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An adaptive harmonic detection and a novel current control strategy for unified power quality conditioner
Simulation Modelling Practice and Theory 17 (2009) 955–966
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Simulation Modelling Practice and Theory journal homepage: www.elsevier.com/locate/simpat
An adaptive harmonic detection and a novel current control strategy for unified power quality conditioner q Yuanjie Rong a,*, Chunwen Li a, Qingqing Ding b a b
Department of Automation, Tsinghua University, Beijing 100084, China Department of Electrical Engineering, Tsinghua University, Beijing 100084, China
a r t i c l e
i n f o
Article history: Received 24 September 2008 Received in revised form 5 December 2008 Accepted 17 February 2009 Available online 13 March 2009
Keywords: Adaptive harmonic detection Linear neuron Unified power quality conditioner One cycle current control
a b s t r a c t This paper proposes an adaptive harmonic detection to precisely detect the voltage with multiple zero crossings and adaptively obtain the reference signals, which makes use of linear neurons to approximate the fundamental component in each phase followed by a symmetric decomposition that calculates the fundamental positive components. According to the compensating requirements, we obtain four different forms of the reference signals. The detected reference signals are then fed into a triangular wave comparison control together with a PI controller and a one cycle current control to force the compensating voltage and current to track the reference signals. The one cycle current control (OCCC) is a combination of the one cycle control and the hysteresis control, which guarantees both tracking performances and constant frequency. The integration of the adaptive detection method and the one cycle current control in a three-phase unified power quality conditioner (UPQC) are simulated, where the effectiveness and reliability of the proposed strategies are demonstrated. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction The electric power network is extremely complex and mutually influent [1]. To attenuate the mutual influence, unified power quality conditioner (UPQC) was presented to synchronously deal with the current and voltage distortion and isolate the loads from the supply system [2]. The current and voltage detection are critical to the implementation of the UPQC and there are various algorithms including instantaneous reactive power theory, Fourier transformation, adaptive algorithms, etc. [3–16]. Among those algorithms, instantaneous reactive power theory based detection algorithms, the high pass filter (HPF) and the low pass filter (LPF) are the most widely used [3–8,11,12]. Usually, the phase of the system voltage is detected by the zero crossing detection [5] and the Phase-Locked Loop (PLL) [6]. However these two approaches have their shortcomings in that the zero crossing detection suffers from the non-stiff voltage and the latter is affected by the inherent delay of the PLL. In this regard, a method using a LPF with a phase corrector is presented to obtain the precise phase of a single-phase system voltage that is non-stiff and has multiple zero crossings via manual regulation of the phase corrector parameters [7]. Gu et al. [8] extends this method to a three-phase system which utilizes the LPF to get the fundamental voltage of each phase and the symmetric decomposition to calculate the phase unit reference. However additional phase-shift generated by LPF downgrades the detecting precision. There are other schemes such as neural-based voltage harmonic detection [9] and wavelet transform-based detection [10], but their practicability is to be further investigated. q
This work was supported part by the NNSF of China under Grants: 60674039. * Corresponding author. Tel.: +86 10 62799024; mobile: +86 13811560784; fax: +86 10 62795356. E-mail address: [email protected] (Y. Rong).
1569-190X/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.simpat.2009.02.011
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Nomenclature V_ s V_ L L1 R1 C1 C dc + V_ c I_c I_s I_L L2 R2 C2 j; l V_ c I_ c
the system voltage vector the load voltage vector the series side smoothing inductance the series side smoothing resistance the series side smoothing capacitor the DC-link capacitor positive sequence the compensating voltage vector the compensating current vector the system current vector the load current vector the shunt side smoothing inductance the shunt side smoothing resistance the shunt side smoothing capacitor j ¼ a; b; c; l ¼ 1; 2 negative sequence the voltage reference vector the current reference vector
As to the determination of the current reference, the instantaneous reactive power theory based methods (e.g. the p–q algorithm, the ip —iq algorithm and the d–q algorithm) are often used [11], whose application in the shunt APF has shown the good effectiveness. However, due to the conceptual limitation of instantaneous reactive power theory, these algorithms can only be applied in a three-phase system without zero-sequence currents or voltages [12]. There is a great tendency to focus on neural network because of its simplicity, learning and generalization ability. Moreover, artificial neural networks are reliable in handling high nonlinearities and uncertainties [13]. For examples, a feed forward and Elman’s recurrent neural network for harmonic detection process in active power filter is shown to be capable of improving the processing speed and simplify harmonic detection process [14]; harmonics of the power line distorted waveforms are detected using a three-layer neural network which is trained by several hundred distorted current waveforms including noise cases [15]. As well as in [9,10], the proposed neural networks based current detection methods are complicated and hard for hardware implementation. Although, an adaptive noise canceling technology based current detection is realizable by an analog circuit [16], the selection of learning rate is difficult and this is a greater impact on the performance. In this paper, a novel adaptive detection method using linear neurons is presented which can be utilized in both current and voltage detection. Each phase current or voltage is approximated by a neuron, whose filtered parameters are synchronously transformed to the unified structure neuron to acquire the fundamental component of each phase current or voltage. This method can precisely obtain the fundamental current and voltage of each phase and is not influenced by multiple zero crossings and the phase-shift generated by the LPF. The learning rate can be regulated in a wide range with little affection on the performance. Owing to its simple structure and theory, the detection method can be realized by digital chips such as DSP or FPGA. Moreover, the detection is done independent for each phase, which can be easily extended to three-phase systems, even three-phase four-wire systems. In this paper, this method is applied in a three-phase three-wire system with non-stiff voltage and non-balance loads. Based on the detected reference signals, control strategies are designed to guide the outputs of the inverters to follow the references. Among existing control strategies such as triangular wave comparison, hysteresis control and one cycle control, the first two can be applied in both current and voltage control, while the third one is applied in voltage tracking [8,17,18]. The hysteresis control is a closed loop control strategy, but the frequency of the PWM signals generated by the hysteresis control is not constant which is difficult for the passive filter design. The triangular wave comparison strategy can deal with PWM signals with variant frequency, however it is an open-loop controller. The one cycle control provides a good solution to both problems, but it is presently only applied in voltage tracking. Combining the advantages of the hysteresis control and the one cycle control, we propose a novel close-loop control strategy with constant frequency in current tracking called one cycle current control (OCCC), which can self-adjust when filter parameters are within a certain range. To demonstrate the overall effectiveness, the adaptive harmonic detection and the one cycle current control are applied in a three-phase three-wire system. We choose one of the four forms of compensating references in order to maintain the compensated load voltage at the nominal value and keep the compensated system current sinusoidal and in the phase with the load voltage. The simulation results show the effectiveness and reliability of the proposed strategies. 2. Mitigation of harmonics by UPQC As shown in Fig. 1, the UPQC isolates the source from the load by a series inverter, a shunt inverter and a DC-link capacitor. The series inverter is connected to the source through the transformer and the shunt inverter links the system by induc-
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isa vca vsa Ls Rs vsb
vsc N
vLa iLa
isb
vLb
vcb
isc
vLc
vcc C2
C1
R1 L 1
K1
K3
K5
S5
B
C
Cdc
A
K2
K4
K6
icc icb ica L2
S1
S3
+
C
S6
Rd1
iLc
Nonlinear Load
R2
UPQC
SOURCE
Ld1
iLb
Ld2 Rd2
Linear Load
LOADS
B A
S4
S2
Fig. 1. The topology of a three-phase UPQC with different loads.
tances. Due to the presence of Rs and Ls , the system voltage becomes non-stiff and hence the distorted system current that in turn affects the voltage of the point of common coupling (PCC) which can be also distorted by any occurrence of lighting stroke, system faults, starting of large asynchronous motors, allopatry harmonics, etc. The series inverter is utilized to generate the corresponding compensating voltage to maintain the PCC voltage at the nominal value and free of distortion. The shunt inverter has the same function as the series inverter which generates compensating current to keep the system current sinusoidal and in the phase with the load voltage. The loads include linear loads and nonlinear loads. Therefore, the system is unbalanced and the voltage and current are interacting. The distorted system voltage can be expanded using Fourier transformation
3 V sinðixt þ baiþ Þ þ V ai sinðixt þ bai Þ 7 6 i¼1 aiþ 7 6 vsa 7 6P 1 7 6 7 6 4 vsb 5 ¼ 6 V biþ sinðixt þ bbiþ Þ þ V bi sinðixt þ bbi Þ 7; 7 6 i¼1 7 6 1 vsc 5 4P V ciþ sinðixt þ bciþ Þ þ V ci sinðixt þ bci Þ 2
2P 1
3
ð1Þ
i¼1
where V jiþ and V ji are the amplitudes of the harmonic positive and negative sequence, respectively (the fundamental components correspond to i ¼ 1Þ; bjiþ and bji are the initial phases. Let
2
V a1 sinðxt þ ba1 Þ þ
1 P
V aiþ sinðixt þ baiþ Þ þ V ai sinðixt þ bai Þ
3
7 6 i¼2 7 6 7 6 1 P 7 6 7 6V 4 vcb 5 ¼ 6 b1 sinðxt þ bb1 Þ þ V biþ sinðixt þ bbiþ Þ þ V bi sinðixt þ bbi Þ 7; 7 6 i¼2 7 6 vcc 1 5 4 P V c1 sinðxt þ bc1 Þ þ V ciþ sinðixt þ bciþ Þ þ V ci sinðixt þ bci Þ 2
3
vca
ð2Þ
i¼2
vcj
where is the reference of the compensating voltage. The objective of the voltage detection is to get the compensating voltage vcj ðj ¼ a; b; cÞ of each phase, by which, the load voltage vLj ; j ¼ a; b; c, are free of distortion
2
vLa
3
2
vsa vca
3
2
V a1þ sinðxt þ ba1þ Þ
3
7 6 7 6 7 6 4 vLb 5 ¼ 4 vsb vcb 5 ¼ 4 V b1þ sinðxt þ bb1þ Þ 5: vsc vcc V c1þ sinðxt þ bc1þ Þ vLc
ð3Þ
Similarly, the distorted load current iLj can also be decomposed as the sum of the fundamental active positive sequence iLjp , the fundamental reactive positive sequence iLjq , the fundamental negative sequence iLj and the harmonic components iLjh as below (see Appendix A for more details)
2
iLa
3
2
iLap þ iLaq þ iLa þ iLah
3
6 7 6 7 4 iLb 5 ¼ 4 iLbp þ iLbq þ iLb þ iLbh 5: iLcp þ iLcq þ iLc þ iLch iLc Let I_c ¼ ica
2
icb
ð4Þ
T icc , where icj is the reference of the compensating current. If one can generate I_c as follows:
2 3 3 iLaq þ iLa þ iLah ica 6 7 6 7 4 icb 5 ¼ 4 iLbq þ iLb þ iLbh 5; iLcq þ iLc þ iLch icc
ð5Þ
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then the resulting system current is to be compensated sinusoidal and in phase with the load voltage
2
3 2 3 2 3 2 3 iLap iLa isa ica 6 7 6 7 6 7 6 7 4 isb 5 ¼ 4 iLb 5 4 icb 5 ¼ 4 iLbp 5: iLcp isc iLc icc
ð6Þ
From the above derivations (3) and (6), the reference voltage and current signals can be obtained by subtracting the fundamental positive voltage and the fundamental positive active current from the system voltage and the load current. Usually, to reduce the size of the compensating device, the fundamental reactive positive sequence may not need compensation. Therefore, there are two schemes in current compensation depending on whether or not compensating the reactive power. For the same reason, in voltage compensation, there are two compensating schemes depending on whether or not compensating the fundamental positive voltage. Therefore, there are four schemes in obtaining the reference signals of the UPQC. 3. Harmonic detection using linear neurons Harmonic detection is the critical part of the UPQC control. Fig. 2 displays a harmonic detection algorithm using linear neurons, which provides the reference values for the shunt and series inverters, respectively. The neurons are used to identify the fundamental voltage and current of each phase followed by the symmetric decomposition to calculate the fundamental positive sequence components. These components are then subtracted from the system voltage and the load current to give the reference voltage of PCC and the fundamental active current. Firstly, we describe how the voltage is detected in Fig. 2. Denote the error between V_ s and Y_ s as
e_ v ¼ V_ s Y_ v ;
ð7Þ
where V_ s is the system voltage vector and Y_ v ¼ ½ yva
yvb
T
yvc . The outputs of neurons Y_ v can be calculated as
Y_ v ¼ FðWXÞ;
ð8Þ 2
3
wa1 wa2 x where the elements of W ¼ 4 wb1 wb2 5 are the weights, X ¼ 1 are the inputs and F is an activation function selected as x2 wc1 wc2 FðxÞ ¼ x, i.e. the neurons are linear. Since, the neurons are used to obtain the fundamental component of each phase, the objective function is chosen as
Ej ¼
1 2 e ; 2 vj
j ¼ a; b; c:
ð9Þ
To minimize the objective function, a back-propagation algorithm is applied to tune the weights
Wðk þ 1Þ ¼ 2 WðkÞ þ DWðkÞ; 3 Dwa1 ðkÞ Dwa2 ðkÞ where DWðkÞ ¼ 4 Dwb1 ðkÞ Dwb2 ðkÞ 5, whose matrix elements are calculated as Dwc1 ðkÞ Dwc2 ðkÞ
Function generator
sin cos
sin Neurons1
cos
Neurons3
MAF
MAF
Neurons2
Neurons4
Fig. 2. Schematic diagram of the adaptive harmonic detection using linear neurons.
ð10Þ
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Dwjl ¼ g
@Ej @Ej @yvj ðkÞ ¼ g ¼ gðvsj yvj Þxl ; @wjl ðkÞ @yvj ðkÞ @wjl ðkÞ
ð11Þ
where j ¼ a; b; c; l ¼ 1; 2 and 0 < g < 1. Therefore, the outputs of neurons1 track the system voltage after k steps. To calculate the fundamental components, the weights matrix is transformed to neurons 2, whose structure are similar to that of the neurons 1, through a Moving Average Filter (MAF) to get the constant part of the weights matrix. The outputs of neurons 2 turn out to be
V_ 1 ¼ WX; V_ 01 ¼ WX 0 ;
ð12Þ
where W is the constant part of the weights matrix W and X 0 ¼ ½ x2 x1 T . Furthermore, the outputs of neurons 2 are symmetrically decomposed to calculate the fundamental positive sequence
v1a
1 _ ¼ V 3 1
v01a
2 3 1 T 6 7 V_ 01 4 a 5;
ð13Þ
a2
2
where a ¼ ej3p ; v1a is the A-phase voltage of the fundamental positive sequence and v01a leads 90° of v1a . Therefore, the fundamental positive sequence voltage V_ 1þ is
2
1
3
6 7 V_ 1þ ¼ 4 a 5v1a : 2 a
ð14Þ
The phases of v1a and v01a can be calculated as
ua u0a
v1a 1 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 : v1a v21a þ v02 1a
ð15Þ
If the system voltage needs to be maintained at the nominal value V_ pcc , the reference value can be calculated by multiplying the phase of the fundamental positive sequence voltages with the nominal amplitude. Finally, depending on what to be compensated, the value of V_ 1þ or V_ pcc is subtracted from the system voltage to calculate the reference values for the series inverter (see Fig. 2). Taking phase signals ua and u0 a as the inputs of the neurons 3 and 4, one can obtain the fundamental positive sequence components and the fundamental active components of the load current. The regulation of the weights of neurons 3 is similar with that of neurons 1 and the structure of neurons 4 is the same with that of neurons 2. Similar to the calculation of V_ 1þ , the fundamental positive sequence current I_1þ can be calculated (see Appendix B for details). In cases that the reactive current also needs to be compensated, the fundamental active current has to be calculated
2
I_1p
3 6 7 0 ¼ 4 a 5 ua i1a þ u0a i1a ua ; a2 1
ð16Þ
0
where i1a and i1a can be identified as v1a and v01a . According to the objective of the system current compensation, the reference values for the shunt inverter are calculated by subtracting the fundamental positive sequence current I_1þ or the fundamental active current I_1p from the load current. In summary, there are four cases for determining the reference signals as listed in Table 1. 4. Control strategies for UPQC Based on the detected reference signals, the controllers are designed to force the inverters to track the corresponding references. Combining the hysteresis control and the one cycle control, we propose a novel current tracking control strategy called one cycle current control (see Fig. 3). The principle of the one cycle current control is that the compensating current
Table 1 Four different forms of reference signals for UPQC. Case
Voltage reference signal
1 2 3 4
V_ c V_ c V_ c V_ c
¼ V_ s ¼ V_ s ¼ V_ s ¼ V_ s
V_ 1þ V_ pcc V_ 1þ V_ pcc
Current reference signal I_c I_c I_c I_ c
¼ I_s ¼ I_s ¼ I_s ¼ I_s
I_1þ I_1p I_1p I_1þ
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tracks the reference current in each cycle whose period is decided by the clock signal added to the set input of the RS flipflop. As shown in Fig. 3, the controller includes a comparator, a NOT gate, a RS flip-flop and two switches. To reduce the harmonic distortion of the compensated system current, we adopt different signals generating methods based on ua which is the A-phase unit reference phase (As shown in Fig. 3, ua is the control signal of the switches and the port 1 (port 2) is selected when ua < 0 ðua P 0Þ). As shown in Fig. 1, the A-phase compensating current is generated as
dica V A vLa ¼ ; dt L
ð17Þ
where V A is the output voltage of the shunt inverter. Suppose that V A ¼ vdc ðvdc Þ (where vdc is the DC-link voltage) if the driving signal equals to 1(0). As shown in Figs. 3 and 4a, when the ua P 0 and ica > ica ; R ¼ 1. Therefore the output of the RS flip-flop Q is based on the signal S. After the falling edge of the clock signal, Q equals to 0 and then the compensating current ica is
dica vdc vLaz ¼ ; dt L
ð18Þ
where vLaz presents that vLa is in a nonnegative half cycle. Therefore the compensating current ica is steepest descent until ica ¼ ica , and then R ¼ 0. Thereby the driving signal equals to 1, V A changes to vdc . The A-phase compensating current ascends and satisfies that
dica vdc vLaz ¼ : dt L
ð19Þ
Comparing Eqs. (18) and (19), the ascending rate is obviously lower than the decent rate (see Fig. 4a), and thereby, the deviation of the compensating current can be controlled to be small, which lowers the harmonic distortion of the compensated system current. Similar is the case when ua is negative. Therefore, the one cycle current control can be used phase by phase to track the detected reference currents. As shown in Eqs. (17)–(19), the increase of the inductance can decrease the slope of the current change and hence the harmonic distortion of the compensated system current. However a larger inductance may downgrade the dynamic tracking performance. Another function of the shunt inverter is to maintain the DC-link voltage, for which a PI controller is introduced to derive the amplitude of the active current needed to keep the capacitor voltage constant
ua* ica* ica
1 1
Driving signal
2 cl k
2
Fig. 3. The schematic diagram of the one cycle current control.
Fig. 4. The execution process of the one cycle current control: (a) ua is nonnegative, (b) ua is negative.
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Idc ¼ kp ðV dc vdc Þ þ ki
Z
ðV dc vdc Þdt:
ð20Þ
The output Idc of the PI controller is added to the amplitude of the fundamental active current as shown in Fig. 2.
Vc*
Vc Vc* Fig. 5. The controller for the voltage compensation.
500
a b
c
400
The system voltage (V)
300 200 100 0 -100 -200 -300 -400 -500 0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.18
0.2
0.22
0.24
time(s) Fig. 6. The system voltage V_ S .
250
a b
200
c
The load current (A)
150 100 50 0 -50 -100 -150 -200 -250 0.04
0.06
0.08
0.1
0.12
0.14
0.16
time(s) Fig. 7. The load current I_L .
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The function of the series inverter is used to compensate the load voltage distortion. Based on the known amplitude of the PCC voltage and the detected phase of the system voltage, the reference value V c can be calculated (see Table 1 case 2) and then be compared with a triangular wave to produce open-loop control signals for the series inverter. To further enhance its robustness, a PI controller is applied as shown in Fig. 5, but more voltage sensors will be needed (to detect the compensating voltage of the series inverter) and the parameters of the PI controller have to be manually regulated.
a
b
400
400
a b c 300
The detected fundamental active current
300
The detected PCC voltage
200
100
0
-100
-200
-300
-400
a b c
200
100
0
-100
-200
-300
-400 0.05
0.1
0.15
0.2
0.05
0.1
time(s)
0.15
0.2
time(s)
Fig. 8. The detected signals: (a) the reference voltage of the PCC V_ pcc , (b) the fundamental active current I_1p .
a
b
500
400
a b c
a b
400
c
300
300 200
The system current
The load voltage
200 100
0 -100
100
0
-100
-200 -200 -300 -300
-400
-500
-400 0.05
0.1
0.15
time(s)
0.2
0.05
0.1
0.15
0.2
time(s)
Fig. 9. The compensated results: (a) the compensated load voltage V_ L , (b) the compensated system current I_ s .
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5. Simulation results To demonstrate the effectiveness of the proposed detection method and control strategy, we simulate the system described in Fig. 1 using MATLAB 7.1. The nominal value of the PCC is 380 V/50 Hz and the system impedance Rs ¼ 0:02 X and Ls ¼ 10 lH. The RLC filters are used to mitigate the switching frequency harmonics generated by inverters. The parameters of RLC filters at the series inverter side are R1 ¼ 0:1 X; L1 ¼ 0:3 mH and C 1 ¼ 20 lF, while those at the shunt inverter
vsa (V)
a
500 0 -500 0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.16
0.18
0.2
0.22
0.24
0.16
0.18
0.2
0.22
0.24
time(s)
vsa (V)
b
200 0 -200 0.04
0.06
0.08
0.1
0.12
0.14
time(s)
vsa (V)
c
500 0 -500 0.04
0.06
0.08
0.1
0.12
0.14
time(s) Fig. 10. The compensating process: (a) the A-phase system voltage vsa , (b) the A-phase compensating voltage generated by the series inverter vca , (c) the A-phase load voltage with compensation vLa .
i La(A)
a
500 0 -500 0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.16
0.18
0.2
0.22
0.16
0.18
0.2
0.22
0.16
0.18
0.2
0.22
time(s)
i ca (A)
b
200 0 -200 0.02
0.04
0.06
0.08
0.1
0.12
0.14
time(s)
i sa (A)
c
500 0 -500 0.02
0.04
0.06
0.08
0.1
0.12
0.14
d
1100
vdc (V)
time(s)
1000 900 0.02
0.04
0.06
0.08
0.1
0.12
0.14
time(s) Fig. 11. The compensating process of the shunt inverter: (a) the A-phase load current iLa , (b) the A-phase compensating current generated by the shunt inverter ica , (c) the system current after compensation isa , (d) the DC-side voltage vdc .
Y. Rong et al. / Simulation Modelling Practice and Theory 17 (2009) 955–966
a
200
* (V) vca and v ca
964
100
v*ca vca
0
-100
-200 0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
b
200
i ca and i ca(A)
time(s)
100
i*ca
*
ica
0
-100
-200 0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
time(s) Fig. 12. The tracking characteristic of the UPQC: (a) the A-phase voltage reference value vca and the A-phase compensating voltage vca , (b) the A-phase current reference value ica and the A-phase compensating current ica .
side are R2 ¼ 1:4 X; L2 ¼ 1 mH;C 2 ¼ 100 lF. The DC-link capacitor C dc is 10; 000 lF and the DC-link reference voltage is 1000 V. As shown in Fig. 6, the system voltage with multiple zero crossings is distorted and unsymmetrical which is caused by the allopatry harmonics and local nonlinear loads. Fig. 7 displays the load current generated by local non-balance loads consisting of a three-phase diode rectifier ðRd1 ¼ 5 X; Ld1 ¼ 5 mHÞ and a RL linear load bridged between the A and B phases (Rd2 ¼ 5 X and Ld2 ¼ 50 lH). The DC side of the rectifier changes to Rd1 ¼ 10 X and Ld1 ¼ 1 mH at 0.14 s and the THD (total harmonic distortion) of the load current are larger than 20% both before and after load change. We choose case 2 in Table 1 for the reference signals’ calculation. As described in Fig. 8, with the detected phase of the system voltage and the known nominal amplitude of the PCC, we are able to obtain the detected PCC voltage (see Fig. 8a). Due to the sag of the DC-link voltage (see Fig. 11d), the amplitude of the detected fundamental active current fluctuates as shown in Fig. 8b which is compensated by the PI controller (see Eq. (20), where kp ¼ 2:36 A=V s;ki ¼ 3:57 A=V sÞ that absorbs active power to maintain the DC-link voltage constant. When the load changes at 0.14 s, the adaptive harmonic detection responds fast (see Fig. 8b). In addition, the learning rate g is chosen in a wide range as 0.01–0.5 and the detection results are almost unchanged as shown in Fig. 8. The detected references are fed into the one cycle current controller and the triangular wave comparison controller which force the inverters to track the references. The parameters of the PI controller for enhancing the robustness of the series inverter are kp ¼ 2:16; ki ¼ 1:32. The compensated results are given in Fig. 9, which show that the compensated three-phase load voltages are sinusoidal and at the nominal value, and the compensated threephase system currents are free of distortion. Comparing Fig. 9 with Fig. 8, we can see that the compensated load voltage and system current can fast and precisely track the detected PCC voltage and the fundamental active current which proves that the controllers for the shunt and series inverters are effective. The details of the compensation process are shown in Fig. 10 (Fig. 11) where it is seen that, after compensation, the Aphase load voltage (current) is sinusoidal and nominal. In Fig. 11b, the compensating current is larger in the first 2 cycle due to the sag of the DC-side voltage (see Fig. 11d), including that the shunt inverter has to draw more active power at the beginning to maintain the DC-link voltage around the reference value. The swell of the DC-link voltage is due to the load change at 0.14 s and by the PI controller, the DC-link voltage is pulled back to the reference value in 2–3 cycles (see Fig. 11d), Fig. 12 shows the tracking characteristics of the two controllers for the series inverter and the shunt inverter, the both control strategies can track the reference values fast and precisely. 6. Conclusion We propose an adaptive harmonic detection method and a one cycle current control strategy. The adaptive harmonic detection method can deal with multiple zero crossings in the voltage. By an adaptively regulated neuron networks, this
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detection method is able to quickly identify precise values of the voltage or current reference signals under various circumstance which can be extended to single-phase or three-phase four-wire system because it works independently in each phase. The one cycle current control strategy is also shown to have precise and rapid tracking performance. It is more advantageous than the direct triangular wave comparison controller by its close-loop control strategy which is robust by nature. The strategy is also better than the hysteresis control because the frequency of the control signal by the OCCC is constant. The effectiveness of the detection method and control strategies is exhibited by simulation in a three-phase UPQC. Appendix A The load current can be expanded using Fourier transformation 3 I sinðixt þ haiþ Þ þ Iai sinðixt þ hai Þ 7 6 i¼1 aiþ 7 6 iLa 7 61 6 7 6 P I sinðixt þ h Þ þ I sinðixt þ h Þ 7 4 iLb 5 ¼ 6 biþ biþ bi bi 7 7 6 i¼1 7 6 1 iLc 5 4P Iciþ sinðixt þ hciþ Þ þ Ici sinðixt þ hci Þ 2
2P 1
3
i¼1
3 1 P Iaiþ sinðixt þ haiþ Þ þ Iai sinðixt þ hai Þ 7 6 i¼2 7 6 7 6 1 6 I sinðxt þ b Þ cosðh b Þ þ I cosðxt þ b Þ sinðh b Þ þ I sinðxt þ h Þ þ P I sinðixt þ h Þ þ I sinðixt þ h Þ 7 ¼ 6 b1þ 7 b1þ b1þ b1þ b1 b1 biþ biþ bi bi b1þ b1þ b1þ b1þ 7 6 i¼2 7 6 1 5 4 P Ic1þ sinðxt þ bc1þ Þ cosðhc1þ bc1þ Þ þ Ic1þ cosðxt þ bc1þ Þ sinðhc1þ bc1þ Þ þ Ic1 sinðxt þ hc1 Þ þ Iciþ sinðixt þ hciþ Þ þ Ici sinðixt þ hci Þ i¼2 2 3 iLap þ iLaq þ iLa þ iLah 6 7 ¼ 4 iLbp þ iLbq þ iLb þ iLbh 5; ðA:1Þ iLcp þ iLcq þ iLc þ iLch 2
Ia1þ sinðxt þ ba1þ Þ cosðha1þ ba1þ Þ þ Ia1þ cosðxt þ ba1þ Þ sinðha1þ ba1þ Þ þ Ia1 sinðxt þ ha1 Þ þ
where iLj is the load current, iLjp ¼ Ij1þ sinðxt þ bj1þ Þ cosðhj1þ bj1þ Þ is the fundamental active current, iLjq ¼ Ij1þ cosðxt þ bj1þ Þ sinðhj1þ bj1þ Þ is the fundamental reactive current, iLa ¼ Ia1 sinðxt þ ha1 Þ is the negative sequence P components and iLjh ¼ 1 i¼2 Ijiþ sinðixt þ hjiþ Þ þ Iji sinðixt þ hji Þ is the harmonic current ðj ¼ a; b; cÞ. Appendix B Denote that
e_ i ¼ I_s Y_ i ; Y_ i ¼ FðMXÞ; where I_s is 2 ma1 M ¼ 4 mb1 mc1
Eij ¼
ðB:1Þ ðB:2Þ
ua and the system current, Y_ i ¼ ½ yia yib yic T is the outputs of neurons 3, the inputs of neurons X ¼ u0 a 3 ma2 mb2 5. The neurons are set to be linear so that the activation function FðxÞ ¼ x. Define the objective function as mc2
1 2 e : 2 ij
ðB:3Þ
To minimize the objective function, the back-propagation algorithm is utilized to regulate the weights
Mðk þ 1Þ ¼ MðkÞ þ DMðkÞ; 2
Dma1 ðkÞ where DMðkÞ ¼ 4 Dmb1 ðkÞ Dmc1 ðkÞ
Dmjl ðkÞ ¼ g
ðB:4Þ 3
Dma2 ðkÞ Dmb2 ðkÞ 5, whose matrix elements can be regulated as Dmc2 ðkÞ
@Eij @Eij @yij ðkÞ ¼ g ¼ gðisj yij Þxl ; @mjl ðkÞ @yij ðkÞ @mjl ðkÞ
ðB:5Þ
where 0 < g < 1; j ¼ a; b; c and l ¼ 1; 2. References [1] M.H.J. Bollen, What is power quality, Electric Power System Research 66 (2003) 5–14. [2] H. Akagi, New trends in active filters for power conditioning, IEEE Transactions on Industry Applications 32 (6) (1996) 1312–1322. [3] Leszek S. Czarnecki, Instantaneous reactive power p–q theory and power properties of three-phase systems, IEEE Transactions on Power Delivery 21 (1) (2006) 362–367.
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[4] H. Akagi, Y. Kanazawa, A. Nabae, Instantaneous reactive power compensators comprising switching devices without energy storage components, IEEE Transactions on Industry Applications 20 (1984) 625–630. [5] D.A. Torrey, A.M. Al-Zamel, Single phase active power filter for multiple nonlinear loads, IEEE Transactions on Power Electronics 10 (3) (1995) 263–272. [6] M. Karimi-Ghartemani, H. Mokhtari, M.R. Iravani, A signal processing system for extraction of harmonics and reactive current of single phase systems, IEEE Transactions on Power Delivery 19 (3) (2004) 979–986. [7] Linash P. Kunjumuhammed, Mahesh K. Mishra, A control algorithm for single-phase active power filter under non-stiff voltage source, IEEE Transactions on Power Electronics 21 (3) (2006) 822–825. [8] Jianjun Gu, Dianguo Xu, Hankui Liu, Unified power quality conditioner (UPQC): the principle, control, and application, in: Power Conversion Conference, 2002, PCC, Osaka, Japan, vol. 1, 2–5 April, 2002, pp. 80–84. [9] Hiroyuki Mori, Kenji Itou, Hiroshi Uematsu, Senji Tsuzuki, An artificial neural-net based method for predicting power system voltage harmonics, IEEE Transactions on Power Delivery 7 (1) (1992) 402–409. [10] A. Elnady, A. Goauda, M.M.A. Salama, Unified power quality conditioner with a novel control algorithm based on wavelet transform, in: Canadian Conference on Electrical and Computer Engineering, Toronto, Canada, vol. 2, 13–16 May, 2001, pp. 1041–1045. [11] L. Asiminoaei, F. Blaabjerg, S. Hansen, Detection is key harmonic detection methods for active power filter applications, IEEE Industry Application Magazine (2007) 22–33. [12] J.L. willems, A new interpretation of the Akagi-Nabae power components of non-sinusoidal three phase situations, IEEE Transactions on Instrumentation and Measurement 41 (4) (1992) 523–527. [13] Abdelaziz Zouidi, Farhat Fnaiech, Kamal AL-Haddad, Salem Rahmani, Artificial neural networks as harmonic detectors, in: 32nd Annual Conference on IEEE Industrial Electronics, IECON 2006, Paris, France, 6–10 November, 2006, pp. 2889–2892. [14] F. Temurtas, R. Gunturkun, N. Yumusak, H. Temurtas, Harmonic detection using feed forward and recurrent neural networks for active filters, Electric Power Systems Research 72 (2004) 33–40. [15] Hsiung Cheng Lin, Intelligent neural network-based fast power system harmonic detection, IEEE Transactions on Industrial Electronics 54 (1) (2007) 43–52. [16] Qun Wang, Ning Wu, Zhaoan Wang, A neuron adaptive detecting approach of harmonic current for APF and its realization of analog circuit, IEEE Transactions on Instrumentation and Measurement 50 (1) (2001) 77–84. [17] A.N. Tiwari, P. Agawal, S.P. Srivastava, Modified hysteresis controlled PWM rectifier, IEE Proceedings – Electric Power Applications 150 (4) (2003) 389– 396. [18] Yang Chen, Keyue Ma Smedley, Parallel operation of one-cycle controlled three-phase PFC rectifiers, IEEE Transactions on Industrial Electronics 54 (6) (2007) 3217–3224.
Contents lists available at ScienceDirect
Simulation Modelling Practice and Theory journal homepage: www.elsevier.com/locate/simpat
An adaptive harmonic detection and a novel current control strategy for unified power quality conditioner q Yuanjie Rong a,*, Chunwen Li a, Qingqing Ding b a b
Department of Automation, Tsinghua University, Beijing 100084, China Department of Electrical Engineering, Tsinghua University, Beijing 100084, China
a r t i c l e
i n f o
Article history: Received 24 September 2008 Received in revised form 5 December 2008 Accepted 17 February 2009 Available online 13 March 2009
Keywords: Adaptive harmonic detection Linear neuron Unified power quality conditioner One cycle current control
a b s t r a c t This paper proposes an adaptive harmonic detection to precisely detect the voltage with multiple zero crossings and adaptively obtain the reference signals, which makes use of linear neurons to approximate the fundamental component in each phase followed by a symmetric decomposition that calculates the fundamental positive components. According to the compensating requirements, we obtain four different forms of the reference signals. The detected reference signals are then fed into a triangular wave comparison control together with a PI controller and a one cycle current control to force the compensating voltage and current to track the reference signals. The one cycle current control (OCCC) is a combination of the one cycle control and the hysteresis control, which guarantees both tracking performances and constant frequency. The integration of the adaptive detection method and the one cycle current control in a three-phase unified power quality conditioner (UPQC) are simulated, where the effectiveness and reliability of the proposed strategies are demonstrated. Ó 2009 Elsevier B.V. All rights reserved.
1. Introduction The electric power network is extremely complex and mutually influent [1]. To attenuate the mutual influence, unified power quality conditioner (UPQC) was presented to synchronously deal with the current and voltage distortion and isolate the loads from the supply system [2]. The current and voltage detection are critical to the implementation of the UPQC and there are various algorithms including instantaneous reactive power theory, Fourier transformation, adaptive algorithms, etc. [3–16]. Among those algorithms, instantaneous reactive power theory based detection algorithms, the high pass filter (HPF) and the low pass filter (LPF) are the most widely used [3–8,11,12]. Usually, the phase of the system voltage is detected by the zero crossing detection [5] and the Phase-Locked Loop (PLL) [6]. However these two approaches have their shortcomings in that the zero crossing detection suffers from the non-stiff voltage and the latter is affected by the inherent delay of the PLL. In this regard, a method using a LPF with a phase corrector is presented to obtain the precise phase of a single-phase system voltage that is non-stiff and has multiple zero crossings via manual regulation of the phase corrector parameters [7]. Gu et al. [8] extends this method to a three-phase system which utilizes the LPF to get the fundamental voltage of each phase and the symmetric decomposition to calculate the phase unit reference. However additional phase-shift generated by LPF downgrades the detecting precision. There are other schemes such as neural-based voltage harmonic detection [9] and wavelet transform-based detection [10], but their practicability is to be further investigated. q
This work was supported part by the NNSF of China under Grants: 60674039. * Corresponding author. Tel.: +86 10 62799024; mobile: +86 13811560784; fax: +86 10 62795356. E-mail address: [email protected] (Y. Rong).
1569-190X/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.simpat.2009.02.011
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Nomenclature V_ s V_ L L1 R1 C1 C dc + V_ c I_c I_s I_L L2 R2 C2 j; l V_ c I_ c
the system voltage vector the load voltage vector the series side smoothing inductance the series side smoothing resistance the series side smoothing capacitor the DC-link capacitor positive sequence the compensating voltage vector the compensating current vector the system current vector the load current vector the shunt side smoothing inductance the shunt side smoothing resistance the shunt side smoothing capacitor j ¼ a; b; c; l ¼ 1; 2 negative sequence the voltage reference vector the current reference vector
As to the determination of the current reference, the instantaneous reactive power theory based methods (e.g. the p–q algorithm, the ip —iq algorithm and the d–q algorithm) are often used [11], whose application in the shunt APF has shown the good effectiveness. However, due to the conceptual limitation of instantaneous reactive power theory, these algorithms can only be applied in a three-phase system without zero-sequence currents or voltages [12]. There is a great tendency to focus on neural network because of its simplicity, learning and generalization ability. Moreover, artificial neural networks are reliable in handling high nonlinearities and uncertainties [13]. For examples, a feed forward and Elman’s recurrent neural network for harmonic detection process in active power filter is shown to be capable of improving the processing speed and simplify harmonic detection process [14]; harmonics of the power line distorted waveforms are detected using a three-layer neural network which is trained by several hundred distorted current waveforms including noise cases [15]. As well as in [9,10], the proposed neural networks based current detection methods are complicated and hard for hardware implementation. Although, an adaptive noise canceling technology based current detection is realizable by an analog circuit [16], the selection of learning rate is difficult and this is a greater impact on the performance. In this paper, a novel adaptive detection method using linear neurons is presented which can be utilized in both current and voltage detection. Each phase current or voltage is approximated by a neuron, whose filtered parameters are synchronously transformed to the unified structure neuron to acquire the fundamental component of each phase current or voltage. This method can precisely obtain the fundamental current and voltage of each phase and is not influenced by multiple zero crossings and the phase-shift generated by the LPF. The learning rate can be regulated in a wide range with little affection on the performance. Owing to its simple structure and theory, the detection method can be realized by digital chips such as DSP or FPGA. Moreover, the detection is done independent for each phase, which can be easily extended to three-phase systems, even three-phase four-wire systems. In this paper, this method is applied in a three-phase three-wire system with non-stiff voltage and non-balance loads. Based on the detected reference signals, control strategies are designed to guide the outputs of the inverters to follow the references. Among existing control strategies such as triangular wave comparison, hysteresis control and one cycle control, the first two can be applied in both current and voltage control, while the third one is applied in voltage tracking [8,17,18]. The hysteresis control is a closed loop control strategy, but the frequency of the PWM signals generated by the hysteresis control is not constant which is difficult for the passive filter design. The triangular wave comparison strategy can deal with PWM signals with variant frequency, however it is an open-loop controller. The one cycle control provides a good solution to both problems, but it is presently only applied in voltage tracking. Combining the advantages of the hysteresis control and the one cycle control, we propose a novel close-loop control strategy with constant frequency in current tracking called one cycle current control (OCCC), which can self-adjust when filter parameters are within a certain range. To demonstrate the overall effectiveness, the adaptive harmonic detection and the one cycle current control are applied in a three-phase three-wire system. We choose one of the four forms of compensating references in order to maintain the compensated load voltage at the nominal value and keep the compensated system current sinusoidal and in the phase with the load voltage. The simulation results show the effectiveness and reliability of the proposed strategies. 2. Mitigation of harmonics by UPQC As shown in Fig. 1, the UPQC isolates the source from the load by a series inverter, a shunt inverter and a DC-link capacitor. The series inverter is connected to the source through the transformer and the shunt inverter links the system by induc-
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isa vca vsa Ls Rs vsb
vsc N
vLa iLa
isb
vLb
vcb
isc
vLc
vcc C2
C1
R1 L 1
K1
K3
K5
S5
B
C
Cdc
A
K2
K4
K6
icc icb ica L2
S1
S3
+
C
S6
Rd1
iLc
Nonlinear Load
R2
UPQC
SOURCE
Ld1
iLb
Ld2 Rd2
Linear Load
LOADS
B A
S4
S2
Fig. 1. The topology of a three-phase UPQC with different loads.
tances. Due to the presence of Rs and Ls , the system voltage becomes non-stiff and hence the distorted system current that in turn affects the voltage of the point of common coupling (PCC) which can be also distorted by any occurrence of lighting stroke, system faults, starting of large asynchronous motors, allopatry harmonics, etc. The series inverter is utilized to generate the corresponding compensating voltage to maintain the PCC voltage at the nominal value and free of distortion. The shunt inverter has the same function as the series inverter which generates compensating current to keep the system current sinusoidal and in the phase with the load voltage. The loads include linear loads and nonlinear loads. Therefore, the system is unbalanced and the voltage and current are interacting. The distorted system voltage can be expanded using Fourier transformation
3 V sinðixt þ baiþ Þ þ V ai sinðixt þ bai Þ 7 6 i¼1 aiþ 7 6 vsa 7 6P 1 7 6 7 6 4 vsb 5 ¼ 6 V biþ sinðixt þ bbiþ Þ þ V bi sinðixt þ bbi Þ 7; 7 6 i¼1 7 6 1 vsc 5 4P V ciþ sinðixt þ bciþ Þ þ V ci sinðixt þ bci Þ 2
2P 1
3
ð1Þ
i¼1
where V jiþ and V ji are the amplitudes of the harmonic positive and negative sequence, respectively (the fundamental components correspond to i ¼ 1Þ; bjiþ and bji are the initial phases. Let
2
V a1 sinðxt þ ba1 Þ þ
1 P
V aiþ sinðixt þ baiþ Þ þ V ai sinðixt þ bai Þ
3
7 6 i¼2 7 6 7 6 1 P 7 6 7 6V 4 vcb 5 ¼ 6 b1 sinðxt þ bb1 Þ þ V biþ sinðixt þ bbiþ Þ þ V bi sinðixt þ bbi Þ 7; 7 6 i¼2 7 6 vcc 1 5 4 P V c1 sinðxt þ bc1 Þ þ V ciþ sinðixt þ bciþ Þ þ V ci sinðixt þ bci Þ 2
3
vca
ð2Þ
i¼2
vcj
where is the reference of the compensating voltage. The objective of the voltage detection is to get the compensating voltage vcj ðj ¼ a; b; cÞ of each phase, by which, the load voltage vLj ; j ¼ a; b; c, are free of distortion
2
vLa
3
2
vsa vca
3
2
V a1þ sinðxt þ ba1þ Þ
3
7 6 7 6 7 6 4 vLb 5 ¼ 4 vsb vcb 5 ¼ 4 V b1þ sinðxt þ bb1þ Þ 5: vsc vcc V c1þ sinðxt þ bc1þ Þ vLc
ð3Þ
Similarly, the distorted load current iLj can also be decomposed as the sum of the fundamental active positive sequence iLjp , the fundamental reactive positive sequence iLjq , the fundamental negative sequence iLj and the harmonic components iLjh as below (see Appendix A for more details)
2
iLa
3
2
iLap þ iLaq þ iLa þ iLah
3
6 7 6 7 4 iLb 5 ¼ 4 iLbp þ iLbq þ iLb þ iLbh 5: iLcp þ iLcq þ iLc þ iLch iLc Let I_c ¼ ica
2
icb
ð4Þ
T icc , where icj is the reference of the compensating current. If one can generate I_c as follows:
2 3 3 iLaq þ iLa þ iLah ica 6 7 6 7 4 icb 5 ¼ 4 iLbq þ iLb þ iLbh 5; iLcq þ iLc þ iLch icc
ð5Þ
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then the resulting system current is to be compensated sinusoidal and in phase with the load voltage
2
3 2 3 2 3 2 3 iLap iLa isa ica 6 7 6 7 6 7 6 7 4 isb 5 ¼ 4 iLb 5 4 icb 5 ¼ 4 iLbp 5: iLcp isc iLc icc
ð6Þ
From the above derivations (3) and (6), the reference voltage and current signals can be obtained by subtracting the fundamental positive voltage and the fundamental positive active current from the system voltage and the load current. Usually, to reduce the size of the compensating device, the fundamental reactive positive sequence may not need compensation. Therefore, there are two schemes in current compensation depending on whether or not compensating the reactive power. For the same reason, in voltage compensation, there are two compensating schemes depending on whether or not compensating the fundamental positive voltage. Therefore, there are four schemes in obtaining the reference signals of the UPQC. 3. Harmonic detection using linear neurons Harmonic detection is the critical part of the UPQC control. Fig. 2 displays a harmonic detection algorithm using linear neurons, which provides the reference values for the shunt and series inverters, respectively. The neurons are used to identify the fundamental voltage and current of each phase followed by the symmetric decomposition to calculate the fundamental positive sequence components. These components are then subtracted from the system voltage and the load current to give the reference voltage of PCC and the fundamental active current. Firstly, we describe how the voltage is detected in Fig. 2. Denote the error between V_ s and Y_ s as
e_ v ¼ V_ s Y_ v ;
ð7Þ
where V_ s is the system voltage vector and Y_ v ¼ ½ yva
yvb
T
yvc . The outputs of neurons Y_ v can be calculated as
Y_ v ¼ FðWXÞ;
ð8Þ 2
3
wa1 wa2 x where the elements of W ¼ 4 wb1 wb2 5 are the weights, X ¼ 1 are the inputs and F is an activation function selected as x2 wc1 wc2 FðxÞ ¼ x, i.e. the neurons are linear. Since, the neurons are used to obtain the fundamental component of each phase, the objective function is chosen as
Ej ¼
1 2 e ; 2 vj
j ¼ a; b; c:
ð9Þ
To minimize the objective function, a back-propagation algorithm is applied to tune the weights
Wðk þ 1Þ ¼ 2 WðkÞ þ DWðkÞ; 3 Dwa1 ðkÞ Dwa2 ðkÞ where DWðkÞ ¼ 4 Dwb1 ðkÞ Dwb2 ðkÞ 5, whose matrix elements are calculated as Dwc1 ðkÞ Dwc2 ðkÞ
Function generator
sin cos
sin Neurons1
cos
Neurons3
MAF
MAF
Neurons2
Neurons4
Fig. 2. Schematic diagram of the adaptive harmonic detection using linear neurons.
ð10Þ
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Dwjl ¼ g
@Ej @Ej @yvj ðkÞ ¼ g ¼ gðvsj yvj Þxl ; @wjl ðkÞ @yvj ðkÞ @wjl ðkÞ
ð11Þ
where j ¼ a; b; c; l ¼ 1; 2 and 0 < g < 1. Therefore, the outputs of neurons1 track the system voltage after k steps. To calculate the fundamental components, the weights matrix is transformed to neurons 2, whose structure are similar to that of the neurons 1, through a Moving Average Filter (MAF) to get the constant part of the weights matrix. The outputs of neurons 2 turn out to be
V_ 1 ¼ WX; V_ 01 ¼ WX 0 ;
ð12Þ
where W is the constant part of the weights matrix W and X 0 ¼ ½ x2 x1 T . Furthermore, the outputs of neurons 2 are symmetrically decomposed to calculate the fundamental positive sequence
v1a
1 _ ¼ V 3 1
v01a
2 3 1 T 6 7 V_ 01 4 a 5;
ð13Þ
a2
2
where a ¼ ej3p ; v1a is the A-phase voltage of the fundamental positive sequence and v01a leads 90° of v1a . Therefore, the fundamental positive sequence voltage V_ 1þ is
2
1
3
6 7 V_ 1þ ¼ 4 a 5v1a : 2 a
ð14Þ
The phases of v1a and v01a can be calculated as
ua u0a
v1a 1 ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 0 : v1a v21a þ v02 1a
ð15Þ
If the system voltage needs to be maintained at the nominal value V_ pcc , the reference value can be calculated by multiplying the phase of the fundamental positive sequence voltages with the nominal amplitude. Finally, depending on what to be compensated, the value of V_ 1þ or V_ pcc is subtracted from the system voltage to calculate the reference values for the series inverter (see Fig. 2). Taking phase signals ua and u0 a as the inputs of the neurons 3 and 4, one can obtain the fundamental positive sequence components and the fundamental active components of the load current. The regulation of the weights of neurons 3 is similar with that of neurons 1 and the structure of neurons 4 is the same with that of neurons 2. Similar to the calculation of V_ 1þ , the fundamental positive sequence current I_1þ can be calculated (see Appendix B for details). In cases that the reactive current also needs to be compensated, the fundamental active current has to be calculated
2
I_1p
3 6 7 0 ¼ 4 a 5 ua i1a þ u0a i1a ua ; a2 1
ð16Þ
0
where i1a and i1a can be identified as v1a and v01a . According to the objective of the system current compensation, the reference values for the shunt inverter are calculated by subtracting the fundamental positive sequence current I_1þ or the fundamental active current I_1p from the load current. In summary, there are four cases for determining the reference signals as listed in Table 1. 4. Control strategies for UPQC Based on the detected reference signals, the controllers are designed to force the inverters to track the corresponding references. Combining the hysteresis control and the one cycle control, we propose a novel current tracking control strategy called one cycle current control (see Fig. 3). The principle of the one cycle current control is that the compensating current
Table 1 Four different forms of reference signals for UPQC. Case
Voltage reference signal
1 2 3 4
V_ c V_ c V_ c V_ c
¼ V_ s ¼ V_ s ¼ V_ s ¼ V_ s
V_ 1þ V_ pcc V_ 1þ V_ pcc
Current reference signal I_c I_c I_c I_ c
¼ I_s ¼ I_s ¼ I_s ¼ I_s
I_1þ I_1p I_1p I_1þ
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tracks the reference current in each cycle whose period is decided by the clock signal added to the set input of the RS flipflop. As shown in Fig. 3, the controller includes a comparator, a NOT gate, a RS flip-flop and two switches. To reduce the harmonic distortion of the compensated system current, we adopt different signals generating methods based on ua which is the A-phase unit reference phase (As shown in Fig. 3, ua is the control signal of the switches and the port 1 (port 2) is selected when ua < 0 ðua P 0Þ). As shown in Fig. 1, the A-phase compensating current is generated as
dica V A vLa ¼ ; dt L
ð17Þ
where V A is the output voltage of the shunt inverter. Suppose that V A ¼ vdc ðvdc Þ (where vdc is the DC-link voltage) if the driving signal equals to 1(0). As shown in Figs. 3 and 4a, when the ua P 0 and ica > ica ; R ¼ 1. Therefore the output of the RS flip-flop Q is based on the signal S. After the falling edge of the clock signal, Q equals to 0 and then the compensating current ica is
dica vdc vLaz ¼ ; dt L
ð18Þ
where vLaz presents that vLa is in a nonnegative half cycle. Therefore the compensating current ica is steepest descent until ica ¼ ica , and then R ¼ 0. Thereby the driving signal equals to 1, V A changes to vdc . The A-phase compensating current ascends and satisfies that
dica vdc vLaz ¼ : dt L
ð19Þ
Comparing Eqs. (18) and (19), the ascending rate is obviously lower than the decent rate (see Fig. 4a), and thereby, the deviation of the compensating current can be controlled to be small, which lowers the harmonic distortion of the compensated system current. Similar is the case when ua is negative. Therefore, the one cycle current control can be used phase by phase to track the detected reference currents. As shown in Eqs. (17)–(19), the increase of the inductance can decrease the slope of the current change and hence the harmonic distortion of the compensated system current. However a larger inductance may downgrade the dynamic tracking performance. Another function of the shunt inverter is to maintain the DC-link voltage, for which a PI controller is introduced to derive the amplitude of the active current needed to keep the capacitor voltage constant
ua* ica* ica
1 1
Driving signal
2 cl k
2
Fig. 3. The schematic diagram of the one cycle current control.
Fig. 4. The execution process of the one cycle current control: (a) ua is nonnegative, (b) ua is negative.
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Idc ¼ kp ðV dc vdc Þ þ ki
Z
ðV dc vdc Þdt:
ð20Þ
The output Idc of the PI controller is added to the amplitude of the fundamental active current as shown in Fig. 2.
Vc*
Vc Vc* Fig. 5. The controller for the voltage compensation.
500
a b
c
400
The system voltage (V)
300 200 100 0 -100 -200 -300 -400 -500 0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.18
0.2
0.22
0.24
time(s) Fig. 6. The system voltage V_ S .
250
a b
200
c
The load current (A)
150 100 50 0 -50 -100 -150 -200 -250 0.04
0.06
0.08
0.1
0.12
0.14
0.16
time(s) Fig. 7. The load current I_L .
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The function of the series inverter is used to compensate the load voltage distortion. Based on the known amplitude of the PCC voltage and the detected phase of the system voltage, the reference value V c can be calculated (see Table 1 case 2) and then be compared with a triangular wave to produce open-loop control signals for the series inverter. To further enhance its robustness, a PI controller is applied as shown in Fig. 5, but more voltage sensors will be needed (to detect the compensating voltage of the series inverter) and the parameters of the PI controller have to be manually regulated.
a
b
400
400
a b c 300
The detected fundamental active current
300
The detected PCC voltage
200
100
0
-100
-200
-300
-400
a b c
200
100
0
-100
-200
-300
-400 0.05
0.1
0.15
0.2
0.05
0.1
time(s)
0.15
0.2
time(s)
Fig. 8. The detected signals: (a) the reference voltage of the PCC V_ pcc , (b) the fundamental active current I_1p .
a
b
500
400
a b c
a b
400
c
300
300 200
The system current
The load voltage
200 100
0 -100
100
0
-100
-200 -200 -300 -300
-400
-500
-400 0.05
0.1
0.15
time(s)
0.2
0.05
0.1
0.15
0.2
time(s)
Fig. 9. The compensated results: (a) the compensated load voltage V_ L , (b) the compensated system current I_ s .
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5. Simulation results To demonstrate the effectiveness of the proposed detection method and control strategy, we simulate the system described in Fig. 1 using MATLAB 7.1. The nominal value of the PCC is 380 V/50 Hz and the system impedance Rs ¼ 0:02 X and Ls ¼ 10 lH. The RLC filters are used to mitigate the switching frequency harmonics generated by inverters. The parameters of RLC filters at the series inverter side are R1 ¼ 0:1 X; L1 ¼ 0:3 mH and C 1 ¼ 20 lF, while those at the shunt inverter
vsa (V)
a
500 0 -500 0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
0.16
0.18
0.2
0.22
0.24
0.16
0.18
0.2
0.22
0.24
time(s)
vsa (V)
b
200 0 -200 0.04
0.06
0.08
0.1
0.12
0.14
time(s)
vsa (V)
c
500 0 -500 0.04
0.06
0.08
0.1
0.12
0.14
time(s) Fig. 10. The compensating process: (a) the A-phase system voltage vsa , (b) the A-phase compensating voltage generated by the series inverter vca , (c) the A-phase load voltage with compensation vLa .
i La(A)
a
500 0 -500 0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.16
0.18
0.2
0.22
0.16
0.18
0.2
0.22
0.16
0.18
0.2
0.22
time(s)
i ca (A)
b
200 0 -200 0.02
0.04
0.06
0.08
0.1
0.12
0.14
time(s)
i sa (A)
c
500 0 -500 0.02
0.04
0.06
0.08
0.1
0.12
0.14
d
1100
vdc (V)
time(s)
1000 900 0.02
0.04
0.06
0.08
0.1
0.12
0.14
time(s) Fig. 11. The compensating process of the shunt inverter: (a) the A-phase load current iLa , (b) the A-phase compensating current generated by the shunt inverter ica , (c) the system current after compensation isa , (d) the DC-side voltage vdc .
Y. Rong et al. / Simulation Modelling Practice and Theory 17 (2009) 955–966
a
200
* (V) vca and v ca
964
100
v*ca vca
0
-100
-200 0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
b
200
i ca and i ca(A)
time(s)
100
i*ca
*
ica
0
-100
-200 0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
time(s) Fig. 12. The tracking characteristic of the UPQC: (a) the A-phase voltage reference value vca and the A-phase compensating voltage vca , (b) the A-phase current reference value ica and the A-phase compensating current ica .
side are R2 ¼ 1:4 X; L2 ¼ 1 mH;C 2 ¼ 100 lF. The DC-link capacitor C dc is 10; 000 lF and the DC-link reference voltage is 1000 V. As shown in Fig. 6, the system voltage with multiple zero crossings is distorted and unsymmetrical which is caused by the allopatry harmonics and local nonlinear loads. Fig. 7 displays the load current generated by local non-balance loads consisting of a three-phase diode rectifier ðRd1 ¼ 5 X; Ld1 ¼ 5 mHÞ and a RL linear load bridged between the A and B phases (Rd2 ¼ 5 X and Ld2 ¼ 50 lH). The DC side of the rectifier changes to Rd1 ¼ 10 X and Ld1 ¼ 1 mH at 0.14 s and the THD (total harmonic distortion) of the load current are larger than 20% both before and after load change. We choose case 2 in Table 1 for the reference signals’ calculation. As described in Fig. 8, with the detected phase of the system voltage and the known nominal amplitude of the PCC, we are able to obtain the detected PCC voltage (see Fig. 8a). Due to the sag of the DC-link voltage (see Fig. 11d), the amplitude of the detected fundamental active current fluctuates as shown in Fig. 8b which is compensated by the PI controller (see Eq. (20), where kp ¼ 2:36 A=V s;ki ¼ 3:57 A=V sÞ that absorbs active power to maintain the DC-link voltage constant. When the load changes at 0.14 s, the adaptive harmonic detection responds fast (see Fig. 8b). In addition, the learning rate g is chosen in a wide range as 0.01–0.5 and the detection results are almost unchanged as shown in Fig. 8. The detected references are fed into the one cycle current controller and the triangular wave comparison controller which force the inverters to track the references. The parameters of the PI controller for enhancing the robustness of the series inverter are kp ¼ 2:16; ki ¼ 1:32. The compensated results are given in Fig. 9, which show that the compensated three-phase load voltages are sinusoidal and at the nominal value, and the compensated threephase system currents are free of distortion. Comparing Fig. 9 with Fig. 8, we can see that the compensated load voltage and system current can fast and precisely track the detected PCC voltage and the fundamental active current which proves that the controllers for the shunt and series inverters are effective. The details of the compensation process are shown in Fig. 10 (Fig. 11) where it is seen that, after compensation, the Aphase load voltage (current) is sinusoidal and nominal. In Fig. 11b, the compensating current is larger in the first 2 cycle due to the sag of the DC-side voltage (see Fig. 11d), including that the shunt inverter has to draw more active power at the beginning to maintain the DC-link voltage around the reference value. The swell of the DC-link voltage is due to the load change at 0.14 s and by the PI controller, the DC-link voltage is pulled back to the reference value in 2–3 cycles (see Fig. 11d), Fig. 12 shows the tracking characteristics of the two controllers for the series inverter and the shunt inverter, the both control strategies can track the reference values fast and precisely. 6. Conclusion We propose an adaptive harmonic detection method and a one cycle current control strategy. The adaptive harmonic detection method can deal with multiple zero crossings in the voltage. By an adaptively regulated neuron networks, this
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detection method is able to quickly identify precise values of the voltage or current reference signals under various circumstance which can be extended to single-phase or three-phase four-wire system because it works independently in each phase. The one cycle current control strategy is also shown to have precise and rapid tracking performance. It is more advantageous than the direct triangular wave comparison controller by its close-loop control strategy which is robust by nature. The strategy is also better than the hysteresis control because the frequency of the control signal by the OCCC is constant. The effectiveness of the detection method and control strategies is exhibited by simulation in a three-phase UPQC. Appendix A The load current can be expanded using Fourier transformation 3 I sinðixt þ haiþ Þ þ Iai sinðixt þ hai Þ 7 6 i¼1 aiþ 7 6 iLa 7 61 6 7 6 P I sinðixt þ h Þ þ I sinðixt þ h Þ 7 4 iLb 5 ¼ 6 biþ biþ bi bi 7 7 6 i¼1 7 6 1 iLc 5 4P Iciþ sinðixt þ hciþ Þ þ Ici sinðixt þ hci Þ 2
2P 1
3
i¼1
3 1 P Iaiþ sinðixt þ haiþ Þ þ Iai sinðixt þ hai Þ 7 6 i¼2 7 6 7 6 1 6 I sinðxt þ b Þ cosðh b Þ þ I cosðxt þ b Þ sinðh b Þ þ I sinðxt þ h Þ þ P I sinðixt þ h Þ þ I sinðixt þ h Þ 7 ¼ 6 b1þ 7 b1þ b1þ b1þ b1 b1 biþ biþ bi bi b1þ b1þ b1þ b1þ 7 6 i¼2 7 6 1 5 4 P Ic1þ sinðxt þ bc1þ Þ cosðhc1þ bc1þ Þ þ Ic1þ cosðxt þ bc1þ Þ sinðhc1þ bc1þ Þ þ Ic1 sinðxt þ hc1 Þ þ Iciþ sinðixt þ hciþ Þ þ Ici sinðixt þ hci Þ i¼2 2 3 iLap þ iLaq þ iLa þ iLah 6 7 ¼ 4 iLbp þ iLbq þ iLb þ iLbh 5; ðA:1Þ iLcp þ iLcq þ iLc þ iLch 2
Ia1þ sinðxt þ ba1þ Þ cosðha1þ ba1þ Þ þ Ia1þ cosðxt þ ba1þ Þ sinðha1þ ba1þ Þ þ Ia1 sinðxt þ ha1 Þ þ
where iLj is the load current, iLjp ¼ Ij1þ sinðxt þ bj1þ Þ cosðhj1þ bj1þ Þ is the fundamental active current, iLjq ¼ Ij1þ cosðxt þ bj1þ Þ sinðhj1þ bj1þ Þ is the fundamental reactive current, iLa ¼ Ia1 sinðxt þ ha1 Þ is the negative sequence P components and iLjh ¼ 1 i¼2 Ijiþ sinðixt þ hjiþ Þ þ Iji sinðixt þ hji Þ is the harmonic current ðj ¼ a; b; cÞ. Appendix B Denote that
e_ i ¼ I_s Y_ i ; Y_ i ¼ FðMXÞ; where I_s is 2 ma1 M ¼ 4 mb1 mc1
Eij ¼
ðB:1Þ ðB:2Þ
ua and the system current, Y_ i ¼ ½ yia yib yic T is the outputs of neurons 3, the inputs of neurons X ¼ u0 a 3 ma2 mb2 5. The neurons are set to be linear so that the activation function FðxÞ ¼ x. Define the objective function as mc2
1 2 e : 2 ij
ðB:3Þ
To minimize the objective function, the back-propagation algorithm is utilized to regulate the weights
Mðk þ 1Þ ¼ MðkÞ þ DMðkÞ; 2
Dma1 ðkÞ where DMðkÞ ¼ 4 Dmb1 ðkÞ Dmc1 ðkÞ
Dmjl ðkÞ ¼ g
ðB:4Þ 3
Dma2 ðkÞ Dmb2 ðkÞ 5, whose matrix elements can be regulated as Dmc2 ðkÞ
@Eij @Eij @yij ðkÞ ¼ g ¼ gðisj yij Þxl ; @mjl ðkÞ @yij ðkÞ @mjl ðkÞ
ðB:5Þ
where 0 < g < 1; j ¼ a; b; c and l ¼ 1; 2. References [1] M.H.J. Bollen, What is power quality, Electric Power System Research 66 (2003) 5–14. [2] H. Akagi, New trends in active filters for power conditioning, IEEE Transactions on Industry Applications 32 (6) (1996) 1312–1322. [3] Leszek S. Czarnecki, Instantaneous reactive power p–q theory and power properties of three-phase systems, IEEE Transactions on Power Delivery 21 (1) (2006) 362–367.
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