A New and Efficient Algorithm for Short-circuit

th

THE 9 INTERNATIONAL SYMPOSIUM ON ADVANCED TOPICS IN ELECTRICAL ENGINEERING May 7-9, 2015 Bucharest, Romania

A New and Efficient Algorithm for Short-circuit Calculation in Distribution Networks with Distributed Generation Ion Triştiu, Member IEEE, Constantin Bulac, Member IEEE, Sorina Costinaş, Member IEEE, Lucian Toma, Member IEEE, Alexandru Mandiş, Tudor Zăbavă University POLITEHNICA of Bucharest, Power Engineering Faculty, 313 Spl. Independenţei, 060042 Bucharest, Romania [email protected], [email protected], [email protected], [email protected], [email protected], [email protected] Abstract - This paper presents a new algorithm for short-circuit currents calculation in distribution networks in which distributed generators are connected. The specifications of the IEC 60909 Standard are applied, in which the fault is replaced by an equivalent voltage source. The algorithm consists in two steps: a forward sweep, in which the aggregated impedances between each bus and the neutral point are calculated, and the backward sweep, in which the short-circuit currents flowing in the network branches are determined. The IEEE 33 bus test network is used for numerical calculations, considering 5 distributed generators. Keywords- distributed generation (DG), distribution network, short-circuit calculation algorithm

I.

INTRODUCTION

The use of small energy sources has been increasingly developed to meet the customer’s needs at the highest efficiency. The integration of distributed generation into the low voltage and medium voltage distribution networks has changed the traditional radial operation. One of the most important topics is the calculation of the short-circuit currents. The short-circuits that occurs in electrical networks generates high intensity currents and low level of voltages. Knowing the value of short-circuit current values is necessary for various purposes, such as: electrical installations sizing and verification for dynamic and thermal requirements; choosing the type and setting the protection adjustments from electrical installations; to determine the level of switching overvoltages; to study dynamic regimes; to analyse the functioning of consumers. The value of residual voltages, that occurs during the appearance of various types of shortcircuits, is necessary to analyze the power supply quality provided to consumers. Thus, paper [1] studies the disturbances in electrical networks as voltage sags caused by short-circuits. The voltage sags represents an important aspect for power quality of power systems [2]. Considering different assumptions, have been developed several methods for calculating short-circuit currents in electrical networks. The “impedance” method, used to calculate fault currents at any point in an installation with a high degree of accuracy [3]. Standard IEC 60909 applies to

978-1-4799-7514-3/15/$31.00 ©2015 IEEE

all networks, radial or meshed, up to 550 kV. This method, based on the Thévenin theorem, calculates an equivalent voltage source at the short-circuit location and then determines the corresponding short-circuit current [4]. In order to reduce the short-circuit currents in power systems, high short-circuit impedance electrical transformers are used [5]. Although a number of simplifying assumptions are accepted, the calculation of short-circuit currents, especially in meshed networks, represents a complex problem. In order to solve this problem specialized calculation programs are used, based on numerical calculation matrix. These methods involve a significant amount of calculations, requiring the completion of several steps: the calculation of the nodal admittance matrix, matrix inversion to obtain the nodal impedance matrix, the calculation of short-circuit current at the fault location, determination of residual voltages at nodes and short-circuit currents flowing thru branches. A particular case in which it is necessary to calculate the short-circuit currents is represented by the integration study of DG in power systems. This case aims to verify the compliance of technical connection requirements of DG in electrical networks. Generally, the methods developed for the calculation of short-circuit currents do not take into account the presence of DG in electrical networks. American standard [6] treats extensively various aspects related with short-circuit currents calculation in electrical network without considering the presence of DG. Recent articles suggest adapting traditional methods for different types of DGs. The paper [7] presents the available analytical equations to calculate the short-circuit current, and makes a comparison between the IEC 60909 and the results obtained by the simulations in a test network that incorporates these units. The methodology of IEC Standard 60909 is also applied to distribution networks with DG resources, to determine the maximum fault level [8]-[10]. DG sources are characterized by relatively low installed capacity, relative to classical power plants (thermal, nuclear and hydraulic). Based on this observation, the integration of DG in high, medium and low voltage electrical networks is recommended [11]. These networks, especially the urban one,

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can have a meshed configuration, but in order to limit the affected area by various defects and reducing the short-circuit currents, these networks operate in radial or arborescent configuration. On the basis of this constraint, in such configuration there are no closed loops, and the source node supply on a single path each consumer node. Previous observation was used to develop a computational method for load flow, known in literature as the “backward/forward sweep”. The principle of this method consists on two steps: the backward sweep for current calculation and the forward sweep for voltage drop calculation [12]-[14]. The constraint imposed to operating configurations of distribution networks, simplifies the calculation process of short-circuit currents, no longer being necessary the use of matrix numerical computation. Thus, this paper proposed a simplified process for calculating short-circuit currents, by using an efficient algorithm that can be applied for distribution networks with DG. Based on the method of equivalent generator voltage at the fault location, the shortcircuit currents are calculated in the upstream and downstream areas. The algorithm principle proposed in this paper is similar to the “backward-forward method” used for load flow calculation in distribution networks. II.

the considered fault regime (maximum or minimum). Figure 1 shows an example of application of this method. For a three-phase fault at the point F of the network from Figure 1, the initial symmetrical short-circuit current value is given by: E cU n cU n = = Zk 3Z k 3 (Z S + ZT + Z L )

''

Ik =

where Z k is the equivalent short-circuit impedance of the electric network at the short-circuit location F. The impedances of the network feeder ( Z S ) and the transformer ( Z T ) are calculated relative to the rated voltage U n at the fault location. For the impedance Z T a correction factor KT must be applied.

S

T

HV S ZT

ZS

Nr:1 A

A

F

The three-phase short-circuit is characterized by a low frequency of occurrence (5-10% of cases), but represents a basic element in calculations made in power systems.

MV ZL F

Un Zk cUn 3

F Ik

Fig. 1. Illustrations for calculating the initial symmetrical short-circuit " current I k in compliance with the procedure for the equivalent voltage source [7].

B. Short-circuit calculation in network with DG In order to determine the contribution of DGs on shortcircuit currents, the method of equivalent voltage source at the fault location is used. Figure 2 shows an example of application of this method.

k3

A. Basic principle of short-circuit calculation During the occurrence of a short-circuit, the phase currents have variable values over time in a transient regime. This regime is followed by a steady state regime in which the currents have constant amplitude. One of the important quantities for short-circuit regimes could be the initial symmetrical short-circuit current I k" , which is the effective value of the a.c. symmetrical component and serves as a basis for the calculation of the peak asymmetrical short-circuit current, ip , as well as the breaking current and capacity [15]. In order to simplify the short-circuit currents calculation some assumptions are considered [4]. For the calculation of short-circuit currents, the method of the equivalent voltage source at the fault location is used. An ideal voltage source E = cU n 3 , connected at the fault location, is considered as the only source in the network, present only in positive sequence diagram. All network feeders are replaced by their internal impedance (positive, negative and zero sequence). The value of voltage factor c depends on the rated voltage U n at the fault location and by

k3

L

Ik

OVERVIEW OF SHORT-CIRCUIT CALCULATION

In a three-phase electrical network the following types of short-circuits can occur: − symmetrical three-phase short-circuit (k3); − phase-to-phase short-circuit clear of earth (k2); − phase-to-phase-to-earth short-circuit (k2E); − phase-to-earth short circuit (k1).

(1)

B

F L

cUn

Un ZL

F

3

B

ZT

T

G

DG 3~

N :1 MV r LV G ZDG F Ik

Zk

Ik

Fig. 2. Contribution to the fault in distribution network of a DG station [9], [10].

For a three-phase fault at the point F of the electrical network from figure 3, the initial symmetrical short-circuit current is given by: ''

Ik =

E cU n cU n = = Zk 3Z k 3 ( Z DG + Z T + Z L )

(2)

where Z DG is the equivalent impedance of DG calculated relative to the rated voltage U n at the fault location. For the impedance Z T a correction factor KT must be applied.

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III.

CALCULATION ALGORITHM OF SHORT-CIRCUIT CURRENTS IN DISTRIBUTION NETWORKS WITH GD

A. Basic principle of algorithm In an arborescent network, all branches can be approached using a simple algorithm, starting from any bus taken as reference. For the network from figure 3, all branches are approached starting from bus n0 . Relative to the reference bus n0 , the branches can be approached in two directions: − forward, from the reference bus n0 towards the terminal busses ( n4 , n5 , n6 and n7 );

−

backward, from the terminal busses towards the reference bus.

3 n2 1 n0

5

2 n1

7 8

14

n4 4 n5 n6

6 9 10

13 n3

11 12

n7

Fig. 3. Approaching the network busses.

Since no loop exists in arborescent network, when a shortcircuit occurs, the network can be separated into two areas (fig. 4): − upstream area, situated between the supplying bus and the fault point; for this area, the contribution of the short-circuit current is from the supply bus and eventually from the DGs; − one or more downstream areas, situated between the fault point and the end points; for these areas, the contribution of the short-circuit current is exclusively from the DGs.

upstream area

downstream area 1

Ik DG up SI

kS

Ik up

By successive network reduction with respect to the fault location, the equivalent impedance Z k is obtained, which is used to determine the current at the short-circuit location: ''

Ik =

E c ⋅Un = Zk 3Z k ''

Starting from the current I k , one can calculate the shortcircuit currents flowing through branches and the contribution of the distributed generators and the main source to the sortcircuit. The calculation procedure presented above is applied for each network area (upstream and downstream). The fault point can be taken as the reference for approaching the network on the calculation procedure of the short-circuit current. The calculation procedure consists into two steps: − the backward sweep, in which, approaching the network from the generator busses as well as from the supply bus towards the fault point, the equivalent impedances between these busses and the neutral point are calculated; − the forward sweep, in which, approaching the network in opposite direction, from the fault point, for which the short-circuit current was calculated, towards the generator busses, as well as towards the supply bus, the currents through the network branches are calculated. The equivalent impedances between the source busses and the neutral bus are determined using simple transfiguration procedures of the series and parallel elements. In order to determine the calculation expression for the two steps, let us consider the arborescent network from figure 5, in which a short-circuit occurring at the bus n is assumed. The impedances Z 1 , Z 2 , ..., Z n represents the impedances of the network branches of the equivalent network.

p1

Ik DG down 1

1

pi

2

Ik down 1 F

Ik down 2

(3)

q

k3 n

r

pm

Ik DG down 2

a)

p1

downstream area 2

Z1

Fig. 4. Areas of an arborescent network with respect to the fault point.

In order to calculate the short-circuit currents using the equivalent voltage source method, the load current is neglected, the DGs and the supply source are replaced by equivalent impedances, while a voltage source E is introduced at the fault location, which is defined in the positive sequence network only.

818

1

Z2

Zq i

2 pi pm

Zq1 q Zq m b)

Zr

r

Zn

n E N

Fig. 5. Arborescent network: a) one-line diagram; b) equivalent diagram for calculating the three-phase short-circuit current.

In the backward stage, in order to determine the equivalent impedance Z k , the network section between bus 1 and the fault bus n is successively reduced thus resulting the equivalent impedances Z k1 , Z k 2 , ..., Z kn between all busses and fault bus n. Figure 6 illustrates the reduced equivalent diagram between busses p and r used to determine the equivalent impedances Z k q and Z k r of these busses with respect to the neutral bus N. p1 Ik q1 Zk q1 I Zk qi q pi k q i

pm

Ik qm

q Ik r

principles illustrated in figure 6,b, the short-circuit current through the bus q equivalent impedance Z k q is: ''

Zr

r

In order to determine the short-circuit currents through the branches situated upstream the bus q (fig. 6, a) the current divider rule is applied:

N q Ik r Zk r

''

Ikq =

Vr

Vr N

b)

c)

The equivalent impedance Z k q is determined based on the fact that the bus q is a separation bus to which m branches are connected upstream, with the following equivalent impedances with respect to the neutral bus N: Z k q1 , Z k q2 , ..., Z k qm (fig. 6, a). Since the points p1, p2, ..., pm are linked to

the neutral point N, all m branches are connected in parallel, and the equivalent impedance is: (4)

In order to determine the equivalent impedance Z k r one can start from the fact that on the upstream side the bus r is connected with bus q only (fig. 6, b), so that the equivalent impedance is: Zkr = Zkq + Zr

(5)

In the forward sweep, using the relationship (3) one can '' calculate the short-circuit current I k at the fault location. The equivalent impedance

Zk

Z k qi

''

I k q , i = 1, 2,..., m

(7)

'' k qi

=

Zkq V pi − V q Z k qi

=

E −V q

=

Zkq E −V q Z k qi

(8) , i = 1, 2,...m

in which the bus q potential have to be calculated in terms of '' the bus r potential, that is V q = V r + Z r ⋅ I k r .

N

Fig. 6. Reducing the equivalent diagram with respect to busses q and r: a) the initial diagram; b) the reduced diagram with respect to bus q; c) the reduced diagram with respect to bus r.

m 1 1 =∑ Z k q i =1 Z k qi

Zkq

V p −V q

r I

Vq

(6)

The currents through the equivalent impedances can be calculated also by applying the Ohm’s low at the branches terminals. In this way, for the situation presented in figure 6, the following equations are successively applied:

Vr

r

''

Ikq = Ikr

''

Zk q m Vq

Zr

''

I k qi =

a) p Ik q Zk q

''

..., I k 2 , I k 1 are successively calculated. Based on the

is equal to the equivalent

impedance Z k n of the bus n obtained the end of the backward ''

sweep. Using the short-circuit current I k at the fault location, ''

the currents through the branches from bus n to bus 1, I k n ,

By employing this calculation procedure, one can start from the fault bus potential V n = 0 (considering a metallic short-circuit). B. Calculation algorithm Following the calculus principle presented above, the algorithm for calculating the short-circuit currents is based on the proposed steps: 1. Establish the fault bus and upstream and downstream areas with respect to this point; 2. For each area (upstream and downstream) we should follow steps 3-7; 3. Arranging the network elements (establishing the previous node and the previous branch for each node); 4. Remove branches through which short-circuit currents are not passing; 5. Backward sweep: going from the generator busses as well as from the supply bus towards the fault bus and doing the next operations: 5.1. Calculation of the equivalent impedance of de upstream side of the bus q, given by the formula (4); 5.2. Calculation of the equivalent impedance of de upstream side of the bus r, given by the formula (5); 6. Short-circuit current calculation to the fault point, given by the formula (3); 7. Forward sweep, the calculation of the currents through the network branches, going from the fault point towards the generator busses, as well as towards the supply bus: 7.1. In order to determine the short-circuit currents through the branches situated upstream the bus q the current divider rule is applied, given by the formula (7);

819

Zk1

7.2. The currents through the equivalent impedances can be calculated also by applying the Ohm’s low at the branches terminals, given by the formula (8); 8. Calculation of total short-circuit current at the fault location. IV.

0

Zk2

Z0-1 Ik1 1

Ik S

CASE STUDY

ZkS

Ik DG20

Ik DG23

Zk1’

Zk2’

Zk down 8

22

DGs transformers

18 19 20 21 Fig. 7. IEEE 33-bus distribution network system with 5 DGs.

Assuming a short-circuit occurring at bus 8, the equivalent diagram is as shown in figure 8 and the reduced equivalent diagram is as shown in figure 9. Z5-8

Ik DG20

Ik DG23

Ik DG29 Ik up

ZS

Z1-20

Z2-23

Z5-29

ZDG20

23 ZDG23

Z8-11 11 Z11-15 15

8

Ik S

20

Ik down

Ik

29

Ik DG11

Ik DG15

ZDG11

ZDG15

Z DG = K G ⋅ Z G ⋅ N r2 + KT ⋅ Z T ⎫ ⎪ U nMV 20 ⎬ ⇒ Z DG = (15.632 + j101.185 ) Ω Nr = = = 28.99 ⎪ U nLV 0.69 ⎭

E

ZDG29

2 ΔPk ⋅ U nMV 10 ⋅ 202 = =4Ω 2 10002 SnT

DGs equivalent impedance (generator and transformer)

Network impedances

N Fig. 8. Equivalent diagram for short-circuit calculation.

The equations solved according to the above-presented procedure for short-circuit currents calculation are presented as follows. i) Impedances calculation Network feeder ⎫ c ⋅ U n2 1.1 ⋅ 202 = = 0.88 Ω ⎪ S kS 500 ⎬ ⇒ Z kS = ( 0.8756 + j 0.0876 ) Ω ⎪ X kS = 0.1 ⎭

Z 0−1 = ( 0.0922 + j 0.047 ) Ω Z 2−5 = (1.5661 + j 01.0875 ) Ω Z 8−11 = (1.615 + j 0.9288 ) Ω Z 1−20 = ( 2.0777 + j1.9903) Ω Z 5−29 = ( 2.8579 + j 2.1409 ) Ω

Z 1− 2 = ( 0.493 + j 0.2511) Ω Z 5−8 = (1.9286 + j 01.5939 ) Ω Z 11−15 = ( 3.3469 + j 2.9389 ) Ω Z 2−23 = (1.3492 + j1.0174 ) Ω

DGs branch impedances

Z kS = RkS

⎫ ⎪ ⎪ ⎬ ⇒ Z T = ( 4 + j 23.6643) Ω 2 uk U nMV 6 202 3 10 = 24 Ω ⎪ ZT = = ⎪ 100 SnT 100 1000 ⎭ 0.95 ⋅ cmax 0.95 ⋅ 1.1 KT = = = 1.009178 1 + 0.06 ⋅ xT 1 + 0.06 ⋅ 0.05916 RT =

Z2-5 5

Zk11

b)

2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17

Z1-2 2

E

Fig. 9. Reduced equivalent diagram for short-circuit calculation: a) upstream area; b) downstream area.

k3

Z0-1 1

Zk5’

8

Ik DG15 Zk15’

Zk11’

26 27 28 29 30 31 32

0 1

0

Ik DG11

25 23 24

a)

Ik DG29

Ik down Z8-11 11 Ik11 Z11-15 15

E

supply bus is SkS = 500 MVA .

Zk up

Z2-5 Ik5 5 Z5-8 Ik up

Z1-2 Ik2 2

The numerical calculation was performed on the IEEE 33bus network [16], that operated at 20 kV (fig. 7). Assumes that distributed generators are connected to busses 11, 15, 20, 23 and 29, having the parameters: SnG = 950 kVA , U nG = 0.69 kV , cos ϕ nG = 0.9 , xd" = 18 % and R G X G = 0.15 . The rated parameters of the transformers: SnT =1000 kVA, UnMV = 20 kV, UnLV = 0.69 kV, ΔPk = 10 kW and uk = 6 % . The short-circuit power at the

Zk5

Z k1' = Z DG + Z 1−20 = (17.7099 + j103.175) Ω

Z k 2 ' = Z DG + Z 2−23 = (16.9814 + j102.2021) Ω

DGs generators

Z k 5' = Z DG + Z 5− 29 = (18.4901 + j103.3256 ) Ω

⎫ x" U 2 18 0.692 3 10 = 0.0902 Ω ⎪ X G = d nG = 100 SnG 100 950 ⎬ ⇒ Z G = ( 0.0902 + j 0.0135) Ω ⎪ RG X G = 0.15 ⎭ cmax 1.1 KG = = = 1.019973 1 + xd" sin ϕnG 1 + 0.18 ⋅ sin(acos(0.9))

Z k11' = Z DG = (15.6322 + j101.1847 ) Ω

Z k15' = Z DG = (15.6322 + j101.1847 ) Ω

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efficient, because it does not involve a great computational effort. It is not necessary to calculate the nodal admittance matrix and its inverse. The proposed algorithm can be implemented in software program, which will be used for studying integration of distributed generators into distribution networks. The case study for algorithm application is based on IEEE 33-bus distribution network, with 5 DGs. The algorithm can be used for any type of short-circuit, by considering the corresponding symmetrical sequence schemes.

ii) Forward sweep (impedance calculation) Upstream area Z k1 = Z kS + Z 0−1 = ( 0.1798 + j 0.9226 ) Ω Z k 1 ⋅ Z k 1' = ( 0.671 + j1.1656 ) Ω Z k 1 + Z k1' Z ⋅Z Z k 5 = Z 2−5 + k 2 k 2' = ( 2.2238 + j 2.2420 ) Ω Z k 2 + Z k 2' Z ⋅Z Z k 8 up = Z 5−8 + k 5 k 5' = (1.037 + j1.352 ) Ω Z k 5 + Z k 5' Downstream area Z k 2 = Z 1−2 +

ACKNOWLEDGMENT The work has been funded by the Sectorial Operational Programme Human Resources Development 2007-2013 of the Ministry of European Funds through the Financial Agreement POSDRU/159/1.5/S/132397.

Z k11 = Z DG + Z 11−15 = (18.9791 + j104.1236 ) Ω Z k 11 ⋅ Z k 11' = (10.244 + j 52.255 ) Ω Z k 11 + Z k 11'

Z k 8 down = Z 8−11 +

REFERENCES

iii) Backward sweep (short-circuit currents calculation) Upstream area

[1]

c ⋅U n = (1.66 − j1.561) kA 3 Z k 8 up

''

I k up =

[2]

Z k 5' = (1.645 − j1.495 ) kA Z k 5 + Z k 5' Z k5 '' '' = ( 0.015 − j 0.065 ) kA I kDG 29 = I k up Z k 5 + Z k 5' Z k 2' '' '' = (1.632 − j1.47 ) kA I k 2 = I k5 Z k 2 + Z k 2' Z k2 '' '' = ( 0.013 − j 0.025) kA I kDG 23 = I k 5 Z k 2 + Z k 2' Z k 1' '' '' I k1 = I k 2 = (1.618 − j1.457 ) kA Z k 1 + Z k 1' ''

''

I k 5 = I k up

''

''

I kDG 20 = I k 2

[3] [4] [5] [6] [7]

[8]

Z k1 = ( 0.014 − j 0.013) kA Z k1 + Z k 1'

Downstream area

[9]

c ⋅U n = ( 0.046 − j 0.234 ) kA 3 Z k 8 down

''

I k down = ''

''

''

''

''

I kDG11 = I k 2 = I k down I kDG15 = I k down

[10]

Z k11' = ( 0.024 − j 0.115 ) kA Z k 11 + Z k 11'

[11]

Z k 11 = ( 0.024 − j 0.115 ) kA Z k 11 + Z k 11'

[12] [13]

iv) Short-circuit current at the fault location I k = I k up + I k down = (1.706 − j1.795 ) kA ''

''

''

[14]

I k'' = 2.476 kA

V.

[15]

CONCLUSIONS

The paper presents an original algorithm for calculating the short-circuit currents in arborescent distribution networks whit distributed generators. This new algorithm is simple and

[16]

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