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ScienceDirect Procedia Technology 25 (2016) 808 – 815
Global Colloquium in Recent Advancement and Effectual Researches in Engineering, Science and Technology (RAEREST 2016)
PV Systems with Continuous Sliding Mode Controlled Quadratic Boost Converter Ashly Dhanesana*, Ravishankar A Nb, Anudev Jc a
Amrita Vishwa Vidyapeetham , Kollam -691001, India Amrita Vishwa Vidyapeetham, Kollam -691001, India c Amrita Vishwa Vidyapeetham, Kollam -691001, India
b
Abstract Photovoltaic (PV) systems can provide maximum power with higher efficiency at best operating point with respect to incident solar irradiation. The locus of maximum power operating point varies with panel surface and cell temperature. An effective maximum power point tracking algorithm can always match the solar and load characteristics continuously so that maximum power is transferred to the load. This paper proposes the use of Quadratic Boost Converter (QBC) as a M PPT converter with existing modified incremental conductance algorithm. The performance of the converter is improved with continuous sliding mode controller such that the system is effective for fast and large variations in input solar irradiation. The result is stu died in M ATLAB/Simulink platform and validates the efficiency of the p roposed M PPT controller. © Published by Elsevier Ltd. Ltd. This is an open access article under the CC BY-NC-ND license ©2016 2015The TheAuthors. Authors. Published by Elsevier (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of RAEREST 2016. Peer-review under responsibility of the organizing committee of RAEREST 2016 Keywords: Photovoltaic (PV) systems; M aximum Power Point Tracker(M PPT); Incremental Conductance; Quadratic Boost
Converter(QBC); Sliding M ode Control(SM C).
1. Introduction Over the past few decades the demand for renewable energy has been increasing significantly. This is mainly because of greenhouse effect and shortage of fossil fuels. Among the various types of renewable energy sources, solar energy has become very popular due to advancements in power electronics techniques [2]. But the power of PV module varies according to solar irradiat ion as well as load resistance [3]. In order to ensure that PV system always
* Corresponding author. Tel.: +918893596061 E-mail address:
[email protected]
2212-0173 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Peer-review under responsibility of the organizing committee of RAEREST 2016 doi:10.1016/j.protcy.2016.08.182
Ashly Dhanesan et al. / Procedia Technology 25 (2016) 808 – 815
provide high efficiency despite this variation, maximu m power point tracking (MPPT) algorithm is used[3]-[5]. The purpose of MPPT system is to samp le the output of PV and apply the load to obtain maximu m power. There are many M PPT algorith ms to optimize the power output of an array . Here a modified incremental conductance algorithm [7] is used which will provide fast response and also reduces complexity of the system.
Fig. 1. PV System with MPPT controller
The proposed PV system consists of a quadratic boost converter connected in between PV module and the load as power conditioner. The current and voltage of the PV module are given to the MPPT algorith m to calculate the duty cycle. It is then used as the control input by continuous sliding mode control to ensure that the PV system always operate without any disturbance under fast and large variation in solar irradiat ion [12]-[15]. Figure 1 shows the block diagram of proposed system. Here, QBC is selected in order to provide high voltage gain without any conduction losses and to provide highest efficiency with a single active switch [17]. Continuous sliding mode control results in robust and stable PV system when applied to switching converters. Nomenclature ୭ ୭ ୭ୡ ୱୡ ୫୮୮
PV voltage PV current output voltage of the converter output current of the converter open circuit voltage of the solar module short circuit current of the solar module voltage at maximu m power point
୫୮୮ ୫ୟ ୶
current at maximu m power point maximu m power
This paper is organized as follo ws. The modified MPPT algorith m used to extract maximu m power fro m the PV source is explained in detail with the flowchart in section 2. Section 3 gives an idea of imp lementing continuous sliding mode control for the quadratic boost converter. Section 4 p resents the simulation results for the system. Finally, the paper is concluded in section 5. 2. Modified Incremental Conductance Algorithm The drawbacks of co mmon ly used MPPT algorith ms like, perturbation and observation and incremental conductance, are oscillations around MPP and sluggish response. These two drawbacks are significant if the changes in solar irradiat ion are more and rapid. These problems are eliminated by the modified incremental cond uctance
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algorith m where relationship between load line and the I-V curve is used to obtain fas t and accurate response. Hence, any variation in voltage and current of PV module due to any variation in load or solar irradiat ion must be considered by the MPPT algorithm. The possible changes are given in Table 1. T able 1. Variation in Voltage and Current of PV module for variation in Solar Irradiation and Load. Causes
Direction
Solar Irradiation Load Resistance
Voltage Variation(dV)
Current Variation (dI)
Increase
Positive
Positive
Decrease
Negative
Negative
Increase
Positive
Positive
Decrease
Negative
Negative
2.1. Decrease in Solar Irradiation Level When the solar irradiat ion is 1000 W/݉ଶ , let the PV module operates at load line 1, Figure 2(a). Then the current and voltage of PV module are ܸ and ܫ. Then, if the solar irradiat ion decreases to 400 W/ ݉ଶ and the duty cycle of the converter remains same, the operating point of the PV module is at point P ( ܸଵ ǡ ܫଵ) of load line 1. But this is far away fro m actual MPP of 400 W/ ݉ଶ , point R. In order to perturb the operating point of the PV module to the new MPP using duty cycle equation (11), voltage and current of new MPP is to be obtained. For this, approximated values are substituted in (11). As shown in Figure 2(a), ܫଵ is close to the short circuit current of 400 W/݉ଶ . Hence, ܫଵ is approximated as the current of new MPP. Also, it is clear that vo ltages of MPP fo r each solar irradiation are close to one another. Hence, ܸ is appro ximated as the voltage of new MPP. Thus, ( ܸ ǡ ܫଵ) are substituted in (11) to perturb the operating point to load line 3 at point Q (ܸଶ ǡ ܫଶ). Finally, a few steps of conventional incremental conductance algorith m helps in tracking the new MPP at point R. Thereby the convergence time fro m P to R is greatly reduced. 2.2. Increase in Solar Irradiation Level When the solar irradiat ion is 400 W/ଶ , let the PV module operates at load line 2. Then the current and voltage of PV module are ୫୮୮ బǤర and ୫୮୮ బǤర. Then, if the solar irrad iation increases to 1000 W/ ଶ and the duty cycle of the converter remains same, the operating point of the PV module is at point S (ଵ ǡ ଵ ) of load line 2. But this is far away fro m actual MPP o f 1000 W/ଶ , K. In o rder to perturb the operating point of the PV module to the n ew MPP using (11), voltage and current of new MPP is to be obtained. But ଵ is far away fro m the short circu it current of 1000 W/ ଶ as shown in Figure 2(b). Thus an additional s tep is formu lated. Fro m figure 2(b), T, V, W forms a right triangle. Using similarity properties of two triangles, the operating current ୶ is obtained. భ ିౣ౦౦ ୍౮ ି୍భ
୶ =
ൌ
ౙ ିౣ౦౦
ౙ ିౣ౦౦ ౙ ିభ
୍౮
ͳ
(1)
(2)
Now, ୶ and ୫୮୮ బǤర are substituted in (11) to obtain the new duty cycle. With this new duty cycle, PV module operates at U (ଶ ǡ ଶ ) of load line 4, wh ich is very near to the new MPP of 1000 W/ ଶ . Then few steps of incremental conductance algorithm are used to track the exact MPP.
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Current (A)
1000 W/݉ ଶ
ሺሺ୫୮୮ ǡ ୫୮୮ ሻ
ሺܸଵǡ ܫଵ ሻ ሺܸଶǡܫଶ ሻ
Voltage (V)
b (ܸଶ ǡ ܫଶ ሻ
Curent (A)
a
ܫଵ far away from new ܫௌ
400 W/݉ ଶ
ሺܸబǤరǡ ܫబǤరሻ
Voltage (V)
Fig. 2. Load lines on I-V Curves for (a) Decrease in Solar Irradiation Level (b) Increase in Solar Irradiation Level
2.3. Load Variation After determining load variation, load line no longer cut through MPP. It means PV module diverts away fro m MPP. Then a new duty cycle is required for the PV to operate at MPP again. Here, voltage and current at the MPP remains unchanged. Using these values, the load resistance can be calculated. Th en substituting these values in (11), new duty cycle will be obtained which will make the PV to operate close to the MPP. Then few steps of conventional incremental conductance algorithm are used to track the actual MPP. 2.4 MPPT Algorithm
Fig. 3. Flowchart of Modified Incremental Conductance Algorithm
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Figure 3 shows the flowchart o f the algorith m. Initially, the flag value is set to 0. When the flag value is set to 1, it indicates that the PV system is operating at MPP. In itially, the conventional incremental conductance algorithm is used to track the MPP. In order to eliminate the steady state oscillation in the system after the MPP is reached, a permitted error of 0.06 is used. ୢ୍ ୍ │ + ሃᦪͲǤͲ (3) ୢ
After the MPP is tracked, flag value is set to 1 and then modified algorith m is fo llo wed. First step is to check equation (3). If it is satisfied, no further regulation of duty cycle is required. When the solar irrad iation or load is varied, (3) will not be satisfied and hence the flag value will be set to 0. Now, load resistance is calculated using (9). If both current and voltage of PV module are decreased, then d uty cycle equation is used to obtain the new duty cycle. If both current and voltage are increased, then (2) is used to calculate ୶ and then calculate new duty cycle. Conventional algorith m is used until the difference in power is smaller than 0.06. For load variation, the new duty cycle is calculated after obtaining load resistance from (9). 3. Quadratic Boost Converter The quadratic boost converter is a fourth-order structure consisting of two commutation cells. The main advantage of QBC co mpared to conventional boost converters is the possibility to obtain a higher gain with an inferior duty cycle and without any saturation in the control signal. The voltage conversion ratio of the converter is given as బ
=
ଵ ሺଵିୈሻ మ
(4)
Since voltage conversion ratio of QBC is square that of boost converter, it is capable of producing a higher output voltage than the boost converter for the same input voltage and duty cycle. 3.1 QBC Steady State Equations For a quadratic boost converter, relationship between voltage and current is given by (5) and (6) ୧୬ = (1-Dሻଶ
(5)
ଵ ሺଵିୈሻమ
(6)
୧୬ =
where ୧୬ is the input voltage of the converter or the voltage of PV module ( ) and ୧୬ is the input current of the converter or the current of PV module ( ). (5) divided by (6) to get (7): ୧୬ = ሺͳ െ ሻସ ୭୳୲
(7)
where ୧୬ is the input resistance of the converter and ୭୳୲ is the load resistance. ౌ ୍ౌ
= ሺͳ െ ሻସ ୪୭ୟୢ
୪୭ୟୢ =
ଵ
ౌ
ሺଵିୈሻర
୍ౌ
(8)
(9)
Thus the load resistance can be calculated by substituting voltage and current of PV module and duty cycle in (9). Above equation can be rewritten to get (11) which is the duty cycle equation of the converter. Then the duty cycle can be calculated by substituting ୫୮୮ and ୫୮୮ of PV module in (11).
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Ashly Dhanesan et al. / Procedia Technology 25 (2016) 808 – 815 ଵ
=
ሺଵିୈሻర
୍ౌ ౌ
(10)
ర
D= where a =
ξ ିଵ
(11)
ర
ξ
୍ౌ
ౌ
.
3.2 Continuous Sliding Mode Control for Quadratic Boost Converter When subjected to load and input voltage variations, output voltage of a DC-DC converter varies. Hence it is necessary to regulate the output voltage of converters. The control of output voltage is difficult because of its non minimu m phase structure. Since switching converters are non-linear and time-variant systems, a non- linear control technique called sliding mode control which is derived fro m the variab le structure control system theory (VSCS), is used to get robust output voltage. But sliding mode controlled converter suffers fro m switching frequency variations called chattering. This can be eliminated by using continuous sliding mode control method. In this method, robust output voltage is obtained by comparing inductor current and reference current. This is because; controlling the current can indirectly control the output voltage. Hence, in steady state, భ = ୰ୣ . Sliding surface is selected as: (12) S = ჴଵ ଵ +ჴଶ ଶ ; ჴଵ = 0.2, ჴଶ = 0.4 ଵ = ୰ୣ - భ
(13)
Since current reference is generated from the voltage error, ୰ୣ = β (୰ୣ െ ୱ); β=0.25
(14)
ଶ = ୰ୣ െ ୭
(15)
On assuming a Lyapunov function V= ½ S2 and on designing the controller in such a way that equivalent control vector ୣ୯ which controls the switch when sliding mode condition is satisfied. ୣ୯ = 1- 0.025
ሺଵିୈሻ మ ሺଶିୈሻ
Control input U is represented as, U= ୣ୯ + kS
ୢ ୢ୲
= Ṡ=0, then the
(16)
(17)
Now, value of k can be calculated from reachability condition, SṠ˂0 Thus, k = 0.24 4. Simulation Results Simu lations were performed for the system in MATLA B/SIMULINK. The specificat ions of the PV module (KC85T) and the values of the co mponents in the quadratic boost converter are given in Tab le 2 and 3 respectively. The switching frequency for the insulated-gate bipolar transistor (IGBT) is set to 20 kHz.
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T able 2.Parameters of KC85T PV Module at ST C
Values 87 W 17.4 V 5.02 A 21.7 V 5.34 A
Parameters ଵ ଶ ଵ ଶ
Values 1.14 μH 21.56 μH 1.097 mF 1.155 μF
X axis = 1 unit=0.2 s Y axis = 1 unit =10 W, 10 V, 10 A
Current (A)
Voltage (V)
Power (W)
Parameters ୫ୟ୶ ୫୮୮ ୫୮୮ ୭ୡ ୱୡ
T able 3. Design Parameters of the Converter
T ime (sec) Fig. 4. Waveforms of PV current, voltage and power during varying solar irradiation of 400 W/ଶ and 1000 W/ଶ
Figure 4 shows the simu lation results for the mod ified algorith m for variation in solar irradiation level. Init ially, the irradiation is 400 W/m2 . Then conventional incremental conductance algorithm is used to track the MPP, and it is tracked at t=0.015s. The power of the PV module is fixed at 75 W. After the MPP is tracked, the flag value is set to 1, and no variation in the duty cycle until a variation in the solar irradiation level is found at t=0.75 s. After the solar irradiat ion is increased to 1000 W/m2 , the PV modu le operates at another point. Hence, (9) is used to calculate the resistance of the load, and then, (11) and (2) are used to calculate ୶ as well as the new duty cycle. The duty cycle remains constant at 0.77, and the power of the PV module is at 86 W.
a
b =395 V
X axis= 1 unit =2 s Y axis = 1 unit =100 V
T ime (sec)
Voltage (V)
Voltage (v)
୭=392 V
X axis =1 unit=2 s Y axis = 1 unit =100 V
T ime (sec)
Ashly Dhanesan et al. / Procedia Technology 25 (2016) 808 – 815 Fig. 5. Voltage waveform of Quadratic Boost Converter (a) without controller (b) with controller
Conventional DC-DC converters can step up low dc voltage level to h igh voltage level with a maximu m gain of 10. But quadratic boost converters can step up a low dc voltage (15-25V) to a 400 V dc level. Figure 5(a) represents the simulation result of converter connected to the PV system without sliding mode controller. Here output voltage of PV module gets boosted by the converter to 392 V. The voltage waveform gets settled at 0.05 s. It is observed that, the voltage settles after few oscillations which are not satisfactory. These oscillat ions can be avoided by sliding mode control which is verified in figure 5(b). The output voltage when sliding mode control method was imp lemented is shown in Figure 5(b). Even when the output voltage of PV module (input voltage of the converter) was varied fro m 18 -22 V, it is observed that output settles to 395 V at a s maller settling time of 0.03 s without any oscillations. Thus the output voltage of the system obtained was robust. 5. Conclusions The mod ified incremental conductance algorith m was analysed and the result ind icated that the algorith m responds faster than the conventional algorithm. In order to have robust output voltage over varying load conditions, continuous sliding mode control method was applied to the converter. The simulat ion result does not include any overshoot and also the output voltage settles to a stable value at a smaller settling time. As a conclusion, the proposed system is robustly stable. References [1] F.M.Gonzalez-Longatt, “Model of Photovoltaic Module in MATLAB” in Proc. 2do CongresoIberoamericano de Estudiantesde ……IngenieriaElectrica, Electronica y Computacion (II CIBELEC), 2005.pp.1-5. [2] M.N.Kabir, Y.Mishra, G.Ledwich, Z.Y.Dong, and K.P.Wong, “ Coordinated control of grid-connected photovoltaic reactive power and ……battery storage systems to improve the voltage profile of a residential distribution feeder,”IEEE Trans. Ind. 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