Performance Analysis of Short-Term Electricity Demand with Atmospheric Variables
Abstract
:1. Introduction
2. Description of Data
2.1. Electricity Demand Data
2.2. Atmospheric Variables
2.3. Weather Station Selection
3. Related Works
4. Prototype Modeling
4.1. Modeling Trend
4.2. Modeling Cyclicality and Seasonality
4.3. Mathematical Model
- Model A: This model consists of the variables from deterministic terms, historical demand and historical demand-related interaction (e.g., ) term. Therefore, Model A is the sum of Equations (5), (9) and (10) and consists of a total of 47 variables including six correlated error terms (). The electricity demand from Model A is denoted by and can be generalized as,
- Model C: Model C consists of all the variables from Model B and atmospheric variables (Equation (8)). Therefore, Model C consists of 94 variables. The electricity demand from Model C is represented by and can be generalized as,
5. Estimation and Forecasting
Algorithm Setup
- Set informative priors,
- Starting values, . The suffix ‘’ in the symbol means OLS estimation.
- Set a normal prior for serial correlated coefficient as , with starting value .
- Set an inverse Gamma prior for where and represent the degree of freedom and scale factor, respectively.
- Draw the conditional posterior distribution,
- For , , then (Appendix C, Theorem A1)
- For correlated error , , then (Appendix C, Theorem A1)
- Given a draw from and , draw from its conditional posterior distribution, . (Appendix C, Theorem A2)
- Repeat Steps 2 and 3 M times to obtain and .
6. Results and Discussion
6.1. Atmospheric Variables
6.2. Temperature Variables
6.3. Performance Analysis
6.4. Hypothesis Testing
6.5. Computation Time
7. Conclusions
Acknowledgments
Author Contributions
Conflicts of Interest
Abbreviations
ARMAX | Auto-regressive moving average with exogenous variable |
MAPE | Mean absolute percentage error |
IPCC | Intergovernmental Panel on Climate Change |
MLR | Multiple linear regression |
ANN | Artificial neural network |
SVM | Support vector machine |
GEFCom2012 | Global Energy Forecasting Competition 2012 |
CDD | Cooling degree day |
HDD | Heating degree day |
HEPCO | Hokkaido Electrical Power Company |
JMA | Japan Meteorological Agency |
MW | Megawatt |
OLS | Ordinary least square |
MCMC | Markov chain Monte Carlo |
Appendix A. Weather Station Selection
Appendix A.1. Methodology
Appendix A.2. Algorithm Setup
- Denote the temperature variables (daily average, maximum and minimum temperature) of each stations as , .
- Develop the forecasting model (Equation (A1)) where electricity demand is a function of the temperature and calendar variables.
- For speed and simplicity, use OLS estimation and forecasting for a year out of the sample data.
- Calculate the forecasting error and MAPE for all the weather stations separately.
- Sort the resulting error measures in ascending order to find the best individual’s (weather stations) impact on demand.
- Combine (average and weighted average with population) the temperature data of the top k weather stations to create a new temperature series and fit all these combinations to the same forecasting model.
- Calculate the forecasting error and find the combinations of weather stations that give the best (smallest) MAPE.
Weather Station | Forecasting Results of Weather Stations When Their Data Combined as: | |||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|
Simple Mean | Weighted by Population | |||||||||||
Sub-Prefecture | Area (m2) | Population | Name | Index | MAPE (%) | Combination | MAPE (%) Variance | R2 | Adjusted-R2 | MAPE (%) Variance | R2 | Adjusted-R2 |
Ishikari | 3539.86 | 2,324,878 | Sapporo | 1 | 2.959 | 1, and 2 | 3.012(1.702) | 0.943 | 0.938 | 2.945(1.70) | 0.965 | 0.962 |
Kamikawa | 10,619.20 | 527,575 | Hakodate | 2 | 3.042 | 1, 2 and 7 | 2.894(1.667) | 0.946 | 0.941 | 2.909(1.689) | 0.968 | 0.965 |
Oshima | 3936.46 | 433,475 | Kitami | 3 | 3.318 | 1, 2, 7 and 8 | 2.967(1.841) | 0.943 | 0.938 | 2.942(1.744) | 0.966 | 0.963 |
Iburi | 3698 | 419,115 | Abashiri | 4 | 3.323 | 1, 2, 7, 8 and 6 | 3.324(1.909) | 0.930 | 0.924 | 3.324(1.90) | 0.962 | 0.959 |
Ashahikawa | 5 | 3.174 | 1, 2, 7, 8, 6 and 5 | 2.970(1.792) | 0.943 | 0.937 | 2.946(1.725) | 0.965 | 0.962 | |||
Tokachi | 10,831.24 | 353,291 | Obihiro | 6 | 3.169 | 1, 2, 7, 8, 6, 5 and 3 | 2.899(1.730) | 0.945 | 0.940 | 2.905(1.710) | 0.967 | 0.964 |
Okhotsk | 10,690.62 | 309487 | Moruran | 7 | 3.010 | 1, 2, 7, 8, 6, 5, 3 and 4 | 2.925(1.670) | 0.945 | 0.940 | 2.927(1.675) | 0.968 | 0.965 |
Tomakomai | 8 | 3.156 |
Appendix B. Forecasting Example
Appendix C. Theorems
Appendix C.1. Theorem A1
Appendix C.2. Theorem A2
Appendix D. Figures and Tables
Hour | Model | Sunday | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | WDH | WDNH | WEH | WENH | HWD | HWE | Holiday | NH |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
1 | Model A | 1.6726 | 1.7407 | 1.7456 | 1.8309 | 1.5394 | 1.4631 | 1.4922 | 1.6639 | 0.7753 | 1.5824 | 1.6213 | 1.9812 | 0.8121 | 1.7474 | 1.6325 |
Model B | 1.1504 | 1.4382 | 1.2741 | 1.4257 | 1.2117 | 1.4709 | 1.2896 | 1.3642 | 0.7606 | 1.2200 | 1.2131 | 1.4685 | 1.3576 | 1.4463 | 1.3136 | |
Model C | 1.1919 | 1.4357 | 1.3395 | 1.4745 | 1.1992 | 1.5799 | 1.2373 | 1.4057 | 0.8193 | 1.1919 | 1.2274 | 1.6611 | 0.9614 | 1.5212 | 1.3382 | |
2 | Model A | 1.8561 | 1.7041 | 1.6715 | 1.8159 | 1.5774 | 1.5581 | 1.5430 | 1.6654 | 0.8006 | 1.6996 | 1.7156 | 2.1112 | 1.3818 | 1.9653 | 1.6535 |
Model B | 1.2177 | 1.4480 | 1.1882 | 1.4230 | 1.2913 | 1.5818 | 1.4109 | 1.3865 | 0.7887 | 1.3143 | 1.3056 | 1.3492 | 1.4865 | 1.3767 | 1.3648 | |
Model C | 1.2970 | 1.4602 | 1.1697 | 1.4413 | 1.2717 | 1.6941 | 1.3749 | 1.4074 | 0.8426 | 1.2970 | 1.3407 | 1.5256 | 1.2430 | 1.4691 | 1.3806 | |
3 | Model A | 1.8299 | 1.6551 | 1.7280 | 1.8782 | 1.5712 | 1.3902 | 1.3610 | 1.6445 | 0.6908 | 1.5954 | 1.6039 | 2.2782 | 1.4283 | 2.1082 | 1.5952 |
Model B | 1.2882 | 1.3785 | 1.1462 | 1.4060 | 1.1784 | 1.3799 | 1.3110 | 1.2978 | 0.7097 | 1.2996 | 1.3006 | 1.2319 | 1.2804 | 1.2416 | 1.3021 | |
Model C | 1.3373 | 1.3129 | 1.1836 | 1.3597 | 1.1587 | 1.4631 | 1.3420 | 1.2956 | 0.7436 | 1.3373 | 1.3548 | 1.3017 | 1.0399 | 1.2494 | 1.3121 | |
4 | Model A | 1.7652 | 1.6379 | 1.8458 | 1.8160 | 1.6098 | 1.3923 | 1.3475 | 1.6604 | 0.6981 | 1.5563 | 1.5657 | 2.2030 | 1.3701 | 2.0364 | 1.6007 |
Model B | 1.1658 | 1.2604 | 1.1607 | 1.3288 | 1.2750 | 1.4508 | 1.3543 | 1.2952 | 0.7567 | 1.2600 | 1.2595 | 1.1060 | 1.2704 | 1.1389 | 1.2958 | |
Model C | 1.1385 | 1.2825 | 1.1582 | 1.3299 | 1.1545 | 1.4228 | 1.3618 | 1.2696 | 0.7364 | 1.1385 | 1.2624 | 1.0859 | 1.0082 | 1.0704 | 1.2779 | |
5 | Model A | 1.8329 | 1.6645 | 1.9004 | 1.9173 | 1.5649 | 1.5715 | 1.3441 | 1.7237 | 0.7901 | 1.5885 | 1.5814 | 2.3748 | 1.7288 | 2.2456 | 1.6435 |
Model B | 1.3387 | 1.3066 | 1.3126 | 1.3861 | 1.2598 | 1.4386 | 1.3605 | 1.3407 | 0.7509 | 1.3496 | 1.3297 | 1.4274 | 1.7425 | 1.4904 | 1.3322 | |
Model C | 1.3420 | 1.3241 | 1.2364 | 1.4013 | 1.1265 | 1.4575 | 1.2308 | 1.3092 | 0.7773 | 1.3420 | 1.2897 | 1.3027 | 1.2207 | 1.2863 | 1.3033 | |
6 | Model A | 1.9198 | 1.9072 | 2.0596 | 1.9769 | 1.5467 | 1.5389 | 1.6301 | 1.8059 | 0.7545 | 1.7750 | 1.8003 | 2.5605 | 1.2725 | 2.3029 | 1.7591 |
Model B | 1.6503 | 1.5450 | 1.6708 | 1.5754 | 1.1965 | 1.4065 | 1.5892 | 1.4789 | 0.7142 | 1.6197 | 1.5820 | 1.6762 | 2.3669 | 1.8144 | 1.4965 | |
Model C | 1.6451 | 1.5607 | 1.5380 | 1.5917 | 1.1067 | 1.3907 | 1.4814 | 1.4376 | 0.7524 | 1.6451 | 1.5595 | 1.4951 | 1.6376 | 1.5236 | 1.4687 | |
7 | Model A | 2.0690 | 2.1267 | 2.2502 | 2.2338 | 1.8833 | 1.6164 | 1.9340 | 2.0221 | 0.7776 | 2.0015 | 2.0574 | 2.9955 | 0.8951 | 2.5754 | 1.9747 |
Model B | 1.7640 | 1.7209 | 1.7645 | 1.6313 | 1.4183 | 1.4893 | 2.0553 | 1.6049 | 0.7315 | 1.9097 | 1.9323 | 2.4035 | 1.4605 | 2.2149 | 1.6527 | |
Model C | 1.6466 | 1.7467 | 1.5595 | 1.5090 | 1.2270 | 1.4631 | 1.7972 | 1.5011 | 0.7673 | 1.6466 | 1.7573 | 2.0983 | 1.0206 | 1.8828 | 1.5397 | |
8 | Model A | 2.2325 | 2.3071 | 2.2233 | 2.5286 | 2.4832 | 2.1212 | 2.4363 | 2.3327 | 1.0441 | 2.3344 | 2.3803 | 3.4155 | 1.4263 | 3.0177 | 2.2833 |
Model B | 1.8220 | 1.8314 | 1.9199 | 1.9725 | 1.8258 | 1.7969 | 2.5240 | 1.8693 | 0.8740 | 2.1730 | 2.1622 | 2.8535 | 2.3874 | 2.7603 | 1.8966 | |
Model C | 1.5913 | 1.5995 | 1.5147 | 1.6427 | 1.4574 | 1.5827 | 2.1622 | 1.5594 | 0.8269 | 1.5913 | 1.8738 | 2.2654 | 1.9355 | 2.1994 | 1.6091 | |
9 | Model A | 2.6461 | 2.4470 | 2.7248 | 2.7950 | 2.8503 | 2.4008 | 3.1912 | 2.6436 | 1.1834 | 2.9187 | 2.8304 | 4.3900 | 4.6659 | 4.4452 | 2.5959 |
Model B | 2.1982 | 2.0883 | 2.2785 | 2.2846 | 2.4666 | 2.1374 | 3.1797 | 2.2511 | 1.0574 | 2.6890 | 2.5874 | 3.8711 | 4.6995 | 4.0367 | 2.2544 | |
Model C | 1.9150 | 1.7530 | 1.7447 | 1.9969 | 1.9034 | 1.8084 | 2.8321 | 1.8413 | 0.9390 | 1.9150 | 2.2789 | 3.4363 | 4.2477 | 3.5986 | 1.8751 | |
10 | Model A | 2.9442 | 2.6022 | 3.2205 | 3.0529 | 3.1272 | 2.6851 | 3.6793 | 2.9376 | 1.3814 | 3.3117 | 3.1540 | 4.5038 | 6.4350 | 4.8900 | 2.9090 |
Model B | 2.4234 | 2.3307 | 2.6872 | 2.3936 | 2.7461 | 2.7183 | 3.5322 | 2.5752 | 1.4121 | 2.9778 | 2.8153 | 4.0603 | 6.1947 | 4.4871 | 2.5583 | |
Model C | 2.1795 | 2.0551 | 2.1036 | 1.9529 | 2.1555 | 2.0213 | 3.0005 | 2.0577 | 1.1097 | 2.1795 | 2.4479 | 3.4744 | 5.4029 | 3.8601 | 2.0883 | |
11 | Model A | 3.2398 | 2.6796 | 3.3393 | 3.2835 | 3.2169 | 2.9312 | 3.9262 | 3.0901 | 1.5203 | 3.5830 | 3.3519 | 4.4814 | 8.1586 | 5.2168 | 3.0849 |
Model B | 2.5062 | 2.3502 | 2.7765 | 2.5841 | 2.6018 | 2.9451 | 3.6375 | 2.6516 | 1.5283 | 3.0718 | 2.8516 | 4.2028 | 7.4327 | 4.8488 | 2.6184 | |
Model C | 2.3283 | 1.9570 | 1.9768 | 2.2351 | 2.1442 | 2.2174 | 3.0316 | 2.1061 | 1.2075 | 2.3283 | 2.4878 | 3.2880 | 6.4853 | 3.9274 | 2.1478 | |
12 | Model A | 3.1075 | 2.8537 | 3.4770 | 3.4629 | 3.4499 | 3.1050 | 3.9691 | 3.2697 | 1.6391 | 3.5383 | 3.3037 | 4.9317 | 8.1837 | 5.5821 | 3.1824 |
Model B | 2.5170 | 2.5425 | 2.9768 | 2.7074 | 2.8006 | 3.0701 | 3.5237 | 2.8195 | 1.6153 | 3.0203 | 2.8234 | 4.9172 | 6.9190 | 5.3175 | 2.6972 | |
Model C | 2.3383 | 2.1527 | 2.0263 | 2.2816 | 2.2020 | 2.3525 | 2.9905 | 2.2030 | 1.2876 | 2.3383 | 2.4675 | 3.6795 | 6.5631 | 4.2562 | 2.1932 | |
13 | Model A | 3.3161 | 2.8978 | 4.0335 | 3.7530 | 3.3656 | 3.5846 | 3.8910 | 3.5269 | 1.8386 | 3.6036 | 3.3948 | 4.6860 | 7.7364 | 5.2961 | 3.4198 |
Model B | 2.4320 | 2.6308 | 3.2304 | 2.9576 | 2.7321 | 3.1860 | 3.3674 | 2.9474 | 1.6902 | 2.8997 | 2.7367 | 3.8506 | 6.1283 | 4.3061 | 2.8323 | |
Model C | 2.2623 | 2.1179 | 2.1186 | 2.3961 | 2.2355 | 2.5430 | 2.7583 | 2.2822 | 1.3922 | 2.2623 | 2.3490 | 3.0000 | 5.7045 | 3.5409 | 2.2593 | |
14 | Model A | 3.6238 | 3.0059 | 4.0271 | 3.8494 | 3.3133 | 3.9163 | 4.3122 | 3.6224 | 1.9851 | 3.9680 | 3.7592 | 5.5966 | 8.1018 | 6.0977 | 3.5452 |
Model B | 2.5357 | 2.6686 | 3.3307 | 3.2034 | 2.7270 | 3.4654 | 3.7935 | 3.0790 | 1.8339 | 3.1646 | 2.9757 | 4.8298 | 6.9040 | 5.2447 | 2.9449 | |
Model C | 2.2401 | 2.2966 | 2.0473 | 2.6013 | 2.1359 | 2.5819 | 3.0670 | 2.3326 | 1.3972 | 2.2401 | 2.4697 | 3.7217 | 6.2939 | 4.2362 | 2.2902 | |
15 | Model A | 3.6812 | 3.0742 | 3.9871 | 3.7488 | 3.0118 | 3.9572 | 4.2087 | 3.5558 | 2.0035 | 3.9449 | 3.7478 | 5.2494 | 7.8475 | 5.7690 | 3.5105 |
Model B | 2.7848 | 2.6771 | 3.1999 | 3.3373 | 2.5674 | 3.2893 | 3.4836 | 3.0142 | 1.7151 | 3.1342 | 2.9288 | 4.9817 | 7.2022 | 5.4258 | 2.8723 | |
Model C | 2.3425 | 2.2175 | 2.2240 | 2.4928 | 2.1483 | 2.6142 | 2.9446 | 2.3394 | 1.3864 | 2.3425 | 2.4668 | 4.1316 | 6.1436 | 4.5340 | 2.2705 | |
16 | Model A | 3.5173 | 3.0099 | 3.5821 | 3.5607 | 2.7995 | 3.2589 | 3.8668 | 3.2422 | 1.6404 | 3.6920 | 3.6108 | 4.8270 | 5.2998 | 4.9216 | 3.2550 |
Model B | 2.7110 | 2.6691 | 2.7547 | 3.0173 | 2.3450 | 2.8460 | 3.2405 | 2.7264 | 1.4517 | 2.9758 | 2.8676 | 4.1300 | 5.1174 | 4.3275 | 2.6838 | |
Model C | 2.2337 | 2.1280 | 2.0626 | 2.3022 | 1.9723 | 2.1713 | 2.6555 | 2.1273 | 1.1495 | 2.2337 | 2.3272 | 3.4206 | 4.7688 | 3.6903 | 2.1090 | |
17 | Model A | 2.8113 | 2.2691 | 2.6527 | 2.8911 | 2.4075 | 2.5460 | 3.7121 | 2.5533 | 1.2941 | 3.2617 | 3.1543 | 3.3655 | 5.3881 | 3.7700 | 2.6801 |
Model B | 2.3903 | 2.2728 | 2.0630 | 2.4652 | 1.9515 | 2.1243 | 3.0331 | 2.1754 | 1.1075 | 2.7117 | 2.6350 | 3.1321 | 4.2301 | 3.3517 | 2.2523 | |
Model C | 2.1376 | 1.9282 | 1.6517 | 1.8570 | 1.8850 | 1.7124 | 2.4634 | 1.8069 | 0.9375 | 2.1376 | 2.2313 | 2.5008 | 3.6711 | 2.7349 | 1.8899 | |
18 | Model A | 2.2690 | 2.1932 | 2.2601 | 2.4965 | 2.2489 | 2.2088 | 3.0329 | 2.2815 | 1.1026 | 2.6509 | 2.6016 | 3.4705 | 3.6273 | 3.5019 | 2.3047 |
Model B | 1.8041 | 2.0382 | 1.7465 | 2.0586 | 1.7992 | 1.8877 | 2.4489 | 1.9061 | 0.9407 | 2.1265 | 2.0982 | 2.6811 | 2.6862 | 2.6822 | 1.9161 | |
Model C | 1.8099 | 1.6286 | 1.3981 | 1.7202 | 1.7559 | 1.5168 | 1.8188 | 1.6039 | 0.7631 | 1.8099 | 1.7890 | 2.0452 | 2.3158 | 2.0993 | 1.6323 | |
19 | Model A | 1.9400 | 2.1032 | 2.4597 | 1.7876 | 2.0171 | 2.0373 | 2.6626 | 2.0810 | 1.0018 | 2.3013 | 2.2479 | 3.1036 | 3.3588 | 3.1546 | 2.0693 |
Model B | 1.5986 | 1.9853 | 1.5508 | 1.5214 | 1.5875 | 1.7703 | 2.1094 | 1.6831 | 0.8720 | 1.8540 | 1.8295 | 2.9165 | 2.3402 | 2.8012 | 1.6528 | |
Model C | 1.5358 | 1.7506 | 1.3152 | 1.1828 | 1.6486 | 1.3373 | 1.6731 | 1.4469 | 0.6953 | 1.5358 | 1.5810 | 2.3915 | 2.0686 | 2.3269 | 1.4310 | |
20 | Model A | 1.7961 | 1.8596 | 1.7109 | 1.6868 | 1.8195 | 1.6626 | 2.3081 | 1.7479 | 0.8015 | 2.0521 | 1.9965 | 2.8977 | 3.1537 | 2.9489 | 1.7528 |
Model B | 1.3819 | 1.3910 | 0.9991 | 1.2920 | 1.2984 | 1.1858 | 1.6894 | 1.2333 | 0.5791 | 1.5357 | 1.5211 | 2.4375 | 1.8249 | 2.3150 | 1.2464 | |
Model C | 1.3681 | 1.2429 | 0.9897 | 1.2038 | 1.2219 | 1.0033 | 1.4228 | 1.1323 | 0.5094 | 1.3681 | 1.3759 | 2.1167 | 1.7822 | 2.0498 | 1.1456 | |
21 | Model A | 1.9851 | 1.8714 | 1.9007 | 1.7697 | 1.8257 | 1.7998 | 2.1877 | 1.8334 | 0.8843 | 2.0864 | 2.0404 | 2.9103 | 2.9981 | 2.9278 | 1.8303 |
Model B | 1.4202 | 1.4070 | 1.0795 | 1.1981 | 1.2286 | 1.1109 | 1.6524 | 1.2048 | 0.5500 | 1.5363 | 1.5231 | 2.2684 | 1.7980 | 2.1743 | 1.2350 | |
Model C | 1.4664 | 1.2926 | 0.9844 | 1.0369 | 1.2318 | 1.0341 | 1.3425 | 1.1159 | 0.5441 | 1.4664 | 1.3868 | 2.1136 | 1.7543 | 2.0417 | 1.1364 | |
22 | Model A | 2.1472 | 2.0246 | 1.9386 | 2.0494 | 1.8935 | 1.8998 | 2.1253 | 1.9612 | 0.9233 | 2.1363 | 2.0900 | 2.8940 | 3.0530 | 2.9258 | 1.9436 |
Model B | 1.4406 | 1.4008 | 1.3538 | 1.4628 | 1.3684 | 1.3452 | 1.6044 | 1.3862 | 0.6642 | 1.5225 | 1.5329 | 2.3268 | 1.3174 | 2.1249 | 1.3735 | |
Model C | 1.4462 | 1.4146 | 1.2637 | 1.2127 | 1.3508 | 1.1255 | 1.3280 | 1.2734 | 0.6027 | 1.4462 | 1.3866 | 2.0830 | 1.3962 | 1.9457 | 1.2590 | |
23 | Model A | 2.2922 | 1.9065 | 2.1283 | 2.2634 | 2.0251 | 2.0859 | 2.0248 | 2.0819 | 1.0168 | 2.1585 | 2.1233 | 2.6635 | 2.8549 | 2.7018 | 2.0595 |
Model B | 1.5580 | 1.5780 | 1.4537 | 1.5983 | 1.6215 | 1.5366 | 1.3977 | 1.5576 | 0.7889 | 1.4779 | 1.4828 | 1.7395 | 1.3809 | 1.6678 | 1.5253 | |
Model C | 1.4426 | 1.4823 | 1.3921 | 1.4256 | 1.5368 | 1.4081 | 1.2703 | 1.4490 | 0.7731 | 1.4426 | 1.3404 | 1.5004 | 1.6744 | 1.5352 | 1.4146 | |
24 | Model A | 2.2812 | 1.8947 | 2.3251 | 2.3162 | 1.9561 | 2.3125 | 1.9756 | 2.1609 | 1.1198 | 2.1284 | 2.0778 | 2.1986 | 3.1313 | 2.3852 | 2.1339 |
Model B | 1.7227 | 1.5818 | 1.6329 | 1.5357 | 1.8184 | 1.5679 | 1.5059 | 1.6273 | 0.8113 | 1.6143 | 1.6001 | 1.6980 | 1.8959 | 1.7376 | 1.6158 | |
Model C | 1.6399 | 1.4829 | 1.4895 | 1.3902 | 1.5656 | 1.4349 | 1.3684 | 1.4726 | 0.7713 | 1.6399 | 1.4723 | 1.5999 | 2.1355 | 1.7070 | 1.4653 |
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Variables | Winter (January) | Summer (August) |
---|---|---|
Temperature | −0.3495 | 0.5302 |
Rain | 0.0727 | −0.0078 |
Humid | 0.1385 | −0.4348 |
Radiation | −0.2321 | 0.4141 |
Snow | 0.1013 | No snowfall data |
Region | Electrical Data | Base Temperature (°C) | Relationship | Reference |
---|---|---|---|---|
USA | Weekly | 18.3 | Linear with CDD | [32] |
Spain | Daily (1983–1999) | 18.5 | Non-linear | [33] |
Italy | Hourly (2002–September 2003) | 18.7 (HDD), 22 (CDD) | Linear with CDD, HDD | [34] |
London | Hourly (1997–2001) | 16 | CDD HDD | [21] |
South Korea | Monthly (2001–2010) | 16.2–19.4 | CDD HDD | [35] |
Tokyo | Hourly | 15 (HDD), 21.3 (CDD) | Piecewise | [36] |
Tokyo | 2 p.m. data | 17.25 | Piecewise | [37] |
Brisbane | Half-hourly | 18.6 | Linear with CDD, HDD | [38] |
Sydney | Weekly (1999–2000) | 17.5 | Linear with CDD, HDD | [38] |
Melbourne | Weekly (1999–2000) | 16.9 | Linear with CDD, HDD | [38] |
Adelaide | Weekly (1999–2000) | 16.8 | Linear with CDD, HDD | [38] |
Hokkaido | Hourly (2013–2015) | 15.65 (HDD), 21.53 (CDD), 17.1 (min. demand) (2 p.m. data) | Piecewise | This study |
−10.2 (min. exhaustion), 33.18 (max. exhaustion), 16.28 (min. demand) | Polynomial | This study |
Temperature °C | Hour 1 | Hour 14 | Hour 19 | ||||||
---|---|---|---|---|---|---|---|---|---|
CDD_val | Deviation | CDD_val | Deviation | CDD_val | Deviation | ||||
19.000 | −5.3611 | −0.0178 | −1.7623 | −3.0000 | −0.0194 | −1.9206 | −1.1465 | 0.0068 | 0.6854 |
20.000 | −4.3611 | −0.0119 | −1.1783 | −2.0000 | −0.0134 | −1.3303 | −0.1465 | 0.0165 | 1.6629 |
21.000 | −3.3611 | −0.0059 | −0.5909 | −1.0000 | −0.0074 | −0.7365 | 0.8535 | 0.0262 | 2.6498 |
22.000 | −2.3611 | 0.0000 | 0.0000 | 0.0000 | −0.0014 | −0.1392 | 1.8535 | 0.0358 | 3.6463 |
23.000 | −1.3611 | 0.0059 | 0.5944 | 1.0000 | 0.0046 | 0.4618 | 2.8535 | 0.0455 | 4.6525 |
24.000 | −0.3611 | 0.0119 | 1.1924 | 2.0000 | 0.0106 | 1.0664 | 3.8535 | 0.0551 | 5.6684 |
25.000 | 0.6389 | 0.0178 | 1.7939 | 3.0000 | 0.0166 | 1.6746 | 4.8535 | 0.0648 | 6.6942 |
26.000 | 1.6389 | 0.0237 | 2.3990 | 4.0000 | 0.0226 | 2.2865 | 5.8535 | 0.0745 | 7.7299 |
27.000 | 2.6389 | 0.0296 | 3.0077 | 5.0000 | 0.0286 | 2.9021 | 6.8535 | 0.0841 | 8.7758 |
28.000 | 3.6389 | 0.0356 | 3.6200 | 6.0000 | 0.0346 | 3.5213 | 7.8535 | 0.0938 | 9.8317 |
29.000 | 4.6389 | 0.0415 | 4.2359 | 7.0000 | 0.0406 | 4.1443 | 8.8535 | 0.1034 | 10.8979 |
30.000 | 5.6389 | 0.0474 | 4.8555 | 8.0000 | 0.0466 | 4.7711 | 9.8535 | 0.1131 | 11.9745 |
31.000 | 6.6389 | 0.0533 | 5.4788 | 9.0000 | 0.0526 | 5.4016 | 10.8535 | 0.1228 | 13.0615 |
32.000 | 7.6389 | 0.0593 | 6.1058 | 10.0000 | 0.0586 | 6.0359 | 11.8535 | 0.1324 | 14.1591 |
Model Types | Overall MAPE (%) | Maximum MAPE (%) | MAPE ≤ 2% | MAPE > 2% | MAPE ≥ 5% | MAPE ≥ 10% | MAPE ≥ 15% | Observations | |
---|---|---|---|---|---|---|---|---|---|
Overall | Model A | 2.43 | 19.32 | 53.5 | 46.5 | 11.56 | 1.09 | 0.19 | 8760 |
Model B | 1.98 | 15.41 | 62.49 | 37.51 | 6.97 | 0.53 | 0.01 | ||
Model C | 1.72 | 14.06 | 67.93 | 32.07 | 4.05 | 0.23 | 0 | ||
Working days | Model A | 1.15 | 19.04 | 54.78 | 45.22 | 9.71 | 0.69 | 0.12 | 5784 |
Model B | 1.03 | 13.8 | 64.93 | 35.07 | 5.53 | 0.32 | 0 | ||
Model C | 0.90 | 13.35 | 70.35 | 29.65 | 2.71 | 0.172 | 0 | ||
Weekends | Model A | 2.49 | 11.93 | 52.87 | 47.13 | 12.66 | 0.92 | 0 | 2376 |
Model B | 2.03 | 11.75 | 60.56 | 39.44 | 7.82 | 0.21 | 0 | ||
Model C | 1.81 | 9.2746 | 66.28 | 33.71 | 5.57 | 0 | 0 | ||
Holidays | Model A | 3.52 | 19.33 | 43.5 | 56.5 | 25 | 5.66 | 1.66 | 600 |
Model B | 2.93 | 15.42 | 46.5 | 53.5 | 17.5 | 3.83 | 0.16 | ||
Model C | 2.51 | 14.06 | 51.17 | 48.83 | 11.33 | 1.66 | 0 |
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Chapagain, K.; Kittipiyakul, S. Performance Analysis of Short-Term Electricity Demand with Atmospheric Variables. Energies 2018, 11, 818. https://doi.org/10.3390/en11040818
Chapagain K, Kittipiyakul S. Performance Analysis of Short-Term Electricity Demand with Atmospheric Variables. Energies. 2018; 11(4):818. https://doi.org/10.3390/en11040818
Chicago/Turabian StyleChapagain, Kamal, and Somsak Kittipiyakul. 2018. "Performance Analysis of Short-Term Electricity Demand with Atmospheric Variables" Energies 11, no. 4: 818. https://doi.org/10.3390/en11040818