T \ P CHJ KHOA HOC & CONG NGHE C.^C TRLONG DAI HOC KV THUAT * SO 80-2011
SLIDING-MODE CONTROL FOR A SINGLE-PHASE ACTIVE POWER FILTER
DIEU KHIEN TRUOT BO LOC CONG SUAT TICH CUC M O T PHA Son. T.Nguyen, Thanh. V.Sguyen
Hanoi University of Science and Technology ABSTRACT
This paper presents the methgd of designing a non-linear controller for a single-phase active power filter (APF) that is connected power electronic loads in parallel. In particular, a controller with sliding-mode control is developed for this application. A single-phase APF has the topology of an H- bridge with four MOSFET switches connected the load via an inductor and connected a capacitor In the DC bus. With the structure like this, the model of the APF can be seen as a variable structure model and is well suited with the sliding-mode control. In this application, the sliding mode control always guarantees the shape of the main current to be sinusoidal and coincide with the phase of the main voltage. The simulation results show that the sliding-mode control always maintains the good performance of the APF when working at different conditions. Moreover, the control algorithm is easily deployed on low-cost digital control systems.
TOM T.\T
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I. INTRODUCTION
The wide application of power electronic dev ices causes the distortion of the main current due to the power electronic devices work as non-linear loads. One of the methods for eliminating the harmonic distortion of the single-phase load is using the active power niter (.-VPF) connected with the load in parallel,
•fhe function of the active filtere is generating a hamionie compensation current that is able to eliminate harmonic components generated by the load.
Recenllv. there have been some methods of designing the single-phase APF. Most of these methods include two following steps:
• Step 1: Detennining the compensation current for the active fitlter with the line frequenev of the non-linear load.
• Step 2: Designing the controller for AC current of the filter computed in step I.
Essentially, the compensation current is the inverse of the hannonic current via the load.
According to [1, 2], there are some methods of determining the hannonic current such as Fast Fourier Transform (FFT), instantaneous power theorv', synchronous d-q theory, instantaneous p-q theory. For FFT method, the exact computation method requires two cycles of the wave needed to be analysed: the first cvcle for data acquisition and another cycle for analyzing data. For other method, the implementation is quite complicated. Recently, the use of adaptive linear neural networks can be seen one of the methods for determining the compensation current [3], However, this method requires costly hardware such as digital signal processor (DSP) or specific digital control svstems.
T.AP CHi KHOA HOC & CONG NGHE CAC T R L 6 > G DAI HOC K\ THL.\T • SO 80 - 2011
This paper decribes a simple method that is able to combine Uvo steps when designing the single-phase .APF. In particular, a sliding- mode control is developed to guarantee the main current to be sinusoidal and coincide with the phase of the main voltage. The main advantage of this method is that it has the fast computation and is easy to be deployed on cheap digital control systems.
This paper is organized as follows.
Section 2 summarizes the model of a single- phase APF. In section 3. the authors mention the development of sliding-mode control for this application. Section 4 are simulation results obtained bv using Matlab/Simulink. Finally, Section 5 is the conclusion of this research.
II. MODEL OF A SINGLE-PHASE APF The single-phase APF is connected with a non-linear load in parallel as shown in Figure. 1. The power of the resistive load is changed by adjusting the firing angle of the Triac. The APF has four controllable switches 5",,.S,,,S', and .S'^ and is connected with the non-linear load via an inductor L and connected with a capacitor ('in the DC bus.
The values of the inductor L and the capacitor ('depend on the maximum power of the resistive load.
In order to guarantee the APF working correctly, the switches in the same legs of the H-bridge have to work in reverse order. This means that if ,9, is closed then ,S', is open, if .V, is closed then S^ is open. Therefore, the control of the H-bridge is essentially controlling tw o switches 5, and .9^.
^.' • S
Fig. I. .1 single-phase .4PF is connected with a power electronic load in parallel
The model of the single-phase APF is a votage source inverter with the DC votage is formed on the capacitor (depending on switching status of the swiches on the H-bridge as shown in Figure.2. Another matter is that the law of switching 5, and .S, has to guarantee the voltage on the capacitor greater than the maximum voltage of the AC source at am moment. Therefore, the control law has to be satified the first condition as follows:
c : • ' • o ) > ^ ' ; (1) where V,, is the voltage on the capacitor C, K, is the reference voltage and !', the r.m.s votlage of the AC source.
Fig.2. The APF is developed by the principle oj a voltage-source inverter
If ^', and »j are called logic signals (Oor I) for closing and opening the switches 5, and S, with the rule below:
• If i/| = 1 then 5", is closed, if u^ = 0 then 5", is open.
• If t/j = 1 then .S', is closed, if »_, = 0 then S.^ is open.
Two equations of the inverter have the following forms:
1
y. = ^.(u.^iu--\)i,]
(21
(3!
According to equations (2) and (3), the current ;, is governed bv the voltage on the capacitor and the switching status ol ,S' and .S', 68
TAPCHl KHOA HOC & CONG NGHE CAC TRLOAG DAI HOC KV T H U A T * SO 80-2011
III. SLIDING-MODE CONTROL
In control theory, sliding-mode control (SMC) is a control form that has variable structure. This is a non-linear control method that changes the dynamics of a non-linear system by high-frequency switching control.
SMC is concemed with forcing one or more force variables (often, but not necessary, state variables) to follow a specific trajectory. The trajectory is known as the sliding surface. The location of the variables relative to the sliding surface governs the control law which is applied to the system. As the system variables of interest pass through the sliding surface, the control law changes. The nonlinear control law is chosen so that regardless of where the system is with respect to the sliding surface, control actions always drive the system toward the sliding surface. Power electronic systems are natural candidates for sliding-mode control because topologies of power electronic circuits always change with the operation of semiconductor switches.
The starting point with the sliding mode control is the defination of a sliding surface. For the single-phase APF, we are interseted in forcing the source current to be the same shape as, and in phase with, the source voltage.
fherefore, the trajectory for the line current is defined as follows:
/• = kV (4)
where ^ is a scaling factor based on the real power demand of the loads. In the standard form, the sliding surface is written as follows:
s = I = 0 (5)
when the source current is on the sliding surface. In order to guarantee the sv stem on the sliding surface, the following condition has to be satisfied at any moment:
s s < 0 (6)
In order to have condition (6) to be
f
alwavs satislled, the sign of s has to be controlled approximately. .Al anv time, the APF can make the sign csi i positive or negative
due to the switching status of the switches on the H-bridge. In addition, the procedure of designing a correct power circuit will always guarantee kV. Therefore, we can control s following the non-linear control law as shows in Table.I.
In other words, we have:
S i ? y
i = ;,- kV, (7) The source current /, is the sum of the
determination i, and the load current /. When /, is on the sliding surface, from (7) vve have:
' + y f , (",+ "4- i X i kV'=0 (8)
According to Table.I, we can use logic value of switch 4 as follows:
1 -f-sgn{V^)
(9) where sgn{Tj = \ if (;>0 and sgn(V^) = -\ if
i; < 0 .
Substitute (9) into (8) and solve equation (8) with variable u, we have:
• ^'( , ,. ] K l - s g n ( F )
"' "Fl'" T "f^^—2^ ^'°^
Equation (10) is popularly used in inverter simulations.
Table. I The non-linear conirol law used to implement Ihe sliding mode control for the APF
"•
".
/ <AK 0
1
/, > A t ; 1 0
",
"e
'•, < o
1 0
i ; > o 0
1
TAP CHI KHOA HOC & CONG NGHE ( A C T R L 6 ? V G DAI HOC K\ THI AT * SO 80 - 2011
I \ , SIMULATION AND RESULTS
In this part, the control algorithm of the APF was tested in Matlab/Simulink environment. The simulation procedure includes four following steps:
• Step I: Determining the maximum powei"
of the load. In this case, vve assume that the resistive power of the load is adjustable bv changing the firing angle of the Triac. The maximum resistive power is \OklV The r.m.s value of the source voltage is 220K
• Step 2: Determining the values of the inductor L and the capacitor (' In this circumstance, 1 = 0.001// and
C = 1000///" are suitable for compensating the minimum to the maximum power.
• Step 3: Choosing the parameter for the non- linear controller. For the convenience, vve choose ^, = I.
• Step 4: Choosing the parameters for the PI controller including the reference voltage on the DC bus r„, the proportional coefficient AT^, the integral coefllcient A", and the saturation output of the Pl controller .\l In this case, those coefficients are chosen as shown in Table.2.
Table. 2 The coefficients of the PI controller used to stabilize the voltage on the capacitor C
K K
P '
0,001 0,08 A/
5
In order to verifv the control algorithm at different conditions, the load was supplied by the source voltage with different firing angles of the Triac 30 .60 .90 and 120" The switching frequenev of the DFETs on the H- bridge is 50 Hz
Figure 3. 4. 5 and 6 are waveforms of currents without and with the use o f l h e APF.
Table.3 is the summarv of the total harmonic distortion (THD) of the source current when usim; the .\PI The THD of the source current
after the compensation reduces to half of THD of the source current before filtering
07 0 08 0 09 0 1
Fig.3. Weivcfonns of the currents when firing angle of Triac a = 30": load current (above curve) and grid side current (below curve)
0 0 01 0 ; ; o oi o o* o a i 0 06 007 time(s)
Fig.4. Wave forms of the currents when firing angle of Triac a = 60°.' load current (above curve) and grid side current (below curve)
001 0 0 2 0 0 3 004 0 05 O X 0 0 7 0 08 0 09 0 1 time<t)
Fig.5. lias eh inns of the currents when firing angle of Triac a = 9 0 load current labovt curve/ and grid side current /below curve) 70
TAP C H I K H O A H O C & CONG NGHE C.AC TRLONG DAI HOC KY THUAT * SO 80 - 2011
GO' 0C2 0 03 0 0 4 0 05 0 0 6 0 07 0 0 8 0 0 9 0 1 time(s)
0 32 0 03 0 0 4 0 05 0 0 6 0 07 0 0 8 0O9 0 1 time(s)
vA„A-'- \i^..:^e.i\):,'X
0 0 01 0 0 2 0 03 0 0 4 0 05 0 0 6 0 07 0 0 6 0 09 0 1 bme(s)
0 01 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 0 1 time<s)
Fig.6. Waveforms of the currents when firing Fig.". Source current aflerfdtering (above curve) angle of Triac a = 120°.' load current (above and the voltage on the capacitor C (below curve) curve) and grid side current (below curve) when the firing angle of Triac a = 90°
Table. 3 THD oflhe source current according to different working schemes oflhe load
Firing angle (a )
30"
60"
90"
120"
THD (%) wilhoul filler
15.12 37.75 65.06 102.6
THD (%) with filter
7.89 15.49 33.69 63.27
V. CONCLUSIONS
The simulation results obtained show that the advantage of sliding-mode control for this application is simple. Therefore, the control algorithm is easily deployed on low-cost digital control systems. The THD of the source current after the compensation reduces to half of THD of the source current before filtering.
REFERENCES
M.Rukonuzzaman and M.Nakaoka, "Single-phase shunt APF with Adaptive Neural Network Method for Determining Compensating Current," The 27th Annual Conference of the IEEE Industrial Electronics Society, pp. 2032 - 2037, 2001.
J.-Q. W. Shu-Guang Sun, Shun-Quan Shi, "Study on Two Detection Methods for Harmonics and Reactive Currents," Proceedings of the Seventh Intemational Conference on Machine Leaming and Cybernetics, Kunming, 12-15 Julv 2008, pp. 1445 - 1449, 2008.
P. Sahiieion and J. R. Vazquez, "Practical Design of a Three-Phase Active Power-Line Conditioner Controlled by Artificial Neural Networks," IEEE Transactions on Power Delivery, Vol. 20. No. 2, April 2005, vol. 20, pp. 1037 - 1044. 2005.
David A. Torrey and A. M. A. M. Al-Zamel, "Single-phase Active Power Filters for Multiple Nonlinear Loads," IEEE Transactions on Power Electronics, Vol. 10, No. 3, May 1995, vol. 10, pp. 263-272. 1995.
D. Ibrahim. Microcontroller Based Applied Digital Control: Wiley, 2006.
Author s eieldress-. Nguven Thanh Son-Tel:(+844)3869.2511. Ernail:[email protected] School of Electrical Engineering. Hanoi Universitv of Science and Technology No. I, Dai Co Viet Str.. Ha Noi, Viet Nam.
