DTTrans: PV Power Forecasting Using Delaunay Triangulation and TransGRU
<p>Overall process of the DTTrans framework.</p> "> Figure 2
<p>PV sites (red cross), Voronoi diagram and Delaunay triangulation of weather stations (blue circle) in Korea. (<b>a</b>) Voronoi diagram of weather stations. (<b>b</b>) Delaunay triangulation of weather stations.</p> "> Figure 3
<p>Extension of DT to DT+ using union-inner triangles algorithm. (<b>a</b>) Union-inner triangles. (<b>b</b>) Cases for the union set of DT weather stations and 3 nearest weather stations.</p> "> Figure 4
<p>Input vector <math display="inline"><semantics> <mi mathvariant="bold">x</mi> </semantics></math> for Voronoi Tessellation and Delaunay Triangulation.</p> "> Figure 5
<p>Architecture of Transformer encoder and multi-head attention.</p> "> Figure 6
<p>Architecture of the GRU unit.</p> "> Figure 7
<p>Learning curve comparison during training and validation.</p> "> Figure 8
<p>The result of union-inner triangles preprocessing. (<b>a</b>) When DT weather stations and 3-nearest weather stations are different, 66% of PV sites (red triangle) use DT weather stations and 34% of PV sites (green cross) use the 3 nearest weather stations. (<b>b</b>) An example when DT is not a good choice.</p> "> Figure 9
<p>An example of union-inner triangles test results.</p> "> Figure 10
<p>Comparison of raw input data and transformed input feature.</p> "> Figure 11
<p>The location of 3 weather stations and the target PV site.</p> "> Figure 12
<p>CDF comparison (individual PV sites forecasting).</p> "> Figure 13
<p>CDF comparison in terms of randomized VPP in Korea.</p> ">
Abstract
:1. Introduction
- We develop a framework for PV generation forecasting by using Delaunay triangulation. Unlike the previous methods that use the weather data from the closest weather station, our method can select three weather stations that enclose the target PV site. We will see that this Delaunay triangulation-based approach outperforms selecting the three-nearest weather stations when the target PV site is well positioned in the corresponding Delaunay triangle.
- An interpretable AI model for PV power forecasting has not been actively studied so far. Considering this, we design an interpretable AI model called TransGRU, which is robust against weather forecast errors, by using a Transformer encoder. TransGRU learns input data through the Transformer encoder, which builds the feature importance for PV power generation in terms of feature representation learning. From the transformed feature data, our model can selectively exploit the weather stations and meteorological factors that are highly related to the target PV site.
- Our framework is simple but effective, specifically for newly built PV sites having a short period of data, e.g., one and a half years. We show that our framework overcomes the dependency on historical PV data by using Delaunay triangulation and a Transformer encoder. Specifically, we provide extensive experiments using 1034 PV sites nationwide and 86 weather stations in Korea. The results show that our framework achieves a 7–15% improvement in forecasting individual PV power generation and a 41–60% improvement in PV aggregation in forming a virtual power plant (VPP). As a result, we achieved a 3–4% of forecast error for VPP, which sufficiently satisfies the requirement of 6% or less error to participate in the renewable energy wholesale market run by the Korea Power Exchange (KPX).
2. Proposed Methodologies
2.1. Overall Framework
2.2. Voronoi Tessellation and Delaunay Triangulation
2.3. Union-Inner Triangles Algorithm
Algorithm 1 Union-Inner Triangles Algorithm |
|
2.4. Proposed TransGRU Model
2.4.1. Transformer Encoder
2.4.2. Gated Recurrent Unit (GRU)
3. Model Selection
3.1. Data Description
3.2. Hyperparameters of the Proposed TransGRU
3.3. Hyperparameters of the Compared Models
3.4. Hyperparameters of the Model Optimization
4. Experiment Results
4.1. Performance Metric
4.2. Reproduction of Weather Forecast Data
4.3. The Impact of Delaunay Triangulation and Union-Inner Triangles Algorithm
4.4. The Impact of Transformer Encoder
4.5. Forecasting of Individual PV Sites
4.6. Forecasting of Aggregated PV Sites
5. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
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Location | # of PVs | Statistical Parameter of PV Data from Each Location | |||
---|---|---|---|---|---|
Maximum | Mean | Conditional Mean | Standard Deviation | ||
Gangwon | 72 | 0.9439 | 0.1418 | 0.4334 | 0.2377 |
Gyeonggi | 77 | 0.4336 | 0.0697 | 0.1932 | 0.1059 |
Gyeongnam | 112 | 1.3644 | 0.2189 | 0.6407 | 0.3493 |
Gyeongbuk | 147 | 0.8453 | 0.1374 | 0.3798 | 0.2102 |
Gwangju | 39 | 0.9845 | 0.1499 | 0.4373 | 0.2324 |
Daegu | 27 | 1.7818 | 0.3044 | 0.8400 | 0.4550 |
Daejeon | 5 | 0.8604 | 0.0595 | 0.3635 | 0.1419 |
Busan | 12 | 0.0475 | 0.0086 | 0.0229 | 0.0129 |
Seoul | 8 | 1.1770 | 0.1986 | 0.5493 | 0.3030 |
Sejong | 4 | 3.2630 | 0.5486 | 1.5490 | 0.8344 |
Ulsan | 4 | 0.8950 | 0.1454 | 0.4104 | 0.2245 |
Incheon | 10 | 0.7373 | 0.1287 | 0.3522 | 0.1932 |
Jeonnam | 243 | 0.5957 | 0.0985 | 0.2836 | 0.1544 |
Jeonbuk | 110 | 0.4478 | 0.0700 | 0.2030 | 0.1113 |
Chungnam | 113 | 1.8684 | 0.3018 | 0.8458 | 0.4673 |
Chungbuk | 51 | 1.3418 | 0.2063 | 0.5972 | 0.3247 |
Layer | Name | Dimension | Number of Parameters |
---|---|---|---|
0 | Input | 288 | - |
1 | Transformer encoder; Feedforward input | 512 | 147,968 |
2 | Transformer encoder; Feedforward output | 288 | 147,744 |
3 | GRU | 64 | 67,968 |
4 | FC layer 1 | 256 | 16,640 |
5 | FC layer 2 | 256 | 65,792 |
6 | Output | 24 | 6168 |
Hyperparameter | Value |
---|---|
Batch size | 18 |
Learning rate | 0.0001 |
Optimizer | Adam |
Epoch | 1000 |
Loss function | MSE |
Location | Weather Forecast Error (%) | NMAE10 (%) | |||||
---|---|---|---|---|---|---|---|
MLP | GRU | TransGRU | |||||
VT | DT+ | VT | DT+ | VT | DT+ | ||
Gwangju | 5 | 9.47 | 7.97 | 10.23 | 8.85 | 8.11 | 7.49 |
10 | 9.51 | 8.04 | 10.37 | 9.04 | 8.59 | 7.62 | |
15 | 10.04 | 8.66 | 10.92 | 9.29 | 8.74 | 7.67 | |
20 | 10.98 | 8.79 | 11.60 | 9.74 | 9.22 | 8.27 | |
Daegu | 5 | 9.48 | 8.41 | 10.07 | 9.02 | 9.40 | 8.09 |
10 | 10.35 | 8.79 | 10.64 | 9.42 | 9.46 | 8.21 | |
15 | 10.44 | 8.99 | 11.25 | 9.37 | 9.55 | 8.22 | |
20 | 11.14 | 9.48 | 12.12 | 9.94 | 10.01 | 8.79 |
Location | # of PVs | Capacity (MW) | Weather Forecast Error (%) | NMAE10 (%) | |||||
---|---|---|---|---|---|---|---|---|---|
MLP | GRU | TransGRU | |||||||
VT | DT+ | VT | DT+ | VT | DT+ | ||||
Gwangju | 39 | 29.92 | 5 | 5.50 | 4.73 | 5.47 | 5.03 | 5.28 | 4.97 |
10 | 5.64 | 4.8 | 5.68 | 5.21 | 5.36 | 5.0 | |||
15 | 6.13 | 4.81 | 6.09 | 5.49 | 5.59 | 5.12 | |||
20 | 6.20 | 5.03 | 6.07 | 5.54 | 6.05 | 5.54 | |||
Daegu | 27 | 34.47 | 5 | 5.76 | 5.29 | 5.66 | 5.09 | 6.43 | 5.35 |
10 | 6.14 | 5.51 | 6.22 | 5.98 | 6.41 | 5.34 | |||
15 | 6.67 | 5.88 | 6.50 | 5.12 | 6.44 | 5.53 | |||
20 | 7.28 | 5.86 | 7.06 | 5.82 | 7.27 | 6.14 |
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Song, K.; Jeong, J.; Moon, J.-H.; Kwon, S.-C.; Kim, H. DTTrans: PV Power Forecasting Using Delaunay Triangulation and TransGRU. Sensors 2023, 23, 144. https://doi.org/10.3390/s23010144
Song K, Jeong J, Moon J-H, Kwon S-C, Kim H. DTTrans: PV Power Forecasting Using Delaunay Triangulation and TransGRU. Sensors. 2023; 23(1):144. https://doi.org/10.3390/s23010144
Chicago/Turabian StyleSong, Keunju, Jaeik Jeong, Jong-Hee Moon, Seong-Chul Kwon, and Hongseok Kim. 2023. "DTTrans: PV Power Forecasting Using Delaunay Triangulation and TransGRU" Sensors 23, no. 1: 144. https://doi.org/10.3390/s23010144