# Hybrid GA-PSO Optimization of Artificial Neural Network for Forecasting Electricity Demand

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Tamil Nadu Electricity Sector

#### Factors Affecting Electricity Demand

- (1)
**GSDP**: Even though the linkage between GSDP growth and electricity demand growth are not as strong as it was in the past, it is worth considering the impact on the society of high GDP growth itself since they are linked to each other. A high GSDP growth rate year after year means higher manufacture of products and provision of services at an unprecedented pace leading to higher electricity demand. The electricity demand continues to grow in the state because of high level to continue in a business as usual scenario.- (2)
**Electricity consumption per capita (E.Con)**has increased from 510 kWh in year 2000–2001 to 1065 kWh in 2011–2012, that is more than 100% increase. Hence per capita consumption has been taken as an independent factor.- (3)
**Income growth rate (per capita)**: The vision 2023 document of the state of Tamil Nadu aims at doubling the per capita income by 2023. It is also seen that any increase in family income leads to spurt in consumption.- (4)
**Consumer Price Index (CPI)**: Prices have an indirect impact on the electricity demand by affecting the purchase of luxury goods such as air conditioners, washing machines etc.

## 3. Methodology

#### 3.1. Artificial Neural Network

#### 3.2. Particle Swarm Optimization (PSO)

_{1}and C

_{2}are knowledge factors, R

_{1}and R

_{2}are random numbers, g is the location of the leader, p the personal best location, ${v}_{t}$ is the velocity at iteration “t” and ${x}_{t}$ is theposition at iteration “t”. This equation reveals the particle leader location to each particle.

## 4. ANN-GA-PSO Models

#### 4.1. Two Form Estimation Method

#### 4.2. GA-PSO Hybrid Optimization Algorithm

- Step 1:
- First, we initialize a population size of 100 and assign positions and velocities of particles. The number of weights and biases are used to calculate the fitness function for all the particles.
- Step 2:
- The best position value achieved by particle p is set as pbest. The pbest with best value is set as gbest and this value is stored.
- Step 3:
- The desired optimization fitness function f(x) is evaluated for each particle.
- Step 4:
- The evaluated fitness value fp of each particle is compared with its pbest value. If fp < pbest then pbest = fp and bestxp = xp, where xp represents the current coordinates of particle p and bestxp represents the coordinates corresponding to particle p’s best fitness so far.
- Step 5:
- After objective function value is calculated for new positions of each particle the overall best fitness value of the swarm becomes the gbest value of the swarm.
- Step 6:
- Next, the velocity and location of the particle is updated according to Equations (1) and (2). The best position is fed into the General Algorithm as selection.
- Step 7:
- The calculation is stopped when the maximum number of iteration reaches 200 or if the convergence occurs before it otherwise Loop to step 3 until convergence. In the present study, the convergence occurs around 50 iterations as shown in Figure 2.
- Step 8:
- The pop size of M particles obtained by GA and M particles are combined to form new pop size particles.
- Step 9:
- Let ${g}_{en}={g}_{en}+1$, then step 3 is carried out.
- Step 10:
- The best fitness values and solutions, namely, the position are outputted.

#### 4.3. Computational Environment and Data Management

#### 4.4. Evaluation of the Forecast Performance

## 5. Results

#### 5.1. Future Estimation

#### 5.2. Relationship between GSDP and Electricity Demand

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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Year | Electricity (kWr) | Income Growth | GSDP | Price | Demand |
---|---|---|---|---|---|

Consumption | Rate per Capita (%) | (Billion Rs) | Index | (in mWh) | |

1991 | 295 | 10.97 | 4.81 | 48 | 17,173 |

1992 | 303 | 11.9 | 5.27 | 55 | 19,130 |

1993 | 334 | 12.9 | 5.74 | 65 | 20,289 |

1994 | 350 | 13.9 | 6.2 | 79 | 23,193 |

1995 | 421 | 14.8 | 6.6 | 82 | 24,610 |

1996 | 435 | 15.7 | 7.1 | 85 | 25,805 |

1997 | 449 | 16.8 | 7.5 | 89 | 26,943 |

1998 | 459 | 17.9 | 8 | 92 | 27,862 |

1999 | 496 | 18.8 | 8.5 | 94 | 30,434 |

2000 | 510 | 14.7 | 10.9 | 101 | 33,418 |

2001 | 539 | 15 | 10.88 | 103 | 36,578 |

2002 | 708 | 15.2 | 15.01 | 107 | 38,529 |

2003 | 740 | 15.3 | 17.56 | 109 | 46,130 |

2004 | 780 | 15.5 | 18.66 | 110 | 49,712 |

2005 | 860 | 17.23 | 17.73 | 115 | 51,282 |

2006 | 960 | 19.99 | 20.44 | 117 | 49,485 |

2007 | 1000 | 12.58 | 12.98 | 124 | 56,493 |

2008 | 1000 | 13.73 | 14.4 | 136 | 53,506 |

2009 | 1080 | 18.83 | 19.53 | 151 | 57,212 |

2010 | 1040 | 17.27 | 18.07 | 166 | 60,518 |

2011 | 1074 | 18.06 | 16.7 | 163.02 | 61,897 |

2012 | 1118 | 18.29 | 17.66 | 159.01 | 66,391 |

2013 | 1161 | 16.3 | 19.98 | 157.39 | 72,987 |

2014 | 2130 | 17.89 | 42.27 | 143.52 | 74,990 |

2015 | 2007 | 12.94 | 38.45 | 138.77 | 77,218 |

Input Layer | Factors | 1 | E.Con (electricity consumption) |

2 | Income growth rate | ||

3 | GSDP | ||

4 | CPI | ||

Number of Units | 59 | ||

Hidden Layer(s) | Number of Hidden Layers | 1 | |

Number of Units in Hidden Layer 1 | 6 | ||

Activation Function | Hyperbolic tangent | ||

Output Layer | Dependent Variables | 1 | Electricity Demand |

Number of Units | 1 | ||

Rescaling Method for Scale Dependents | Standardized | ||

Activation Function | Identity | ||

Error Function | Sum of Squares |

Training | Sum of Squares Error | 0.004 |

Relative Error | 0.001 | |

Stopping Rule Used | Training error ratio criterion (0.001) achieved | |

Training Time | 0:00:00.23 |

Year | E.Con | Income | GSDP | CPI | Sq-E.Con | Sq-Income | Sq-GSDP | Sq-CPI |

2001 | 0 | 0.153846 | 0 | 0 | 0 | 0.023669 | 0 | 0 |

2002 | 0.313544 | 0.153846 | 0.363636 | 0.038835 | 0.09831 | 0.023669 | 0.132231 | 0.001508 |

2003 | 0.372913 | 0.153846 | 0.636364 | 0.058252 | 0.139064 | 0.023669 | 0.404959 | 0.003393 |

2004 | 0.447124 | 0.230769 | 0.727273 | 0.067961 | 0.19992 | 0.053254 | 0.528926 | 0.004619 |

2005 | 0.595547 | 0.307692 | 0.636364 | 0.116505 | 0.354677 | 0.094675 | 0.404959 | 0.013573 |

2006 | 0.781076 | 0.538462 | 0.818182 | 0.135922 | 0.61008 | 0.289941 | 0.669421 | 0.018475 |

2007 | 0.855288 | 0 | 0.181818 | 0.203883 | 0.731517 | 0 | 0.033058 | 0.041568 |

2008 | 0.855288 | 0.076923 | 0.272727 | 0.320388 | 0.731517 | 0.005917 | 0.07438 | 0.102649 |

2009 | 1.003711 | 0.461538 | 0.818182 | 0.466019 | 1.007435 | 0.213018 | 0.669421 | 0.217174 |

2010 | 0.929499 | 0.307692 | 0.636364 | 0.61165 | 0.863969 | 0.094675 | 0.404959 | 0.374116 |

2011 | 0.992579 | 0.384615 | 0.545455 | 0.582524 | 0.985213 | 0.147929 | 0.297521 | 0.339335 |

2012 | 1.074212 | 0.384615 | 0.636364 | 0.543689 | 1.15393 | 0.147929 | 0.404959 | 0.295598 |

2013 | 1.153989 | 0.230769 | 0.818182 | 0.524272 | 1.33169 | 0.053254 | 0.669421 | 0.274861 |

2014 | 2.953618 | 0.384615 | 2.818182 | 0.398058 | 8.723858 | 0.147929 | 7.942149 | 0.15845 |

2015 | 2.723562 | 0 | 2.454545 | 0.349515 | 7.417791 | 0 | 6.024793 | 0.12216 |

2016 | 3.022263 | 0.153846 | 2.909091 | 0.38835 | 9.134076 | 0.023669 | 8.46281 | 0.150815 |

Year | X12 | X13 | X14 | X23 | X24 | X32 | X34 | Demand |

2001 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

2002 | 0.048237 | 0.055944 | 0.012176 | 0.055944 | 0.005975 | 0.055944 | 0.014122 | 0.053338 |

2003 | 0.057371 | 0.097902 | 0.021723 | 0.097902 | 0.008962 | 0.097902 | 0.03707 | 0.261141 |

2004 | 0.103183 | 0.167832 | 0.030387 | 0.167832 | 0.015683 | 0.167832 | 0.049426 | 0.359068 |

2005 | 0.183245 | 0.195804 | 0.069384 | 0.195804 | 0.035848 | 0.195804 | 0.074139 | 0.40199 |

2006 | 0.420579 | 0.440559 | 0.106166 | 0.440559 | 0.073189 | 0.440559 | 0.111209 | 0.352862 |

2007 | 0 | 0 | 0.174379 | 0 | 0 | 0 | 0.03707 | 0.544453 |

2008 | 0.065791 | 0.020979 | 0.274024 | 0.020979 | 0.024645 | 0.020979 | 0.087379 | 0.462792 |

2009 | 0.463251 | 0.377622 | 0.467749 | 0.377622 | 0.215086 | 0.377622 | 0.381289 | 0.56411 |

2010 | 0.286 | 0.195804 | 0.568529 | 0.195804 | 0.1882 | 0.195804 | 0.389232 | 0.654492 |

2011 | 0.381761 | 0.20979 | 0.578201 | 0.20979 | 0.224048 | 0.20979 | 0.317741 | 0.692192 |

2012 | 0.413158 | 0.244755 | 0.584037 | 0.244755 | 0.209111 | 0.244755 | 0.345984 | 0.815053 |

2013 | 0.266305 | 0.188811 | 0.605004 | 0.188811 | 0.120986 | 0.188811 | 0.42895 | 0.99538 |

2014 | 1.136007 | 1.083916 | 1.175712 | 1.083916 | 0.153099 | 1.083916 | 1.121801 | 1.050139 |

2015 | 0 | 0 | 0.951925 | 0 | 0 | 0 | 0.857899 | 1.11105 |

2016 | 0.464964 | 0.447552 | 1.173695 | 0.447552 | 0.059746 | 0.447552 | 1.129744 | 1.211196 |

Year | E.Con | Income | GSDP | CPI | x1 | x2 | x3 | x4 | x5 |
---|---|---|---|---|---|---|---|---|---|

2016 | 2167 | 14.88 | 43.06 | 142.9 | −1.93 | 0.91 | −1.005 | −1.63 | −1.14 |

2017 | 2341 | 17.11 | 48.23 | 147.22 | −1.94 | 0.54 | −1.56 | −0.41 | −1.25 |

2018 | 22 | 19.68 | 54 | 151.64 | −1.98 | −0.1 | −0.179 | −1.64 | −1.12 |

2019 | 2730 | 22.63 | 60.5 | 156.19 | −2 | 0.39 | −1.05 | −0.86 | 0.77 |

2020 | 2949 | 26.03 | 67.76 | 160.87 | −2 | −1.4 | −0.68 | −0.76 | 0.99 |

2021 | 3185 | 29.93 | 75.89 | 165.7 | −1.99 | 0.19 | −1.58 | −1.23 | −0.63 |

2022 | 3439 | 34.4 | 85 | 170.7 | −2 | −1 | −1.95 | −1.2 | −0.31 |

2023 | 3715 | 39.58 | 95.2 | 175.8 | −1.99 | 0.28 | 0.28 | −1.71 | 0.62 |

2024 | 4012 | 45.52 | 106.6 | 181 | −2 | 0.41 | −0.9 | −0.21 | −0.49 |

2025 | 4333 | 52.35 | 119.42 | 186.5 | −2 | −1.26 | 0.127 | −0.76 | 0.03 |

Year | Act Total | ANN-Pso | Linear | Holts | ANN-BP | ANN-G-P | ARIMA | ANN-GA | A-G-P-Q |
---|---|---|---|---|---|---|---|---|---|

2001 | 36,578 | 36,206 | 39,441 | 37,643 | 36,434 | 36,705 | 36,018 | 36,582 | |

2002 | 38,529 | 38,302 | 43,532 | 40,247 | 38,987 | 38,854 | 39,876 | 38,618 | 38,827 |

2003 | 46,130 | 46,180 | 44,614 | 42,787 | 46,337 | 46,109 | 43,671 | 46,192 | 46,238 |

2004 | 49,712 | 50,054 | 45,595 | 45,829 | 49,786 | 49,484 | 49,214 | 49,323 | 49,731 |

2005 | 51,282 | 51,007 | 48,299 | 48,925 | 51,254 | 51,540 | 51,458 | 51,179 | 51,611 |

2006 | 49,485 | 49,394 | 50,630 | 51,870 | 49,643 | 49,949 | 52,069 | 49,707 | 49,640 |

2007 | 56,493 | 56,927 | 53,094 | 54,343 | 56,282 | 56,546 | 53,244 | 56,795 | 56,586 |

2008 | 53,506 | 53,257 | 56,060 | 57,267 | 53,719 | 53,792 | 56,676 | 53,201 | 53,404 |

2009 | 57,212 | 57,172 | 61,235 | 59,603 | 57,404 | 57,720 | 58,214 | 57,303 | 57,383 |

2010 | 60,518 | 60,737 | 64,208 | 62,076 | 60,205 | 60,465 | 62,391 | 60,302 | 60,522 |

2011 | 61,897 | 62,353 | 64,090 | 64,631 | 62,098 | 61,757 | 64,313 | 62,024 | 62,011 |

2012 | 66,391 | 66,593 | 63,920 | 67,069 | 66,515 | 66,282 | 65,730 | 66,713 | 66,378 |

2013 | 72,987 | 73,023 | 64,302 | 69,712 | 72,635 | 73,126 | 69,779 | 73,164 | 73,160 |

2014 | 74,990 | 74,890 | 78,675 | 72,748 | 74,464 | 75,084 | 72,866 | 74,898 | 75,109 |

2015 | 77,218 | 77,285 | 75,235 | 75,681 | 77,818 | 76,870 | 78,189 | 76,930 | 77,242 |

Linear | Holts | ARIMA | ANN-BP | ANN-GA | ANN-P | ANN-G-P | A-G-P-Q |
---|---|---|---|---|---|---|---|

6.07 | 0.85 | 3.02 | 0.44 | 0.42 | 0.4 | 0.3 | 0.22 |

Linear | Holts | ARIMA | ANN-BP | ANN-GA | ANN-P | ANN-G-P | A-G-P-Q |
---|---|---|---|---|---|---|---|

0 | 0.15 | 0 | 0.56 | 0.58 | 0.6 | 0.7 | 0.78 |

Year | Scenario 1 | Scenario 2 |
---|---|---|

2016 | 80,881 | 80,537 |

2017 | 81,213 | 83,324 |

2018 | 81,142 | 82,726 |

2019 | 82,137 | 84,301 |

2020 | 83,044 | 81,074 |

2021 | 82,752 | 83,469 |

2022 | 83,029 | 85,331 |

2023 | 83,826 | 87,581 |

2024 | 83,401 | 85,636 |

2025 | 84,263 | 87,825 |

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**MDPI and ACS Style**

Anand, A.; Suganthi, L.
Hybrid GA-PSO Optimization of Artificial Neural Network for Forecasting Electricity Demand. *Energies* **2018**, *11*, 728.
https://doi.org/10.3390/en11040728

**AMA Style**

Anand A, Suganthi L.
Hybrid GA-PSO Optimization of Artificial Neural Network for Forecasting Electricity Demand. *Energies*. 2018; 11(4):728.
https://doi.org/10.3390/en11040728

**Chicago/Turabian Style**

Anand, Atul, and L Suganthi.
2018. "Hybrid GA-PSO Optimization of Artificial Neural Network for Forecasting Electricity Demand" *Energies* 11, no. 4: 728.
https://doi.org/10.3390/en11040728