, which has obvious volatility and uncertainty, is greatly influenced by natural factors such as sunlight conditions, climate, and seasons. The integration of large-scale PV output may have an impact on the stability of the power grid [1,2,3,4]. Medium–long-term forecasting can be beneficial for power station planning and resource assessment, ensuring the balance of electricity in the power system and improving PV penetration at the macro level [5].

In PV output forecasting, time–frequency decomposition is widely used to handle the volatility of PV power time series due to its ability to reveal the internal structure and local characteristics of the time series. Reference [6] uses the empirical mode decomposition (EMD) signal processing algorithm to decompose the time series into a series of relatively stable component sequences, and then establishes forecasting models for each subsequence. Finally, the forecasting results of each subsequence are stacked to obtain the final forecasting value. Reference [7] introduces the ensemble empirical mode decomposition (EEMD) signal processing algorithm, decomposes historical PV time series into multiple frequencies, and establishes a generalized regression neural network forecasting model to forecast the future output of PV power plants. Reference [8] introduces the Variational Mode Decomposition (VMD) algorithm to avoid mode mixing, boundary effects, and other issues, thereby reducing the non-stationary nature of PV data. Time-frequency decomposition can decompose complex PV power time series into multiple intrinsic mode functions with different frequency characteristics [9,10,11]. The intrinsic mode function can better reveal the intrinsic structure and local characteristics of data, and more accurately capture the dynamic characteristics of PV power changes. In addition, time–frequency decomposition also helps to reduce the complexity of data, improve the generalization ability and forecasting accuracy of the model.

The traditional PV power medium–long-term forecasting method based on time–frequency decomposition usually models each intrinsic mode function obtained from decomposition, forecasts the evolution trend of each intrinsic mode function time series, and then overlays the forecasting results to obtain the final PV power forecasting value. Although each intrinsic mode function is independent in frequency, there may be statistical correlations between them, which can result in similar information entropy [12]. Taking the PV power time series as an example, the decomposed intrinsic mode function may represent rapid power fluctuations caused by cloud cover, or may be related to seasonal changes. Therefore, how to handle the correlation between the modal functions obtained from the decomposition of PV power time series is an important issue.

In deep learning methods, graph neural networks (GNN) are often used to handle multi time series forecasting in various fields [13,14,15]. Reference [16] uses graph convolutional neural networks to capture the topological relationships of power networks, transform them into graphical structures, and transform load forecasting problems into graph node regression tasks, achieving load forecasting. Reference [17] first uses the visibility graph method to transform multiple time series of power loads into undirected graphs, and then trains the GNN with the obtained graph and corresponding adjacency matrix inputs. Finally, real data from high-voltage/medium-voltage substations confirmed that the proposed method outperforms widely used machine learning methods. Reference [18] proposes a traffic flow forecasting model based on a dynamic graph recursive network, which captures hidden spatial dependencies in data through a dynamic graph generator. The generated dynamic graph is trained into special time series data through a dynamic graph recursive neural network, and the excellent forecasting accuracy of the proposed model is verified with a large number of datasets.

The literature indicates that the graph attention network (GAT) in GNN has shown great potential in processing graph structured data [19,20]. GAT allocates adaptive weights to nodes in the graph by introducing attention mechanisms, thereby capturing complex relationships between nodes. Due to its flexibility and generalization ability, it can effectively handle graph structure data from different fields and performs well in various graph related machine learning tasks such as node classification and forecasting, and graph classification [21]. Reference [22] proposes a new dynamic multi granularity spatiotemporal GAT framework for traffic forecasting, which effectively considers the cyclic patterns in traffic data by utilizing the multi granularity spatiotemporal correlations of different time scales and variables. Finally, the effectiveness of the proposed model was verified through simulation. Reference [23] uses GAT to analyze individual speech features to recognize or verify the speaker’s identity, improves the feature fusion strategy in speaker recognition tasks, and enhances recognition performance through a self supervised learning framework. Reference [24] combines GAT with forecast protein contact maps for forecasting whether multi-stage proteins can crystallize, and demonstrate the effectiveness of GAT through simulation experiments.

Although GAT has shown excellent performance in multiple time series forecasting tasks in various fields, it is currently less applied in the field of PV power forecasting. Based on the above background, this paper proposes a medium–long-term PV power forecasting method that combines the time–frequency decomposition algorithm and GAT. By decomposing PV time series using the time–frequency decomposition method and based on amplitude-aware permutation entropy (AAPE), this paper reconstructs the decomposed sequence into a multivariate time series and uses graph attention networks to capture the correlation between various time series, achieving medium–long-term forecasting of PV power. AAPE can be imagined as a special video editor that can split a video into different video tracks. Just like when we watch a video, we can see the picture and hear the sound. AAPE does something similar. It breaks down a complex signal into several simpler parts, each with its own characteristics, and eliminates the parts that have minimal impact. The advantage of this is that we can more easily understand these signals. This article converts the simple parts decomposed by AAPE into nodes, and the GAT is the technology used to more effectively capture complex interactions between nodes. It is like a graph of a social network, which can help us understand the connections between different nodes and predict their subsequent changes.

The method proposed in this paper provides a new feasible approach for medium–long-term forecasting of PV output. The contributions of this paper are as follows:

(1)

A PV power feature extraction method based on AAPE is proposed. Through AAPE analysis, the changing characteristics of PV power generation time series are effectively captured, providing a new quantitative description method for PV power generation fluctuation patterns.

(2)

A method is creatively designed to convert the reconstructed sequence into node features and adjacency matrix form as the input of GAT. And the relationship between nodes is extracted through the attention mechanism, allowing the model to focus on nodes that are more important to the prediction task.

(3)

The proposed algorithm is empirically evaluated in a campus PV-microgrid demonstration system in East China and a public dataset in Australia, respectively. By comparing with existing technologies, the effectiveness and superiority of the proposed method in PV power prediction at different time scales are verified.

2. IMF Component Reconstruction of PV Output Sequences Based on Amplitude Perception Permutation Entropy

2.1. EEMD Decomposition of PV Output Sequences

EEMD automatically separates PV power sequences at different time scales to their corresponding reference scales by adding Gaussian white noise to the original PV output sequence and performing multiple EMD decomposition, effectively suppressing EMD mode aliasing [25] and possessing stronger scale separation ability. The process of EEMD decomposition for $x(t)$ is as follows:

Firstly, add Gaussian white noise $n_m(t)$ to $x(t)$, i.e.,

$$x_m(t)=x(t)+k{n}_m(t)$$

(1)

where $x_m(t)$ is the m-th PV power sequence after adding Gaussian white noise.

Then, perform EMD decomposition on $x_m(t)$ to obtain J intrinsic mode function (IMF) components $c_{j,m}(t)$ and residual component $r_m(t)$, i.e.,

$$x_m(t)={\displaystyle \sum _{j=1}^J{c}_{j.m}(t)}+r_m(t),j=1,2,\cdots ,J$$

(2)

Finally, calculate the mean of the IMF and residual components obtained after M rounds of EMD decomposition as shown in Equations (3) and (4), From this, ${\overline{c}}_i(t)$($i=1,2,\cdots ,n$) and ${\overline{r}}_n(t)$ are obtained as the nth IMF component and residual component obtained by EEMD decomposition of the original PV power sequence, respectively.

$${\overline{c}}_i(t)={\displaystyle \sum _{m=1}^M{c}_{i.m}(t)/M},i=1,2,\cdots ,n$$

(3)

$${\overline{r}}_n(t)={\displaystyle \sum _{m=1}^M{r}_{n,m}(t)/M}$$

(4)

2.2. IMF Component Reconstruction Based on Amplitude Perception Permutation Entropy

The n IMF components and residual components obtained by EEMD decomposition of the PV power series contain local features of the original PV power series at different time scales. However, indiscriminate forecasting and stacking of too many components can not only be computationally cumbersome, but may also lead to error accumulation. Therefore, this paper proposes an IMF component reconstruction method based on amplitude-aware permutation entropy (AAPE). Using AAPE as a measure of sequence complexity, IMF components are classified and reconstructed according to their complexity. This not only reduces time and computational costs, but also provides conditions for using different forecasting algorithms for sequences with different complexities.

Using the theory of phase space reconstruction, the decomposed components of PV output can be reconstructed into vectors as shown in Equation (5)

$${{\overline{c}}_i}^{d,\tau }(t)=\{{\overline{c}}_i(t),{\overline{c}}_i(t+\tau ),\cdots ,{\overline{c}}_i(t+(d-1)\tau )\}$$

(5)

where $d$ and $\tau$ are the embedding dimension and delay time, respectively, $t=1,2,\cdots ,N-(d-1)\tau$, $N$ is the total length of the PV power sequence. Arrange the elements in each sequence of ${{\overline{c}}_i}^{d,\tau }(t)$ in ascending order of size, and denote the $j$th order as ${\pi }_j$. The probability of the occurrence of each order of ${\pi }_j$ is as follows:

$$p({\pi }_j)={\displaystyle \frac{f({\pi }_j)}{N-d+1}}$$

(6)

where $f({\pi }_j)$ represents the number of occurrences of arrangement order ${\pi }_j$; $p({\pi }_j)$ represents the probability of occurrence of arrangement order ${\pi }_j$.

The permutation entropy (PE) can be calculated from Equation (7)

$$H_{PE}(d)=-{\displaystyle \frac{1}{\ln (d!)}}{\displaystyle \sum _{{\pi }_j=1}^{{\pi }_j=d!}p({\pi }_j)\ln p({\pi }_j)}$$

(7)

where $H_{PE}(d)$ represents the calculated value of the PV power sequence component PE. However, PE only considered the order of amplitude in the PV power sequence components, and did not fully extract the amplitude characteristics of the elements in the components. This paper uses the AAPE algorithm to evaluate the complexity of PV power sequence components. Compared to traditional PE algorithms, AAPE considers the deviation between the mean and amplitude of the sequence amplitude in the calculation process, and uses relatively normalized probabilities to replace the counting rules in traditional PE algorithms [26]. The average value (AA) and relative amplitude (RA) of the reconstructed sequence can be represented as follows:

$$A{A}_j={\displaystyle \frac{1}{d}}{\displaystyle \sum _{k=1}^d|{\overline{c}}_i(t+(k-1)\tau )|}$$

(8)

$$R{A}_j={\displaystyle \frac{1}{d-1}}{\displaystyle \sum _{k=2}^d|{\overline{c}}_i(t+(k-1)\tau )-{\overline{c}}_i(t+(k-2)\tau )|}$$

(9)

The initial value of $p({\pi }_j^{d,\tau })$ is set to 0, and during the process of t in reconstructing vector ${{\overline{c}}_i}^{d,\tau }(\mathrm{t})$ gradually increases from 1 to $N-d+1$, Whenever the order of arrangement is ${{\overline{c}}_i}^{d,\tau }(\mathrm{t})$, $p({\pi }_j^{d,\tau })$ is calculated once. The formula is as follows:

$$p({\pi }_j^{d,\tau })=p({\pi }_j^{d,\tau })+(\alpha \cdot A{A}_j+(1-\alpha )R{A}_j)$$

(10)

where $\alpha \in (0,1)$ is the weight used to adjust the mean amplitude of the component and the deviation between component amplitudes, generally taken as 0.5. The probability of each arrangement order appearing at this time is

$$p*({\pi }_j)={\displaystyle \frac{f({\pi }_j^{d,\tau })}{{\displaystyle \sum _{t=1}^{N-d+1}(\alpha \cdot A{A}_j+(1-\alpha )R{A}_j)}}}$$

(11)

Then, the AAPE of the PV power sequence component can be expressed as

$$H_{AAPE}(d)=-{\displaystyle \frac{1}{\ln (d!)}}{\displaystyle \sum _{{\pi }_k=1}^{{\pi }_k=d!}{p}^{*}({\pi }_k)\ln p^{*}({\pi }_k)}$$

(12)

where $H_{AAPE}(d)$ represents the AAPE value of the PV power sequence component. AAPE reflects the complexity of each component, with IMF components with higher AAPE values representing the characteristics of short period components with stronger randomness in PV power sequences, and IMF components with lower AAPE values representing the trend of long period changes with stronger regularity in PV power sequences.

From the perspective of feature extraction, forecasting and modeling components with similar complexity separately have limited effect on improving forecasting accuracy and will greatly increase the workload of model training. To improve the training efficiency of the forecasting model, this paper uses the AAPE difference between adjacent components as the judgment condition to reconstruct the EEMD component. When the AAPE difference between adjacent subsequences is greater than a certain value, it can be considered that there is a significant difference in complexity between components, and they need to be processed separately as subsequences S₁~S_z. When the AAPE difference between adjacent components is less than a certain value, it can be considered that the complexity between components is close, and the components contain similar information, which can be merged and recorded as S_z+1.The residual component generally has a large difference from adjacent components and is used as a separate subsequence S_z+2.

3. PV Output Forecasting Modeling Based on the Graph Attention Network

GAT introduces an attention mechanism into graph neural networks based on spatial domains. Unlike graph convolutional networks (GCNs) based on spectral domains, graph attention networks do not require complex calculations using matrices such as Laplacian, and only update node features through the representation of first-order neighboring nodes. The algorithm principle is relatively simple [27,28]. Taking the five subsequences formed after decomposition and reconstruction of the original sequence as an example, the GAT forecasting model constructed in this paper is shown in Figure 1. The model consists of a graph data input layer, a graph attention layer, a fully connected layer, and an output layer.

At the input layer, the node feature sequence and node adjacency matrix obtained from the PV power decomposition and reconstruction sequence together constitute the graph data sequence. Among them, the node feature sequence is composed of the subsequence set S obtained from reconstructing the PV power sequence through the IMF component based on AAPE, where the nodes in each graph data are column elements of the node feature sequence. The edges of each graph data in the graph data sequence are elements of the node adjacency matrix. In this paper, the node adjacency matrix is composed of the mutual information between any two subsequences $S_i$ and $S_j$ in the node feature sequence, as shown in Equations (13) and (14).

$$A=\left[\begin{array}{cccc}0& I\left(S_1,S_2\right)& \cdots & I\left(S_1,S_n\right)\\ I\left(S_2,S_1\right)& 0& \cdots & I\left(S_2,S_n\right)\\ ⋮& ⋮& \ddots & ⋮\\ I\left(S_n,S_1\right)& I\left(S_n,S_2\right)& \cdots & 0\end{array}\right]$$

(13)

$$I(S_i,S_j)={\displaystyle \int p(S_i,S_j){\log }_2\frac{p(S_i,S_j)}{p(S_i)p(S_j)}\mathrm{d}{S}_i\mathrm{d}{S}_j}$$

(14)

where A is the node adjacency matrix; n is the number of nodes; $I(S_i,S_j)$ represents the mutual information between $S_i$ and $S_j$; $p(S_i,S_j)$ is the joint probability of variables $S_i$ and $S_j$; $p(S_i)$ and $p(S_j)$ are the edge probability density functions of $S_i$ and $S_j$ respectively.

The core of the GAT neural network is the graph attention layer, which uses an attention mechanism to calculate the hidden representation of each node in the graph, that is, the hidden features of factors in the PV power sequence. Each layer inputs a set of node features and outputs a new set of node features. Firstly, in order to enable the model to obtain sufficient expressive power to transform input features into higher-level features, at least one learnable linear transformation is required to be applied to each node. Therefore, a shared linear transformation $\mathbf{W}\in {ℝ}^{{\mathrm{F}}^{\prime }\times \mathrm{F}}$ parameterized by a weight matrix is used in the attention layer of the graph, and the attention coefficients shown in Equation (15) are calculated for the nodes [29].

$$e_{ij}=a(\mathbf{W}\overrightarrow{h_i},\mathbf{W}\overrightarrow{h_j})$$

(15)

where represents the attention coefficient of node j’s features to node I which is the unidirectional relationship between each subsequence of the PV power sequence, and the number attention coefficient calculation head in this paper is 3; $\overrightarrow{h_i}$ and $\overrightarrow{h_j}$ represent node features.

Then, the GAT neural network allows for interaction between each node by injecting the graph structure into the mechanism using attention mechanisms to compute $e_{ij}$, $j\in N_i$, where $N_i$ is an adjacent node. In order to make the coefficients easy to compare between different nodes, the softmax function shown in Equation (16) is used to normalize the attention system [30].

$${\alpha }_{ij}={\mathrm{softmax}}_j(e_{ij})={\displaystyle \frac{\exp (e_{ij})}{{\displaystyle {\sum }_{k\in N_i}\exp (e_{ik})}}}$$

(16)

Next, the attention mechanism of each layer in the GAT neural network serves as a single-layer feedforward neural network, parameterized by a weight vector and non-linearized using LeakyReLU with a negative slope of 0.2. The specific formula is as follows [31]:

$${\alpha }_{ij}={\displaystyle \frac{\exp (\mathrm{Leaky} \mathrm{ReLU}({\overrightarrow{a}}^{\mathsf{{\rm T}}}[\mathbf{W}\overrightarrow{h_i}\parallel \mathbf{W}\overrightarrow{h_j}])}{{\displaystyle {\sum }_{k\in N_i}\exp (\mathrm{Leaky} \mathrm{ReLU}({\overrightarrow{a}}^{\mathsf{{\rm T}}}[\mathbf{W}\overrightarrow{h_i}\parallel \mathbf{W}\overrightarrow{h_k}])}}}$$

(17)

where ${\alpha }_{ij}$ is the attention mechanism coefficient of node $i$ to node $j$; $\overrightarrow{a}$ is the weight vector of the attention mechanism; $\mathbf{W}$ is the weight matrix; $\mathsf{{\rm T}}$ represents transpose operation; $\parallel$ represents the splicing operation. Finally, through fully connected layers for feature integration, the sequence forecasting results are output, and the sequence is stacked to obtain the PV output at the time of forecasting.

4. A Combined Forecasting Model Based on the AAPE-GAT Neural Network

In summary, considering the factors of forecasting accuracy and forecasting time, the proposed AAPE-GAT neural network combination forecasting process in this paper is shown in Figure 2.

(1)

Perform EEMD decomposition on the PV sequence data in the dataset to obtain IMF and residual components for different frequency components.

(2)

Calculate the AAPE of the components and perform reconstruction to obtain the node feature sequence.

(3)

Calculate the mutual information of node feature sequences to obtain the adjacency matrix of nodes, and generate a graph data sequence together with the node feature sequence.

(4)

Input the graph data sequence into the GAT neural network, and finally output the forecasting results.

5. Example Analysis

5.1. Datasets and Preprocessing

The simulation and verification of this paper uses the PV output power data collected from the PV output system of Hangzhou Dianzi University(HDU) from January 2022 to January 2024 as the dataset. The installed capacity of the PV system is 120 kWp, and the sampling period is from 8:00 to 17:00 every day, with a sampling interval of 60 min. Therefore, the number of sampling points per day is 10. The original data consists of 820 days, corresponding to 8200 sampling points. To obtain statistical results, this paper constructs a time series of raw data for training and forecasting, using 730 days from January 2022 to December 2023 as the training set, using the last 90 days as the forecasting set. The forecast time span is 15 days.

To test the generalizability and robustness of the proposed forecasting model from different geographical locations, we also apply our model to the dataset from the Desert Knowledge Australia Solar Centre (DKASC), Alice Springs which contains a range of solar technologies operating at Desert Knowledge Precinct in Central Australia. The sampling period is from 8:00 to 17:00 every day, with a sampling interval of 60 min. We use 730 days from January 2021 to December 2022 as the training set, using the last 90 days as the forecasting set and the forecast time span is 15 days.

5.2. EEMD Decomposition of PV Output Sequence

Perform EEMD decomposition on the original sequence set of historical PV power to obtain the corresponding IMF and residual components. The original power sequence and EEMD decomposition results are shown in Figure 3. This paper combines the experience of selecting parameters K and M in reference [32], and sets K = 0.1 and M = 100 in the experiment.

5.3. Component Merging Based on Amplitude Perception Permutation Entropy

AAPE is used to evaluate the complexity of IMF components and then the components with similar complexity are reconstructed to reduce computational complexity. The time delay $\tau$ has a small impact on the results, so usually taking $\tau$ = 1, and the embedding dimension m is determined by the pseudo neighbor method. In this paper, m = 5. The AAPE calculation results of the PV power sequence components are shown in Figure 4.

From Figure 4, it can be seen that the AAPE value of the high-frequency component of the original PV power sequence after decomposition is larger, indicating a higher complexity. The lower AAPE value of the low-frequency component indicates lower complexity. The AAPE values of the lower-frequency components, namely IMF₇~IMF₁₂, are very close, and the difference between adjacent components is less than 0.04 [33]. Therefore, these components are combined into a subsequence S₆. The AAPE values of components IMF₂~IMF₆ differ significantly, so the original components remain unchanged and are, respectively, used as subsequences S₁~S₅. The residual components have a significant difference from adjacent components and are separately used as subsequences S7. The reconstructed subsequence is shown in Figure 5.

5.4. Forecasting Model Parameters

In order to verify the effectiveness of the method proposed, two deep learning algorithms commonly used in time series prediction, graph convolutional networks (GCNs) and Long Short-Term Memory (LSTM), were also used for the simulation comparison verification.

Reasonable neural network parameter settings determine the reliability and accuracy of PV power sequence forecasting. The parameters of the GAT neural network constructed in this chapter are shown in

Table 1. Parameters in the GAT neural network.

Item	Parameter Values	Item	Parameter Values
Number of hidden layers	1	Time interval	60
Training frequency	10	Historical length	6
Batch size	64	Number of nodes	8
Discard rate	0.56	Number of parallel working processes	32

, which includes one hidden layer and is trained 10 times. The batch size for each training is 64, with a time interval of 60, and the number of parallel working processes is 32. And parameters of the other models are shown in

Table 2. Parameters in the GCN.

Item	Parameter Values	Item	Parameter Values
Number of hidden layers	1	Time interval	60
Training frequency	10	Historical length	6
Batch size	64	Number of nodes	8
Discard rate	0.51	Number of parallel working processes	32

and

Table 3. Parameters in LSTM.

Item	Parameter Values	Item	Parameter Values
Number of hidden layers	1	Verbose	2
Epoch	10	Optimizer	Adam
Batch size	64	Number of nodes	120

. This not only ensures the stability of model training, but also accelerates training speed and completes training better.

5.5. Analysis of Forecasting Results

To verify the effectiveness of introducing AAPE reconstruction and GAT neural networks in improving forecasting accuracy, EEMD-GCN-based models and EEMD-GAT-based models were constructed as comparative models. The above model parameters are consistent with the network parameters used in this paper. The error evaluation parameters are Relative Error, MAPE, and rRMSE as shown in Equations (18)–(20), respectively.

$$RelativeError={\displaystyle \frac{\left|L_{\mu }-L_x\right|}{L_{\mu }}}\times 100\%$$

(18)

$$MAPE={\displaystyle \frac{1}{p}}{\displaystyle \sum _{i=1}^p\left|\frac{{\tilde{L}}_i-L_i}{L_i}\right|}\times 100\%$$

(19)

$$rRMSE={\displaystyle \frac{\sqrt{\frac{1}{p}{\displaystyle \sum _{i=1}^p{({\tilde{L}}_i-L_i)}^2}}}{\sqrt{\frac{1}{p}{\displaystyle \sum _{i=1}^p{L_i}^2}}}}\times 100\%$$

(20)

where $L_{\mu }$ represents the actual cumulative power generation value; $L_x$ represents the forecast cumulative power generation value; p represents the number of PV power sampling points in a day; $L_i$ represents the actual output of PV power on a certain day; ${\tilde{L}}_i$ represents the forecast output of PV power for that day. In the above indicators, relative error and MAPE, respectively, express the degree of deviation between cumulative days and specific daily forecast values and actual values, while rRMSE is highly sensitive to the error value of deviation from the mean in a certain group of forecast values.

Table 4. Results of PV output forecasting to dataset from HDU.

Model	Actual Cumulative PV Output (kWh)	Forecasting Cumulative PV Output (kWh)	Error Index
			Relative Error (%)	MAPE (%)	rRMSE (%)
EEMD-GCN	4639.35	4162.74	10.27	44.83	27.85
EEMD-GAT		4155.00	10.44	47.22	29.45
AAPE-GAT		4647.61	0.18	33.25	23.06
LSTM		3830.89	17.4	94.81	69.86

and

Table 5. Results of PV output forecasting to dataset from the DKASC, Alice Springs.

Model	Actual Cumulative PV Output (kWh)	Forecasting Cumulative PV Output (kWh)	Error Index
			Relative Error (%)	MAPE (%)	rRMSE (%)
EEMD-GCN	741.57	1176.63	58.67	61.33	58.79
EEMD-GAT		810.75	9.32	11.46	12.69
AAPE-GAT		787.94	6.25	10.12	12.20
LSTM		449.28	39.42	38.94	39.88

present a comparison of the cumulative power generation forecasting values and forecasting errors for each forecasting model over a total of 15 days.

From Table 4 and Table 5, it can be seen that in terms of the absolute value of cumulative forecast power generation, the forecast value of the method proposed in this paper is significantly closer to the actual value. From the perspective of relative error indicators, the proposed method in this paper has significantly lower Relative Error, MAPE, and rRMSE compared to the other two models. It can be seen that the model proposed in this paper has significantly improved learning ability and forecasting accuracy.

In addition, from the comparison of daily forecast power generation shown in Figure 6 and Figure 7, it can be seen that the method proposed in this paper has significantly more points similar to the actual power generation in the 15 day forecasting results than the other two models. Using GPU3060 (Colorful GeForce RTX 3060 DUO 12G, Hangzhou, China), the proposed model took only 8 min at training stage, and 2 min at testing stage. The comparison results are shown in

Table 6. Comparative results of different models’ running time.

Model	Training Time (min)	Testing Time (min)
EEMD-GCN	9	3
EEMD-GAT	9	2
AAPE-GAT	8	2
LSTM	4	2

. From Table 6, the running time is shorter and the calculation efficiency is higher than the other two networks.

This is because the use of the EEMD decomposition algorithm and the mutual information method improves the extraction of data features. In the forecasting process, the node adjacency matrix and reconstructed data can help the model better find the relationships between subsequences with similar features, improving the accuracy of PV sequence forecasting. The IMFs obtained by AAPE decomposition can capture the local change characteristics of the signal. These characteristics provide GAT with rich information and help to model and predict system behavior more accurately. In addition, the multi-scale signal features obtained by AAPE are combined with the attention mechanism of GAT to achieve cross-scale information fusion and improve the model’s ability to capture changes in different time scales. And the combined use of AAPE and GAT can resist the influence of noise interference and outliers to a certain extent, because both the decomposition process of AAPE and the attention mechanism of GAT have certain denoising capabilities. These are advantages that the compared models do not have.

6. Conclusions

This paper proposes a method for extracting data features based on the EEMD data decomposition method, AAPE and the mutual information method, as well as a PV output forecasting model using the GAT neural network. In this model, the PV power series data are first decomposed by EEMD to obtain IMF and residual components of different frequency components. Then, AAPE is calculated for the decomposed IMF and residual components, and the lower-complexity components are merged into a PV power subsequence. Afterwards, node feature sequences are obtained from each subsequence, and mutual information values are calculated for the node feature sequences. A calculation method for the node adjacency matrix is designed. Finally, a sequence of graph data is generated and the GAT neural network is used to obtain the forecasting results. The comparative experimental results show that the proposed model improves the forecasting accuracy in PV power sequence forecasting and can effectively forecasting medium–long-term PV power series. This method has certain practical application and promotion value. However, it should be noted that the proposed method requires a large amount of historical data for training, and is only suitable for PV power plants that have been built and operated for several years, because these power plants will have rich historical data. It is not applicable to new PV power stations, and one of the solutions is to use the transfer learning algorithm to establish the corresponding model by using the historical data of power stations with similar geographical locations.