Synchronous Сlosing During High-speed Transfer System Operation

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The MAIN JOURNAL for POWER GRID SPECIALISTS in RUSSIA


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44

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ection

Synchronous Сlosing 
During High-speed 
Transfer System Operation

O

ne of the requirements to 
high-speed transfer systems 
is busbar coupler (BC) clos-
ing when voltage vector on 

the intact busbar section and EMF vec-
tor of the generalized motor running 
down to the busbar section with power 
failure have a small phase difference 
(a range is up to 30° in [1]).

This requirement is valid since it al-

lows to minimize transient current when 
the busbar coupler is closed. However, 
non-zero time of BC closing (

T

ON

), ignor-

ing the rate of frequency change and 
methodical errors when determining 
angle and frequency in digital blocks can 
lead to a violation of this requirement.

Let’s consider the power loss mode 

on busbar section no.1 (BS1) to which 
the synchronous motor (SM) is connect-
ed. It is assumed that voltage magnitude 
and frequency are constant on the intact 
busbar section no. 2 (BS2) (Figure 1).

The equation of motion for the vol-

tage vector of busbar section 2 (BS2) is:

BS2

 = 

r

 · 

t

 + 

0 BS2

where 

BS2

 – current phase, rad; 

r

 – ra-

ted circular frequency (rotating speed), 
rad/s; 

0 BS2

 – initial phase, rad.

The motion law for BS 1 voltage 

vector depends on the law of motor 
rundown (see below). During power 
failure, the voltage on BS 1 is induced 
only by motor excitation 

fi

 eld. In this 

case, voltage frequency and phase are 
clearly associated with rotor spinning 
frequency and phase. In general, the 
motor rundown law is Newton's second 
law for spinning bodies:
 

d

2

 

— = 

M

 (1)

 

d

t

2

where 

J

 is inertia moment of rotating 

mass, kg·m

2

 – rotor rotation angle 

relative to the preselected 

fi

 xed  axis, 

rad; 

M

 – total moment of forces acting 

on the body, N·m.

When the equation (1) is integrated 

two times in the course of 

fi

 nding  the  

(

t

) dependence, two constants pre-

sent themselves, which are determined 
by the initial conditions: 

0

 – initial angle 

(the angle at the initial moment of time), 

rad; (

d

/

d

t

)

t

 = 0

 = 

0

 – 

initial rotating speed, 
rad/s.

In order to give the 

BC closing command, it 
is necessary to predict 
the angle at the time of 
breaker closing. For this 
prediction, it is essential 
to know the angle be-
tween voltages (

i

), the 

rotating speed (

i

) and 

the formula for 

M

-func-

tion (dependence/inde-
pendence of the total 

BB1

СB

Q

SM

VT BS 1

VT BS 2

BB2

Figure 1.

ВВ

 – air blast breaker;

СВ

 – bus section breaker;

SM – synchronous motor;

VT BS – VT of bus section


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45

47th CIGRE Session 

Special issue, August 2018

moment on other variables) at the moment of calculation 
(

i

-th moment of time).

Let’s analyze each of those parameters and estimate 

the closing angle error related to the inaccurate determi-
nation of the parameters.

FREQUENCY

Frequency calculation in protection relays is a non-trivial 
task and can be carried out in various ways [2, 3]. We 
assume here that the algorithm calculates frequency 
without error, but has an averaging window to improve 
result reliability (for example, the standard [4] requires 
frequency calculation for no longer than 60 ms).

As a result, when frequency varies linearly and fre-

quency values are averaged over the time 

T

AV

, the algo-

rithm gives an error equal to:

f

 = –

 

T

AV 

/

 

2 (2)

where 

 – rate of frequency change, Hz/s; 

T

AV

 – averag-

ing time, s.

According to the equation (2) above, in case of fre-

quency increase, the measured frequency will be under-
valued, and vice versa.

When estimating the angle of voltage vector rota-

tion during breaker closing time, the frequency error (2) 
gives an error in the angle equal to:



1

 = 2

 · 

f

 · 

T

ON

. (3)

Moreover, the real vector will describe an arc larger 

than the calculated one.

ANGLE

In order to analyze angle error, let us consider one of 
the most common methods of transition from sample 
values to vectors. This is separation of the main har-
monic by means of the Fourier series expansion:

 

t

C

 = 

 

jy

 · 

e

j

t

 

d

t

.

 

t

 – 

T

If input signal frequency differs from the frequency 

used to calculate the orthogonal components (and we 
have already identi

fi

 ed it is so, even if frequency adjust-

ment is taking place in the protection relay), then the 
function under the integral is:

 

y

 = 

· 

sin

[(

 + 



)

 

t

 + 

]. (4)

The Fourier calculation is performed for one period 

of the signal, therefore, linear frequency decrease is not 
taken into account in the formula (4).

We can expect that the vector will no longer be un-

moved, but will rotate with a difference frequency 



.

Subsequent to integration we obtain:

 1 

1

C

 = 

· 

sin



·   — 

e

j

(



t + 



– 

)

 – — 

e

j

((2

 + 



)

t

 + 



– 

))

 

 



2



where 

 = 

 



/

.

The assumption turned out to be true. The vector ac-

tually has a low-frequency component 



. However, in 

accordance with the amplitude-frequency response of 
discrete Fourier transformation, vector amplitude was 
changed (by 

sin

/

 times) and high-frequency compo-

nent 2

 + 



 was added. The end of the vector de-

scribes a hypocycloid.

It should be pointed that the vector on average al-

ways lags behind the "real" vector by an angle 

:



2

 = 

 



/

. (5)

Thus, when forecasting, the actual vector is already 

slightly "further" than protection relay calculates.

MOTOR RUNDOWN LAW

Motor rundown is described by the equation [5, 6, 7]:
 

d

ˆ

k

LF

 

— = – — [

m'

0

 + (1 – 

m'

0

) · 

ˆ

] (6)

 

d

t

 

j

where 

k

LF

 – motor load factor for active power; 

j

 – inertia 

constant of motor driving unit system, s; 

m'

0

 – reduced 

initial negative torque, 

M

0

/(

k

LF

 · 

M

rt

); 

ˆ

 – reduced rotating 

speed, 

/

rt

.

The pace of motor rundown is determined by the ini-

tial acceleration (

d

ˆ

/

d

t

)

t

 = 0

 = –

k

LF 

/

 

j

 = 

ˆ

0

.

It is also evident that regardless of motor type (

), 

rundown occurs identically at the initial moment of time 
and is determined only by load factor 

k

LF

 and inertia con-

stant 

j

.

It is not necessary to numerically solve the equa-

tion (6) in the protection relay, because under real initial 
accelerations from 40 to 400 rad/s

2

 [5], the deviation of 

the rotating speed (frequency) variation law from the li-
near one is small during the time of calculating and ave-
raging performed by protection relays.

However, for the purpose of synchronization, the 

angle prediction can be ful

fi

 lled based on the assump-

tion that frequency is constant during the time of circuit 
breaker closing. In this case, the angle error is equal to:



3

 = 

 · 

T

2

ON 

/

 

2 (7)

where 

 – angular acceleration (frequency derivative), 

rad/s

2

.

All errors have the same sign and may 

cause a condition under which the actual 
voltage vector phase differs more from the 
voltage phase of the intact busbar section at 
the moment of BC closing than it is allowed 
as per the calculations.

Figure 2 shows the angular errors, de-

pending on the initial acceleration when us-
ing ISM15_Shell_FT2 high-speed circuit 

0

50

100

150

200

250

300

0

5

10

15

20

25

Initial acceleration 

ε

0

, rad/s

2

 

Angular error 

Δϕ

, deg

 

Dependence on the frequency error
Dependence on the angle error
Dependence on ignoring the linear frequency change
Total error

T

ON

 = 22 ms

Figure 2. Dependence of angular errors on the 

initial acceleration. 

T

ON

 = 22 ms


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46

RELAY PROTECTION

breaker with CM_1501_01 electronic control module (4) and 
with closing time of 22 ms [8]. Figure 3 represents the same 
functional relation when using a slow circuit breaker with 
closing time of 50 ms (closing time of modern circuit break-
ers may be up to 100 ms).

The inertia constant for gas compressor units with STD-

4000-2 (three-phase synchronous motors) and 280-12-7 
supercharger is 3.25 s [9]. Through the inertia constant, 
it is possible to calculate the initial acceleration with mo-
tor rundown being 96.6 rad/s

2

 . The graphs show that the 

methodical error only will be 7 and 18 degrees respectively. 
Taking into account the protection relay cyclical calculation, 
the angular error will further increase because the "correct" 
time for issuing the command may come in the middle of the 
program cycle. For high initial acceleration values and CBs 
closing within 70-100 ms, the methodical error will be tens 
of degrees.

In the BMRZ-BAVR high-speed transfer system pro-

duced by LLC "NTC Mekhanotronika" the following solu-
tions are used for exact determination of the moment of is-
suing the BC closing command:
1.  The device analyzes not only the speed but also the ac-

celeration of busbar section vectors rotation relative to 
each other.

2.  The linear frequency change during breaker closing is 

taken into account, because without considering this fact 
the error depends on the time of breaker closing qua-
dratically.

3. Adaptive change of 

fi

 lter order is used for faster re-

sponse to network mode change. The maximum value 
of the observation window is half the period. It makes 
possible to ignore angular errors when calculating the 
orthogonal components.

4.  It is preferable to use high-speed circuit breakers, as the 

accuracy of prediction decreases for longer periods of 
time. 

 

Р

Figure 3. Dependence of angu-

lar errors on the initial accelera-

tion. 

T

ON

 = 50 ms

REFERENCES
1. OTT-29.130.00-KTN-119-17. General technical re-

quirements. Fast automatic transfer switch devices on 
the basis of vacuum circuit breaker with rated voltage 
above 1000 V. Moscow, PJSC "Transneft" Publ., 2017. 
48 p. (In Russian). 

2.  Ivanov N.G., Soldatov A.V., Naumov V.A., Antonov V.I. 

Frequency estimation based on zero crossing in digital 
systems of relay protection and automation. Charac-
teristics of accuracy. 

Releynaya zashchita i avtomati-

zatsiya

 [Relay protection and automation], 2013, no. 4, 

pp. 22-26. (in Russian)

3.  Antonov V.I., Naumov V.A., Shevtsov V.M. Frequency 

estimation in electrical network. Theoretical founda-
tions and practical algorithms. 

Sbornik nauchnykh 

statey. Tsifrovaya elektrotekhnika: problemy i dostizhe-
niya. Vypusk 1 

[Collection of scienti

fi

 c articles. Digital 

electrical engineering: problems and achievements. 
First edition], 2012, pp. 20-39.

4.  STO 59012820.29.020.003-2016. Relay protection and 

automation. Automatic emergency control of power 
system modes. Microprocessor devices for automatic 
frequency load shedding. Standards and requirements. 
Moscow, SO UPS, JSC Publ., 2016. 19 p. (In Russian).

5.  Kryshnev Y.V. Investigation of the dynamics of synchro-

nous motors rundown taking into account drive mecha-
nisms characteristics. 

Vestnik GGTU 

[GSTU news], 

2002, no. 3-4, pp. 74-81. (in Russian)

6. Syromyatnikov I.A. 

Rezhimy raboty asinkhronnykh i sin -

khronnykh dvigateley

 [Operation modes of asynchro-

nous and synchronous motors]. Moscow, Energo-
atomizdat Publ., 1984. 240 p.

7.  Kurganov V.V., Kryshnev Y.V., Veriga B.A. Accounting 

of mechanical characteristics for a generalized drive in 
the algorithm for high-speed self-starting of high-voltage 
synchronous motors. 

Energetika. Izvestiya vysshikh 

uchebnykh zavedeniy i energeticheskikh obyedineniy 
SNG 

[ENERGETIKA. Proceedings of CIS higher edu-

cation institutions and power engineering associations], 
2007, no. 2, pp. 17-33. (in Russian)

8. Belyayev A.V. 

Avtomatika i zashchita na podstantsiyakh 

s sin khronnymi i chastotno reguliruyemymi elektrod-
vigatelyami bolshoy moshchnosti

 [Automation and pro-

tection in substations with synchronous and frequency-
controlled high-power electric motors]. St. Petersburg, 
FGAOU DPO "PEIPK" Publ., 2012. 72 p.

0

0

10

20

30

40

50

60

 

 

50

100

150

200

250

300

Initial acceleration 

ε

0

, rad/s

2

 

Angular error 

Δϕ

, deg

T

ON

 = 50 ms

Dependence on the frequency error
Dependence on the angle error
Dependence on ignoring the linear frequency change
Total error

"NTC Mekhanotronika", LLC

Russia, Saint-Petersburg

Tel: +7(812)244-70-15

www.mtrele.ru


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One of the requirements to high-speed transfer systems is busbar coupler (BC) closing when voltage vector on the intact busbar section and EMF vector of the generalized motor running down to the busbar section with power failure have a small phase difference.

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