Development of a Sliding Control Maximum Power Point Tracker
for Photovoltaic
Jui-Liang Yang,Ding-Tsair Suand Ying-Shing Shiao
Department of Electrical EngineeringNationalChanghuaUniversity of Education
E-mail:
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Abstract
This paper proposes arobustsliding mode controller as atmosphericchanges in a second. Usingsliding mode controltheory to the Boost type converter in solar array and loads tracks the Maximum Power Point(MPP). Amicro processor, PIC16F877A, is used to implement the sliding mode controller in this paper. Moreover, using the Lyapunov functioncan prove the sliding mode controller that selected sliding surface function exists. Simulationand experimentalresults show the proposed sliding mode controller has improved the PV power system speed of tracking the PV power system.
Index Terms- MPPT, variable structure control, sliding mode control,Lyapunov function.
1. Introduction
High technology makes economy grow. Manufacture and consumer pollutereduce the nature resources. Therefore, problems such as global incalescence, oil shortage and so on increase.
According to the BP Statistical Review of World Energy [1], the quantity of oil on the earth can only be used about 50 years if continuing consumes oil as much.Hence, the technology of new energy and energy efficiencyare an important issue to be discussed.
The reason why solar array can not reach maximum power output is affected bythe temperature and isolationconditions and of load electrical characteristics. Some tracking maximum power were discussed as the following lists.
1.1Perturb and Observe (P&O)[2][3]
P&O shows when the disturbance voltage increases, the output power of solar cellalso increases ,therefore, the disturbance voltage should be increased. Supposethe disturbance voltage continuingly increases and the power of solar cell decreases, therefore, the disturbance voltage should be decreased. That is.Table 1 depictssummary of P&O algorithm.
Table 1. Summary P&O algorithm
Perturbation / Changein Power / Next Perturbation
Positive / Positive / Positive
Positive / Negation / Negation
Negation / Positive / Negation
Negation / Negation / Positive
1.2 Incremental Conductance(IncCond)[4]
Three phenomenon of Incremental Conductance are listed as the following lists.
, at MPPT (1)
, left of MPPT (2)
, right of MPPT (3)
As,
, at MPPT (4)
,left of MPPT (5)
, right of MPPT (6)
1.3 Fractional Open-Circuit Voltage [5][6]
The near linear relationship between and of the PV array, under varying isolationand temperature levels, has given rise the fractional method.
(7)
where the value of is between 0.71 and 0.78 to approach MPPT.
1.4 Fractional Short-Circuit Current[8]
is approximately linearly related to the of the PV array shown in (8).
(8)
where the value of is between 0.78 and 0.92 to approach MPPT.
1.5 Fuzzy Logic Control [7][9]
There are three designc steps of fuzzy controller.
1.5.1 Fuzzification
1.5.2 Rule base table lookup
1.5.3 Defuzzification
where
(9)
(10)
Using (9) and (10) as input variables can have the fuzzy output. Therefore, this paper proposes a sliding mode controller to adjust and control the circuit that meet the requirement of MPPT. Also, the proposed sliding mode controller [11] is better on response time than the method of fuzzy and P&O (perturbation and observation) controller.
2.Variable Structure Control andSliding-mode Control
2.1 Variable Structure Control(VSC)
Variable Structure Control [10]need to have two or more sub-structure generated first, and then add switching condition as shown Fig. 1 that has two different control structures: A and B. Structure A’s speed is faster but oscillation. Structure B’s speed is lower but more stable. Therefore, Fig. 2 shows faster-response and more stable that used structure A for a period of time and then switched to Structure B.
Fig.1 Structure A and B response
Fig.2Variable structure control response
2.2 Sliding mode control
Design steps of Slidingmode control are the following lists.
2.2.1. Choosing sliding function
According to the theory of sliding mode control, choose sliding function () will be considered as and as shown in Fig. 3. When, the system status,, will be pushed to sliding surface which means. Moreover, approaching mode is 3D transformation to 2D as the limit time of .
2.2.2. Switch control signal
The sliding mode[13]is when, system will be in the surface of 2D as shown in Fig. 4 and the switch control signal can be selected as (11)
(11)
where is a switching function and .
Fig.3 Approaching and sliding mode
Fig.4 Switch condition on the sliding surface
2.2.3.Approachingand Sliding Condition
In order to prove the sliding and approaching conditions that exist, the following lists are necessary.
(1) Approaching condition (12)
(2) Sliding Condition (13)
2.2.4. Equivalent Control
Approaching mode is continuous, however, but sliding mode is not continuous. The reason why sliding mode not continuous is the switching condition, and. According to the theory of Filippov[12], equivalent control was proposed that is as , is continuous .
(14)
where (14) is equivalent control and .
Fig. 5 Equivalent control
Table 2: Specification of solar array
Characteristics / SPECOpen circuit voltage / 21.3(V)
Short circuit current / 1.6(A)
Voltage at peak power / 17.3(V)
Current at peak power / 1.5(A)
Typical peak power / 25(W)
Temperatures coefficient of short-circuit current( / 2.03(
Temperatures coefficient of short-circuit voltage( / -0.077(
3. Design of Sliding Mode Controller
3.1 Analysis of solar arraycharacteristics
Mathematical model of the solar array can be expresses as shown in (15)
(15)
where denotes a current of a solar array, denotes an output voltage of a solar array, denotes an electron charge (C) , denotes a cell reverse saturation current (A), is the Boltzman’s constant (J/K),is a cell temperature (K), denotes the ideality factor。
The output power of solararray is usually affected by temperature, sunshine, and so on. Therefore, Fig. 6 shows the relationship among output power, current and output voltage under different isolation.
(a) PV terminal V-I characteristics
(b) PV terminal V-P characteristics
(C) PV terminal V-I characteristics
(d)PV terminal V-P characteristics
Fig.6 Simulated characteristics of ideal PV panel
Fig.7The circuit diagram of PV DC-DC converter system
3.2 DC-DC converter modeling
Fig. 7 shows the Boost Converter to transfer power to load from solar array. When, power will be switched to off. When, power will be switched to on.From Fig. 7, we can draw the system dynamic model as follows.
(16-a)
(16-b)
(16-C)
(16-d)
By Fig. 6, the characteristic curve of solar array depicts the design method. PV array output power is.When the solar array is operating in its maximum output power state. We can have (17).
(17)
where (17) represents maximum power achieved.
3.3 Switching functiocn
By choosing switcching function,will be shown in (18).
(18)
Switch control signal can be selected as shown below.
(19-a)
(19-b)
Therefore, the equivalent control variablec is shown below.
(19-c)
By Lyapunov function, it proves exists.
Let
Using (15) will have (18) as shown below.
(20)
(1)When
Fig. 6(d), (18) and (19-a)，，must increase.
(21)
(22)
Using (21) for (22) depicts and .
(2)When and ,must decrease.
(23)
Finally, using (23) for (22) shows and .Obviously, the system could reach global stability.
4. Simulation and Experiment results
This paper used Matlab/Simulink to simulate P&O, fuzzy and sliding mode control. Fig. 8 shows comparison of the tracking maximum power which reveals the sliding mode controller only needs 2ms, fuzzy controller needs 6ms and P&O controller needs 10ms. Therefore, the proposed sliding mode controller is improved its performance of MPPT.Fig. 9 and 10 show the comparison of voltage and current that the performance of the sliding mode controller is better than P&O and fuzzy controller. Fig. 11 shows the tracking condition of the sliding mode controller as the light changes in a second. As the time changes in 0.02sec, the isolation changes from 600kW/m2 to 800kW/m2 and the time changes in 0.04sec, the isolation changes from 800kW/m2 to 1000kW/m2. Hence, the MPPT changes from 14.6W (600kW/m2) to 19.8W(800kW/m2)in 0.02sec and 19.8W(800kW/m2) to 25W(1000kW/m2)in 0.04sec.
Fig. 12 shows the control architecture, the control system comprises Microcontroller PIC16F877A, MOSFET, L etc. Fig. 13(a) shows the circuit of solar. Fig. 13(b) shows the circuit of booster type converter. Fig. 14 shows the tracking performance of the sliding mode controller as light changes in a second. Fig. 15 and 16 show the voltage and current of Solar cell tracking. Experimental results show the proposed sliding mode controller is robust as the light changes in a second.
Fig. 8 Power characteristic tracking
Fig. 9 Voltage characteristics tracking
Fig. 10 Current characteristics tracking
Fig. 11 Power, voltage, and current of sliding mode controller tracking
Fig. 12 Control architecture
(a)
(b)
Fig. 13 (a) Circuit of solar (b) Circuit of booster type converter
5. Conclusion
This paper presents the sliding mode controller from VSC that controls Booster type converter of solar cell and load to compete the tracking of MPP. After using Matlab and Simulink to simulate P&O, fuzzy control and sliding mode control, compare its response time. Experimental results show the response time of the proposed sliding mode control is better than P&O and fuzzy control.
Fig. 14 Power of solar cell tracking
Fig. 15Voltage of Solar cell tracking
Fig. 16 Current of solar celltracking
6. Reference
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