Optimal Design of a Medium Voltage Hybrid Fault ... - IEEE Xplore

ENERGYCON 2014 • May 13-16, 2014 • Dubrovnik, Croatia

Optimal Design of a Medium Voltage Hybrid Fault Current Limiter Jesper Magnusson #1 , Juan A. Martinez-Velasco ∗2 , Ara Bissal #3 , Göran Engdahl #4 , Lars Liljestrand o5 #

Dept. Electromagnetic Engineering, Royal Institute of Technology (KTH) Teknikringen 33, 100 44 Stockholm, Sweden 1

∗

[email protected] 3 [email protected] 4 [email protected]

Dept. Enginyeria Electrica - ETSEIB, Universitat Politecnica de Catalunya Diagonal 647, 08028 Barcelona, Spain 2

5

[email protected] o ABB AB Väster˚as, Sweden

[email protected]

be increased [1]. With the transition from overhead lines to power cables, the number of faults decreases, but the faults tend to be permanent and the reparation time increases [2]. A fast limitation of the fault current can minimize the damage in the cable and reduce the reparation cost and down time of the network. Fault current limiters have been a topic in the power grid for a long time and several possible topologies have been proposed. The solid-state FCL [3] uses a semiconductor component in the current path and provides an interruption within 100 μs. The main drawback is the high conduction losses. Other solutions, including the superconducting FCL [4] and resonant circuits [5], only limit the fault current while the existing CB takes care of the current interruption. The solutions used today in distribution systems are based on the current limiting fuse [6]. The fuse is both simple and cheap, but has to be replaced after each use. The ABB “Islimiter” [7] utilizes a current limiting fuse in parallel with a copper conductor. As a resettable fuse, positive temperature coefficient materials have been proposed [8]. In this project, a mechanical power electronic (PE) hybrid solution [9], [10] is investigated. The aim is to optimize the parameters of the hybrid FCL using a transient analysis model in combination with an optimization module.

Abstract—The connection of distributed generation increases the short circuit power which in turn might exceed the ratings of the installed circuit breakers. A solution is to limit the available short circuit power by increasing the grid impedance, but since there is a constant strive for lower losses and higher power transfer capabilities, this is not desired. The application of a fault current limiter (FCL) that can limit the current before the first peak enables a power system with high short circuit power and low short circuit current. This can increase the stability of the grid and reduce the requirements of other equipment. This work presents a simulation model to be used as an aid in the design of a hybrid FCL for a 12 kV AC system. The proposed model combines a transient analysis circuit model with an optimization module to obtain multiple sets of possible design parameters. The design is not straight forward since there is a trade-off between several of the design parameters. Index Terms—Fault current limiter, hybrid switch, modelling, optimization, power systems, transient analysis.

I. I NTRODUCTION

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ECHANICAL circuit breakers (CBs) use the natural current zero crossing for interrupting the current. In normal operation this means just another half-cycle of the current flows before interruption, but in case of a fault, the delay might be more severe. As a consequence of this delay at least one half-cycle of full short-circuit current will flow into the system before the current is interrupted. Because of the delays in detection systems and mechanical movements, in reality about five full cycles of short circuit current flows into the system before it is interrupted. If a fault current limiter (FCL) or a CB with the ability to force a current zero would be installed, all equipment downstream in the network could be dimensioned for a lower peak current resulting in simpler and cheaper components. Due to the lower fault current, the transformer life time could be extended and the overall capacity of the grid can

II. T HE HYBRID FAULT CURRENT LIMITER A. Principles of operation and circuit topology The hybrid FCL may consist of a parallel combination of three branches as shown in Fig. 1: a mechanical switch, a PE branch, and an energy absorbing branch (e.g. a metal oxide varistor, MOV). The mechanical switch should carry the nominal current in normal operation providing the same low resistive losses as a conventional CB. The PE branch will take care of the current interruption under full current and voltage stress, and the third branch will absorb the energy in the system to force the current to zero.

The work in this project was partially financed by SweGRIDS and KIC Innoenergy.

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Compared to a conventional CB, the demands on the mechanical switch are lower, except for the opening speed. The switch does not interrupt the system current, it only commutates it to a parallel branch and the current ceases under a low voltage stress. The required arc voltage is low and the arcing time should be short. Compared to a solid-state FCL, the PE branch does not carry the nominal current so the inherent on-state losses are avoided. The decreased conduction time of the PE branch means that the cooling system can be decreased in complexity and capacity or even avoided.

Fig. 2. The circuit diagram of the main circuit of the FCL as implemented into PSCAD.

and hence the current is forced to zero. The magnetic energy stored in the inductive power system is absorbed and converted into heat. When interrupting a nominal current, the interruption sequence can be simplified by interrupting the current at a current zero crossing. Under such arrangements, no magnetic energy needs to be dissipated in the MOV and a passive turnoff PE switch (e.g. a thyristor) could be used. However, this is not possible in the case of a rising fault current when the current must be limited before its first peak.

Fig. 1. The hybrid FCL consists of three parallel branches: the mechanical switch, the power electronics, and an energy absorbing element.

B. Simulation model of the hybrid FCL Fig. 2 shows the circuit diagram of the main FCL model. The model has been implemented in the simulation package PSCAD. The circuit consists of a one-phase equivalent of a 12 kV system. The nominal current is set to 2 kA and the prospective fault current to 25 kA. The study is carried out with the system under faulty conditions and the load is represented by a pure resistance. The grid is modelled as a stiff voltage source in series with an L-R impedance. The values of L and R are calculated to give the required fault current and a time constant of 50 ms. The values can be seen in the circuit diagram. As explained before, the FCL shown in the figure consists of three parallel branches whose models are described in detail in Section IV. C. Interruption of the current Fig. 3 shows the current interruption process. The interruption is triggered at t = 0 and the PE switch is turned on. After a delay in the mechanical system, the contacts of the mechanical switch separate. The arc voltage drives the commutation of the current from the mechanical switch to the PE branch. The commutation is slowed down by the undesired stray inductance in the commutation loop and the forward voltage drop of the PE switch. When the current in the mechanical switch reaches zero, the voltage stress is low compared to the system voltage and the current ceases. The PE branch carries the current for a short time interval to allow the gas in the switch to cool down and de-ionize. As the PE switch is turned off, the current is forced into the energy absorbing branch. This branch is designed so that the voltage across the FCL will be higher than the system voltage as seen in Fig. 4

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Fig. 3. The normal operation of the hybrid FCL. When the FCL is triggered at t = 0, the PE is turned on and the mechanical switch is triggered to open. The switch opens and the current is commutated to the PE branch. As all the current is conducted by the PE branch, it can be turned off and the current is forced to the third branch. The magnetic energy stored in the grid is absorbed and the current is forced to zero.

D. Dimensioning of the PE branch The design of the PE branch in this paper is based on IGBTs manufactured by ABB. Given the high current and voltage

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lated using the data sheet. In this project a simple model of a constant voltage drop in series with a resistive component has been used. Considering four parallel branches with five IGBTs (with their respective antiparallel diodes) connected in series, the model parameters become 13.8 V and 1.61 mΩ. III. P ROBLEM DESCRIPTION Several parameters are to get involved in the design of the FCL. In many cases, there is a trade-off between some of the parameters and the best choice will depend on external factors as cost or reliability. Considering the case shown in Fig. 3 as a successful interruption, the case in Fig. 5 is a failure. The combination of the switch opening time and the arc voltage is not sufficient to fully commutate the current from the mechanical switch to the IGBT branch. After the commutation starts, the current in the IGBT branch will increase until it reaches a value where the IGBT voltage drop is equal to the arc voltage. As the system fault current continues to rise, the current in the mechanical switch will increase and the IGBT current will remain constant. Hence, the current in the mechanical switch will not reach zero and the interruption will fail. The extension of the plot is not valid as the IGBTs would fail due to overheating and go into a permanent short-circuit mode.

Fig. 4. The voltage across the FCL during a successful interruption. When the current is commutated into the MOV branch, the voltage across the FCL exceeds the system voltage and the current is forced to zero. The system Is current is shown as reference.

ratings of the components, the ABB “S5SNA 2000K450300 StakPak IGBT Module” [11] has been chosen. This technology facilitates the series connection of several components and hence the design of a compact FCL. The selected components have a maximum current and voltage rating of 4 kA and 4.5 kV, respectively. Considering reasonable values for the parameters involved in the FCL, it is assumed that four semiconductors will be required in parallel to handle the current. Based on the component data sheet, the highest allowed peak current in the IGBT branch is then 16 kA. The voltage requirements of the IGBTs depend on the MOV used as energy absorber. The MOV is generally limited by the leakage current in the blocking state, where the MOV will draw 50 Hz current. Since the FCL should be allowed to be in this state for a long time, the continuous leakage current has to be low enough to not cause over-heating of the MOV. An option could be to connect a load break switch in series with the FCL to obtain more freedom in choosing the MOV voltage level. Considering the basic features of ZnO varistors, the required voltage withstand can be calculated. For a MOV specified to continuously handle an rms voltage of 10 kV, the breakdown voltage is around 20 kV [12], resulting in a requirement of five series-connected IGBTs to handle the transient over-voltage. In addition, the FCL has to be bi-directional and allow equal current conduction in both directions. Since the IGBT is a unipolar device [13], another five components connected in anti-parallel to the first ones are required to handle the reverse current. The ABB IGBTs are equipped with an anti-parallel diode in the same package resulting in a straight forward connection of the components. The total forward voltage drop of the IGBTs can be calcu-

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Fig. 5. Some combinations of arc voltage and switch opening time result in a failed commutation from the switch to the IGBT branch. Since the current in the mechanical switch never reaches zero, the FCL fails to interrupt the current.

The problem with a failed commutation has several solutions. One solution is shown in Fig. 6 where the only change compared to the failed case is an increase of the switch arc voltage. In this new case the voltage becomes higher than the voltage drop of the parallel branch and the current is successfully commutated. Another solution to the failed commutation is shown in Fig. 7. By decreasing the opening time of the mechanical switch, the current to be commutated becomes lower. Hence, the arc

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axis. As shown in the figure, an increase in the arc voltage decreases the peak current because of a faster commutation but increases the demand on the mechanical switch, whereas an increase in the switch opening time increases the peak current and decreases the demands on the switch. The grid impedance is not a direct parameter in the FCL design (see Fig. 3); it is imposed by the grid. However, it is evident that it is a key parameter when designing the FCL as the short circuit current and its rise time are fundamental issues for FCL behaviour.

Fig. 6. Compared to Fig. 5, the arc voltage has been increased. The higher voltage is enough to get a successful commutation and hence the current interruption is successful.

voltage is enough to commutate the current and achieve a successful interruption.

Fig. 8. The table shows how the output parameters on the y-axis are affected by an increase in the design parameters on the x-axis.

To sufficiently design the FCL, a parameter sweep would be required for each parameter that affects the design. As the parameters affect each other, xN simulations would be required, where N is the number of parameters in the design and x is the number of values for each parameter (assuming the same number of values for each parameter). However, many parameter combinations will not be valid since they will not lead to a successful current interruption. The work presented in this paper is based on a model that is built with an optimization algorithm to obtain parameter sets that define the requirements for a successful interruption. IV. D ETAILS OF THE FCL MODEL Fig. 7. Compared to Fig. 5, the switch opening time has been decreased. With the faster response of the switch, the current is lower and the arc voltage is enough to successfully commutate the current.

A. The mechanical switch The mechanical switch is modelled with a voltage source representing the arc voltage in series with the PSCAD built-in breaker model. When the switch is opened, the status “STCB” of the breaker changes from 0 to 1 and the voltage source is controlled to give a voltage “Varc” according to the right part of Fig. 9. The arc voltage is either zero or constant at the value specified by the control variable “Arcvoltage”. When the current in the switch branch crosses zero, the breaker “BRK” changes from 0 to 1, i.e. from conducting to blocking state. Hence, the logic signal changes and the voltage source returns to zero.

It is not obvious which solution is better: to design a faster switch with a lower arc voltage or a slower switch with a higher arc voltage. This example shows the complexity of the design using only two parameters. However, the hybrid FCL contains a number of design parameters that all affect each other. This is illustrated in Fig. 8 in which the y-axis shows the variables that need to be controlled but are a result of the system and FCL behaviour. The cells of the figure contain an indication whether these variables are increased or decreased by an increase in the design parameters listed along the x-

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E. The optimization module The model is equipped with the PSCAD built-in optimization capability [15]. The block takes one parameter, known as the objective function (OF), as input and may have up to 20 parameters as output. A simulation is run with some initial values for all parameters to obtain a value of the OF. Using the Simplex method [16], a new set of parameters is calculated. The procedure is repeated and the iteration stops when the difference in the OF between two consecutive runs is lower than a specified tolerance. The benefit of the Simplex method is that no derivatives are required and the new parameter values are calculated using only the value of the OF and the old parameter values. The OF has to be carefully defined to get the expected system behaviour. In this case, the OF is defined by adding two functions: demand and desire. The goal of the demand function is to guarantee the interruption of the fault current whereas the desire function controls the design of the switch. The point is that no matter how “good” a design is in the sense of a low desire-function, the solution is not valid unless the demand is fulfilled. Considering the previous calculations, the peak current of the system is set to 16 kA. To achieve this target, every ampere above this limit is penalized by 1000, giving the definition of the demand function as 1000. (Iˆ − 16, 000), Iˆ > 16 kA fDemand = (1) 0, Iˆ ≤ 16 kA.

Fig. 9. The mechanical switch is modelled with a constant arc voltage that is active only from contact separation until the current becomes zero.

B. The PE branch The PE branch is shown to the left in Fig. 10. The IGBT stacks are modelled as one single IGBT with the forward voltage drop according to the previous calculations. The IGBTs are turned on and off with the variable “IGBT”. The turn on and turn off processes are ideal and are performed within one simulation time step. In series with the IGBT is an inductor representing the stray inductance in the commutation loop. Its value can be varied; simulations show that 0.8-1.1 μH is a reasonable value. This stray inductance slows down the commutation from the mechanical switch to the IGBT branch, but does not affect the IGBT turn-off since the IGBT behaves as an ideal switch.

Fig. 10. Left: the PE branch with the IGBT model in series with the undesired stray inductance. Right: the built-in PSCAD MOV model with non-linear U − I characteristics.

This function is piecewise linear and helps the system to converge properly. Restrictions in the parameters are also added here. Since all parameters should be larger than zero, the demand function is penalized when any parameter becomes negative. Hence the demand function is zero when its goal is achieved. It should be noted that the system current in the simulation model is used instead of the IGBT current since the use of the latter results in an optimal solution with no arc voltage. In this case, the current is interrupted solely by the mechanical switch at the next current zero crossing, i.e. as a conventional mechanical CB. The desire function is defined to obtain the optimal parameters among the allowed solutions. This is done by summing all parameters, P, with positive sign if the parameter should be minimized and with a negative sign if the parameter should be maximized; that is:

C. The MOV branch The MOV branch is based on the PSCAD built-in MOV model, shown to the right in Fig. 10. The nominal voltage of the MOV is specified to the same level as the system voltage, i.e. 9.8 kVpeak , according to the previous reasoning. Parallel to the MOV is the voltage measurement of the FCL voltage. In reality, there should also be a stray inductance in the commutation loop between the IGBT and MOV that might cause an over-voltage spike during the IGBT turn-off [14]. In that case a snubber circuit might be required to protect the IGBTs. Since the IGBTs are modelled as ideal switches during turn-off, adding this stray inductance would not affect the behaviour of the model. D. The fault A switch in parallel to the load is used to represent a ground fault with zero resistance. During the simulation the entire model must be allowed to reach a steady-state before the fault is triggered. The voltage phase angle at the time of the fault can be controlled to cause different fault cases. The fault detection is modelled with a constant value; as the current passes this level, the system is triggered to interrupt the current. The current is set to a limit of 4 kA, i.e. twice the rms value of the system nominal current.

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fDesire =

i

ki Pi , ki =

+1, Pi is minimized −1, Pi is maximized.

(2)

The parameters are normalized with an initial guess, so that all parameters are 1 in the initial simulation. If the initial guesses of the parameters are of the same order of magnitude as the final values, the desire function will always have a value close to zero, positive or negative. This way, if an optimum is found where the desire function cancels a non-zero value in

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the demand function (i.e. a solution that should be non-valid), the high penalty in the demand function makes sure that the excess current in the IGBTs is small and can be neglected. Since the allowed peak current depends on the number of parallel components and hence is a discrete value design parameter, there is no gain in having a peak current that is lower than just below the allowed limit. However, with the definition of the desire function, the optimal values of the design parameters will push the current towards the limit. Consequently the full capacity of the IGBTs is utilized and there is no need to include this functionality in the demand function. V. R ESULTS A. Design parameters The main objective is to find the design parameters that define the minimum requirements of the mechanical switch and provide a successful current interruption and limitation. Two parameters are considered in this work: • Arc voltage, (Varc ): The arc voltage is assumed constant. The larger part of the arc voltage comes from the anodecathode voltage drop and is basically a function of the contact material and the insulation media (gas). The effect of the arc length is neglected due to the short arcing time. A lower arc voltage means a simpler mechanical switch, so this parameter should be minimized. • Switch open delay, (Tsw ): Due to the control system of the mechanical switch as well as the mass and physical properties of the switch, there will be a delay from fault detection until the contacts separate and the arc voltage appears. This parameter should be maximized to give the lowest possible demands of the mechanical switch. The two parameters were normalized by the initial values of 100 V and 500 μs, respectively.

Fig. 11. The convergence of the OF and the two parameters used in the optimization. The dots indicate the iterations where the OF obtained a value considered to be an allowed solution.

arc will be high and can cause high stresses on the contact system.

B. Model convergence Fig. 11 shows the convergence of a simulation where the two parameters are equally weighted in the desire function. Varc and Tsw are plotted for each iteration whereas the OF is only plotted for the iterations where the demand function is fulfilled. The peak current becomes too high with the initial values and the Simplex module starts increasing Varc and decreasing Tsw until the first valid solution is found in iteration 4. At this point, the demand function becomes zero, and the values of the parameters are varied to decrease the desire function. Each data point that fulfils the demand function is indicated with an asterisk and it can be seen that only 28 of the 50 iterations give valid solutions.

Fig. 12. The asymmetric fault current occurs when the fault is applied at a voltage angle close to zero, or more precisely 90◦ before the angle of the system impedance.

If the fault occurs close to the angle of the complex grid impedance (arctan(ωL/R)), the fault current will be symmetric as shown in Fig. 13. This situation causes a lower current peak than the asymmetric case, but has a higher current derivative in the beginning. Since the main objective of the FCL is to limit the fault current, this has to be done before the first peak, i.e. within 5 ms in a 50 Hz system. Considering the two fault cases, it is clear that the symmetric fault has a higher current for any instant before t = 5 ms. The proposed model has been used to investigate what

C. The worst case From the system perspective, the asymmetric fault case shown in Fig. 12 has to be considered the worst case since it results in a current peak that is almost twice the value of the peak of the steady state fault current. With a low damping in the system, several peaks of high magnitude will occur if the current is not rapidly interrupted. For a CB the current in the

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Fig. 13. The symmetric fault current occurs if the voltage angle of the system voltage is close to the angle of the system impedance at the time of the fault. For a pure inductive system, this would mean ϕ = 90◦ .

Fig. 14. The required arc voltage of the mechanical switch as a function of the switch open delay and the fault angle. All cases show that the worst case is around 80◦ , but shifts slightly to the left as the switch delay increases.

the demands are on the mechanical switch for different fault angles. The fault angle was swept through all faults of interest and Tsw was varied from 100 to 500 μs. In each point, the simulation model was used to minimize Varc with the restriction that the current should not exceed 16 kA and the result is shown in Fig. 14. It can be seen that the highest arc voltage for all three Tsw is required around a fault angle of 80◦ . The studied system has a time constant of 50 ms, and the symmetrical fault occurs at ϕ ≈ 86◦ . The reason for the difference in angle is the delay in detecting the fault, here defined by the fault detection level. The worst case for the FCL is when the highest current derivative occurs at the fault detection level and the current rises after the triggering of the switch. This results in the highest current when the commutation starts and hence requires the highest arc voltage. To be more precise, the worst case occurs when the mean value of the current derivative, during the interval Tsw , is highest. This can be seen by the slight shift of the peak to the left as Tsw is increased. This effect however is minor, and the angle is still close to 80◦ .

By sweeping α from 0 to 1, a set of parameters known as the Pareto frontier can be obtained [17]. The importance of the two parameters can be investigated from using only Varc to ignoring Varc completely. In the two extreme cases, 0 and 1, the algorithm gets convergence problems due to optimization with parameters that do not affect the OF. A final value is found in both cases, but the algorithm does not fully converge. Fig. 15 shows the optimal values obtained for the two parameters with different values of α. Since there is a trade-off between the two parameters, there is an infinite number of possible solutions. Note that the 10 points are situated on a parabola that is on the limit of fulfilling the demand function, i.e. shows the minimum requirements of the mechanical switch. Looking at the two outer most cases, one has the possibility of designing a switch with Varc as low as 42 V, but in that case the switch has to open within 6 μs. The other extreme is a switch with Tsw = 550 μs, but it requires a substantial arc voltage of above 200 V. The design has to be within the area limited by the dashed black lines. In case of a fast switch, the arc voltage has to be higher than the voltage drop of the IGBTs at the end of the commutation. Hence, even a switch with an instant opening will still require an arc voltage to perform the commutation. The horizontal line shows the result of a simulation with Tsw = 0 for which the lowest possible arc voltage is slightly above 40 V. Since there is a fixed delay where the IGBTs are allowed to conduct the current, the commutation has to be finished before this. The vertical line shows a case where Varc was set to a value with which the commutation time can be neglected and the opening time of the switch cannot exceed 620 μs. The parameter sets close to the edges are generally not desired in the design. As the parabola asymptotically approaches the fundamental limits, the demand on one parameter increases rapidly and the other parameter is almost constant. Comparing

D. Different parameter combinations As mentioned before, the main objective is to find different sets of parameters that fulfil the demand rather than finding a real optimal solution. The reason is that it is not easy to define the relationship between the design parameters and the complexity or cost of the switch. Since the model with the Simplex optimization block only finds one optimum that is highly dependent on the initial guess, a sweep was performed to find more sets. Apart from the two parameters Varc and Tsw another weighting parameter, α, is added to obtain the following desire function: fDesire = (1 − α)

Varc Tsw . +α 100 500. 10−6

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(3)

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the cases α = 0 and α = 0.3, it can be seen that an increase in the arc voltage by only 6 V (15%), reduces the demand on the switch opening time from 6 to 170 μs.

R EFERENCES [1] A. J. Power, “An overview of transmission fault current limiters,” IEE Colloquium on Fault Current Limiters - A Look at Tomorrow, June 1995. [2] H. Al-Khalidi and A. Kalam, “The impact of underground cables on power transmission and distribution networks,” in Power and Energy Conference, 2006. PECon ’06. IEEE International, 2006, pp. 576–580. [3] C. Meyer, S. Schroder, and R. De Doncker, “Solid-state circuit breakers and current limiters for medium-voltage systems having distributed power systems,” Power Electronics, IEEE Transactions on, vol. 19, no. 5, pp. 1333–1340, 2004. [4] W. Paul, M. Lakner, J. Rhyner, P. Unternhrer, T. Baumann, M. Chen, L. Widenhorn, and A. Gurig, “Test of 1.2 mva high-tc superconducting fault current limiter,” Superconductor Science and Technology, vol. 10, no. 12, pp. 914–918, 1997. [5] G. Karady, “Principles of fault current limitation by a resonant lc circuit,” Generation, Transmission and Distribution, IEE Proceedings C, vol. 139, no. 1, pp. 1–6, 1992. [6] K. Leix, L. A. Kojovic, M. Marz, and G. Lampley, “Applying currentlimiting fuses to improve power quality and safety,” in Transmission and Distribution Conference, 1999 IEEE, vol. 2, 1999, pp. 636–641 vol.2. [7] K.-H. Hartung and V. Schmidt, “Limitation of short circuit current by an IS-limiter,” in Electrical Power Quality and Utilisation, 2009. EPQU 2009. 10th International Conference on, 2009, pp. 1–4. [8] R. Strumpler, J. Skindhoj, J. Glatz-Reichenbach, J. H. W. Kuhlefelt, and F. Perdoncin, “Novel medium voltage fault current limiter based on polymer ptc resistors,” Power Delivery, IEEE Transactions on, vol. 14, no. 2, pp. 425–430, 1999. [9] M. Francis, J. Dupraz, R. Besrest, and J. Armata, “New topology of hybrid circuit breaker/current limiter for mv aes networks,” in All Electric Ship (AES2005), International Conference on, 2005, pp. 13– 14. [10] H. Kurioka, T. Genji, M. Isozaki, H. Iwai, and M. Yamada, “Development of a high-speed current limiter for a 6 kv distribution system and evaluation of its effectiveness,” Electrical Engineering in Japan, vol. 125, no. 3, pp. 11–20, 1998. [11] ABB, “S5SNA 2000K450300 StakPak IGBT module,” 2013. [Online]. Available: http://www.abb.com/product/us/9AAC30200001.aspx [12] ABB AB, “High voltage surge arresters - buyer’s guide,” 2012. [Online]. Available: http://www.abb.com/product/se/9AAC710009.aspx [13] B. J. Baliga, M. S. Adler, R. Love, P. Gray, and N. Zommer, “The insulated gate transistor: A new three-terminal mos-controlled bipolar power device,” Electron Devices, IEEE Transactions on, vol. 31, no. 6, pp. 821–828, 1984. [14] J. Magnusson, R. Saers, L. Liljestrand, and G. Engdahl, “Separation of the energy absorption and over-voltage protection in solid-state breakers by the use of parallel varistors,” Accepted for publication in IEEE Trans. Power Electron., 2013. [Online]. Available: www.ieeexplore.org [15] A. Gole, S. Filizadeh, R. Menzies, and P. Wilson, “Optimizationenabled electromagnetic transient simulation,” Power Delivery, IEEE Transactions on, vol. 20, no. 1, pp. 512–518, 2005. [16] J. A. Nelder and R. Mead, “A simplex method for function minimization,” The Computer Journal, vol. 7, no. 4, pp. 308–313, 1965. [17] M. Heidari, S. Filizadeh, and A. Gole, “Support tools for simulationbased optimal design of power networks with embedded power electronics,” Power Delivery, IEEE Transactions on, vol. 23, no. 3, pp. 1561– 1570, 2008. [18] K. Kobravi and S. Filizadeh, “An adaptive multi-modal optimization algorithm for simulation-based design of power-electronic circuits,” Engineering Optimization, vol. 41, no. 10, pp. 945–969, 2009. [19] F. Yahyaie and S. Filizadeh, “A surrogate-model based multi-modal optimization algorithm,” Engineering Optimization, vol. 43, no. 7, pp. 779–799, 2011.

Fig. 15. Different sets of Varc and Tsw as a function of α in equation (3). The fault is triggered at ϕ = 80◦ , i.e. the worst fault case.

VI. C ONCLUSIONS It has been shown that using an optimization module in combination with the transient analysis model, several possible designs of a hybrid FCL can be obtained. Each set of parameters represent a possible configuration of the switch and defines the minimum requirements for a successful limitation and interruption of the fault current. It is also shown that the worst fault case for the hybrid FCL is determined by the fault detection system. Compared to a CB where the worst case is an asymmetric fault, the worst case for the FCL is a fault that occurs slightly before the voltage peak. As the fault current rises rapidly while the mechanical switch is opening, fast fault detection is crucial to minimize the peak current. There is also a dependence on the opening time of the mechanical switch, but it is negligible since the opening time of the switch is much lower that the system voltage period time. This simulation model is the first step in the development of a fast commutation switch than could be used as the mechanical switch in a hybrid FCL. A prototype of the switch will be manufactured and tested to validate the model results. The obtained sets of parameters will serve as alternatives from which parameters could be selected when evaluating cost and reliability in the design. Parameters such as cost and reliability cannot be easily implemented into the objective function (OF). In addition, it is fundamental to detect both local and global minima. Since only one optimal solution can be obtained by means of the Simplex optimization algorithm, a more powerful multimodal algorithm, as in [18] and [19], will be applied in future versions.

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