# Day-Ahead Spot Market Price Forecast Based on a Hybrid Extreme Learning Machine Technique: A Case Study in China

^{*}

## Abstract

**:**

## 1. Introduction

- (a)
- Many current studies ignore the useless information brought by the large amount of electricity price data when screening data features, which not only causes a reduction in forecasting accuracy but also affects the operational efficiency of forecasting models [34].
- (b)

- (1)
- Through the analysis of sample factor correlation degree and sample factor similarity, a massive amount of data is cleaned up, the amount of data is reduced, the useful information is fully used, the accuracy of the RELM model is improved, and the calculation efficiency of the model is improved.
- (2)
- Considering the characteristics of the RELM model, the MPA model is used for optimization to reduce the probability of the prediction model falling into the local optimal solution.
- (3)
- A framework of electricity price forecasting based on similar days is proposed, which realizes 96-point forecasting in a day instead of single-point forecasting

## 2. Extraction of Similar Days

#### 2.1. Analysis on the Formation Mechanism of Electricity Price in Spot Market

- (1)
- The power grid dispatching center provides the trading center with the basic information of the power system according to the operation status of the power system, and the trading center releases the market public information to the market subjects according to the trading sequence;
- (2)
- According to market public information, the market subject discriminates the market supply-demand ratio, thermal power output, and New energy output, and formulates the trading strategy according to the market information;
- (3)
- According to the corresponding transaction clearing rules, the trading center will centrally match the transaction strategies of the sender and user sides to form a pre-clearing price;
- (4)
- The trading center sends the pre-clearing results to the power grid dispatching center for security verification. The power grid checks the clearing results according to the power system carrying capacity. If the verification is passed, the trading center forms a formal clearing price. If the verification is not passed, the trading center needs to re-match the transaction;
- (5)
- The trading center will send the final market price to the trading subject.

#### 2.2. Identification of Electricity Price Forecasting Factors in Spot Market

_{i}represents the rank difference between subjects, n represents the number of observations, and ${r}_{s}$ represents the correlation between two subjects.

#### 2.3. Selection of Similar Days Based on Weighted Gray Relational Grade

#### 2.3.1. Improvements to CRITIC

#### 2.3.2. Weighted Gray Correlation

_{i}element on the forecast day and the value of the n

_{i}element on the t day. $\underset{tk}{\mathrm{min}}\underset{{n}_{i}}{\mathrm{min}}{\Delta}_{tk}({n}_{i})$ represents the minimum difference value for all elements, and $\underset{tk}{\mathrm{max}}\underset{{n}_{i}}{\mathrm{max}}{\Delta}_{tk}({n}_{i})$ represents the maximum difference value for all elements. $\mu $ represents the resolution coefficient, which is 0.5. The correlation coefficients between different factors in different historical days can be calculated by the above Equation. The weighted gray relational degrees of different historical days and forecast days can be expressed as follows:

- (a)
- Select the relevant factors of electricity price forecast, and use Spearman correlation to analyze the correlation of relevant factors;
- (b)
- Determine the forecast date, use the improved CRITIC model to calculate the relevant factors of the forecast date and the historical date, and obtain the comprehensive weight between the relevant factors;
- (c)
- Bring the weight of relevant factors obtained by CRITIC into the GRA model to obtain the correlation coefficient between different factors on different historical days;
- (d)
- The correlation coefficients of different historical days are sorted from large to small. The market information similarity between the previous historical day and the forecast day is the highest, and the electricity price similarity is the highest. On the contrary, the electricity price similarity is also lower.
- (e)
- The number of similar days can be selected according to the size of the similarity interval of the whole historical day, and the previous similar days are preferred. If the market is relatively stable and the similarity concentration is high, it can also be further determined according to the number of training arrays of the prediction model.

## 3. Construction of Electricity Price Forecasting Model

#### 3.1. Regularized Extreme Learning Machine (RELM)

#### 3.2. Marine Predator Algorithm (MPA)

- (1)
- Initialization phase. Set algorithm parameters to initialize the location of the prey within the search scope. It can be described as:$${X}_{0}={X}_{\mathrm{min}}+rand({X}_{\mathrm{max}}-{X}_{\mathrm{min}})$$

- (2)
- Optimization stage. The optimization phase is divided into early iteration, middle iteration and late iteration. At the beginning of the iteration, the current iterations are less than 1/3 of the maximum iterations. Predators are faster than prey, performing globes and updating prey through Brown random.$$\{\begin{array}{c}stepsic{e}_{i}={R}_{B}\otimes (Elit{e}_{i}-{R}_{B}\otimes pre{y}_{i})\\ pre{y}_{i}=pre{y}_{i}+P\u2022{R}_{B}\otimes stepsic{e}_{i}\end{array}\phantom{\rule{0ex}{0ex}}Iter<\frac{1}{3}\mathrm{max}\_Iter$$

- (3)
- FADs effect or eddy current. Fish aggregation devices (FADs) or vortex effects often change the behavior of marine predators, which enables the MPA to overcome the premature convergence problem and adjust the local extremum.$$pre{y}_{i}=\{\begin{array}{c}pre{y}_{i}+CF[{X}_{\mathrm{min}}+{R}_{L}\otimes ({X}_{\mathrm{max}}-{X}_{\mathrm{min}})]\otimes U\\ pre{y}_{i}+[FADs(1-r)+r](pre{y}_{r1}-pre{y}_{r2})\end{array}\begin{array}{l}r\le FADs\\ r>FADs\end{array}$$

#### 3.3. MPA-RELM Model Construction

- (1)
- Divide the similar day data selected by CRITIC-GRA above into training and testing sets and normalize them;
- (2)
- Set parameters such as the maximum number of iterations and population size. According to the Equations (1)–(10), the prey initialization position is set and the current iteration number is 0 to calculate the management matrix.
- (3)
- According to the three stages of the optimization process, continuously update the location of prey, complete the elite update, calculate the fitness value, and update the final position.
- (4)
- In combination with the FADs effect, the Equations (1)–(13) are used to update the prey so that the algorithm can iteratively jump out of the local optimal solution.
- (5)
- Evaluate and update the elite matrix and determine the relationship between the number of iterative operations and the maximum number of iterations. If the iterative algorithm is equal to the maximum number of iterations, the best iterative elitist matrix is output. Elitist matrix is the best key parameter of RELM, which is brought into RELM model for prediction. The specific process structure is shown in Figure 3.

#### 3.4. Construction of a Day-Ahead Spot Market Price Prediction Model Based on Hybrid Extreme Learning Machine Technology

- (1)
- Data preprocessing

- (2)
- Identify the core factors of electricity price forecasting

- (3)
- Build a similar day screening model

- (4)
- Select the optimal model to predict

- (5)
- Model prediction result verification

- (6)
- Diebold–Mariano test

_{k}is the autovariance at lag k.

## 4. Case Analysis

#### 4.1. Similar Day Filter

#### 4.2. Day-Ahead Spot Market Price Forecast Based on a Hybrid Extreme Learning Machine Technique

^{−10}, 2

^{−9}, …, 2

^{9}, 2

^{10}), the initial value of the parameter L is 10, and each time it increases by 10, with a maximum increase of 20. At the same time, in order to verify the effectiveness of the model proposed in this paper, MPA-RELM, GA-ELM, GA-SVM, ELM, and SVM models are used as references. The prediction effect of CRITIC-GRA-MPA-RELM is shown in Figure 9.

- (1)
- The prediction error of the ELM model is lower than that of the SVM model, indicating that ELM is more adaptable than SVM for electricity price forecasting. From the forecast trend, it can be seen that the electricity price predicted by SVM is generally higher than that of ELM, and the electricity price trend of SVM during the evening peak is opposite to that of ELM, indicating that the SVM forecast curve is more volatile. The basic RELM model used in this paper is a model further optimized on the basis of ELM, which shows that the model proposed in this paper has a certain model foundation and is more suitable for electricity price forecasting than other machine learning algorithms.
- (2)
- The error of MPA-RELM is lower than that of GA-ELM, indicating that using MPA to optimize RELM can improve the accuracy of machine learning more than the GA model to optimize ELM. The electricity price prediction curve from MPA-RELM is basically the same as that of GA-ELM. The electricity price curve predicted by the MPA-RELM model still has a large deviation, but MPA-RELM reduces the deviation of each time point, especially in the evening peak, meaning MPA-RELM is closer to the real electricity price.
- (3)
- CRITIC-GRA-MPA-RELM has the highest prediction accuracy, and MPA-RELM is second only to the model proposed in this paper, indicating that further screening of historical data, obtaining historical daily data similar to the market on the forecast day, which can better adapt to the volatility of electricity prices in the spot market, can improve the prediction accuracy of the MPA-RELM model and prevent the model from overfitting.

## 5. Conclusions

- (1)
- Through the CRITIC-GRA model to screen the original data, the original data structure can be optimized to ensure the accuracy of the input data of the prediction model.
- (2)
- Through the comparison of several prediction models, it shows that the MPA algorithm has better optimization speed and global search ability than the GA algorithm under the same conditions, and can improve the generalization ability of RELM.
- (3)
- Combined with the relevant data of Shanxi spot pilot, it is verified that CRITIC-GRA-MPA-RELM can deal with peak and trough electricity prices, and the avoided single model can only deal with the problem of low volatility.
- (4)
- The forecasting error of the forecasting model proposed in this paper is concentrated in the electricity price spike period, which shows that, when forecasting electricity price, we should not only consider the market public information, but also pay attention to the means of planning.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

MPA | marine predator algorithm |

RELM | regularized extreme learning machine |

ELM | extreme learning machine |

SVM | support vector machines |

GA | Genetic Algorithm |

RMSE | root mean square error |

MAE | mean absolute error |

MSE | mean square error |

SSE | residual sum of squares |

CRITIC | criteria importance though intercriteria correlation |

GRA | grey relational |

FADs | fish aggregation device |

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**Figure 5.**The historical day-ahead spot electricity price from 19 February 2022 to 25 February 2022.

**Figure 6.**Related factors of day-ahead spot market from 19 February 2022 to 25 February 2022. (

**a**) Load data for Unified scheduling; (

**b**) Inter-provincial demand load; (

**c**) New energy output; (

**d**) Thermal power output.

Species | Factors |
---|---|

History of electricity | Day-ahead spot price, real-time spot price; |

Demand load in the province | Forecasting deviation of market demand load and market load; |

Thermal power output | Historical actual output of thermal power, thermal power pre-dispatch output, thermal power participation in peak adjustment output; |

New energy output | Historical output of new energy, forecast deviation of new energy output, proportion of new energy in market demand; |

Inter-provincial demand load | Provincial adjustment of medium and long term trading electricity, inter-provincial spot trading electricity; |

Time | Similarity | Ranking | Time | Similarity | Ranking |
---|---|---|---|---|---|

24 February 2022 | 0.878184 | 1 | 29 November 2021 | 0.773253 | 26 |

11 December 2021 | 0.846866 | 2 | 14 January 2022 | 0.770666 | 27 |

23 February 2022 | 0.839821 | 3 | 7 February 2022 | 0.766438 | 28 |

1 October 2021 | 0.835788 | 4 | 28 December 2021 | 0.766079 | 29 |

13 February 2022 | 0.824152 | 5 | 16 November 2021 | 0.765566 | 30 |

19 January 2022 | 0.80802 | 6 | 5 December 2021 | 0.763201 | 31 |

7 November 2021 | 0.807764 | 7 | 18 October 2021 | 0.763031 | 32 |

17 October 2021 | 0.805276 | 8 | 14 October 2021 | 0.76284 | 33 |

30 October 2021 | 0.802232 | 9 | 4 February 2022 | 0.758902 | 34 |

22 February 2022 | 0.798048 | 10 | 9 February 2022 | 0.756474 | 35 |

11 February 2022 | 0.79689 | 11 | 10 January 2022 | 0.755527 | 36 |

2 October 2021 | 0.796766 | 12 | 14 February 2022 | 0.755209 | 37 |

29 October 2021 | 0.794495 | 13 | 25 October 2021 | 0.754894 | 38 |

25 December 2021 | 0.792829 | 14 | 12 January 2022 | 0.753398 | 39 |

20 October 2021 | 0.792804 | 15 | 19 November 2021 | 0.750492 | 40 |

2 November 2021 | 0.792363 | 16 | 3 February 2022 | 0.749896 | 41 |

19 February 2022 | 0.7845 | 17 | 24 October 2021 | 0.747245 | 42 |

13 December 2021 | 0.784356 | 18 | 7 December 2021 | 0.745932 | 43 |

20 February 2022 | 0.782755 | 19 | 9 October 2021 | 0.74574 | 44 |

2 January 2022 | 0.778299 | 20 | 24 January 2022 | 0.745663 | 45 |

10 February 2022 | 0.778109 | 21 | 16 January 2022 | 0.745158 | 46 |

21 February 2022 | 0.776506 | 22 | 7 January 2022 | 0.745041 | 47 |

15 November 2021 | 0.776366 | 23 | 24 December 2021 | 0.744753 | 48 |

8 November 2021 | 0.774248 | 24 | 12 December 2021 | 0.744734 | 49 |

15 February 2022 | 0.773299 | 25 | 2 February 2022 | 0.742596 | 50 |

Dataset | Statistic Values | ||||
---|---|---|---|---|---|

Mean | Standard Deviations | Median | Minimun | Maxmun | |

All | 520.15 | 446.08 | 383.57 | 0 | 1500 |

Similar day | 539.99 | 1062.04 | 398.00 | 0 | 1500 |

Forecast day | 242.44 | 154.00 | 315.00 | 0 | 399 |

Dataset | Statistic Values | ||||
---|---|---|---|---|---|

Mean | Standard Deviations | Median | Minimun | Maxmun | |

all | 27,996.96 | 2520.96 | 27,771.85 | 21,663.2 | 34,370.6 |

Similar day | 27,885.57 | 2512.60 | 27,672.05 | 21,663.2 | 34,370.6 |

Forecast day | 29,556.41 | 2093.83 | 28,904.55 | 26,613.5 | 34,014.7 |

Dataset | Statistic Values | ||||
---|---|---|---|---|---|

Mean | Standard Deviations | Median | Minimun | Maxmun | |

All | 5561.96 | 1506.58 | 5687.00 | 2370 | 9358 |

Similar day | 5510.22 | 1519.37 | 5511.00 | 2370 | 9358 |

Forecast day | 6286.35 | 1085.50 | 6779.50 | 4816 | 7571 |

Dataset | Statistic Values | ||||
---|---|---|---|---|---|

Mean | Standard Deviations | Median | Minimun | Maxmun | |

All | 6250.60 | 4564.19 | 4918.57 | 607.35 | 21,412.28 |

Similar day | 5902.42 | 1519.37 | 4498.11 | 607.35 | 21,412.28 |

Forecast day | 11,125.14 | 3961.87 | 10,709.60 | 5652.25 | 18,490.39 |

Dataset | Statistic Values | ||||
---|---|---|---|---|---|

Mean | Standard Deviations | Median | Minimun | Maxmun | |

All | 27,308.31 | 5567.70 | 27,748.21 | 7725.24 | 39,587.33 |

Similar day | 27,493.36 | 5576.35 | 27,868.57 | 7725.24 | 39,587.33 |

Forecast day | 24,717.62 | 4764.13 | 25,339.33 | 15,153.6 | 31,065.95 |

CRITIC-GRA-MPA-RELM | MPA-RELM | GA-ELM | GA-SVM | ELM | SVM | |
---|---|---|---|---|---|---|

residual sum of squares (SSE) | 0.1257 | 0.1893 | 0.2504 | 0.2536 | 0.2789 | 0.4145 |

mean squared error (MSE) | 0.0013 | 0.0020 | 0.0026 | 0.0026 | 0.0029 | 0.0043 |

mean absolute error (MAE) | 0.0165 | 0.0328 | 0.0411 | 0.0436 | 0.0449 | 0.0533 |

root mean square error (RMSE) | 0.0013 | 0.0020 | 0.0026 | 0.0026 | 0.0029 | 0.0043 |

p | MPA-RELM | GA-ELM | GA-SVM | ELM | SVM |
---|---|---|---|---|---|

CRITIC-GRA-MPA-RELM | 0.04 | 0.02 | <0.01 | <0.01 | <0.01 |

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## Share and Cite

**MDPI and ACS Style**

Dong, J.; Dou, X.; Bao, A.; Zhang, Y.; Liu, D.
Day-Ahead Spot Market Price Forecast Based on a Hybrid Extreme Learning Machine Technique: A Case Study in China. *Sustainability* **2022**, *14*, 7767.
https://doi.org/10.3390/su14137767

**AMA Style**

Dong J, Dou X, Bao A, Zhang Y, Liu D.
Day-Ahead Spot Market Price Forecast Based on a Hybrid Extreme Learning Machine Technique: A Case Study in China. *Sustainability*. 2022; 14(13):7767.
https://doi.org/10.3390/su14137767

**Chicago/Turabian Style**

Dong, Jun, Xihao Dou, Aruhan Bao, Yaoyu Zhang, and Dongran Liu.
2022. "Day-Ahead Spot Market Price Forecast Based on a Hybrid Extreme Learning Machine Technique: A Case Study in China" *Sustainability* 14, no. 13: 7767.
https://doi.org/10.3390/su14137767