International Conference on Renewable Energies and Power Quality (ICREPQ’09)
European Association for the Development of Renewable Energies, Environment and Power Quality
Valencia (Spain), 15th to 17th April, 2009
A Control Strategy for Combined SeriesParallel Active Filter System under NonPeriodic Conditions M. Ucar, S. Ozdemir and E. Ozdemir Electrical Education Department Technical Education Faculty, Kocaeli University 41380, Umuttepe, Turkey Phone/Fax number:+90262 3032275 / :+90262 3032203 email:
[email protected],
[email protected],
[email protected]
Abstract. In this study, generalized nonactive power theory based control strategy is proposed for a 3phase 4wire Combined SeriesParallel Active Filter (CSPAF) system using a ThreeDimensional (3D) Space Vector Pulse Width Modulation (SVPWM). The CSPAF system consists of a Series Active Filter (SAF) and a Parallel Active Filter (PAF) combination connected a common Direct Current (DC) link for simultaneous compensating the source voltage and the load current. The generalized nonactive power theory was applied in previous studies for the PAF control, in this study the theory is used for the CSPAF system control under nonsinusoidal and nonperiodic current and voltage conditions. The closed loop control algorithm for the proposed CSPAF system has been described to direct control of filtering performance by measuring source currents and load voltages for the PAF and the SAF, respectively. The proposed control strategy has been verified by simulating the CSPAF system in Matlab/Simulink environment.
Key words
period of the currents is not equal to the period of the line voltage [1], [2]. In this paper, the generalised instantaneous nonactive power theory is used for the CSPAF system under nonsinusoidal and nonperiodic load current and source voltage conditions. The CSPAF system consists of backtoback connection of SAF and PAF with a common DC link. While the PAF compensates current quality problems of load and regulating of DC link, the SAF compensates voltage quality problems of utility [3], [4]. The system configuration of the CSPAF system is shown in Fig. 1. vS
vSF
3∼
L S vS
iS
iS
−
iL
vSF –
+
RSF CSF
iPF CPF RPF LPF
LSF
VDC
SAF
vL
LL
LL Nonlinear loads
Sensitive loads
C
1. Introduction The large use of nonlinear loads and power electronic converters has increased the generation of nonsinusoidal and nonperiodic currents and voltages in electric power systems. Generally, power electronic converters generate harmonic components which frequencies that are integer multiplies of the line frequency. However, in some cases, such as line commutated threephase thyristor based rectifiers, arc furnaces and welding machines, the line currents may contain both frequency lower and higher than the line frequency but not the integer multiple of line frequency. These currents interact with the impedance of the power distribution system and disturb voltage waveforms at Point of Common Coupling (PCC) that can affect other loads. These waveforms are considered as nonperiodic, although mathematically the currents may still have a periodic waveform, but in any event, the
iPF
iL =
+
N1/N2
AA Source
Harmonics, unbalance, reactive power compensation, nonperiodic, active filter, 3DSVPWM.
vL
=
PAF
CSPAF
Fig. 1. System configuration of the CSPAF system.
In 3phase 3wire systems, conventional SVPWM method, which is based on αβ plane, has been widely used to reduce ripples and to get fixed switching frequency. In this study, the 3DSVPWM scheme is used for controlling the CSPAF system, which uses two 3leg 4wire Voltage Source Inverter (VSI) because the zero sequence components must be controlled [5]. In the closed loop control scheme of the proposed CSPAF system, source currents and load voltages are measured and filtering performance is controlled directly. The CSPAF system provides minimum harmonics of these currents and voltages.
2. Generalized NonActive Power Theory The generalised nonactive power theory [6] is based on Fryze’s theory of nonactive power/current [7] and is an extension of the theory proposed in [8] [9]. Voltage vector v(t) and current vector i(t) in a 3phase system,
threephase fundamental sinusoidal systems and are valid in various cases, such as singlephase systems, nonsinusoidal systems, and nonperiodic systems as well, by changing the averaging interval Tc and the reference voltage vp(t) [10]. In this theory, all the definitions are instantaneous values; therefore, they are suitable for realtime control.
v(t ) = [v1 (t ), v2 (t ), v3 (t )]T ,
(1)
3. 3DSVPWM Algorithm
i (t ) = [i1 (t ), i2 (t ), i3 (t )]T .
(2)
In this paper, the 3DSVPWM algorithm is utilized for controlling the CSPAF system, which uses two 3leg 4wire VSI. The switching vectors of the 3leg 4wire VSI are shown into a 3D plane in Fig. 2. The eight switching vectors are distributed in the αβ0 space and the zero switching vectors V0 and V7 are in opposite directions. Since there is a zero axis in the 3D space, two zero switching vectors can be used independently to control the zero sequence voltage [5].
The instantaneous power p(t) and the average power P(t) is defined as the average value of the instantaneous power p(t) over the averaging interval [tTc, t], that is 3
p(t ) = vT (t ) i (t ) =
∑v
p (t ) i p (t ),
(3)
p =1
1
t
1 P (t ) = Tc
∫ p(τ ) dτ .
(4)
V2
V3 beta
t − Tc
0
V7 V4
The averaging time interval Tc can be chosen arbitrarily from zero to infinity for compensation of periodic or nonperiodic waveforms, and for different Tc’s, the resulting active current and nonactive current will have different characteristics [6]. The instantaneous active current ia(t) and nonactive current in(t) are given (5) and (6).
1 1
V6
V5
0 zero
V1
V0
1
1
1
0 alpha
Fig. 2. Switching vectors in 3D space.
i a (t ) =
P(t ) V p2 (t )
v p (t )
in (t ) = i (t ) − ia (t )
(5)
The instantaneous voltage can be transformed to the αβ0 3D space by using (10).
(6)
v0 vα = v β
In (5), voltage vp(t) is the reference voltage, which is chosen on the basis of the characteristics of the system and the desired compensation results. Vp(t) is the corresponding rms value of the reference voltage vp(t), that is
V p (t ) =
1 Tc
t
∫v
T p
(τ ) v p (τ ) dτ .
(7)
t − Tc
The instantaneous nonactive power pn(t) and the average nonactive power Pn(t) is defined over the averaging interval [tTc, t], that is
1/ 2 1/ 2 1/ 2 va 2 1/ 2 1/ 2 vb 1 3 0 3 / 2  3 / 2 vc
(10)
The reference vector in the αβ0 3D space can be written as,
VR (k ) = i.vα + j.v β + k .v0 .
(11)
Once the reference vector VR has been determined, it can be reflected the αβ plane as shown in Fig. 3 to decide which sector and which active switching vectors are to be selected [5]. βaxis
V3αβ
V2αβ
3
pn (t ) = v T (t ) in (t ) =
∑v
p (t ) inp (t ),
(8)
V0
p =1
V4αβ
1 Pn (t ) = Tc
VRαβ VR
V
V1αβ
7
t
∫ p (τ ) dτ . n
αaxis
(9)
t − Tc
0axis
The definitions in the instantaneous nonactive power theory are all consistent with the standard definitions for
V5αβ
V6αβ
Fig. 3. 3DSVPWM method in the 3leg 4wire VSI.
Two zeroswitching vectors V0 and V7 with different effective times t0 and t7 can synthesize the reflection of the reference vector in the zero axis. Along with the different switching functions, the reference space vector VR(k) is presented in Table I. TABLE I. Switching functions and switching voltage space vectors Switching vectors
S a S b S c VR 1
1
0
0
0
1
0
1
1
1
0
0
0 (i.2 + j.0 + k .(− 0 (i.1 + j. 3 + k .(
2 2
)).
Ts=2.ts
V1
6
2 2
va
Vdc
)).
V2
6 2
0 (i.( −1) + j. 3 + k .( −
2
2
1 (i.( −2) + j.0 + k .(
Vdc
2
)).
)).
1 (i.1 + j.(− 3 ) + k .( 3
1
1 (i.0 + j.0 + k .1).
0
0
0 (i.0 + j.0 + k .(−1)).
2
Vdc
2 2
)).
3 2
)).
Vdc
6
6
V5
t 0 + t1 + t 2 + t 7 = t s
In this study, the CSPAF system, which has two 3leg 4wire VSI, uses generalised nonactive power theory based current and voltage control with the 3DSVPWM scheme.
V6
V7 V0
2 Vdc
t7 − t0 =
Voltage control block diagram is shown in Fig. 5. The nonsinusoidal, unbalanced and/or nonperiodic load voltages (vLa, vLb, vLc) is applied to Phase Locked Loop (PLL) circuit and fundamental positive sequence currents (ia1+, ib1+, ic1+), used as a reference current ip(t) and the same phase with the fundamental positive sequence load voltage (vLa1+, vLb1+, vLc1+) and unity amplitude are obtained. Effective value of reference current Ip(t) is
(12) (13)
(14)(17) show the equations involved in the calculation of switching time of each involved switching vector for reference vector happens in sector I.
t1 =
t0
A. Voltage control strategy Vdc
V0 .t 0 + V1.t1 + V2 .t 2 + V7 .t 7 = VR .t s
Vdc
t1
4. Control of the CSPAF System
In Fig. 3, the reference voltage vector VR is located in a sector in which the four switching states (V0, V7, V1 and V2) are adjacent to the reference vector. The effective switching time of each switching vector, within PWM switching period, Ts, can be obtained from an equation (12), (13) [5].
t1 =
t2 t7 t7 t2
Fig. 4. PWM switching time sequence.
Vdc
Vdc
t1
V4
6 2
vc t0
Vdc
2
vb
V3
6
1 (i.( −1) + j.(− 3 ) + k .( −
1
2
The selected switching vectors can be applied in a sequence optimized to reduce switching loss or achieve a better voltage Total Harmonic Distortion (THD). Symmetrical sequencing gives the lowest THD output, due to the fact that all switching vectors are arranged symmetrically [11]. So this sequencing method is chosen in this paper. In symmetrical sequencing strategy, the switching sequence is arranged as V0  V1  V2  V7  V7 V2  V1  V0. Fig. 4 shows the sequencing of switching states for a time period of Ts for sector I.
3 1 ⋅ t s ⋅ ( ) ⋅ v Rα + (− ) ⋅ v Rβ 2 2
(14)
⋅ t s ⋅ v Rβ
(15)
I p (t ) =
1 Tc
t
∫i
T p
(τ ) i p (τ ) dτ
(18)
t −Tc
vL
Phase i1+ Locked Loop (PLL)
Referance vSF* Voltage Calculation
1

+ ∑
PI
+ ∑
+
3D SVPWM
vL1+
SAF Switching Signals
vDC
Fig. 5. Voltage control block diagram.
vR 0 ⋅ t s − (t 2 − t1 ) / 3 3 Vdc
2
⋅
t 7 + t 0 = t s − (t 2 + t1 )
(16)
(17)
The average power calculated given (4) by using this reference currents and source voltages. Desired sinusoidal load voltages (vLa1+, vLb1+, vLc1+) as compensation reference voltages (vSFa*, vSFb*, vSFc*) of SAF, is derived by using (19) from amplitude and phase angle of fundamental positive sequence component of the load voltages. Reference voltage is compared load
Iabc Vabc a b N c
A
A
B
B
A
C
C
B
2
A B C
B. Current control strategy
Vdc
∑
PI
∑
+
3D SVPWM
vL1+
Vdc1
A B C
PAF Control
400 200 0 200 400 0.35
0.36
0.37
0.38
0.39
0.4 t (s)
0.41
0.42
0.43
0.44
0.45
0.44
0.45
400
PAF Switching Signals
200 0 200 400 0.35
0.36
0.37
0.38
0.39
0.4 t (s)
0.41
0.42
0.43
100 0 100 0.35
X ∑
iSabc1+
Fig. 8 demonstrate the simulation results for the periodic current and voltage compensation. 3phase source current and load voltage is sinusoidal and balanced and neutral current eliminated after compensation. Table III shows a summary of measured components.
vS VDC*
Vdc2
B C
+v 
(a) 3phase source voltage waveforms.
1
+

C2
vLabc1+ Vdc
A
(b) 3phase load voltages after compensation.
+
ica
1

iSabc
pulses
g +
Fig. 7. The CSPAF system Matlab/Simulink block diagram.
iLabc(A)
vL1+

+
C
+
+v 
Discrete, Ts = 1e006 s.
iS
iPF*
B
vLabc1+
SAF Control
(20)
0
Referance iPF + ∑ Current Calculation +
A
t
∫ (VDC − vDC ) dt ]
C1
g
pulses
iSabc1+
vLabc(V)
ica (t ) = v L [ K P (VDC − v DC ) + K I
vLabc
vSabc(V)
The reference currents are compared source currents to realize the closed loop control scheme. Then, using 3DSVPWM controller, PAF switching signals are obtained. Current control block diagram of the CSPAF system is shown in Fig. 6. The CSPAF system Matlab/Simulink block diagram is shown in Fig. 7.
Lpf A B C
Lsf
The average power calculated given (4) by using source currents and fundamental positive sequence (vLa1+, vLb1+, vLc1+) load voltages over the averaging interval [tTc, t]. Desired sinusoidal source currents (iSa1+, iSb1+, iSc1+) are derived by using (5). Also, the additional active current ica(t) required to meet the losses in (20) is drawn from the source by regulating the DC link voltage vDC to the reference VDC. A Proportional Integral (PI) controller is used to regulate the DC link voltage vDC. Thus, the compensation reference currents (iPFa*, iPFb*, iPFc*) of PAF is obtained.
Nonperiodic Loads
Iabc Vabc a b c N
A
A A B B C C Rpf Cpf
B
+ i
A A B B C C Rsf Csf
A B C N
C
2
Iabc Vabc a b c N
(19)
A B C LL
A B C
i p (t )
A
I p2 (t )
B
va (t ) =
A B C
+ i
1
+ i
C
P(t )
Iabc Vabc a b c N C
2
Nonperiodic AC Source
1
N
1
voltages and applied to 3DSVPWM and thus SAF switching signals are obtained.
PI
0.36
0.37
0.38
0.39
0.4 t (s)
0.41
0.42
0.43
0.44
0.45
0.44
0.45
(c) 3phase load current waveforms.

vDC
Fig. 6. Current control block diagram.
iSabc(A)
100 0 100 0.35
5. Periodic Current and Voltage
0.36
0.37
0.38
0.39
0.4 t (s)
0.41
0.42
0.43
(d) 3phase source currents after compensation.
TABLE II. 3phase source voltage components
iNLabc(A)
50 0 50 0.35
0.37
0.38
0.39
0.4 t (s)
0.41
0.42
0.43
0.44
0.45
0.44
0.45
50 0 50 0.35
Fundamental Unbalance (%) Harmonics (%) 50 Hz 5. 7. 9. 11. 13. 17. 19. 20 220 V 10 7,5 15 5 2,5 1,25 1
0.36
(e) Load neutral current waveforms. iNSabc(A)
For compensation of periodic currents and voltages with fundamental period T, using a compensation period Tc that is a multiple of T/2 is enough for complete compensation [6]. In this study, 3phase source voltage components is given in Table II. 3phase RL loaded tyristor rectifier and 1phase RC loaded diode rectifier in each phase connected 3phase 4wire power system. Thyristor rectifier firing angles are 30°.
0.36
0.37
0.38
0.39
0.4 t (s)
0.41
0.42
0.43
(f) Source neutral current after compensation. Fig. 8. Periodic voltage and current compensation.
RMS (V)
THD (%)
RMS (A)
THD (%)
TABLE III. Summary of measured values under periodic current and voltage condition
a b c n a b c n
a b c a b c
Load Currents (IL) 28,97 29,08 29,04 165,30 81,05 81,01 81,59 47,21 Source Voltages (VS) 22,20 22,20 16,96 206,5 206,5 267,7
Source Currents (IS) 4,34 4,48 4,34 73,74 73,78 74,03 Load Voltages (VL) 2,21 2,30 2,13 219,1 219,2 219,5
6. NonPeriodic Current and Voltage
result in an acceptable both source current and load voltage which are quite close to a sine wave. If Tc is large enough, increasing Tc further will not typically improve the compensation results significantly [10]. In this work, 3phase source voltage and load current components is given in Table V. Fig. 10 shows the stochastic nonperiodic voltage and current compensation choosing the period as Tc=5T. After compensation, load voltages and source currents are balanced and almost sinusoidal with low THD. In addition, source neutral current have been reduced considerably. The system parameters used for the simulation are given in Table VI. TABLE V. 3phase source voltage and load current components Parameters Freq. (Hz) Currents Voltages
Fund. 50 104 50 A 30 220 V 7,5
Components (%) 117 134 147 40 20 20 10 5 5
250 50 12,5
0 200 400 0.35
0.4
0.45
0.5
0.55
0.6
(a) 3phase source voltage waveforms. vLabc(V)
400 200 0 200 400 0.35
0.4
0.45
0.5
0.55
0.6
t (s)
(b) 3phase load voltages after compensation. 100
iLabc(A)
In this study, 3phase source voltage and load current components are given in Table IV. Subharmonic current and voltage compensation simulation results are shown in Fig. 9. The subharmonic component can be completely compensated by choosing Tc=2.5T, and the source currents and load voltages are balanced and sinusoidal. Additionally, the neutral current component is compensated.
200
t (s)
50 0 50 100 0.35
0.4
0.45
0.5
0.55
0.6
t (s)
(c) 3phase load current waveforms. 100
iSabc(A)
The subharmonic currents are (frequency lower than fundamental frequency) typically generated by power electronic converters. The main feature of these nonperiodic currents is that the currents may have a repetitive period. When the fundamental frequency of the source voltage is an odd multiple of the subharmonic frequency, the minimum Tc for complete compensation is 1/2 of the common period of both fs and fsub. When fs is an even multiple of fsub, the minimum Tc for complete compensation is the common period of both fs and fsub [6].
vSabc(V)
400
A. Subharmonic current and voltages
TABLE IV. 3phase source voltage and load current values
50 0 50 100 0.35
0.4
0.45
0.5
0.55
0.6
t (s)
(e) Load neutral current waveforms.
Parameters Freq. (Hz) Currents Voltages
Fundamental 50 50 A 220 V
Subharmonic 10 % 20 % 20
iNLabc(A)
50
0 50 0.35
0.4
0.45
0.5
0.55
0.6
t (s)
(e) Load neutral current waveforms.
B. Stochastic nonperiodic currents and voltages The arc furnace load currents may contain stochastic nonperiodic currents (frequency higher than fundamental frequency but not an integer multiple of it). Theoretically, the period T of a nonperiodic load is infinite [12]. The nonactive components in these loads cannot be completely compensated by choosing Tc as T/2 or T, or even several multiples of T. Choosing that period as may
iNSabc(A)
50
0 50 0.35
0.4
0.45
0.5
0.55
0.6
t (s)
(f) Source neutral current after compensation. Fig. 9. Subharmonic voltage and current compensation.
vSa(V) vSb(V) vSc(V)
7. Conclusion
400 200 0 200 400 0.35 400 200 0 200 400 0.35 400 200 0 200 400 0.35
0.4
0.45
0.5
0.4
0.45
0.5
0.45
0.5
0.4 t (s)
(a) 3phase source voltage waveforms. vLabc(V)
400 200 0 200 400 0.35
0.4
0.45
0.5
t (s)
(b) 3phase load voltages after compensation. iLa(A)
0.45
0.5
100 0 100 0.35
0.4
0.45
0.5
100 0 100 0.35
0.4
0.45
0.5
iLc(A)
0.4
iLb(A)
Acknowledgement
100 0 100 0.35
t (s)
iSabc(A)
(c) 3phase load current waveforms. 100 0 100 0.35
0.4
0.45
0.5
t (s)
iNLabc(A)
(d) 3phase source currents after compensation. 50 0 50 0.35
0.4
0.45
0.5
t (s)
(e) Load neutral current waveforms. iNSabc(A)
In this paper, the generalized nonactive power theory, which is applicable to sinusoidal or nonsinusoidal, periodic or nonperiodic, balanced or unbalanced electrical systems, is presented. It has been applied to the 3phase 4wire CSPAF system with the 3DSVPWM to get fixed switching frequency. The theory is adapted to different compensation objectives by changing the averaging interval Tc. The closed loop control algorithm has been described by measuring source currents and load voltages in the proposed CSPAF system to direct control of filtering performance. The simulation results based on Matlab/Simulink software are presented to show the effectiveness of the CSPAF system for the compensation of a variety of nonsinusoidal and nonperiodic voltages and currents in power systems.
50 0 50 0.35
0.4
0.45
0.5
t (s)
(f) Source neutral current after compensation. Fig. 10. Stochastics nonperiodic voltage and current compensation. TABLE VI. The system parameters Power system Series transformer SAF AA filter PAF AA filter DC bus Switching freq. 3phase thristor 1phase diode
VSabc, fs, Ls N1/N2 LSF, RSF, CSF LPF, RPF, CPF VDC,C1, C2 fSAF, fPAF LL1, LDC, RDC1 LL2, CDC, RDC2
220V, 50Hz, 50µH 1 2mH, 2Ω, 30µF 1mH, 1Ω, 30µF 800V, 5600µF 10kHz 3mH, 20mH, 5Ω 3mH, 470µF, 15Ω
This work is supported by TUBITAK Research Fund, (Project No: 108E083).
References [1] Watanabe, E. H. and Aredes, M., “Compensation of Nonperiodic Currents Using The Instantaneous Power Theory”, IEEE Power Engineering Soc. Summer Meeting, 2000, 994999. [2] Czarnecki, L. S., “NonPeriodic Currents: Their Properties, Identification and Compensation Fundamentals”, IEEE Power Engineering Soc. Summer Meeting, 2000, 971976. [3] Fujita, H. and Akagi, H., “The Unified Power Quality Conditioner: The Integration of Series and Shunt Active Filters”, IEEE Trans. on Power Electr., 13 (2), 1998. [4] Aredes, M., “Active Power Line Conditioners”, Ph.D. Dissertation, Technischen Universität, Berlin, 1996. [5] C. Zhan, A. Arulampalam, V. K. Ramachandaramurthy, C. Fitzer, M. Barnes, N. Jenkins, “Novel voltage space vector PWM algorithm of 3phase 4wire power conditioner”, IEEE Power Eng. Soc., pp. 10451050, 2001. [6] Xu, Y., Tolbert, L. M., Peng, F. Z., Chiasson, J. N. and Chen, J. “CompensationBased NonActive Power Definition”, IEEE Power Electr. Letter, 1 (2), 4550, 2003. [7] Fryze, S. “Active, Reactive, and Apparent Power in NonSinusoidal Systems”, Przeglad Elektrot., 7, 193203 (in Polish), 1931. [8] Peng, F. Z., and Tolbert, L. M. “Compensation of NonActive Current In Power Systems  Definitions from Compensation Standpoint”, IEEE Power Eng. Soc. Summer Meeting, 2000, 983987. [9] Xu, Y., Tolbert, L. M., Chiasson, J. N., Campbell, J. B. and Peng, F. Z., “A Generalised Instantaneous NonActive Power Theory for STATCOM”, Electric Power Applications, IET, 853861, 2007. [10] Xu, Y., Tolbert, L. M., Chiasson, J. N., Campbell, J. B. and Peng, F.Z., “Active Filter Implementation Using a Generalized Nonactive Power Theory”, IEEE Industry Applications Conference, 2006, 153160. [11] H.Pinheiro, F. Botteron, C. Rech. Schuch and et al., “Space Vector Modulation for VoltageSource Inverter: A Unified Approach,” IECON02, Industrial Electronics Society, IEEE 2002, 28th Annual Conference. [12] Tolbert, L. M., Xu, Y., Chen, J., Peng, F. Z, Chiasson, J. N., “Compensation of Irregular Currents with Active Filters,” IEEE Power Engineering Society General Meeting, 2003, 12781283.