International Journal of Engineering Practical Research (IJEPR) Volume 3 Issue 4, November 2014 www.seipub.org/ijepr doi: 10.14355/ijepr.2014.0304.01
Maximum Power Point Tracking Simulations for PV Applications Using Matlab Simulink Mohammed Bekhti*‡, Tekkouk Adda Benattia* *Centre for Satellites Development, Po Box 4065, Ibn Rochd, USTO, Oran, 31130, Algeria Mobile: +213 663 025 823 m_bekhti@yahoo.fr Abstract
Operating Principle
The problem being solved using maximum power point tracking MPPT techniques is to find the voltage VMPP or current IMPP at which a photovoltaic module should operate to obtain the maximum power output PMAX under a given temperature and illumination (solar irradiation). This paper gives an overview about some used techniques for power point tracking. The results which will be presented will also demonstrate the influence of temperature and solar irradiation (illumination) on the output power. Keywords Maximum Power Point Tracking; DC‐DC Converter; Load; Matching; Solar Generator; Command
Introduction Specific commands laws existing to bring devices to operate at maximum points of their characteristics without neither the knowledge in advance of these points nor the knowledge when they have been changed or what are the reasons for this change. This type of control is often referred to as maximum power point tracking (MPPT). The principle of these commands is to conduct a search of the point of maximum power while ensuring a perfect matching between the generator and load. Figure 1 shows a bloc diagram for an elementary photovoltaic system with an MPPT control. The system is based on a solar array, a DC‐DC converter and a load. In our case the power supplied by the photovoltaic generator corresponds to the maximum power PMAX generated and then transferred to the load.
FIG 1 BLOC DIAGRAM FOR AN ELEMENTARY PHOTOVOLTAIC SYSTEM WITH AN MPPT COMMAND
The commonly used control technique is to act on the duty cycle automatically to bring the generator to its optimum operating value because of sudden load variations that can occur at any time. Figure 2 illustrates three (03) sorts of disturbances. Depending on the type of disturbance, the operating point moves from the maximum power point MPP1 to a new operating point P1 more or less far from the optimum. For a variation of sunshine (case a), one needs to adjust the duty cycle value to converge to the new MPP2. For a load variation (case b), we may note a change in the operating point which can find a new optimum position due to the action of a command. To a lesser extent, the last case of variation of the operating point may occur due to the variations in operating temperature of the photovoltaic module (case c). Although we have to act at the command level, the latter does not have the same time constraints as the previous two cases.
FIG 2 SEARCH AND RECOVERY OF MPP, A) SUNSHINE VARIATION, B) LOAD VARIATION, C) TEMPERATURE VARIATION.
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Different MPPT Commands Synthesis
1)
Various works on MPPT commands appear regularly in the literature since 1968, the date of publication of the first command law adapted to renewable energy (photovoltaic). Given the large number of publications in this field, we have a classification of different MPPT according to their basic principles.
The principle of MPPT commands of P & O types is to disrupt the voltage VPV with a low amplitude around its initial value and analyze the behavior of the resulting power variation PPV. Thus, as shown in Figure 4, we can deduce that if a positive increment of voltage VPV generates an increase of power PPV, this means that the operating point is to the left of the MPP. If, however, the power decreases, this implies that the system has exceeded the MPP.
First MPPT Commands Types The algorithm implemented in the first MPPT command was relatively simple. Indeed, the capacity of microcontrollers available at that time was low and applications, especially, for space had fewer constraints regarding temperature and solar irradiation. The first command to be applied to a photovoltaic system was described by A.F. Boehringer. The command was based on an algorithm of adaptive control, to maintain the system at its maximum power point PPM. This is described in Figure 3 and can be easily implemented on a computer. The system calculates the power at time ti from the measurements of IPV and VPV, and compares it to the one stored in memory (time ti‐1). From there, a new duty cycle D is calculated and applied to the static converter.
Perturb and Observe Command Principle
FIG 4 PPV VS VPV CHARACTERISTIC OF A SOLAR PANEL
Figure 5 shows the algorithm associated with a conventional MPPT command of the P & O type, where the evolution of the power is analyzed after each voltage disturbance. For this type of command, two sensors (current and voltage) are needed to determine the power of the solar generator at every instant of time. The Perturb & Observe method is nowadays widely used because of its ease of implementation. However, it has some problems associated with oscillations around the MPP it generates in steady state because the search of the MPP should be repeated periodically, causing the system to oscillate continuously around the MPP.
FIG 3 BLOC DIAGRAM OF A DIGITAL MPPT COMMAND.
This principle is always valid from a theoretical point of view and applied nowadays to more efficient numerical algorithms. However, the response time has been improved as well as the PPM search accuracy. Efficient MPPT Commands Algorithms The three (03) methods most commonly encountered are commonly referred to respectively as Hill Climbing, Perturb & Observe and incremental conductance.
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FIG 5 DIVERGENCE OF THE P & O COMMAND DUE TO RADIATION VARIATIONS
Figure 6 shows a detailed algorithm of the P & O command.
International Journal of Engineering Practical Research (IJEPR) Volume 3 Issue 4, November 2014 www.seipub.org/ijepr
FIG 7 HILL CLIMBING COMMAND PRINCIPLE
FIG 6 ALGORITHM OF THE P & O TYPE OF COMMAND
To understand this, consider the example of a given solar irradiation, E1, with an operating point lying in A. following a voltage disturbance of value V, it switches to B, implying a variation of operating without illumination, a reversal of the sign of the disturbance due to the detection of a negative sign for the derivative of the power resulting, in equilibrium, in oscillations around the MPP due to the path of the operating point between points B and C. it can be noted that losses of power transfer will be more or less important depending on the respective positions of points B and C with respect to A. When changing the irradiation of the module from E1 to E2, the operating point then moves from A to D, which is interpreted in this case as a positive power variation. 2)
The method’s algorithm is depicted in Figure 8. The slope corresponds to a variable that takes the value 1 or ‐1 depending on the direction we give to our search to increase the power output of the panel. α and PPV represent respectively the duty cycle and power, a represents the increment of the duty cycle. Periodically, the PPP power (n) is compared with the previous one PPV (n‐1), depending on the comparison’s result; the sign of the slope remains the same or changes. This has the effect of incrementing or decrementing the duty cycle value. Once the MPP is reached, the system oscillates around it indefinitely while making a tradeoff between speed and accuracy.
Hill Climbing Command Principle
The Hill Climbing technique consists of putting high the operating point along the generator characteristic having a maximum. For this, two slopes are possible. The search stops when the theoretically maximum power point is reached. This method is based on the relationship between the panel output power and the value of the duty cycle applied to the solar generator. Mathematically, the MPP is reached when DPPV / dD is forced to zero by the command, as shown in Figure 7.
FIG 8 HILL CLIMBING COMMAND ALGORITHM
The advantage of this technique is its simplicity of implementation. However, it has the same disadvantages as the Perturb and Observe method with regard of oscillations around the MPP in steady state and an occasional loss of search of the MPP for rapidly changing weather conditions. 3)
Conductance Increment Command Principle
The conductance of the photovoltaic module is defined by the ratio between the current and voltage as follows:
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G
I
(1)
V
The conductance increment can be defined as: I
dG
V
(2)
On the other hand, the evolution of the module power PPV versus voltage VPV gives the operating point position with respect to the MPP. When the power derivative is zero, it means that we are on the MPP, if positive, the operating point is to the left of the maximum, and otherwise it is on the right. Figure 9 is used to write the following conditions: The maximum power MPP is obtained when: P
0
V
(3)
The source output power can be written as: P Expressing
P V
I V
(4)
0 we find: dP dV
I
dV dV
dI dV
V
P
I
I
V
V
V
P V
V
G
(5)
∆G
(6)
And
In general, the source voltage is a positive quantity; this gives the key results for this method:
dP/dV > 0 G > ‐ ΔG dP/dV = 0 G = ‐ ΔG dP/dV < 0 G < ‐ ΔG
G > ‐ ΔG increase Vp reduce α. G = ‐ ΔG keep Vp do not modify α. G < ‐ ΔG reduce Vp increase α.
There is a case where you cannot compare the conductance. This is when the system was indeed in the MPP at the previous iteration. In this case, the duty cycle was not modified and therefore Vp remained constant (dVp = 0). Incremental conductance G is then not defined. For this, we just need to observe the variations of Ip.
dIp =0 Vp constant do not modify α. dIp > 0 increase Vp reduce α. dIp < 0 reduce Vp increase α.
4) MPPT Commands Based on Proportional Relationships The operating mode of these commands is based on proportional relationships between optimal parameters, characterizing the MPP (VOPT & IOPT) and the characteristic parameters of the module (Voc and Isc).
Thus: V
Measure of Voc (Fraction of Voc).
This technique consists of comparing the panel voltage VP with a reference voltage corresponding to the optimum voltage Vopt. The reference voltage is obtained from the knowledge of the linear relationship, existing between Vopt and Voc of the solar generator (7): V
K
V
(7)
Measure of Isc (Fraction of Isc).
This method is based on the knowledge of the linear relationship between of IOPT and Isc of the equation (8):
Figure 9 shows the different cases shown above:
I
= K
IS
(8)
With ki a power factor which depends on the solar generator used and is generally between 0.78 and 0.92. Definition of a Power Chain and Associated Efficiencies The maximum conversion efficiency photon‐electron of the solar panel noted ηPV is defined in equation (9): ηPV
FIG 9 EVOLUTION OF POWER AS A FUNCTION OF VOLTAGE ACROSS A SOLAR GENERATOR
We then get:
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P G A
Where: ‐ PMAX output available power from solar generator. ‐ Aeff effective area of solar generator.
(9)
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Th he efficiency y of the op perating poiint brings that t den noted ηMPPT can measu ure the effecctiveness of the com mmand thatt is responssible for thee control of the power converrter so that the photovoltaic mod dule pro ovides a max ximum of po ower. P
ηMPPT
P
(10)
No ote the poweer at the outp put Pout, the eefficiency off the con nverter ηconv can be defineed as followss (11), P
η
P
(11)
Th he total efficieency of the cconversion ch hain ηtotal can n be deffined as the product of th he three (03) efficiencies (12). η η
P G A
P P
= ηMPPTT η
pplied by th he generatorr according to the output sup volltage of thee generator with time. The electrical mo odel used forr this study iis based on o one hand on the jun nction tempeerature of th he cells and d on the otther han nd on the sollar irradiatio on. The resultts show that the too ol, used ʺMattlab / Simuliinkʺ, proves to be great for pho otovoltaic en nergy converrsion. This alllows operatting thee photovoltaiic generatorss in optimal conditions aand theerefore gets better b use off the solar energy. e For this t wo ork, we consiider a panell comprising g 6 strings off 48 solar cells in series. Figure 110 shows a b bloc diagram for thee photovoltaiic generator u under ʺMatla ab / Simulink kʺ. TA ABLE 1 ALSAT‐1 AVERAGE ELECT TRICAL PERFORMA ANCE DATA FRO OM MANUFA ACTURER
P P
ηPVV
(12)
Simulations Results mulation of a a Solar Geneerator Sim Th he objective of o this work k is to present the electrrical chaaracterization and mo odeling und der ʺMatlab b / Sim mulinkʺ for ssolar generattors. We anaalyze the currrent sup pplied by th he generator and the electrical e pow wer
Isc (mA A) Voc (V)) Pm (mW W) Im (mA A) Vm (V)) Fill facttor Eff. %
254.6 1.022 214.2 238.0 0.900 0.82 19.8
To check the vaalidity of ourr model, we give on figu ures 14 and 15 the evolution of tthe two main n characterisstics (I, V V) and (P, V)) with a solarr radiation o of 1370w/m2 aand a temperature of 25 ° C. T Table 1 sum mmarizes all the datta from the supplier o of solar cellss used for the sim mulations
FIIG 10 REPRESENTATION OF T THE SOLAR GE ENERATOR UN NDER SIMULIN NK
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FIG 11 I‐V CHARACTERISTICS OF THE SOLAR GENERATOR
FIG 15 SOLAR RADIATION INFLUENCE ON THE I‐V CHARACTERISTICS
FIG 12 P‐V CHARACTERISTICS OF THE SOLAR GENERATOR
FIG 16 SOLAR RADIATION INFLUENCE ON THE P‐V CHARACTERISTICS
Conclusion From the simulation’s results, one can conclude that the performance of the solar generator degrade with an increase in temperature and a decrease of the intensity of the solar irradiation. The performance of the photovoltaic generator is evaluated by using standard conditions 1370W/m2 and 25°C. As a summary, the MPPT controller performs a permanent monitoring of the MPP, necessary to know the variations of the output power of the photovoltaic generator and adjust the duty cycle of the static converter and thus ensure the matching between the photovoltaic generator and the load.
FIG 13 TEMPERATURE INFLUENCE ON THE I‐V CHARACTERISTICS
REFERENCES
FIG 14 TEMPERATURE INFLUENCE ON THE P‐V CHARACTRISTICS
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International Journal of Engineering Practical Research (IJEPR) Volume 3 Issue 4, November 2014 www.seipub.org/ijepr
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