A Multi-Stage Price Forecasting Model for Day-Ahead Electricity Markets
<p>Flowchart of the proposed two-stage approach.</p> "> Figure 2
<p>Comparison of MAPE for one week (24 July 2015 to 30 July 2015) to predict day-ahead price (31 July 2015).</p> "> Figure 3
<p>Comparison of MAPE for two weeks (17 July 2015 to 30 July 2015) to predict day-ahead price (31 July 2015).</p> "> Figure 4
<p>Comparison of MAPE for three weeks (10 July 2015 to 30 July 2015) to predict day-ahead price (31 July 2015).</p> "> Figure 5
<p>Comparison of MAPE for one month (1 July 2015 to 30 July 2015) to predict day-ahead price (31 July 2015).</p> "> Figure 6
<p>Comparison of MAPE for 45 days (16 June 2015 to 30 July 2015) to predict day-ahead price (31 July 2015).</p> "> Figure 7
<p>Comparison of MAPE for 60 days (1 June 2015 to 30 July 2015) to predict day-ahead price (31 July 2015).</p> "> Figure 8
<p>Comparison of MAPE for 75 days (17 May 2015 to 30 July 2015) to predict day-ahead price (31 July 2015).</p> "> Figure 9
<p>Comparison of MAPE for 90 days (1 May 2015 to 30 July 2015) to predict day-ahead price (31 July 2015).</p> "> Figure 10
<p>Comparison of MAPE for all dataset from one week to 75 days to predict day-ahead price (31 July 2015).</p> "> Figure 11
<p>Comparison of MAPE for 1, 2, 3 and 6-month weekdays dataset to predict day-ahead price (31 July 2015).</p> "> Figure 12
<p>Comparison of MAPE for 1, 2, 3 and 6-month weekend dataset to predict day-ahead price (26 July 2015).</p> ">
Abstract
:1. Introduction
2. Modelling of Electricity Price & Forecasting Methods
2.1. ARIMA
2.2. Locally Weighted Scatterplot Smoothing (LOWESS)
2.3. Support Vector Machines (SVM)
2.4. Random Forest (RF)
2.5. Generalized Linear Model (GLM)
3. Proposed Hybrid 2-Stage Model
3.1. Stage-1: Initial Price Forecast (F) Using ARIMA
3.2. Stage-1: Input Residuals to the Hybrid Model
3.2.1. ARIMA-SVM
3.2.2. ARIMA-RF
3.2.3. ARIMA-LOWESS
3.2.4. ARIMA-ARIMA
4. Explanatory (Input) Variables for Day-Ahead Price Forecast
Data Explanation
- (a)
- Hourly electricity price for day D and day D-6.
- (b)
- Hourly load data, including total load demand, hydro power demand, solar power demand, coal power demand, wind power demand and combined cycle power demand for day D and day D-6.
- (c)
- Hourly weather data, including temperature, wind speed and solar irradiance.
5. Results and Discussion
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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Data Duration | p | d | q | MAPE |
---|---|---|---|---|
One week | 4 | 1 | 3 | 5.36 |
Two weeks | 2 | 0 | 1 | 4.23 |
Three weeks | 4 | 0 | 4 | 4.07 |
One month | 5 | 0 | 4 | 5.64 |
45 days | 2 | 1 | 2 | 2.7 |
60 days | 1 | 1 | 0 | 1.99 |
75 days | 4 | 1 | 3 | 1.99 |
90 days | 4 | 1 | 3 | 2.80 |
Weekday-one month | 5 | 0 | 4 | 8.16 |
Weekday-two months | 3 | 1 | 1 | 1.81 |
Weekday-three months | 2 | 1 | 2 | 3.58 |
Weekday-six months | 1 | 1 | 0 | 4.48 |
Weekend-one month | 2 | 0 | 1 | 13.07 |
Weekend-two months | 2 | 1 | 3 | 9.94 |
Weekend-three months | 5 | 1 | 1 | 9.73 |
Weekday-six months | 2 | 1 | 2 | 9.91 |
Variable No. | Description |
---|---|
1, 2 | Hourly Price D, Hourly Price D-6 |
3, 4 | Hourly Power Demand D-1 & D-6 |
5, 6 | Hourly Hydropower Generation D-1 & D-6 |
7, 8 | Hourly Solar Power D-1 & D-6 |
9, 10 | Hourly Coal Power Generation D-1 & D-6 |
11, 12 | Hourly Wind Power Generation D-1 & D-6 |
13, 14 | Hourly Combined Cycle Power Generation D-1 & D-6 |
15, 16, 17 | Hourly Temperature, Wind speed, Radiation D+1 |
MAPE | ARIMA | ARIMA-GLM | ARIMA-SVM | ARIMA-RF |
---|---|---|---|---|
Short-Term Price Forecast (Day-Ahead) | ||||
5.36 | 5.00 | 3.73 | 5.24 | |
4.23 | 4.43 | 3.98 | 4.01 | |
4.07 | 4.14 | 3.64 | 3.69 | |
5.64 | 5.54 | 5.05 | 5.44 | |
2.7 | 2.54 | 2.49 | 2.38 | |
1.99 | 1.92 | 2.037 | 2.027 | |
1.99 | 1.92 | 2.009 | 2.2263 |
MAPE | ARIMA | ARIMA-GLM | ARIMA-SVM | ARIMA-LOWESS | ARIMA-RF |
---|---|---|---|---|---|
2.80 | 2.59 | 2.73 | 2.66 | 3.12 |
MAPE | ARIMA | ARIMA-GLM | ARIMA-SVM | ARIMA-RF |
---|---|---|---|---|
8.16 | 8.30 | 7.41 | 7.01 | |
1.81 | 1.86 | 1.84 | 2.33 | |
3.58 | 3.83 | 3.82 | 4.72 | |
4.48 | 4.54 | 4.62 | 5.78 |
MAPE | ARIMA | ARIMA-GLM | ARIMA-SVM | ARIMA-RF |
---|---|---|---|---|
13.07 | 12.4 | 12.01 | 13.7 | |
9.94 | 9.15 | 9.26 | 9.52 | |
9.73 | 9.22 | 9.15 | 9.19 | |
9.91 | 9.63 | 9.53 | 9.88 |
MAPE | ARIMA | ARIMA-ARIMA (with Explanatory Variables in Stage-2) | ARIMA-ARIMA (without Explanatory Variables in Stage-2) |
---|---|---|---|
5.36 | 4.66 | 5.34 | |
4.23 | 4.44 | 3.79 | |
4.07 | 4.14 | 4.02 | |
5.64 | 5.54 | 5.65 | |
2.7 | 2.54 | 2.73 | |
1.99 | 1.78 | 1.91 | |
1.99 | 1.84 | 1.98 |
Methods | MAPE |
---|---|
Mixed Model [46]—one week | 14.90 |
ARIMA with 2 Variables—five months [47] | 13.39 |
Neural Network—40 days [48] | 11.40 |
Weighted Nearest Neighbor—23 months [49] | 10.89 |
Wavelet-ARIMA with 4 Variables—47 days [50] | 10.70 |
Fuzzy Neural Network [51] | 9.84 |
Adaptive Wavelet Neural Network with 2 variables [52] | 9.64 |
Neural network Wavelet Transform with 1 variable [53] | 9.5 |
WNF with 1 variable—42 days [54] | 9.47 |
Elman Network [55] | 9.09 |
Hybrid Intelligent systems with 3 Variables | 7.47 |
Wavelet-ARIMA-RBFN | 6.76 |
Hybrid wavelet-PSO-ANFIS [56] | 6.50 |
Cascaded Neuro-evolutionary Algorithm with 2 variables-50 days [57] | 5.79 |
MAPE | ARIMA | ARIMA-GLM | ARIMA-SVM | ARIMA-RF |
---|---|---|---|---|
Short-Term Price Forecast (Day-Ahead) | ||||
Average | Average | Good | Average | |
Good | Good | Good | Good | |
Good | Good | Good | Good | |
Average | Average | Average | Average | |
Good | Good | Good | Good | |
Good | Good | Good | Good | |
Good | Good | Good | Good |
Parameter | ARIMA | ARIMA-GLM | ARIMA-SVM | ARIMA-RF |
---|---|---|---|---|
Short-Term Price Forecast (Day-Ahead) | ||||
0.941 | 0.947 | 0.964 | 0.946 | |
0.958 | 0.970 | 0.973 | 0.957 | |
0.963 | 0.971 | 0.969 | 0.963 | |
0.966 | 0.971 | 0.967 | 0.962 | |
0.977 | 0.979 | 0.976 | 0.974 | |
0.982 | 0.983 | 0.982 | 0.981 | |
0.979 | 0.981 | 0.979 | 0.976 |
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Angamuthu Chinnathambi, R.; Mukherjee, A.; Campion, M.; Salehfar, H.; Hansen, T.M.; Lin, J.; Ranganathan, P. A Multi-Stage Price Forecasting Model for Day-Ahead Electricity Markets. Forecasting 2019, 1, 26-46. https://doi.org/10.3390/forecast1010003
Angamuthu Chinnathambi R, Mukherjee A, Campion M, Salehfar H, Hansen TM, Lin J, Ranganathan P. A Multi-Stage Price Forecasting Model for Day-Ahead Electricity Markets. Forecasting. 2019; 1(1):26-46. https://doi.org/10.3390/forecast1010003
Chicago/Turabian StyleAngamuthu Chinnathambi, Radhakrishnan, Anupam Mukherjee, Mitch Campion, Hossein Salehfar, Timothy M. Hansen, Jeremy Lin, and Prakash Ranganathan. 2019. "A Multi-Stage Price Forecasting Model for Day-Ahead Electricity Markets" Forecasting 1, no. 1: 26-46. https://doi.org/10.3390/forecast1010003