Surge Arrester Selection Algorithm for Protection of Parallel Passive Filters Against Lightning Surges Under Harmonic Voltage Conditions

Parallel passive filters are used for decrease of harmonic components of load currents. In electrical distribution systems, over voltages such as switching and lightning over voltages are applied to the parallel passive filters. Th is paper analyses the behaviour of parallel passive filter employed to decrease the load harmonic currents under travelling wave conditions. The parallel passive filter is vulnerable to lightning surges. Therefore, protection of it against lightning surges is necessary. Equipment protection against lightning surges is usually done by gapless surge arrester. This paper presents important points of gapless surge arrester to protect parallel passive filters. A lso an algorithm is presented to select gapless arrester under harmonic conditions in this paper. The presented algorithm is based on the IEEE standards C62.22 and 1531. Finally the simulat ion results are provided to verify the presented algorithm.


Introduction
Discharges of lightning surges on electrical distribution lines cause electrical breakdown of insulators. So metimes cutting of the electrical line and outage are occurred because of lightning discharges. Concrete poles utilized in low voltage electrical systems (up to 20kV) have no grounding systems and no grounding conductors. Therefore, they cannot suppress the lightening surges effectively due to their large surge impedances. Also probability of the simu ltaneous lightning discharges on three-phase system is high, because of short height of the insulators and shape of utilized cross arms in distribution systems.
If the voltage magnitude of the lightning surge is higher than LPL (lightning protection level) of the insulators, the flashes are occurred on the insulators of three-phase. Chopped surges voltages which are produced by the flashes, travel through conductors named travelling waves [2] Today the parallel passive filters (PPFs) are widely used to decrease harmonic currents of non-linear loads in the electrical distribution system. Whereas number of the lightning surges is h igh , th e p rotect ion of the PPFs is necessary.
Design of the PPFs is based on limitation of the harmon ic currents as mentioned in standard IEEE519 [1] but the details of protection of the PPFs during lightning surges are not discussed in the standard. The surge arresters are used in installation of the PPFs to prevent failures of their co mponents during lightning surges. If the PPFs are not protected appropriately, they will damage [2]. For example in HVDC transmission system, the arresters are emp loyed to protect series capacitors [3]. In [4] various approaches are discussed to protect electrical equip ment but they are not under harmonic conditions. The subject of [5] is estimation of heating with mixtures of fundamental and harmonic voltages in order to select an appropriate rating of arrester, but the paper does not examine effects of the lightening surges on parallel passive filters. Reliability of the PPF is impo rtant too, use of surge arresters for lightning protection improve reliability of the system [6].
This paper examines equivalent surge impedance in conjunction point to analyse behaviour of travelling wave in electrical d istribution lines. Also the PPF is examined under travelling wave conditions in this paper. To selection of arrester, an algorith m is presented for protection of the PPF. The IEEE standards C62.22 and 1531 are emp loyed to extract the algorithm. Finally a case study is simulated to verify the presented equations and algorithm. There are several model for analysis of the surge arrester, such as IEEE model, Pinceti model, Popov model [7], this paper uses IEEE model of the surge arrester in simulation.

Travelling Waves in Distribution System
To reduce the harmonic currents, the PPFs are utilized in 20kV or 0.4kV electrical systems. Where the PPFs are employed in 20kV electrical systems, they must be protected against the lightning surges by gapless arresters. The arrester is placed across passive filter or across capacitor of the parallel passive filter [2]. Figure (1) shows a simp le electrical distribution system co mprising a radial d istribution line, a PPF and an arrester. Also the equal surge impedance of the electrical d istribution system in conjunction point is shown in figure (1). When lightning surge hits on the line, tow travelling waves appear on the each phase of the electrical distribution line as shown in figure (1). Therefore, six travelling wave are appeared when lightning surge hits on the conductors. After conjunction, the lightning surges move towards the arrester and the filter through the conductors. In conjunction of lightning surges with the PPF and the arrester, the arrester should protect the PPF.
A radial electrical d istribution line without branches and ignoring of other loads is the worst case for analysis of the conjunction of lightning surges with electrical distribution line, as shown in figure(1).
where V LI , I LI and Z eq denote lightning voltage, lightning current and equivalent surge impedance of conjunction point, respectively. Equivalent surge impedance will be: Where, Z pole is surge impedance of the concrete pole, Z ch is surge impedance of the discharge channel of air, and Z ph is surge impedance of the conductor.
Lightning current(I LI ) depends on the climate conditions, but the lightning voltage depends on the surge impedance and the lightning current wave form as seen in figure (2).
General solution of no-loss equations is: Where Z o =(L/ C) 0.5 is the surge impedance Z ph =Z O and u=(LC) -0.5 is the velocity of the wave which is 300000km/sec approximately in air distribution lines. Vo ltages v F and v B are named the forward and the backward waves respectively.
When a travelling wave on a distribution line reaches the PPF, a part of the wave reflects back along the line, and another part passes to the PPF. W ithout protection, if the voltage magnitude of the lightning surge encountering to the PPF is larger than the base insulation level (BIL) of the PPF, the PPF will be damaged. To avoid parallel passive filter failure, there are two strategies: Decreasing of Z eq Utilizing of surge arrester To reduce Z eq , grounding system is necessary to be in-Lightning Surges Under Harmonic Voltage Conditions stalled for each pole, but this method is costive. Therefore, utilizing of the surge arrester is economic.

Behaviours of the PPF under Travelling Wave Condition
The behaviours of the travelling waves reaching to the PPF depend on the shapes of the waves and the values of the elements(L and C) employed in the PPF. The PPF behaves similar to capacitor where X C >>X L and behaves similar to inductor where X C <<X L [ 8].
The PPF consists of a capacitor is connected in serries with an inductor. To examine behaviour of the PPF during travelling wave, it is needed to drive differential equations.
To protect the PPF perfectly, investigation of the worst case is necessary too. Figure ( (5), it can be written as: The filter current is equal to the capacitor current, so: Fro m equations (6)(7)(8), the capacitor voltage can be written as: The behaviours of the PPF at the initial and ending times of travelling wave are shown in Table(I). Considering table(I), the voltages of the capacitor and the inductor will be t wo t imes of peak value o f V F without protection. Therefore, it is necessary to protect the PPF against the travelling waves.

Selection of Surge Arrester under Harmonic Conditions for Protection of the PPF
Gapless arresters are used to protect the PPF. They utilize a single stacked column or two or more parallel co lu mns of meta l-o xide valve elements. Voltage-current characteristic and the structure of a gapless arrester are shown in Figure(5). The nonlinear behaviour of arrester can be approximated by: (10) Where k is calculated by fitting of the curve, and α normally varies fro m 10 to 50 for metal-o xide [3].
Three parameters are considered to select an arrester: • voltage rating • ma ximu m continuous operating voltage(MCOV) • temporary overvoltage(TOV) The voltage rating of an arrester is determined by the manufacturer. The MCOV of the arrester is typically in the range of 75% to 85% of the voltage rating.
To prevent activation of arrester in contingent over voltage such as load rejection, single phase short circuit or entrance of PPF, TOV of arrester should be greater than magnitudes short-time over voltages.
a system TOV TOV > If there are no voltage harmonic co mponents, the arresters located at the line terminals of a PPF are applied in the same way as other arresters located on a power system. In the otherwise, the peak applied voltage and harmonic heating should be considered in selecting the arrester rating [2,9] Fro m equation (12), the peak voltage of the arrester(rated voltage) will be equalled to sum of the fundamental and the harmonic co mponents.
To prevent heating of the arrester, the maximu m continuous operating voltage (MCOV) of the arrester should be higher than sum of the fundamental and the harmonic voltages [2,8].
The harmonic (dielectric) heating of the arrester is proportional to the order of the harmonic and the square of the voltage of each harmonic (including the fundamental). To avoid heating of arrester dielectric at rated frequency, the arrester MCOV rating should be selected as [2,9]: For continuous operation, the MCOV for arrester should be based on the higher value of equations (13) and (14).

Flowchart of Arrester Selection under Harmonic Conditions
Figure (7) shows the algorithm of the arrester selection under harmonic conditions. The steps of the flowchart are as follows: Step1: The elements of the PPFs are designed according to [1,2].
Step2: The harmonic voltages and the temporary over voltage are calculated by load flow.
Step3: V r , M COV and TOV of the arrester are determined fro m equations (11) to (14).
Step4:The insulation coordination is calculated as fo llows [2]: Degree of coordination is calcu lated by the protective ratio (PR): tan Pr

Insulation Withs d Level PR
Voltage at otected Equipment = (15) Three protective ratios are in co mmon use which compare protective levels with corresponding insulation withstands. Step5: The maximu m allowable separation distance between the arrester junction and the PPF terminal is calculated as below: It is necessary to calculate acceptable separation distances between the arrester and the PPF. Equation (19)   Step6: The discharge energy is calculated as follows: When metal-o xide arresters are energized, it will absorb energy that results in a temperature increase of its elements. If the temperatures of the elements reach a high enough level, damage to the valve elements can occur, leading to an electrical breakdown and failure of the arrester. The energy that an arrester can absorb during an overvoltage event without impairing the arrester's ability to serve the intended function following the event is usually called "energy handling capability" or "energy withstands capability." This capability is often expressed in terms of kilo joules per kV of arrester MCOV or per kV of duty-cycle rat ing [2].
The amount of energy is proportional to surge magnitude, wave shape, the system impedance, circuit topology, the arrester voltage-current characteristics, and the nu mber of operations (single/mult iple events). The energy which is discharged by an arrester, W, in joule, may be conservatively estimated by [2]: The equation (20) assumes that the entire line is charged to Lightning Surges Under Harmonic Voltage Conditions a surge voltage (which exists at the arrester location) and is discharged through the arrester during n propagation and reflection. n is supposed 10 in co mmon. The discharge voltage and current are related by the equation (21): Finally, considering the application guides of the manufacturer, and calculated W, thermal class of arrester is determined. Figure(7) shows the steps of the arrester selection under harmonic conditions.

Case Study and Simulation
Figure (9) shows a simp le system studied in this paper. The system may not be a very practical distribution system, but it is interesting fro m the point of view of arrester design in harmonic conditions. The simu lation is carried out based on ATP software.
Lightning protection must be designed for the worst case. Therefore, it is supposed that, the line is cut during lightning as shown in figure (9).
The harmonic voltage spectrum in the terms of the fundamental in the PPFs bus is according to table(II).
The wave shape of the lightning voltage is designated by a combination of t wo numbers. At the first, an index of the wave front, is the virtual duration of the wave front in microseconds (T f ). At the second, an index of the wave tail, is the time in microseconds (T tail ). In this paper, they are supposed as: 1.  (2) shows the voltage at the terminals of the PPFs where lightning discharge occurs at point placed 20km fro m the PPFs. As shown, the voltage peak of the PPFs reaches two times the peak value of the lightning voltage. The peak of curve (2) decreases because of resistive losses of the inductors employed in the PPF.  (10), the voltage peak of the PPFs is around 280kV and the PPFs cannot withstand it. Therefore, if the PPFs are not protected against lightning surges, they will be damaged certainly.

Simulation result wi th arrester
An arrester (V rated =24kV, MCOV=19kV) is selected which its V-I characteristic is shown in table (III).

Conclusions
In this paper, an algorith m for consideration of arrester selection is presented where harmon ic voltages may be significant. The presented selection method consists of the harmonic condit ion and occurrence of the lightning surges at the terminals of the PPFs. The analysis of the PPFs under harmonic conditions with and without metal-o xide arrester protection has been studied in this paper. Two cases are studied, and it is seen that the presented method is effective to protect the PPFs in allowable limitation.