2013 Annual IEEE India Conference (INDICON)
Performance Comparison of Direct and Indirect Current Control Techniques Applied to a Sliding Mode Based Shunt Active Power Filter Rajesh K Patjoshi
Kamala Kanta Mahapatra
Electronics and Communication Engg.Dept. National Institute of Technology Rourkela, India
[email protected]
Abstract— This paper presents a new and efficient control scheme which adopted the voltage source inverter to decrease current harmonics generated by the nonlinear load. The sliding mode control is used in the current control loop to achieve fast dynamics and a simple proportional-integral controller is adopted in the outer voltage control loop to achieve slow dynamics. The proposed scheme implements simplified control algorithms based on direct current control (DCC) and indirect current control (ICC) for designing trajectories in sliding mode control based shunt active power filter (SAPF). The performances of the DCC and ICC techniques were verified through a simulation with MATLAB. Simulation results confirm that compared to the conventional DCC scheme, the ICC scheme using sliding mode control can achieve high power factor and current harmonics elimination in SAPF. Keywords-Shunt Active Power Filter;Sliding Mode Control;unit vector;Direct current control;Indirect current control .
I.
INTRODUCTION
With the development of modern industry, a variety of nonlinear and time-varying electronic devices such as inverters, rectifiers, and switching power supplies are widely used. These solid-state converters inject harmonics into the grid and lead to serious distortion of the power supply current and voltage, decreasing the quality of power supply. Power quality problems endanger the safe operation of the power supply and electrical equipment seriously, attracting more and more attention in the modern society. Shunt active power filter [SAPF] is an effective device to compensate the harmonic currents in power system. The models of active power filter have been established using various methods, and the behaviour of reference signal tracking has been improved using advanced control approaches. Singh et al. [2] compared two types of current control techniques, and showed that active power filter with indirect current control technique had simpler structure and better harmonic treating effect than direct current control. Active power filter using the indirect current control method is designed in [3, 4], where the power supply current harmonics with sliding mode control was calculated and indirect current control technique did not need compensation current measurement, but only detection devices for power supply
Electronics and Communication Engg.Dept National Institute of Technology Rourkela,India
[email protected]
voltage, power supply current and DC voltage. Therefore, such technique can effectively reduce the system requirement for the hardware environment and is easy to implement with DSP technique. Matas et al. [5] succeeded in linearizing the mathematical model of active power filter with feedback linearization method. The reference currents tracking behavior were improved by novel sliding mode control, reducing the power supply current harmonic content obviously in [6, 7]. Here an integer portion of the traditional hysteresis control method is added and reduced the steady tracking error by the designed sliding mode controller. Cheng et al. [7] adopted sliding mode control method based on proportion switch function in the controller and analyzed the robustness and stability of the system by the simulation analysis. Singh et al. [8] designed a simple fuzzy logic-based robust active power filter to minimize the harmonics for a wide range of variation of load current under stochastic conditions. As per [14,15], sliding mode control (SMC) technique, which combines design and analysis closely, has the robustness to model uncertainty as well as external disturbance. The SMC is composed of an equivalent control part that describes the behaviour of the system when the trajectories stay over the sliding manifold and a variable structure control part that enforces the trajectories to reach the sliding manifold and prevent them leaving the sliding manifold. In this paper, a novel sliding mode controller is implemented in SAPF for tracking reference currents using direct and indirect current control methods. Compared with direct current control technique, the indirect current control has simpler system structure and better harmonic treating performances.Organization of the paper is as follows: This paper initially focuses on the development of shunt active power filter .Then the control strategy of active power filter is presented. The performances of DCC and ICC were analyzed by means of a simulation with MATLAB. Finally, the most relevant conclusions of this paper are summarized. II. DEVELOPMENT OF SHUNT ACTIVE POWER FILTER The functional diagram of a shunt active power filter, based on a voltage source converter, for the compensation of current harmonics generated by the nonlinear load is shown in
978-1-4799-2275-8/13/$31.00 ©2013 IEEE
vdc −
iload
vsb
vsc
v
LL
3 phase Source
Nonlinear Load
icomp
I max
+
RL
v sa v sb v sc
∗ dc
PI Controller
unit vector generation
i sa∗
usa usb usc
+
i sb∗ i
vdc
isa
−
∗ sc
isb
Sliding
− −
isc
Controller
+
+
Mode
gate pulse
iline
vsa
Fig.3 Control Algorithm of SAPF using ICC scheme
vdc −
Sliding Mode Controller
vdc∗ PI Controller
icomp = iL
n
vln
S2
D2
L S1
D1
2C
+v
v sa v sb v sc
c
−2
i sb∗ isc∗
+v c 2 −
+
+ +
−
ica∗
−
icb∗
−
icc∗
ica
+ + +
−
i
Sliding
icc
Controller
−cb −
Mode
Fig.4 Control Algorithm of SAPF using DCC scheme
Fig.2 Equivalent Circuit for a single phase of the converter
Fig.1. A three phase voltage source inverter is employed as a shunt active power filter. The inverter is controlled through two controllers. A fast inner loop is used to control the shape of the line currents, forcing them to be of the same shape, and in phase with, the phase voltages. The inner current loop is based on a sliding-mode controller which is conceptually simple and very easy to implement. An outer proportionalintegral (PI) voltage loop is used to set the proper magnitude of the phase current. A. Sliding Modes and equivalent control The single phase Model of Fig. 2 does not take into consideration the shift in the voltage of the common capacitor node relative to the neutral of the source and this leads to a valid sliding-mode control law. If a switching function u is defined such that u = 1 when either S1 or D1 is conducting and u = −1 when either S2 or D2 is conducting, then the inductor current is given by dic vln v (1) = − u c − Rc ic dt L 2L An expression for capacitor voltage taking into account the ripple due to compensating currents can be written as dvc 1 i i i = − [ua ca + ub cb + uc cc ] dt 2 C C C
unit vector generation
i sa∗
usa usb usc
gate pulse
Fig.1 Functional structure of shunt active power filter
2C
I max
+
i ilblc ila
(2)
Where ua , ub , uc are the independent controls for phases a, b, and c, respectively, and ica , icb , icc are the compensating currents for phases a, b, and c, respectively. The filter can be
broken into three first-order independent systems which are expressed as ilinex = iload x + icomp x
v ⎤ ⎡v = iload x + ⎢ xn + u x c ⎥ dt L L⎦ 2 ⎣
∫
(3)
Where x denotes the phase. To apply a sliding mode control theory to the active power filter, the sliding surfaces, or the trajectories, first must be defined that we wish the system to follow. Here the trajectories are defined using the following two control strategies. B. Indirect Current Control (ICC) Fig.3 shows the ICC scheme for designing trajectory in SMC. ∗ ∗ ∗ Here the trajectories for line currents isa , isb , isc are obtained by multiplying the unit vectors usa , usb , usc generated from source voltages vsa , vsb , vsc with the continuous peak source current I max . vsa = vm sin(ωt ) vsb = vm sin(ωt − 120° )
(4)
°
vsc = vm sin(ωt + 120 ) v v v usa = sa , usb = sb , usc = sc vm vm vm
(5)
∗ isa = I max × usa ∗ isb = I max × usb ∗ isc = I max × usc
(6)
C. Direct Current Control (DCC) Fig.4 shows the DCC scheme for designing trajectory in SMC. Here the trajectories for compensating currents ∗ ∗ ∗ are obtained by subtracting source reference ica , icb , icc currents from the load currents. ∗ ica ∗ icb ∗ icc
∗ = isa − ila ∗ = isb − ilb ∗ = isc − ilc
(7)
Table I (Simulation Parameters)
vm
100V
* vdc
220V
RL
6.8 Ω
Rc
0.1 Ω
LL C
20 mH
Lc
20mH
1800 μ F
Kp
0.033
Ki
0.3
The sliding surfaces are chosen according to ICC and DCC schemes and are given by, ∗ sx = [isa − isa ] = 0 (For Indirect Current Control)
25 20
∗ s y = [ica − ica ] = 0 (For Direct Current Control)
15 10 A m plitude (A)
To assure that the system can be maintained on the sliding surface, it must be shown that there is a natural control which satisfies ss ≤ 0 at all times, i.e., for all values that the state may experience. It u is within the natural control's bounds of the physical system for s = 0 , then it is possible to remain on the sliding surface at all times and maintain perfect tracking. Setting s x = 0 or s y = 0 , the equivalent control can be found
5 0 -5 -10 -15 -20 -25 0
0.05
to be
0.1
0.15
0.2
0.25 Time (sec)
0.3
0.35
0.4
0.45
0.5
0.35
0.4
0.45
0.5
0.35
0.4
0.45
0.5
Fig.5 Waveform of the load current
⎛ di ∗ di v ⎞ ⎛ 2L ⎞ (8) ueqx = ⎜⎜ sx − loadx − xn ⎟⎟ ⎜ ⎟ dt L ⎠ ⎝ vc ⎠ ⎝ dt The natural control limits of the circuit are −1 ≤ ueq ≤ 1 .To
If s0 then u= -1
200 V o lta g e (V )
satisfy ss ≤ 0 , the discontinuous control law can be seen
250
150
(9)
100 50
III. RESULTS AND DISCUSSIONS The control units have been tested using MATLAB according to the structure shown in Fig.3 and Fig.4. A three phase diode bridge rectifier feeding RL load is considered as nonlinear load. The parameters used in simulation are shown in Table I, where Rc and Lc correspond to the link inductor
Here the simulation results are displayed using the proposed control techniques. Fig. 5 shows the applied load current waveform. The capacitor voltage waveforms for DCC and ICC techniques are shown in Fig.6. They become steady at about 220V, but ICC takes less time ( ≈ 0.01 sec) as compared to DCC ( ≈ 0.25 sec) showing better voltage regulation in the ICC. The compensating current waveforms for both techniques are presented in Fig.7, which contain equal and opposite harmonics to that of load current. Fig.8 shows the source current after compensation. From the figure it is clear that the current source is nearly sinusoidal and in phase with the source voltage even after compensating for both DCC and ICC
0.05
0.1
0.15
0.2
0.25 0.3 Time (sec)
(a) 250
200
Vo ltag e (V)
* model, C is the capacitance of dc bus, vdc is the reference dc bus voltage, and K P and K i are the PI-controller constants, and vm is the peak value of the source voltage.
0 0
150
100
50
0 0
0.05
0.1
0.15
0.2
0.25 Time (sec)
0.3
(b) Fig.6 Capacitor voltage waveforms for a) DCC, b) ICC
techniques. But on the basis of calculation of Total Harmonics Distortion (THD %), Table II shows the superiority of the ICC method (4.94%) over the DCC method (5.19%). The source current spectra before and after compensation are given in Fig.9 and 10 for both DCC and ICC schemes. The
Table II (Calculation of THD %)
50 40 30
Amplitude (A)
20 10
Control Techniques
Source Current Before Compensation
Source Current After Compensation
DCC
29.7
5.19
ICC
29.7
4.94
0 -10 -20 -30 -40 -50 0
0.05
0.1
0.15
0.2
0.25 Time (sec)
0.3
0.35
0.4
0.45
0.5
0.3
0.35
0.4
0.45
0.5
(a) 50 40 30
Amplitude (A)
20 10 0 -10 -20 -30 -40 -50 0
Fig.9 Source current spectrum before compensation 0.05
0.1
0.15
0.2
0.25 Time (sec)
(b) Fig.7 Compensating Current waveforms for a) DCC, b) ICC 200 SOURCE CURRENT SOURCE VOLTAGE A M P L IT U D E
100
0
(a)
-100
-200 0
0.5
0.1
0.15
0.2
0.25 TIME(S)
0.3
0.35
0.4
0.45
0.5
(a)
200
SOURCE CURRENT SOURCE VOLTAGE
150
A M P L IT U D E
100 50
(b)
0
Fig.10 Source current spectrum after compensation
-50
Using a) DCC, b) ICC
-100 -150 -200 0
0.05
0.1
0.15
0.2
0.25 TIME(S)
0.3
0.35
0.4
(b)
Fig.8 Source current waveform after compensation With a) DCC, b) ICC
0.45
0.5
amplitudes of different harmonic orders (5th.....25th) are analysed using the above two methods, which are shown in a tabular form given below. According to amplitude measurements of harmonics specified in Table III, it can be found that the amplitude of harmonics are minimum in ICC as compared to DCC showing the higher priority of previous one than the later.
Table III (Amplitude of harmonics in source current) Harmonic order
DCC
ICC
5th
0.44
0.30
7th
0.46
0.29
11th
0.49
0.29
13th
0.39
0.28
17th
0.44
0.29
19th
0.40
0.28
23rd
0.47
0.32
25th
0.39
0.27
IV. CONCLUSIONS The implementation of Direct and Indirect current control techniques applied to sliding mode based SAPF has been presented.A novel sliding mode control is proposed in reference current tracking to reduce the tracking error. A PI regulator is used to generate the amplitude of the reference currents. Multiplying this with unit sinusoidal signals, reference currents having the same phase with power supply voltage can be formed. The advantage of using the novel sliding mode controller for the SAPF with indirect current control technique is that it does not need harmonic detection component and minimizes the harmonics for a wide range of variation of load current under nonlinear load conditions. Compared with direct current control technique, it has simpler system structure and better harmonic treating performances. Therefore, it is easy to implement with digital signal processing system. The simulation results reveal that the designed active power filter with Indirect current control technique has a superior harmonic compensation effect as compared to the Direct current control technique. REFERENCES [1] S. Saetieo and R. Devaraj, “The design and implementation of a three phase active power filter based on sliding mode control”, IEEE Transactions on Industry applications, vol. 31, no. 5, pp. 993-1000, 1995. [2] B. Singh, A. Chandra, and K. Haddad, “Performance comparison of two current control techniques applied to an active power filter,” in Proceedings of the International Conference on Harmonics and Quality of Power, pp. 133–138, Athens, USA, 1998. [3] D. Nedeljkovic, M. Nemec, K. Drobnic, and V. Ambrozic, “Direct current control of active power filter without filter current measurement,” in Proceedings of the International Symposium on Power Electronics, Electrical Drives, Automation and Motion (SPEEDAM ’08), pp. 72–76, 2008.
[4] B. Singh, “Sliding mode control technique for indirect current controlled active power filter,” in Proceedings of the Annual Technical Conference of IEEE Region 5, pp. 51–58, 2003. [5] J. Matas, L. Garcia de Vicuna, J. Miret, J. M. Guerrero, and M. Castilla, “Feedback linearization of a single-phase active power filter via sliding mode control,” IEEE Transactions on Power Electronics, vol. 23, no. 1, pp. 116–125, 2008. [6] D. Stanciu, M. Teodorescu, A. Florescu, and D. A. Stoichescu, “Single-phase active power filter with improved sliding mode control,” in Proceedings of the 17th IEEE International Conference on Automation, Quality and Testing, Robotics (AQTR ’10), pp. 15–19, May 2010. [7] B. Cheng, P.Wang, and Z. Zhang, “Sliding mode control for a shunt active power filter,” in Proceedings of the 3rd International Conference on Measuring Technology and Mechatronics Automation (ICMTMA ’11), vol. 3, pp. 282–285, 2011. [8] G. K. Singh, A. K. Singh, and R. Mitra, “A simple fuzzy logic based robust active power filter for harmonics minimization under random load variation,” Electric Power Systems Research, vol. 77, no. 8, pp. 1101–1111, 2007. [9] B. Singh, A. Chandra, and K. Haddad, “DSP based control method of active filter : elimination of switching ripples,” in Proceedings of the 15th IEEE International Conference on Applied Power Electronics and Exposition (APEC’2000), vol. 1, pp. 427–433, 2000. [10] V. S. Bandal and P. N. Madurwar, “Performance analysis of shunt active power filter using sliding mode control strategies”, in 12th International workshop on Variable Structure Systems (VSS ), March 2012. [11] T. Thomas, and A. Jaffart, ‘Design and performance of active power filters’, IEEE Industry Applications magazine, September/October, pp. 38-46, 1998. [12] B. Singh, A. Chandra, and K. Haddad,"A new control approach to three-phase active filter for harmonics and reactive power compensation",IEEE Trans.on Power Systems, vol. 13, no. 1 , pp. 133-138, Feb 1998. [13] S. Buso, L. Malesani, P. Mattavelli, “Comparison of Current Control Techniques for Active Filter Applications”, IEEE Trans. On Industrial Electron., vol. 45, pp.722-729, Oct 1998. [14] H. De Battista and R. J. Mantz, “Harmonic series compensators in power systems: their control via sliding mode,” IEEE Transactions on Control Systems Technology, vol. 8, no. 6, pp. 939–947, 2000. [15] H. Wang, Q. Li, Y. Gong, and Y. Duan, “An adaptive sliding mode control methodology applied to shunt active power filter,” in Asia-Pacific Power and Energy Engineering Conference (APPEEC ’10), March 2010. [16] S. Rahmani, K.Haddad, “Experimental design and simulation of a modified pwm with an indirect current control technique applied to a single-phase shunt active power filter,” IEEE International Symposium on Industrial Electronics, vol. 2, pp. 519-524, 2005.
