# Forecasting for Ultra-Short-Term Electric Power Load Based on Integrated Artificial Neural Networks

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## Abstract

**:**

## 1. Introduction

- Ultra-short-term load forecasting: The forecasting unit ranges from several minutes to several hours. Such a model is often used in flow control and used for detecting the stability of an electric power system and forecasting its reserve capacity, so as to prevent the occurrence of insufficient electric power dispatching.
- Short-term load forecasting: The forecasting unit ranges from 1 h to several weeks. Such a model is often used for adjusting the economic dispatching of electric power, analyzing electric power demand and supply and power flow, forecasting crisis in the case of accidents, and for corporate operations and equipment maintenance.
- Mid-term load forecasting: the forecasting unit ranges from several days to 1 month. Such a model is often used for estimating the peak electric power consumption and maintenance of power equipment. It can be used for detecting the time for maintenance and shutdown of power generators and is mainly used for decision making on energy management, such as electricity pricing and procurement of fuels used in power generation.
- Long-term load forecasting: The forecasting unit ranges from 1 year to several years. Such a model is often used for research on electric power policies. New generator sets can be developed or constructed thereby for the future electric power planning of power industry, planning of power transmission and distribution system, procurement of fuels, signing contracts on outsourced electricity, electricity pricing and price structure analysis, corporate operation management and earnings estimation, load management, etc. This load forecasting considers the economic growth, energy proportion planning, industrial structure, construction of electric power development, electric power demand management and other conditions, such as population, temperature, power saving effect of research organizations or government agencies.

## 2. Literature Review

## 3. Proposed Method

#### 3.1. Adaptive-Network-Based Fuzzy Inference System (ANFIS)

- R
_{i}: If x_{1}is ${A}_{1}^{i}$ and x_{2}is ${A}_{2}^{i}$ and …x_{k}is ${A}_{k}^{i}$ - Then ${f}^{i}=\text{}{a}_{k}^{i}{x}_{k}$ + ${a}_{k-1}^{i}{x}_{k-1}$ +…+ ${a}_{0}^{i}$

**X**= (x

_{1}, x

_{2}, x

_{3},) be input load data; from x

_{1}to x

_{3}in sequence, x

_{1}was the load value for the first period of time prior to the forecasting time point, x

_{2}was the load value for the second period of time; x

_{3}was the load value for the third period of time. The node at the output layer was the forecasting value of electric power load at the forecasting time point.

_{j}that is fed to node i of Layer 2. The output of each node of layer 2 represents the firing strength of a rule.

#### 3.2. Ultra-Short Term Load Forecasting Based on Back-Propagation Neural Network

_{1}to x

_{3}at the input layer were the actual values of electric power load for the three periods of time prior to forecasting. The gradient descent approach is adopted for adjusting the parameters of the BPN. The node at the output layer was the forecasting value of the electric power load in the forecasting period of time.

#### 3.3. Persistence

_{a}is the current actual load value; L

_{f}is forecasting value. As seen, the value of L

_{f}was forecasted from the first period of time on the first day prior to the actual load value to the next period of time in sequence. However, in the case of bad weather or hot weather, such external conditions would lead to dramatic changes in the load line and hence forecasting based on persistence would not be so accurate. If the weather conditions and other external factors on that day are the same as that on the previous day, the forecasting based on the method will be quite accurate. Persistence is one of the most efficient methods in some cases.

_{f}(t + 1) is the forecasting value of time t+1, L

_{a}is the actual value of time t.

#### 3.4. Integrated Search Method

_{i}$\le $ 1, i = 1,2,3); w

_{1}+ w

_{2}+ w

_{3}= 1; and the output y

_{es}was evaluated as Equation (7).

_{1}, y

_{2}; y

_{3}are the outputs of ANFIS; BPN; and persistence, respectively. The optimal weight value was determined by applying the search algorithm, as shown in Algorithm 1.

_{i}$\le $ 1, i = 1,2,3, and w

_{1}+w

_{2}+w

_{3}= 1. ${y}^{\prime}$ was actual load value; n was data volume. In Equation (8), all training data were used for calculating the difference between the weight of load estimates of the three methods and the actual load value, and obtaining the w

_{i}at the time of the minimal error value as the weight of training model.

Algorithm 1. Integrated search algorithm | ||

Input: ANFIS, BPN, Persistence model, load dataset (X, ${y}^{\prime}$) | ||

Output: w_{1,opt}, w_{2,opt}, w_{3,opt} | ||

Step | 1: | Input X, calculate ANFIS, BPN, Persistence output: y_{1}, y_{2}, y_{3}. |

Step | 2: | E_{min} = $\infty $ |

Step | 3: | For w_{1} = 0: 1: step 0.01 |

Step | 4: | For w_{2} = 0: (1 − w_{1}): step 0.01 |

Step | 5: | w_{3} = 1 − (w_{1}+w_{2}) |

Step | 6: | ${E}_{new}={{\displaystyle \sum}}_{t=1}^{n}\left|\left({w}_{1}{y}_{1}\left(t\right)+\text{}{w}_{2}{y}_{2}\left(t\right)\text{}+\text{}{w}_{3}{y}_{3}\left(t\right)-{y}^{\prime}\left(t\right)\right)\right|$ |

Step | 7: | If (E_{min} > ${E}_{new}$) Then |

Step | 8 | E_{min} = ${E}_{new}$; w_{1,opt} = w_{1};w_{2,opt} = w_{2}; w_{3,opt} = w_{3}; |

Step | 9 | End if |

Step | 10 | Next w_{2} |

Step | 11 | Next w_{1} |

Step | 12 | End |

## 4. Experimental Results

#### 4.1. The Data Set

_{1}, x

_{2}, x

_{3}. x

_{1}was the load value for the first period of time prior to the forecasting time point; x

_{2}was the load value for the second period of time, and x

_{3}was the load value for the third period of time. Output y

_{i}(t), i = 1, 2, 3 was the load at the forecasting time point, t; ${y}^{\prime}\left(t\right)$ was the actual load. In model training, define $\epsilon \left(t\right)=\mathrm{y}\left(t\right)-{y}^{\prime}\left(\mathrm{t}\right)$ as the error value. For adjustment of parameters, please refer to [15].

#### 4.2. Ultra-Short Term Electric Power Load Forecasting

_{ave}):

_{L}was the actual load value at the time t, P

_{f}was the forecasting load value at the time t.

_{max}):

#### 4.2.1. Workday Ultra-Short-Term Electric Power Load Forecasting Experiment

#### 4.2.2. Non-workday Ultra-Short-Term Electric Power Load Forecasting Experiment

#### 4.2.3. National Workday Ultra-Short-Term Electric Power Load Forecasting Experiment

#### 4.2.4. National Non-Workday Ultra-Short-Term Electric Power Load Forecasting Experiment

## 5. Discussion

_{1}, w

_{2}, and w

_{3}parameter values. Since there are only three parameters to decide, using the search algorithm can find the best value in a short time. Since the current load value is estimated using the power load values of the previous three 10-min periods, the experimental results show that the predicted value of this paper is more accurate than the other three methods. When future research considers long-term or mid-term electric power load forecasting, the search algorithm requires more calculation time because of the longer estimation time and the need to consider the weather and temperature. In future research, gene algorithms, bee colony algorithms, and PSO algorithms can be used to estimate parameters for long-term or mid-term electric power load forecasting.

## Author Contributions

## Funding

## Conflicts of Interest

## References

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Date | Method | E_{ave} (%) | E_{max} (%) |
---|---|---|---|

20 | ANFIS | 0.78 | 4.73 |

BPN | 2.33 | 12.79 | |

Persistence | 0.95 | 6.03 | |

Proposed Method | 0.75 | 4.7 | |

21 | ANFIS | 0.74 | 3.19 |

BPN | 2.3 | 12.56 | |

Persistence | 0.93 | 5.308 | |

Proposed Method | 0.73 | 3.09 | |

22 | ANFIS | 0.79 | 3.67 |

BPN | 2.17 | 13.4 | |

22 | Persistence | 0.94 | 5.69 |

Proposed Method | 0.74 | 3.63 | |

23 | ANFIS | 0.66 | 3.26 |

BPN | 2.22 | 12.08 | |

Persistence | 0.9 | 5.09 | |

Proposed Method | 0.65 | 3.23 | |

26 | ANFIS | 0.68 | 3.65 |

BPN | 2.31 | 15.8 | |

Persistence | 0.92 | 5.31 | |

Proposed Method | 0.67 | 3.64 |

Methods | E_{ave} (%) | E_{max} (%) |
---|---|---|

ANFIS | 0.73 | 3.70 |

BPN | 2.27 | 13.32 |

Persistence | 0.93 | 5.48 |

Proposed Method | 0.71 | 3.65 |

Date | Methods | E_{ave} (%) | E_{max} (%) |
---|---|---|---|

24 June | ANFIS | 0.72 | 3.12 |

BPN | 1.73 | 8.69 | |

Persistence | 0.83 | 3.10 | |

Proposed Method | 0.71 | 3.05 | |

25 June | ANFIS | 0.81 | 3.54 |

BPN | 1.94 | 6.99 | |

Persistence | 0.86 | 3.53 | |

Proposed Method | 0.79 | 3.34 |

Methods | E_{ave} (%) | E_{max}(%) |
---|---|---|

ANFIS | 0.77 | 3.33 |

BPN | 2.18 | 7.84 |

Persistence | 0.86 | 3.32 |

Proposed Method | 0.75 | 3.19 |

Date | Method | E_{ave} (%) | E_{max} (%) |
---|---|---|---|

20 | ANFIS | 0.61 | 5.4 |

BPN | 1.74 | 11.63 | |

Persistence | 0.74 | 5.42 | |

Proposed Method | 0.59 | 4.6 | |

21 | ANFIS | 0.58 | 2.86 |

BPN | 1.76 | 12.44 | |

Persistence | 0.73 | 5.51 | |

Proposed Method | 0.56 | 2.86 | |

22 | ANFIS | 0.66 | 3.53 |

BPN | 1.87 | 1.87 | |

Persistence | 0.707 | 4.74 | |

Proposed Method | 0.587 | 2.46 | |

23 | ANFIS | 0.51 | 2.2 |

BPN | 1.78 | 10.82 | |

Persistence | 0.7 | 4.62 | |

Proposed Method | 0.5 | 2.2 | |

26 | ANFIS | 0.51 | 2.15 |

BPN | 1.86 | 12.05 | |

Persistence | 0.73 | 5.06 | |

Proposed Method | 0.5 | 2.08 |

Methods | E_{ave} (%) | E_{max}(%) |
---|---|---|

ANFIS | 0.57 | 3.17 |

BPN | 1.80 | 9.76 |

Persistence | 0.72 | 5.07 |

Proposed Method | 0.54 | 2.84 |

Date | Methods | E_{ave} (%) | E_{max} (%) |
---|---|---|---|

24 June | ANFIS | 0.59 | 2.05 |

BPN | 1.44 | 4.24 | |

Persistence | 0.62 | 2.17 | |

Proposed Method | 0.52 | 2.05 | |

25 June | ANFIS | 0.63 | 2.48 |

BPN | 1.27 | 4.65 | |

Persistence | 0.62 | 2.80 | |

Proposed Method | 0.59 | 2.50 |

**Table 8.**Comparison of average forecasting errors in non-workdays across Taiwan on 24 June and 25 June.

Methods | E_{ave} (%) | E_{max}(%) |
---|---|---|

ANFIS | 0.61 | 2.27 |

BPN | 1.36 | 4.45 |

Persistence | 0.62 | 2.49 |

Proposed Method | 0.56 | 2.27 |

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**MDPI and ACS Style**

Shieh, H.-L.; Chen, F.-H.
Forecasting for Ultra-Short-Term Electric Power Load Based on Integrated Artificial Neural Networks. *Symmetry* **2019**, *11*, 1063.
https://doi.org/10.3390/sym11081063

**AMA Style**

Shieh H-L, Chen F-H.
Forecasting for Ultra-Short-Term Electric Power Load Based on Integrated Artificial Neural Networks. *Symmetry*. 2019; 11(8):1063.
https://doi.org/10.3390/sym11081063

**Chicago/Turabian Style**

Shieh, Horng-Lin, and Fu-Hsien Chen.
2019. "Forecasting for Ultra-Short-Term Electric Power Load Based on Integrated Artificial Neural Networks" *Symmetry* 11, no. 8: 1063.
https://doi.org/10.3390/sym11081063