Download Measurement, Modeling and Simulation of Capacitor Bank

Measurement, Modeling and Simulation
of Capacitor Bank Switching Transients
Mirza Softić*, Amir Tokić**, Ivo Uglešić***
*Kreka - “Dubrave” Mine, Dubrave, Bosnia and Herzegovina
(e-mail: [email protected]).
** Faculty of Electrical Engineering, University of Tuzla, Tuzla, Bosnia and Herzegovina
(e-mail: [email protected])
*** Faculty of Electrical Engineering and Computing, University of Zagreb, Zagreb, Croatia
(e-mail: [email protected])
Abstract: This paper presents the results of experimental and simulated investigations of electromagnetic
transient phenomena during energizing of industry capacitor banks. Experimental and simulated
investigations based on the electrical network model having the nominal voltage of 6 kV are carried out.
In addition, sensitive analyses of characteristic impact factors are performed. It is shown how capacitor
banks switching transients influence a degradation of the power quality in electrical distribution system.
Keywords: Power quality, capacitor banks, switching transients, overcurrents, overvoltages.
Ls – inductance of system
1. INTRODUCTION
Power quality is a topic of constant study as problem inherent
to it can lead to economical losses, mainly in industrial
processes. Although many factors influence the power
quality, the paper presented here focuses on electromagnetic
switching transients originating from capacitor bank
switching in typical mining distribution systems, Adams et al.
(1998), Bollen et al. (2006), Grebe (1996), McCoy et al.
(1994). Two main advantages of capacitor banks connecting
are: improvement of the network’s voltage profile and
reducing the network’s losses. In general, these capacitors are
not connected all of the time, since the network loads are
changing with time according to certain load curves. Hence,
they may be switched on and off several times during a
typical day. These switching actions will be accompanied by
low or medium frequency of electromagnetic transient
voltages and currents which may have an influence on
sensitive electrical equipment connected in local networks.
The capacitor banks switching provokes transient
overvoltages that theoretically can reach peak phase-to-phase
values of 2.0 p.u., Saided (2004). Generally, the frequency of
capacitor banks switching transients is below 2 kHz. Other
factors that affect amplification of the transient voltages
during the banks switching should also be mentioned: size of
the capacitor banks switched, short circuit capacity at the
capacitor banks location, rated power of the distribution
transformer and characteristics of the connected loads.
Frequency of transient during energizing of industry
capacitor banks is calculated by the equation ( LS >> L) :
f =
1
2π
(L
where are:
S
+ L )C
≈
1
2π LS C
C – capacity of capacitor banks
L – inductance of capacitor banks.
2. EXPERIMENTAL MEASUREMENTS
Characteristics of electromagnetic transients originating from
industry capacitor banks switching are studied in this paper.
Moreover, factors that influence the intensity of such
transients are investigated in order to identify the conditions
in which these effects can be undermined. It should be
pointed out that the electrical network which represents a
real-life feeder of the typical 6 kV mining distribution system
is investigated in this paper. The feeder supplies mining loads
(total power is approximately 2.5 MVA) with installed three
phase, star connected, capacitor banks (rated power 500
kVAr), Fig. 1.
The results of experimental investigations of capacitor banks
switching transients are presented in this chapter. Current
waveforms and phase to phase voltage waveforms are
measured during energizing of three phase capacitor banks.
(1)
Fig. 1. Simplified configuration of 6 kV electrical network
Phase current waveforms and phase to phase voltage
waveforms during energizing of 500 kVAr capacitor banks at
the 6 kV electrical network with isolated neutral point are
presented in Fig. 2 and Fig. 3.
3. MODELING AND SIMULATIONS
Simulations of electromagnetic transient phenomena during
energizing of capacitor banks are carried out in electrical
networks of 6 kV. An equivalent three phase electrical model
is implemented within the MATLAB/Simulink software.
Here are being modelled: power system equivalent, industrial
loads, distribution transformer, breaker, supply cable,
capacitor banks equivalent and protection inductors.
A stiff differential equation system, describing the behaviour
of three phase capacitor banks switching transient, is solved
by using the numerical method of L – stable backward
differentiation formulas (BDFs), Tokić et al. (2005).
The results of simulating phase current waveforms and phase
to phase voltage waveforms during energizing of three phase
500 kVAr capacitor banks in electrical networks of 6 kV with
isolated neutral point are presented in Fig. 4 and Fig. 5.
Currents [simulation]
1000
Fig. 2. Measured phase currents during energizing of
capacitor banks
I1
I2
I3
800
600
400
Current [A]
200
0
-200
-400
-600
-800
-1000
0
0.005
0.01
0.015 0.02 0.025
Time [sec]
0.03
0.035
0.04
Fig. 4. Simulated phase currents during energizing of
capacitor banks
1.5
Fig. 3. Measured phase to phase voltages during energizing
of capacitor banks
x 10
4
Voltages [simulation]
U12
U23
U31
1
Values of characteristic parameters of phase transient
currents and phase to phase transient voltage waveforms
(amplitude, duration and frequency) obtained as a result of
experimental measurements during energizing of a 500 kVAr
three phase capacitor banks at the 6 kV mining electrical
network with isolated neutral point are presented in Table 1.
Voltage [V]
0.5
0
-0.5
-1
-1.5
Table 1. Characteristics of transient during energizing of a
500 kVAr three phase capacitor banks (measurements)
Max/ Min
current I1 (A)
266/−122
Max
voltage U12 (V)
8000
Steady state
currents Is (A)
53
Max/ Min
current I2 (A)
544/−444
Max
voltage U23 (V)
11333
Duration of
transient T (ms)
7.87
Max/ Min
current I3 (A)
522/−800
Min
voltage U31 (V)
−9000
Frequency of
transient f (Hz)
1124
0
0.005
0.01
0.015 0.02 0.025
Time [sec]
0.03
0.035
0.04
Fig. 5. Simulated phase to phase voltages during energizing
of capacitor banks
Values of characteristic parameters of phase transient
currents and phase to phase transient voltage waveforms
(amplitude, duration and frequency) resulting from the
simulation during switching/energizing of a 500 kVAr three
phase capacitor banks at the typical 6 kV mining electrical
network with isolated neutral point are presented in Table 2.
Table 2. Characteristics of transient during energizing of a
500 kVAr three phase capacitor banks (simulations)
Max/ Min
current I1 (A)
285/−125
Max
voltage U12 (V)
8000
Steady state
currents Is (A)
53
Max/ Min
current I2 (A)
580/−500
Max
voltage U23 (V)
12000
Duration of
transient T (ms)
8.25
Max/ Min
current I3 (A)
630/−860
Min
voltage U31 (V)
−9000
Frequency of
transient f (Hz)
1124
Waveforms of phase currents and phase to phase voltages
obtained as a result of experimental measurements and
simulations during energizing of a 500 kVAr capacitor banks
at the 6 kV network are in very good agreement. It should be
noted there are no many papers that show both measured and
simulated three phase currents and voltages during industry
capacitor banks energizing.
Fig. 6. Simulated phase currents during energizing of
capacitor banks
4. SENSITIVE ANALYSIS OF THE SYSTEM
PARAMETERS
Based on an implemented equivalent model, different
simulation scenarios of system parameters are investigated.
This chapter focuses on the sensitive analysis of influential
parameters within a three phase system by observing
characteristic parameters of phase transient currents and
phase to phase transient voltage waveforms (amplitude,
duration, frequency).
Influential parameters on a three-phase system are: initial
conditions, impedance of system, consumers’ characteristics,
capacity of capacitor banks and moment of circuit breaker
switching.
Fig. 7. Simulated phase to phase voltages during energizing
of capacitor banks
The important parameters of a three-phase system had the
following values:
The results of simulating the waveforms of phase transient
currents and phase to phase transient voltages are presented
in Fig. 8 and Fig. 9.
•
peak of system voltage/per phase: Um = 8000 V
•
initial conditions (residual voltage of capacitor banks at
the moment of circuit breaker switching): Ures = 1 kV
•
impedance of system: R = 0.0025 Ω, L = 0.55 mH
•
consumers’ characteristics: S = 2.5 MVA
•
capacity of capacitor banks/per phase: C = 36.5 µF
•
moment of circuit breaker switching: T0 = 15.75 ms
Second case: Reducing the system impedance twice in the
equivalent three-phase electrical simulation model.
First case: Disregarding the residual voltage in the
equivalent three-phase electrical simulation model.
The results of simulating the waveforms of phase transient
currents and phase to phase transient voltages are presented
in Fig. 6 and Fig. 7.
Fig. 8. Simulated phase currents during energizing of
capacitor bank
The results of simulating the waveforms of phase transient
currents and phase to phase transient voltages are presented
in Fig. 12 and Fig. 13.
Fig. 9. Simulated phase to phase voltages during energizing
of capacitor banks
Third case: Increasing the industrial load twice in the
equivalent three-phase electrical simulation model.
The results of simulating the waveforms of phase transient
currents and phase to phase transient voltages are presented
in Fig. 10 and Fig. 11.
Fig. 12. Simulated phase currents during energizing of
capacitor banks
Fig. 13. Simulated phase to phase voltages during energizing
of capacitor banks
Fig. 10. Simulated phase currents during energizing of
capacitor banks
Fifth case: Moving the moment of circuit breaker switching
in phase 2 for 0.1 ms (pole asynchronism of circuit breaker
switching) in the equivalent three-phase simulation model.
The results of simulating the waveforms of phase transient
currents and phase to phase transient voltages are presented
in Fig. 14 and Fig. 15.
Fig. 11. Simulated phase to phase voltages during energizing
of capacitor bank
Fourth case: Increasing the capacity of capacitor bank twice
in the equivalent three-phase electrical simulation model.
Fig. 14. Simulated phase currents during energizing of
capacitor banks
(d) S’ = 2S
Max/ Min
current I1 (A)
260/−70
Max
voltage U12 (V)
8000
Steady state
currents Is (A)
53
Max/ Min
current I2 (A)
560/−375
Max
voltage U23 (V)
11150
Duration of
transient T (ms)
3.25
Max/ Min
current I3 (A)
445/−820
Min
voltage U31 (V)
−8150
Frequency of
transient f (Hz)
1124
(e) C’ = 2C
Fig. 15. Simulated phase to phase voltages during energizing
of capacitor banks
The results of investigation change the initial conditions
(residual voltage), serial system impedance, consumers’
characteristics, capacity of capacitor banks and pole moments
of circuit breaker switching into the values of characteristic
parameters of phase transient currents and phase to phase
transient voltage waveforms, as presented in Table 3.
Table 3. The results of investigation change the system
parameters: different scenarios
(a) S = 500 kVAr
Max/ Min
current I1 (A)
285/−125
Max
voltage U12 (V)
8000
Steady state
currents Is (A)
53
Max/ Min
current I2 (A)
580/−500
Max
voltage U23 (V)
12000
Duration of
transient T (ms)
8.25
Max/ Min
current I3 (A)
630/−860
Min
voltage U31 (V)
−9000
Frequency of
transient f (Hz)
1124
(b) Ures = 0 V
Max/ Min
current I1 (A)
185/−50
Max
voltage U12 (V)
8000
Steady state
currents Is (A)
53
Max/ Min
current I2 (A)
740/−620
Max
voltage U23 (V)
12700
Duration of
transient T (ms)
8.25
Max/ Min
current I3 (A)
670/−910
Min
voltage U31 (V)
−8920
Frequency of
transient f (Hz)
1124
(c) z’ = z/2 V
Max/ Min
current I1 (A)
383/−235
Max
voltage U12 (V)
8100
Steady state
currents Is (A)
53
Max/ Min
current I2 (A)
795/−750
Max
voltage U23 (V)
11950
Duration of
transient T (ms)
12.25
Max/ Min
current I3 (A)
980/−1175
Min
voltage U31 (V)
−9350
Frequency of
transient f (Hz)
1589
Max/ Min
current I1 (A)
450/−190
Max
voltage U12 (V)
8150
Steady state
currents Is (A)
106
Max/ Min
current I2 (A)
820/−815
Max
voltage U23 (V)
12200
Duration of
transient T (ms)
16.75
Max/ Min
current I3 (A)
1260/−1000
Min
voltage U31 (V)
−10000
Frequency of
transient f (Hz)
1589
(f) Tbreaker asynchronism
Max/ Min
current I1 (A)
2060/−1110
Max
voltage U12 (V)
8000
Steady state
currents Is (A)
53
Max/ Min
current I2 (A)
565/−490
Max
voltage U23 (V)
13150
Duration of
transient T (ms)
8.25
Max/ Min
current I3 (A)
1170/−2060
Min
voltage U31 (V)
−14550
Frequency of
transient f (Hz)
1124
The collected simulation results, for different electrical
system scenarios, are shown in Table 3. It can be concluded
that the last case represents the most critical case where the
worst-case transient phenomena in terms of amplitude
overvoltages and overcurrents transients occur.
High values of amplitude overvoltages and overcurrents
transients result from induced waveforms of voltages in
phase 1 and phase 3, generated by the waveform of voltage in
phase 2 at the moment of three phase circuit breaker
switching.
In order to reduce overvoltages and overcurrent transient
peak values in three phase system, the following measures
can be applied: preresistors/inductors adding, fixed inductors
(reactors) and applying of controlled (intelligent) switching.
A fixed inductor (reactor) of rated inductance 125 µH can be
applied in real life to reduce the overvoltages and overcurrent
transients during energizing of a 500 kVAr three phase
capacitor banks. Practical experience have showed to be very
effective in case of electromagnetic transients mitigation
generated by energizing of a 500 kVAr three phase capacitor
banks at the typical 6 kV mining electrical network.
5. CONCLUSIONS
Based on the results of experimental measurements and
simulations of electromagnetic transient phenomena during
energizing of three phase industry capacitor banks, the
amplitude of overvoltages occurs in phase to phase voltage
U23 and approaches the value 2Umax, whereas the amplitude
of overcurrents occurs in phase current I3, that is 15÷20 times
greater than the current amplitude of a capacitor banks in the
steady state Is. Duration of electromagnetic transient
phenomena during energizing of three phase industry
capacitor banks is approximately 8 ms, that is less than one
time period of the system. Frequency of electromagnetic
transient phenomena during energizing of three phase
industry capacitor banks is 1124 Hz.
On the basis of characteristic parameters values of phase
transient currents and phase to phase transient voltage
waveforms (amplitude, duration and frequency) obtained as a
result of experimental measurements and simulations during
energizing of a 500 kVAr three phase capacitor banks at the
typical 6 kV mining electrical network with isolated neutral
point, it can be concluded that the transient phenomena are
classified as medium frequency electromagnetic transients.
REFERENCES
Adams, R.A. and Middlekauff, S.W. (1998). Solving
customer power quality problems due to voltage
magifications. IEEE Transaction on Power Delivery,
volume 13 (number 4), 1515-1520.
Bollen, M.H. and Gu, I. Y. (2006). Signal processing of
power quality disturbances, IEEE Press, Wiley, New
York.
Grebe, T.E. (1996). Application of distribution system
capacitor banks and their impact on power quality. IEEE
Transaction on Industry Applications, volume 32
(number 3), 714-719.
McCoy, C.E. and Floryancic B.L. (1994). Characteristics and
measurements of capacitor switching at medium voltage
distribution level. IEEE Transaction on Industry
Applications, volume 30 (number 6), 1480-1489.
Saided, M.M. (2004). Capacitor switching transients: analysis
and proposed technique for identifying capacitor size and
location. IEEE Transaction on Power Delivery, volume
19 (number 2), 759-765.
Tokić, A., Madžarević V. And Uglešić I. (2005). Numerical
calculations of three-phase transformer transients. IEEE
Transaction on Power Delivery, volume 20 (number 4),
2493-2500.