Effective two-terminal numerical algorithm for overhead ... - Springer Link

Electr Eng (2007) 89: 425–432 DOI 10.1007/s00202-006-0014-6

O R I G I NA L PA P E R

Zoran Radojevi´c · Vladimir Terzija

Effective two-terminal numerical algorithm for overhead lines protection

Received: 14 October 2005 / Accepted: 26 November 2005 / Published online: 23 March 2006 © Springer-Verlag 2006

Abstract In the paper an effective numerical algorithm for overhead lines protection, particularly fault location and adaptive autoreclosure, is presented. It is based on the two terminal line currents and voltages acquisition. For this purposes the synchronized sampling of all analogue input variables, i.e. the application of the Global Position System/Phasor Measurement Units, was assumed. The algorithm presented is derived in the spectral domain. By this the set of third harmonics variables and line parameters was also used. The prerequisite for successfully adaptive autoreclosure functionality realization was the suitable modelling of the electrical arc. Arc was considered as a source of higher harmonics, distorting by this other electrical variables. In the arc modelling, results of laboratory testing were used. Algorithm is tested for a typical network configuration, assuming by this that the line considered was short enough to neglect its capacitive nature. Based on the results obtained, it is very realistic that the algorithm presented could be implemented in praxis in modern Intelligent Electronic Devices (IEDs). Keywords Fault location · Electrical arc · Protection · Transmission lines · Spectral analysis · Synchronized phasors 1 Introduction In today’s competitive market, manufacturers and utilities are trying to maximize the benefit of existing technology while continually exploring new ways to implement advanced technologies and algorithms into products. Z. Radojevi´c (B) Department of Electrical Engineering Konkuk University, Seoul, Korea E-mail: [email protected] Tel.: +82-2-4503752 Fax.: +82-2-4479186 V. Terzija ABB AG, ABB/PTPM-AS, Oberhausener Str. 33, 40472 Ratingen, Germany E-mail: [email protected]

Determination of fault location on overhead lines is extremely important to utilities to aid in fast fault analysis and power restoration to improve the quality of power delivery. Various fault location methods with sufficient accuracy for most practical applications have been developed using one-terminal information (voltages and currents measured and processed by the installed protective device at one line terminal, only). A major advantage by this is that communications between line terminals are not needed. The microprocessor/multiprocessor fault locators and digital devices with the fault location algorithms using local data have been marketed in early 1980s. Since in the previous 20 years the use of communications and digital technology have been continued to expand, the integration of power system functions in existing applications dramatically increased. When communication channels are available, or when the synchronized phasor measurement is available (e.g. phasor synchronization over the Global Positioning System and dedicated Fieldbus technology, i.e. application of communication protocols), the two terminal fault location methods may be used following the disturbance. The pure post-fault off-line analysis technique does not require high-speed communications link so that the advantages of modern microprocessor and communication technology is not essential here. Compared to one-terminal techniques, the two-terminal techniques offer improved fault location estimation without assumptions and without information concerning the external network such as source impedances. In addition, fault resistance here does not influence fault location determination, so in this sense faults must not me classified into two main categories: (a) high and (b) low resistance faults. However, the post-fault on-line analysis requires fast links between two line terminals, so the use of modern communication technology is the prerequisite for the successful protection. Some selected papers in the field of line protection are listed as [1–9]. Takagi et al. [1] use current and voltage phasors from one terminal for their method based on reactive power. Girgis et al. [2], Abe et al. [3], Jiang et al. [4] and Gopalakrishnan et al. [5] use voltage and current phasors from both ends. References [2] and [3] also show techniques

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to remove synchronization errors. Reference [2] uses threephase analysis and uses a least square estimate to obtain the fault point distance by solving six equations. Reference [3] presents a reactive power based method and extends it to a multiterminal single transmission line. Reference [4] derives a fault-location index from a phasor model based on transmission line equations. Reference [5] adopts a time domain model of a transmission line for development of their algorithm. Djuri´c et al. [6,9] present numerical algorithms in phasor and time domain utilizing pre-fault and post-fault current samples from one end of the line. Tawfik et al. [7] use Prony method to convert time domain samples to frequency domain and then use artificial neural network to estimate the fault location. The global positioning system (GPS) is a system with ability to provide time synchronization to a ±1 µs accuracy over a wide area as covered by a power system network. Some modern techniques for fault location/detection using the GPS are presented in [10–13]. Modern digital relays, today called intelligent electronic devices (IED) and manufactured as multiprocessor architectures, use various communication protocols for vertical and horizontal communication. Among various protocols used, the following are recognized as the mostly used: SPABUS, PROFIBUS, LON, MODBUS, IEC 608705-103 [14]. All of these protocols do not support the time synchronization of IEDs and have a serious drawback that they are not offering a full compatibility between IEDs manufactured by different manufacturers (e.g. ABB, Siemens, Areva, SEL etc.). That was the reason for development of a new communication protocol IEC 61850 [15] which should bring the compatibility between aforementioned IEDs. In addition, this protocol provides the time synchronization with accuracy of 1 µs. In this paper authors present a new effective numerical algorithm for fault location calculation and for the blocking of unsuccessful autoreclosing. It uses synchronized phasors, measured by e.g. phasor measuring units (PMUs) installed at both line terminals. In order to determine the fault nature (permanent, or transient fault), the information of the arc voltage, existing at the fault location, is obtained and evaluated. For these purposes the arc is mathematically modelled, based on a great number of arc voltage records obtained by transient recorder [16]. The calculated arc voltage amplitude was used as an input for making a decision whether the fault is permanent or transient one, similar like in [17]. The algorithm uses a classical discrete Fourier transformation (DFT) for phasor calculation. In other words, the algorithm is derived in spectral domain, using voltage/current phasors synchronously sampled on both line terminals.

Z. Radojevi´c and V. Terzija

around the earth. Since a GPS receiver provides time synchronization with the ±1 µs accuracy, the PMUs using GPS-synchronization in power system can be successfully applied for the fault location and protection of overhead lines. The GPS is used to synchronize the clocks of the measuring devices, sampling voltages and currents at line terminals. In Fig. 1 two synchronized measuring devices (IED) at each end of the transmission line are presented. In Fig. 1 the IEDs constantly acquire voltage and current data from PT and CT at each end of the line. The voltage and current data collected from the IEDs are forwarded to a central control computer in which the processing of simultaneously sampled voltages and currents can be carried out. As an alternative, the IEDs can communicate between each other and exchange simultaneously obtained variables to be processed. In other words, by this is opened the way for successfully realization of a two terminal overhead line protection numerical algorithm. Both IEDs are processing data sampled on both line terminals. If faulty conditions are detected, the numerical algorithm for fault location is being started. Based on the fault nature, autoreclosing is being blocked, or released.

2.2 Characteristics of a long electric arc The long electric arc in free air is a plasma discharge and has nonlinear nature. Nonlinear characteristics of an arcing fault on transmission line cause distortions in voltage and current waveforms at the each end of the transmission line. That means that an arc, as a source of higher harmonics, distorted other electrical variables (voltages and currents) and offered us the possibility to develop sophisticated numerical algorithms using information about these distortions. Simply formulated, harmonics detected in voltages and currents measured at line terminals can be used in determining if a fault is transient, or permanent one. If the fault is transient, autoreclosure should operate. Contrary, if the fault is permanent, autoreclosure must be blocked. Otherwise, the

satelite busbar 1

busbar 2 CT 2

CT 1

CB 2

CB 1

PT 1

PT 2 IED 2

IED 1

2 The new algorithm 2.1 Synchronized sampling technique The GPS is a space-based positioning, navigation, and timing system, consisted of 24 satellites that constantly revolve

receiver Fig. 1 Synchronized sampling arrangement. CT Current transformer, PT Potential transformer, CB Circuit breaker, IED Intelligent electronic device

Effective two-terminal numerical algorithm for overhead lines protection

autoreclosure should cause unnecessary reclosure onto a permanent fault, what could have serious consequences (e.g. damages on expensive equipment, power system stability problems, or chain reaction which could bring a power system to dangerous brown/blackout conditions and unexpected losses). That is why an approach of blocking unnecessary autoreclosure is extremely important from the praxis point of view. The starting point for analysing arcing faults presents the suitable modelling of an electric arc. In the problem solved the subject of the investigation is the so called “long arc in free air”, which should not be treated as a short electric arc existing in switching devices, like circuit breaker. In [18] the arc voltage was modelled by a nonlinear arc resistance. In [19] the arc is modelled by the piecewise arc voltage–current characteristics. A typical arc voltage wave form can be approximated as a rectangular waveform, as shown in Fig. 2 [16,20]. The arc voltage wave form from Fig. 2 gives a normalized single cycle of a real arc wave form with arc voltage amplitude Va =1.0 p.u. The arc voltage wave form from Fig. 2 can be mathematically modelled by the Fourier series containing the odd sine components only, and the coefficients (k h ) of the h-th harmonic, obtained using the DFT, as shown in Table 1. Following the Table 1, one obtains the following model for arc voltage: va (t) =

∞


∞


vah (t) =

h=1,3,5,.

k h Va sin(hωt),

(1)

h=1,3,5,.

where h=1, 3, 5, 7, . . . is the odd harmonic order, vah (t) is the h-th harmonic of arc voltage (in the time domain), Va is a scalar value of arc voltage amplitude, ω is the fundamental radian frequency and k h is the coefficient of the h-th harmonic. Both the arc voltage wave form and the arc voltage model (Eq. 1) are the proof that an arc can be considered as 1.5

arc voltgae (p.u).

1.0

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a source of higher harmonics being spread over the power system and causing the distortions in neighbouring electrical variables. The advantage of the arc voltage presentation through the sequence of numerical values is its simplicity and flexibility. Up to the concrete application and the application analyzed, one can create various wave form shapes and calculate the corresponding coefficients k h . For example, in [9,17,20] it was assumed that an electrical arc can be assumed to be a pure rectangular wave form, so another set of coefficients k h are used in the numerical algorithms presented. By this, in [9,17, 20] an analytical expression for coefficients k h was derived and successfully applied. Theoretically, this approach could be also implemented in the algorithm presented in the next paragraph of this paper. 2.3 Derivation of the arcing fault location algorithm Faults on overhead lines can be divided into two groups. Approximately about 70–90% of faults on overhead lines are transient faults and the remaining 10–30% of faults are permanent (metallic) faults. In this paper, the most frequent single line to ground arcing fault on transmission line will be analysed. In Fig. 3 the representation of a single line to ground arcing fault in spectrum domain is shown [20]. The introduction of higher harmonics modelled the nonlinear arc nature, as discussed in previous paragraph. Arcing fault from Fig. 3 is represented as a serial connection of an arc voltage and a fault resistance R F . Thus, from Fig. 3 the h-th harmonic of the fault voltage can be expressed as follows: V Fh = V ah + RF I Fh ,

(2) I Fh

V ah

is the h-th harmonic of the arc voltage and is where the h-th harmonic of the fault current. Let us assume an a-phase single line to ground arcing fault on a transmission lines at l distance away from the left line terminal, as presented in Fig. 4. Under the assumption that the line is a short one (e.g. lines at HV/MV level up to 100 km), the shunt capacitance and the shunt conductance of the transmission line can be neglected. In Fig. 4 all variables

Va

0.5

fault location

0.0

F -0.5 h

IF

-1.0

+

-1.5 0

5

10

15

V ah

20

time (ms)

arc

Fig. 2 A typical arc voltage wave form

RF Table 1 Harmonic coefficients

kh

h

1

3

5

7

kh

1.23

0.393

0.213

0.135

Fig. 3 Single line to ground arcing fault

V hF

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Z. Radojevi´c and V. Terzija

D D-l

l

sending end

receiving end

transmissi on line

c b a

F

I hF

I Sh

I hR

+

V Sh

V ah

arc

V hF

V hR

RF

Fig. 4 Single line to ground arcing fault

have radian frequency multiplied by the harmonics order h and all line parameters are calculated in term of (hω). The fault location is denoted by F and the fault distance by l . In Fig. 4 index h denotes the order of harmonic, D is line length, subscript S and R denote the sending and receiving end of the line, respectively. By using the well known methodology of symmetrical components (positive, negative and zero sequence symmetrical components), the unsymmetrical three phase circuit from Fig. 4 can be represented by three single-phase equivalent circuits [positive (p), negative (n), and zero (0) sequence circuits, respectively], as shown in Fig. 5. For the circuit depicted in Fig. 5 the following equations hold: V Sh p = z h I Sh p + V Fh p , (3) V Sh n = z h I Sh n + V Fh n ,

(4)

z 0h I Sh 0

(5)

V Sh 0

=

S

V Shp

+

z hl

V Fh 0 ,

F

V hFp

h

I Sp

z hl

1 h IF 3

R

z h ( D − l) I hR p

V hR p +

z h ( D − l)

V ah V Shn

I Shn

V hFn h z 0l

h

V S0

I Sh0

I hR n

V hR n

3RF

h z 0 ( D − l)

V hF0

I hR 0

V hR 0

Fig. 5 Equivalent sequence network connection of faulted lines

h h VR = z h (D − )I R + V Fh p , p p

(6)

h h = z h (D − )I R + V Fh n , VR n n

(7)

h h = z 0h (D − )I R + V Fh 0 , VR 0 0

(8)

where h the h-th harmonic of positive-, negative-, V Sh p, n, 0 , V R p, n, 0 and zero sequence phase voltage at both ends of the lines; h I Sh p, n, 0 , I R the h-th harmonic of positive-, negative-, p, n, 0 and zero sequence phase current at both ends of the lines; h V Fp, n, 0 the h-th harmonic of positive-, negative-, and zero sequence faulted phase voltage at the fault point; positive- or negative sequence line zh impedances for the h-th harmonic, are zero sequence line impedances for the z 0h h-th harmonic. By adding the above six equations, and by using the following basic symmetrical component equations: V Sh = V Sh p + V Sh n + V Sh 0

(9)

I Sh = I Sh p + I Sh n + I Sh 0

(10)

h h h h = VR + VR + VR VR p n 0

(11)

h h h h = IR + IR + IR IR p n 0

(12)

V Fh = V Fh p + V Fh n + V Fh 0

(13)

the h-th harmonic of phase voltage of sending and receiving end can be expressed as follows: h)

V Sh = z h (I Sh + k zh I S0 ) + V Fh ,

(14)

h) h h = z h (I R + k zh I R )(D − ) + V Fh) , VR 0

(15)

z 0h −z h zh

is the zero sequence compensation factor, where k zh = which depends on line parameters and which can be calculated in advance. Equations (14) and (15), written for the first harmonics, becomes the following forms: V 1S = z 1 (I 1S + k 1z I 1S0 ) + V 1F ,

(16)

V 1R = z 1 (I 1R + k 1z I 1R0 )(D − ) + V 1F .

(17)

Equations (16) and (17) represent a system of two equations with two unknowns: the fault distance and fault voltage. By subtracting Eq. (17) from Eq. (16), the following equation with unknown fault distance can be obtained: V 1S − V 1R = z 1 (I 1S + k 1z I 1S0 ) − z 1 (I 1R + k 1z I 1R0 )(D − ). (18)

Effective two-terminal numerical algorithm for overhead lines protection

The fault distance l from Eq. (18) can be now calculated as follows: =

V 1S − V 1R + z 1 (I 1R + k 1z I 1R0 )D z 1 [I 1S + I 1R + k 1z (I 1S0 + I 1R0 )]

.

(19)

Equation (19) is the explicit fault location expression for the short three-phase transmission line. In the next step, a formula for the unknown arc voltage amplitude is derived. For this calculation the third harmonics must be used, because the equations of the first harmonics are not sufficient to obtain the explicit expression for the arc voltage amplitude. Firstly, the fault distance (Eq. 19) can be incorporated into the following formula for the third harmonics: V 3S = z 3 (I 3S + k 3z I 3S0 ) + V 3F .

(20)

In Eq. (20) only the fault voltage is unknown, so it can be expressed as follows: V 3F = V 3S − z 3 (I 3S + k 3z I 3S0 ).

(21)

The third harmonic of the fault voltage can be expressed (see Eq. 2) as: V 3F = V 3a + RF I 3F .

(22)

At the same time the third harmonic of the arc voltage is given as: V 3a = k 3 Va ,

(23)

where k 3 is the suitable third harmonics coefficient. By this, the following holds: k3 = k3 3 ϕ1,

(24)

ϕ1

is the phase angle of the fundamental harmonic where of the arc voltage. Arc voltage and arc (fault) current are in phase, so that ϕ 1 = arg{I 1F }.

(25)

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As discussed in previous paragraphs, the calculated arc voltage amplitude is used to determine the fault nature. A fault is considered as an arcing transient fault if the calculated value of the arc voltage amplitude is greater than the in advance determined minimal arc voltage amplitude. The minimal arc voltage amplitude is determined as a product of the arc voltage gradient and the length of the arc path, which is equal to the length of a suspension insulator string [17]. The average arc voltage gradient lies between 12 and 15 V/cm [21].

3 Computer simulated tests The Electromagnetic transient program [22] is used to test the validity of the proposed algorithm. The schematic diagram of a 400 kV power system is shown in Fig. 6. By this, the shunt capacitance and conductance of the line are neglected. In Fig. 6 v S,R(t) and I S,R(t) denote the measured voltages and currents, whereas D=100 km, r =0.0325 /km, x=0.3 /km, r0 =0.0975 /km, and x0 =0.9 /km present line parameters. In Table 2 the network parameters are presented. By this, the equivalent electromotive force of networks A and B were E A =416 kV and E B =400 kV, respectively. Single line to ground arcing faults are simulated at different locations of the transmission line. The pre-fault load was also taken into account during simulation. It is assumed that all phasors are ideally synchronized (synchronization error equal to 0 ◦ ). Figures 7, 8, 9 and 10 show the faulted phase voltages and currents at both ends of the transmission line, sampled with the sampling frequency of f s =3, 840 HZ (64 sample/T0 ). It is obvious that all curves correspond to the single line to ground fault. The fault was simulated at the 10th km, observed from the left line terminal. In the simulation the arc voltage wave form and amplitude are assumed to be of square wave form, with typical arc

The fault current is not measurable, but it can be calculated based on the measurements on both line ends as follows: I 1F = I 1S + I 1R .

(26)

From Eqs. (21) and (22) one obtains the following equation: k Va + 3

I 3F RF

=

V 3F

Re{k 3 } Va + Re{I 3F } RF = Re{V 3F }

(28)

Im{k 3 } Va + Im{I 3F } RF = Im{V 3F }.

(29)

From Eqs. (28) and (29) the following explicit equation for the arc voltage amplitude can be derived: Re{V 3F } × Im{I 3F } − Im{V 3F } × Re{I 3F } Re{k 3 } × Im{I 3F } − Im{k 3 } × Re{I 3F }

l

.

(30)

D−l F

network A

(27)

which can be separated into two equations (real and imaginary equation):

Va =

D

iF (t )

is (t )

va (t )

vs (t )

network B iR (t )

arc

vF (t )

vR (t )

RF

Fig. 6 Single line diagram of the simulated test power system Table 2 Network parameters

Network A Network B

R []

L [H]

R0 []

L 0 [H]

1 0.5

0.064 0.032

2 1

0.128 0.064

430

Z. Radojevi´c and V. Terzija

vS, b

15

vS, c

250 0 -250

0

20

40

60

80

5 0 -5

time (ms)

vR, b

vR, c

10

iF(t)

250 0 -250 -500 0

20

40

60

80

60

20

va(t) 10

0

0

-5

-10

40

60

80

100

12

12

l

5

iSb

-10 20

40

60

80

100

time (ms) Fig. 9 Faulted phase currents at the line sending end (S)

ignition wave form deformations and with the amplitude of Va =4.5 (kV), as shown in Fig. 11. The fault inception was 33 ms and the fault resistance was RF =8 . In Fig. 12 the calculated fault location and arc voltage amplitude are presented. It is obvious that accurate values are obtained. From the calculated arc voltage amplitude it can be concluded that the fault is the transient one, so the autoreclosure should be released. In the next test the algorithm sensitivity to the possible synchronization error is investigated. An extremely high error of 1 millisecond was assumed. Fig. 13. It is obvious that large synchronization errors cannot be tolerated, particularly from the fault location calculation point of view. It can be concluded, that the calculation of arc voltage amplitude is less sensitive to the synchronization error. In order to investigate the sensitivity, synchronization error was

arc voltage (kV)

10

0

0

-20 120

time (ms)

10

-15

100

Fig. 11 Arc voltage and fault current

iSc

iSa

-5

80

5

-10 20

Fig. 8 Faulted phase voltages at the line receiving end (R) 15

40

100

time (ms)

phase currents (kA)

20

Fig. 10 Faulted phase currents at the line receiving end (R)

arc voltage (kV)

phase voltages (kV)

vR, a

0

time (ms)

Fig. 7 Faulted phase voltages at the line sending end (S) 500

iRb

-10 -15

100

iRa

fault current (kA)

-500

iRc

10

8

10 8

6

Va

6

4

4

2

2

0 20

40

60

80

fault distance (km)

vS, a

phase currents (kA)

phase voltages (kV)

500

0 100 120 140 160

time (ms) Fig. 12 Estimated fault location (exact value used by EMTP was 10 km), and arc voltage amplitude (exact value used by EMTP was 4.5 kV)

changed from 0 to 1 ms, being selected from the following set of synchronization errors (ms): 0, 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875, 1. In Fig. 14 the corresponding results are presented. It is obvious that the calculation errors are being increased with the increased synchronization error. In Fig. 15 results of the algorithm sensitivity to the synchronization errors are clearly presented. As concluded, the fault location is more sensitive, whereas the arc voltage amplitude errors could be even tolerated. From the praxis point of view, determination of the arc voltage is not sensitive to synchronizing errors. That means that independently on the fault

Effective two-terminal numerical algorithm for overhead lines protection

20

l

15

15

10

10

Va 5

5

0 20

40

60

80

fault distance (km)

arc voltage (kV)

20

0 100 120 140 160

time (ms) Fig. 13 Estimated fault location (exact value used by EMTP was 10 km), and arc voltage amplitude (exact value used by EMTP was 4.5 kV) 20

l

15

15

10

10

5

5

fault distance (km)

arc voltage (kV)

20

Va 0 20

40

60

80

0 100 120 140 160

time (ms) Fig. 14 Results obtained for synchronization error changed in the range of 0–1 ms

relative error

0.8

0.6

a) 0.4

0.2

0.0 0.0

b) 0.2

0.4

0.6

0.8

1.0

synchronization error (ms)

Fig. 15 Relative errors versus synchronization errors a fault location, and b arc voltage

location the presented concept of adaptive autoreclosure is insensitive to these errors, as well. This is an important algorithm feature. 4 Conclusions In the paper a new efficient numerical algorithm for overhead lines protection is presented. Through the realistic modelling of the fault and by introducing a new model of the electrical

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arc, the fault location calculation accuracy was improved and the possibility of controlling the process of autoreclosure is achieved. Based on the calculated arc voltage, a way to block/release autoreclosure was determined. Algorithm is based on synchronized measured voltages and currents sampled at both line terminals and fast communication channels between two IEDs installed at line terminals. It uses higher harmonic of processed voltages and currents and for this purposes apply discrete Fourier transformation. Through algorithm testing for the most probable single line to ground arcing/metallic fault, proved that the algorithm could be implemented in today praxis. From one side, the novel communication protocols, like IEC 61850, provide synchronization error small enough to prevent algorithm errors caused by inaccurate synchronization. From other side, the opportunity to control autoreclosure by blocking it for permanent faults, open a more sophisticated functionality of modern IEDs improving by this power system stability, power quality and preventing the potential damage of expensive equipment. These goals are particularly important in deregulated power systems in which reliable system operation became extremely important, in order to reduce unexpected costs of system outages.

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Z. Radojevi´c and V. Terzija

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