# Adjusting the Parameters of Metal Oxide Gapless Surge Arresters’ Equivalent Circuits Using the Harmony Search Method

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Equivalent Circuit Models of Metal Oxide Gapless Arresters

- I is the discharge current that passes through the arrester,
- k is a measure of its current-carrying capacity depending on geometrical configuration and characteristics of the arrester (cross-sectional area, length),
- V is the residual voltage at the terminals of the arrester, and
- α is a measure of non-linearity between V and I, depending on the composition of the oxides.

_{0}) for low currents, as low-value bulk resistance (R

_{B}) is the dominant component for high current levels [9,10,14,23].

_{0}and A

_{1}and a filter R-L. The voltage–current characteristics of A

_{0}and A

_{1}are illustrated in Figure 4. For currents with high rising times, the filter R-L presents a low impedance, resulting in a parallel connection between A

_{0}and A

_{1}. For impulse currents with low rising times, the filter R-L presents a high impedance, diverting the current to A

_{0}.

## 3. Definition and Analysis of the Optimization Problem

_{1}, x

_{2}, …, x

_{n})

^{T}is carried out. Considering the great impact of the parameter values of each model on the accuracy of the simulated results, the following objective function must be minimized:

- V
_{res}is the magnitude of the residual voltage of the arrester, - s is an indicator for the results obtained by simulation procedures,
- m is an indicator for the data provided by the manufacturer,
- I is the injected impulse current (peak value, time),
- i is an indicator that corresponds to the curve of the injected impulse current (i = 1: 8/20 μs, i = 2: 1/20 μs, i = 3: 30/60 μs, i = 4: long duration impulse),
- E is the absorbed energy by the arrester in Joules, given as following:$$\mathrm{E}={{\displaystyle \int}}_{0}^{\mathrm{T}}\mathrm{u}\left(\mathrm{t}\right)\xb7\mathrm{i}\left(\mathrm{t}\right)\mathrm{dt}$$

- u(t) is the waveform of the residual voltage of the arrester,
- i(t) is the waveform of the discharge current that passes through the arrester, and
- is the duration of the injected impulse current.

_{i}. The aim of the optimization procedure is to minimize Equation (2), which is a function of several variables. It is infeasible to attain the optimum procedure in a single step, but instead an iteration technique is required. In the current work, the harmony search method (presented in Section 4) is applied.

## 4. Harmony Search Method

_{i}, i = 1, 2, …, n, where

- x is the set of each decision variable xi,
- n is the number of decision variables,
- X
_{i}is the set of the possible range of values for each decision variable, considering lower and upper bounds for each decision variable.

- ${\mathrm{x}}_{\mathrm{i}}^{\mathrm{j}}$ are randomly generated solutions,
- HMS is the harmony memory size,
- i = 1, 2, …, n, and
- j = 1, 2, …, HMS

## 5. Results and Discussion

- Case 1: implementation of the algorithm considering the response for a 10 kA, 8/20 μs current.
- Case 2: implementation of the algorithm considering the response for all the current waveforms of Table 1.
- Case 3: implementation of the algorithm considering the response for all the current curves and the energy for long duration impulse of Table 1.

## 6. Conclusions

## Author Contributions

## Conflicts of Interest

## References

- Agrawal, K.C. Electrical Power Engineering: Reference and Applications Handbook; CRC Press: Boca Raton, FL, USA, 2007. [Google Scholar]
- Laughton, M.A.; Warne, J. Electrical Engineer’s Reference Book, 16th ed.; Newnes: Amsterdam, The Netherlands, 2003. [Google Scholar]
- Christodoulou, C.A.; Vita, V.; Maris, T.I. Lightning protection of distribution substations by using metal oxide gapless surge arresters connected in parallel. Int. J. Power Energy Res.
**2017**, 1, 1–7. [Google Scholar] [CrossRef] - Tarchini, J.A.; Gimenez, W. Line surge arrester selection to improve lightning performance of transmission lines. In Proceedings of the IEEE PowerTech Conference, Bologna, Italy, 23–26 June 2003. [Google Scholar]
- Christodoulou, C.A.; Ekonomou, L.; Fotis, G.P.; Gonos, I.F.; Stathopulos, I.A. Assessment of surge arrester failure rate and application studies in Hellenic high voltage transmission lines. Electr. Power Syst. Res.
**2010**, 80, 176–183. [Google Scholar] [CrossRef] - IEEE. IEEE Std 1243-1997: IEEE Guide for Improving the Lightning Performance of Transmission Lines; IEEE: New York, NY, USA, 1997. [Google Scholar]
- IEC. IEC 60099-4: Surge Arresters-Part 4: Metal-Oxide Surge Arresters without Gaps for a.c. Systems, 2nd ed.; IEC: Geneva, Switzerland, 2004–2005.
- IEEE Working Group 3.4.11. Modeling of metal oxide surge arresters. IEEE Trans. Power Deliv.
**1992**, 7, 302–309. - Pinceti, P.; Giannettoni, M. A simplified model for zinc oxide surge arresters. IEEE Trans. Power Deliv.
**1999**, 14, 393–398. [Google Scholar] [CrossRef] - Ceaki, O.; Seritan, G.; Vatu, R.; Mancasi, M. Analysis of power quality improvement in smart grids. In Proceedings of the 10th International Symposium on Advanced Topics in Electrical Engineering (ATEE), Bucharest, Romania, 23–25 March 2017; pp. 797–801. [Google Scholar] [CrossRef]
- Nieto, A.; Vita, V.; Maris, T.I. Power quality improvement in power grids with the integration of energy storage systems. Int. J. Eng. Res. Technol.
**2016**, 5, 438–443. [Google Scholar] - Ceaki, O.; Vatu, R.; Mancasi, M.; Porumb, R.; Seritan, G. Analysis of electromagnetic disturbances for grid-connected PV. In Proceedings of the 5th International Conference on Modern Electric Power Systems (MEPS2015), Poland, Wroclaw, 6–9 July 2015. [Google Scholar] [CrossRef]
- Fernandez, F.; Diaz, R. Metal oxide surge arrester model for fast transient simulations. In Proceedings of the International Conference on Power System Transients IPAT’01, Rio De Janeiro, Brazil, 24–26 June 2001. [Google Scholar]
- Bayadi, A.; Harid, N.; Zehar, K.; Belkhiat, S. Simulation of metal oxide surge arrester dynamic behavior under fast transients. In Proceedings of the International Conference on Power Systems Transients 2003, New Orleans, LA, USA, 28 September–2 October 2003. [Google Scholar]
- Christodoulou, C.A.; Ekonomou, L.; Fotis, G.P.; Karampelas, P.; Stathopulos, I.A. Parameters’ optimisation for surge arrester circuit models. IET Sci. Meas. Technol.
**2010**, 4, 86–92. [Google Scholar] [CrossRef] - Christodoulou, C.A.; Vita, V.; Ekonomou, L.; Chatzarakis, G.E.; Stathopulos, I.A. Application of Powell’s optimization method to surge arrester circuit models’ parameters. Energy J.
**2010**, 35, 3375–3380. [Google Scholar] [CrossRef] - Christodoulou, C.A.; Gonos, I.F.; Stathopulos, I.A. Estimation of the parameters of metal oxide gapless surge arrester equivalent circuit models using genetic algorithm. Electr. Power Syst. Res.
**2011**, 81, 1881–1886. [Google Scholar] [CrossRef] - Bayadi, A. Parameter identification of ZnO surge arrester models based on genetic algorithms. Electr. Power Syst. Res.
**2008**, 78, 1204–1209. [Google Scholar] [CrossRef] - Nafar, M.; Gharehpetian, G.B.; Niknam, T. Improvement of estimation of surge arrester parameters by using modified particle swarm optimization. Energy
**2011**, 36, 4848–4854. [Google Scholar] [CrossRef] - Lira, G.R.S.; Fernandes, D.; Costa, E.G. Parameter identification technique for a dynamic metal-oxide surge arrester model. In Proceedings of the International Conference on Power Systems Transients (IPST2009), Kyoto, Japan, 2–6 June 2009. [Google Scholar]
- Li, H.J.; Birlasekaran, S.; Choi, S.S. A parameter identification technique for metal-oxide surge arrester models. IEEE Trans. Power Deliv.
**2002**, 17, 736–741. [Google Scholar] [CrossRef] - ABB: High Voltage Surge Arresters, 5th ed.; ABB: Baden, Switzerland, 2004–2010.
- Suljanovic, N.; Mujcic, A.; Murko, V. Practical issues of metal-oxide varistor modeling for numerical simulations. In Proceedings of the 28th International Conference on Lightning Protection, Kazanawa, Japan, 18–22 September 2006; pp. 1149–1154. [Google Scholar]
- Hinrichsen, V. Metal-Oxide Surge Arresters in High Voltage Power Systems, 3rd ed.; Siemens: Munich, Germany, 2011. [Google Scholar]
- Christodoulou, C.A.; Ekonomou, L.; Mitropoulou, A.D.; Vita, V.; Stathopulos, I.A. Surge arresters’ circuit models review and their application to a Hellenic 150 kV transmission line. Simul. Model. Pract. Theory
**2010**, 18, 836–849. [Google Scholar] [CrossRef] - Wang, X.; Gao, X.Z.; Zenger, K. An Introduction to Harmony Search Optimization Method; Springer Briefs in Computational Intelligence; Springer: Berlin/Heidelberg, Germany, 2015. [Google Scholar]
- Omran, M.G.H.; Mahdavi, M. Global-best harmony search. Appl. Math. Comput.
**2008**, 198, 643–656. [Google Scholar] [CrossRef] - Lee, K.S.; Geem, Z.W. A new meta-heuristic algorithm for continuous engineering optimization: Harmony search theory and practice. Comput. Methods Appl. Mech. Eng.
**2005**, 194, 3902–3933. [Google Scholar] [CrossRef] - Engelbrecht, A.P. Fundamentals of Computational Swarm Intelligence; Wiley: Hoboken, NJ, USA, 2005. [Google Scholar]
- Lin, C.J.; Wang, J.G.; Chen, S.M. 2D/3D face recognition using neural network based on hybrid Taguchi-particle swarm optimization. Int. J. Innov. Comput. Inf. Control
**2011**, 7, 537–553. [Google Scholar] - Cai, X.; Cui, Z.; Zeng, J.; Tan, Y. Particle swarm optimization with self-adjusting cognitive selection strategy. Int. J. Innov. Comput. Inf. Control
**2008**, 4, 943–952. [Google Scholar] - Lee, K.S.; Geem, Z.W. A new structural optimization method based on the harmony search algorithm. Comput. Struct.
**2004**, 82, 781–798. [Google Scholar] [CrossRef] - Mahdavi, M.; Fesanghary, M.; Damangir, E. An improved harmony search algorithm for solving optimization problems. Appl. Math. Comput.
**2007**, 188, 1567–1579. [Google Scholar] [CrossRef]

**Figure 3.**The IEEE model [8] (d is the height of the arrester in m, n is the number of varistor columns).

**Figure 5.**The Pinceti–Giannettoni model (V

_{n}is the arrester’s rated voltage, V

_{r8/20}is the residual voltage for an 8/20 10 kA impulse current and V

_{r1/T2}is the residual voltage for a 1/T

_{2}10 kA impulse current) [9].

**Figure 6.**The Fernandez–Diaz model [13].

**Figure 10.**Residual voltage (in kV) and dissipated energy (in kJ/kV) for the three examined models (case 3) (the symbol * corresponds to the absorbed energy by the arresters).

Rated Voltage (U_{r}) | 30 kV | ||

Maximum Continuous Operating Voltage (U_{c}) | 24 kV | ||

Nominal Discharge Current | 10 kA | ||

Line Discharge Class according to IEC 60099-4 | 2 | ||

Long Duration Current Impulse (2000 μs) | 540 A | ||

Energy for Long Duration Impulse | 5.8 kJ/kV U_{c} | ||

Residual Voltage | 8/20 μs | 5 kA | 75.29 kV |

10 kA | 79.27 kV | ||

20 kA | 88.78 kV | ||

1/20 μs | 10 kA | 82.01 kV | |

30/60 μs | 125 A | 58.14 kV | |

500 A | 61.02 kV | ||

Sheds | 11 | ||

Height | 302 mm | ||

Creepage | 762 mm |

IEEE Model [8] | Pinceti–Giannettoni Model [9] | Fernandez–Diaz Model [13] | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Initial | Optimized | Initial | Optimized | Initial | Optimized | |||||||

Case | Case | Case | ||||||||||

1 | 2 | 3 | 1 | 2 | 3 | 1 | 2 | 3 | ||||

R_{0} (Ω) | 30.20 | 17.82 | 94.81 | 54.19 | 1 × 10^{6} | 1 | 0.952 × 10^{6} | 1.102 × 10^{6} | 1 × 10^{6} | 0.998 × 10^{6} | 1.051 × 10^{6} | 1.088 × 10^{6} |

R_{1} (Ω) | 19.63 | 24.48 | 27.88 | 37.54 | - | - | - | - | - | - | - | - |

L_{0} (μΗ) | 0.0604 | 0.108 | 0.141 | 0.421 | 0.259 | 0.192 | 0.314 | 0.419 | - | - | - | - |

L_{1} (μΗ) | 4.530 | 2.470 | 1.982 | 2.217 | 0.086 | 0.057 | 0.028 | 0.041 | 0.630 | 0.587 | 0.681 | 0.701 |

C (pF) | 331.1 | 784.2 | 860.9 | 1008.1 | - | - | - | - | 334.4 | 481.2 | 287.7 | 398.4 |

5 kA 8/20 μs | 10 kA 8/20 μs | 20 kA 8/20 μs | 10 kA 1/20 μs | 125 A 30/60 μs | 500 A 30/60 μs | 540 A 2000 μs | |||
---|---|---|---|---|---|---|---|---|---|

IEEE Model [8] | initial | 6.22 | 3.1 | 3.58 | 4.77 | 7.19 | 6.41 | 8.4 | |

Optimized (Case 1) | Harmony | 5.84 | 0.25 | 3.27 | 5.41 | 9.24 | 7.90 | 12.7 | |

Simplex | 6.81 | 0.66 | 4.2 | 5.20 | 9.51 | 8.38 | 11.4 | ||

Powell | 6.94 | 0.72 | 4.47 | 5.61 | 10.1 | 8.84 | 13.1 | ||

GA | 5.95 | 0.37 | 3.41 | 5.27 | 9.83 | 6.98 | 11.9 | ||

Optimized (Case 2) | Harmony | 3.04 | 0.97 | 1.4 | 3.2 | 3.9 | 4.12 | 8.70 | |

Simplex | trapped in local minima | ||||||||

Powell | trapped in local minima | ||||||||

GA | 3.24 | 1.19 | 1.38 | 3.46 | 4.21 | 4.40 | 9.45 | ||

Optimized (Case 3) | Harmony | 3.65 | 1.21 | 1.85 | 3.58 | 4.42 | 4.87 | 5.10 | |

Simplex | trapped in local minima | ||||||||

Powell | trapped in local minima | ||||||||

GA | 4.03 | 1.58 | 2.24 | 3.92 | 5.10 | 5.51 | 5.95 | ||

Pinceti–Giannettoni Model [9] | initial | 4.21 | 2.87 | 8.74 | 3.87 | 4.24 | 5.08 | 9.2 | |

Optimized (Case 1) | Harmony | 4.52 | 0.35 | 6.89 | 4.10 | 4.21 | 4.89 | 11.1 | |

Simplex | 4.91 | 0.50 | 7.08 | 4.74 | 5.58 | 6.24 | 12.9 | ||

Powell | 4.64 | 0.41 | 6.72 | 4.67 | 5.14 | 5.78 | 12.2 | ||

GA | 4.81 | 0.62 | 6.71 | 4.73 | 4.95 | 5.32 | 12.6 | ||

Optimized (Case 2) | Harmony | 3.31 | 1.04 | 4.84 | 2.1 | 2.91 | 3.70 | 8.91 | |

Simplex | trapped in local minima | ||||||||

Powell | trapped in local minima | ||||||||

GA | 3.68 | 1.41 | 4.58 | 2.43 | 3.08 | 4.12 | 9.21 | ||

Optimized (Case 3) | Harmony | 3.84 | 1.77 | 5.30 | 2.78 | 3.25 | 3.87 | 6.04 | |

Simplex | trapped in local minima | ||||||||

Powell | trapped in local minima | ||||||||

GA | 4.09 | 2.16 | 5.12 | 3.22 | 4.10 | 4.15 | 6.59 | ||

Fernandez–Diaz model [13] | initial | 2.41 | 1.59 | 8.35 | 7.41 | 5.97 | 5.45 | 11.23 | |

Optimized (Case 1) | Harmony | 2.71 | 0.15 | 8.1 | 7.88 | 6.20 | 5.81 | 13.2 | |

Simplex | 3.55 | 0.41 | 8.29 | 8.31 | 6.54 | 6.77 | 15.1 | ||

Powell | 3.29 | 0.37 | 8.15 | 8.04 | 6.31 | 6.28 | 12.2 | ||

GA | 2.94 | 0.30 | 7.82 | 7.94 | 6.48 | 5.59 | 11.7 | ||

Optimized (case 2) | Harmony | 1.1 | 1.31 | 2.21 | 3.08 | 3.45 | 3.64 | 9.4 | |

Simplex | trapped in local minima | ||||||||

Powell | trapped in local minima | ||||||||

GA | 1.54 | 1.92 | 2.73 | 3.50 | 3.68 | 4.01 | 10.7 | ||

Optimized (case 3) | Harmony | 1.77 | 1.91 | 2.89 | 3.71 | 4.81 | 4.19 | 6.81 | |

Simplex | trapped in local minima | ||||||||

Powell | trapped in local minima | ||||||||

GA | 1.95 | 2.24 | 3.11 | 4.02 | 4.61 | 4.42 | 6.40 |

© 2017 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Christodoulou, C.A.; Vita, V.; Perantzakis, G.; Ekonomou, L.; Milushev, G.
Adjusting the Parameters of Metal Oxide Gapless Surge Arresters’ Equivalent Circuits Using the Harmony Search Method. *Energies* **2017**, *10*, 2168.
https://doi.org/10.3390/en10122168

**AMA Style**

Christodoulou CA, Vita V, Perantzakis G, Ekonomou L, Milushev G.
Adjusting the Parameters of Metal Oxide Gapless Surge Arresters’ Equivalent Circuits Using the Harmony Search Method. *Energies*. 2017; 10(12):2168.
https://doi.org/10.3390/en10122168

**Chicago/Turabian Style**

Christodoulou, Christos A., Vasiliki Vita, Georgios Perantzakis, Lambros Ekonomou, and George Milushev.
2017. "Adjusting the Parameters of Metal Oxide Gapless Surge Arresters’ Equivalent Circuits Using the Harmony Search Method" *Energies* 10, no. 12: 2168.
https://doi.org/10.3390/en10122168