Electrical Power and Energy Systems 71 (2015) 123–130
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Electrical Power and Energy Systems journal homepage: www.elsevier.com/locate/ijepes
DSP based proportional integral sliding mode controller for photo-voltaic system Subramanya Bhat a,⇑, H.N. Nagaraja b a b
Department of E&C, Canara Engineering College, Mangalore, VTU, Belgaum, India Indus University, Ahmedabad, India
a r t i c l e
i n f o
a b s t r a c t
Article history: Received 12 June 2014 Received in revised form 11 February 2015 Accepted 20 February 2015
The buck–boost converter is controlled using different algorithms like voltage mode control, current mode control, V2 control, enhanced V2 control, Sliding Mode Control (SMC), and Proportional Integral (PI) control. In all these algorithms the steady state error is more. On combining PI control and sliding mode control the steady error can be minimized. In industry and commercial applications involving Photo-Voltaic (PV) systems, uses buck–boost converter. In this converter above control algorithms are implemented using hardware circuitry or microcontroller. In industry and commercial applications Digital Signal Processor (DSP) is used for automation purposes and the same DSP can be used to implement control algorithms so as to get maximum electrical energy from solar energy. The efficient utilization of resources such as DSP is achieved as we are using the same DSP for implementing control algorithm. In the proposed study, PI control method and sliding mode control methods are combined to obtain a Proportional Integral Sliding Mode Control (PISMC) and it is used to control the buck–boost converter which is used to drive the electrical loads from solar energy. The buck–boost converter is designed, simulated and implemented. The algorithms PI, SMC and PISMC are simulated in using MATLAB simulink and then implemented in DSP TMS 320 2808. In the proposed study PISMC, a stable and efficient output voltage is obtained in which the steady state error and maximum overshoot are minimum. The PISMC is better in terms of transient and steady state performances as validated by our experiments. The proposed study will work in real-time since DSP is used for implementing the control algorithms and found to be better in terms of speed and regulation. The proposed DSP based PISMC can also be used to control other types of DC–DC converters. Ó 2015 Elsevier Ltd. All rights reserved.
Keywords: Steady state error Control algorithm DC loads Regulation
Introduction In a large number of industrial, commercial and residential applications it is required to convert a fixed DC voltage to a different DC voltage level with a regulated output. To perform this task a DC–DC converter is needed. A DC–DC converter converts a DC voltage of one level to another. In the proposed work a DC to DC converter called buck–boost converter is used to drive electrical loads from solar panel input. In industry and commercial applications Digital Signal Processor (DSP) is used for automation purposes and the same DSP can be used to implement control algorithms so as to get maximum electrical energy from solar energy. The DSP is more accurate and it will work in real time. In Industry and commercial applications involving automation using DSP is ⇑ Corresponding author. E-mail addresses:
[email protected] (H.N. Nagaraja).
(S.
Bhat),
http://dx.doi.org/10.1016/j.ijepes.2015.02.038 0142-0615/Ó 2015 Elsevier Ltd. All rights reserved.
[email protected]
underutilized. Hence in the proposed study, the DSP which is used for automation process is used for implementing control algorithms. Photovoltaic generation is reliable and its operation and maintenance cost is low. The PV system also provides social and economical benefits to the society where other forms of electricity are unavailable. The buck–boost converter is used for charging the battery from solar module. In PV power generation system, other than solar modules, many circuits and devices are required to provide a satisfactory electricity supply. Many systems implemented in the literature [1–4] have a provision for energy storage to supply electricity at night and during cloudy weather. In these papers, they have mentioned about different types of battery storage systems. In order to control the energy generated from the solar cell the various power conditioning and control circuits are needed. A microcontroller based stand alone PV system described in [5], uses low cost microcontrollers to control the switching period of the switch used in converter and inverter. In this work, the output waveforms have unexpected even harmonics which is due to the
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low clock speed, microcontroller approximates switching angles instead of accurate values. The DSPs have more computational power than microcontrollers. Hence more advanced control algorithms can be implemented on a DSP. In the proposed method, PISMC is implemented on a DSP TMS320 2808. PI controllers are linear controllers in which steady state error is more. Sliding mode controllers are non linear controllers in which the steady error is less. Hence in the proposed method PI controllers are combined with sliding mode controllers to achieve better control. The sliding mode controllers have good robustness properties. The sliding mode control of DC–DC converters are well discussed in [6–10]. The disadvantages with sliding mode controllers are that they are sensitive to noise and they operate at variable switching frequency which limits the selection of inductor. The implementation of PI controller discussed in [10] is subjected to external disturbances. This can be overcome by adaptive sliding mode control. The methodology of the proposed study is discussed in Section ‘Methodology’. The PI, SMC and the proposed study PISMC are tested and the results are presented in Section ‘Results’. The results are discussed in Section ‘Discussion’. The proposed study is concluded in Section ‘Conclusion’. Methodology The block diagram of proposed study is shown in Fig. 1. The voltage from solar panel is taken as input to the buck–boost converter. The output of buck–boost converter is stored in battery which is used to drive DC loads LED lamp, modem and fan. The buck–boost converter is designed, simulated and implemented. The load voltage and current are sensed and compared with the reference signal and the output of the same is given to ADC. The ADC converts analog value to digital and this output is given to the digital PISMC. The PISMC control algorithm is implemented using a DSP. The DSP will generate PWM wave and it is used to trigger the MOSFET switch in buck–boost converter. The advantage of this DSP is that it can generate PWM wave in real-time [12,13]. The amplitude of PWM wave generated from DSP is more than 3 V and frequency is 50 kHz. Hence, gate drive circuit is not necessary for the proposed study. But Akkaya and Kulaksiz [5] used micro controller for solar PV system which generates PWM wave, the amplitude is less to trigger the switch in buck–boost converter. Hence they used gate driver circuit to increase the amplitude of PWM wave. Because of gate driver circuit the power consumption is increased and size and cost of the system will also be increased.
Input voltage from solar Panel
Mathematical modeling The solar panel is modeled mathematically as follows. The PV generator is formed by connecting many PV cells in series and parallel to get the desired output voltage and current [1]. The PV generator shows a nonlinear V–I characteristics. The V–I characteristics with Ns cells in series and Np cells in parallel is given by Eq. (1)
Ns Np
V g ¼ Ig Rs
þ
Ns Iph Ig Ns ln 1 þ D N p Io
where D = q/AKT where q = electric charge of an electron, A = completion factor, K = Boltzman constant, T = absolute temperature, Io = cell reverse saturation current, Ns = number of cells in series, Np = number of cells in parallel, Iph = insolation dependent photo current, Ig = solar cell array current, Vg = solar cell array voltage. The equivalent circuit is shown in Fig. 2. Here Rs is the series resistance and Rsh is the parallel resistance of cell. We developed a mathematical model for the buck–boost converter used in PV system. The mathematical model is developed using state space equations in the following. The structure of buck–boost converter is shown in Fig. 3. The output voltage of buck–boost converter is more or less than the input voltage which depends on duty ratio of the switch. The switch is implemented using MOSFET. The equations for buck–boost converter using state space averaging method is obtained as follows. When the switch is ON, the state space equations are obtained as dIL ¼ VLin dt dV c 1 ¼ RC dt
) ð2Þ
vo
When the switch is OFF, the state space equations are written as dIL ¼ vLo dt dV c 1 ¼ RC dt
) ð3Þ
v o IC
L
The state space representation for ON mode is given by
x_ ¼ A1 x þ B1 u
ð4Þ
V c ¼ C1x where A1 ¼
0 1=C
1=L 1=RC
B1 ¼
0 C 1 ðxÞ ¼ ½ 0 0
DC Load (LED Lamp ,Modem & Fan)
Buck-Boost Converter Baery
Current Sensor circuit
PWM generaon with DSP TMS 320 2808
ð1Þ
Voltage Sensor circuit
Reference Signal
Comparator
Fig. 1. Block diagram of the proposed method.
Error Amplifier
1 and u ¼ V in .
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S. Bhat, H.N. Nagaraja / Electrical Power and Energy Systems 71 (2015) 123–130 Table 1 The load ratings. Device
Power rating (W)
Output voltage (V)
Current (A)
Tube light Fan Modem
7 16.8 5.5
12 12 10
0.58 1.4 0.55
Switching frequency of the switch is taken as f = 50 kHz,
Fig. 2. Equivalent circuit of solar panel.
Lcr ¼
Vg D f DiL
ð14Þ
Using Eq. (14) we will get the inductor value as L = 1.15 mH
C cr ¼
Dio D f DV o
ð15Þ
The output voltage ripple is taken as DV o ¼ 1% of output voltage. Using Eq. (15) the capacitor value is obtained as 220 lF. Fig. 3. Buck–boost converter structure.
PI control of buck–boost converters
The state space representation for OFF mode is given by
x_ ¼ A2 x þ B2 u
ð5Þ
V c ¼ C2x
0 0 1=L B2 ¼ C 2 ¼ ½ 0 1 and u ¼ V in . 0 1=RC 0 The averaged state space representation of buck–boost converter system is obtained and represented by the following equations: where A2 ¼
x_ ¼ ½aA1 þ ð1 dÞA_ 2 x þ ½dB1 þ ð1 dÞB2 v in
)
ð6Þ
Vc ¼ ½dC 1 þ ð1 dÞC 2 x
where d is the duty ratio of the MOSFET. IL is the inductor current and Vc is the voltage across the capacitor and R is the load resistance. From system point of view, d is the control input, E is the voltage and R is the output resistance. In matrix form the Eqs. (2), (4) and (6) is written as
"
I_L V_ c
#
" ¼
0 1d L
1d L 1 RC
#
IL Vc
þ
d=L 0
v in
ð7Þ
For the state space model the state space variables chosen are; inductor current x1 = IL and capacitor voltage x2 = Vc. Output of the model is taken as capacitor voltage y = x2. The simple form of Eqn.(7) is as follows
x_ ¼ Ax þ Bu
ð8Þ "
Where the system parameter matrix is A ¼
State dependent input matrix as B ¼ And the state matrix is x ¼
IL
d=L 0
0 1d L
1d L 1 RC
#
ð10Þ
ð11Þ
The buck–boost converter is designed as follows. Load specifications are taken as follows (see Table 1). Total load current is obtained as 2.53 A. Output voltage of a buck–boost converter is given by,
Vo ¼ Vi
D 1D
We took;
ð12Þ
DiL ¼ 3%IL
where IL ¼
Io 1D
uðtÞ ¼ K p eðtÞ
ð16Þ
where Kp is the proportional gain e(t) is the error and u(t) is the perturbation in output signal of PI controller from the base value corresponding to normal operating conditions. It with no integration property always exhibit static error in the presence of disturbances and changes in set-point and shows a relatively maximum overshoot and long settling time. To remove steady-state offset in controlled variable of a process, an extra intelligence is added to the P controller and this intelligence is the integral action. The controller is a PI controller whose mathematical notation is depicted in Eq. (17)
Z t uðtÞ ¼ K c eðtÞ þ 1=K i eðtÞdt
ð17Þ
0
The simulink diagram for PI control of buck–boost converter is shown in Fig. 4. In this figure output voltage of converter is compared with a reference source of 12 V and the error signal generated is applied to PI controller. The PI controller output is compared or ANDED with a pulse generator output to obtain PWM wave so as to trigger the MOSFET switch. Sliding mode control of buck–boost converters
ð9Þ
VC
A PI controller fuses the properties of P and I controllers and the algorithm provides a balance of complexity and capability to be widely used in process control applications. It is reported that single input single-output PI controller controls 98% of control loop in paper and pulp industries. Eq. (16) describes P controller.
ð13Þ
In SMC, a controller is forcing the system states to reach, and remain on, a predefined switching surface within the state space. This motion to a predefined switching surface is known as sliding motion. The advantages of this type of motion or control are reduction in system order and control is insensitive to parameter variations. Due to these advantages, the buck–boost converter is controlled using SMC. The buck–boost converter output voltage error and rate of change of voltage are both selected as state variables. The SMC is implemented using two control loops and they are inner current loop and the outer voltage loop as shown in Fig. 5. These two loops are combined in series to achieve SMC for buck–boost converter. The equations used in SMC are explained as follows. Let us consider voltage error as X, rate of change of voltage error as Y and integral of voltage error as Z. Under continuous conduction mode we can write as derived in [11]
X ¼ ðV ref bV o Þ
ð18Þ
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S. Bhat, H.N. Nagaraja / Electrical Power and Energy Systems 71 (2015) 123–130
Fig. 4. Simulink diagram for PI control of buck–boost converters.
Y ¼ X_ ¼ b=C
Z¼
Z
vo
RL
Z
1½uV i V o dt RL
Xdt
ð20Þ 2
X buck-boost
ð19Þ
3
ðV ref bV o Þ h i 6 v o R 1½uV i V o dt 7 7 ¼6 RL 4 b=C RL 5 R ðV ref bV o Þdt
X_ buck-boost ¼ AX buck-boost þ BU 2
0 6 .. . . 6. . Where A ¼ 6 6 40
1 .. . 1 R1 C
1 ... 2
0
3 0 .. 7 .7 7 7 05
ð21Þ
ð22Þ
ð23Þ
where s is the instantaneous state variable trajectory and is described as
s ¼ a1X1 þ a2X2 þ a3X3 ¼ J T X
ð26Þ
where JT ¼ ½/ 1 / 2 / 3. Where / 1; / 2 and / 3 represents control parameters and these are known as sliding coefficients. A sliding surface is obtained by substituting S = 0. The mapping of the equivalent control function on the duty ratio control d is done as follows.
0
