Comparison of the performance of maximum power point tracking schemes applied to single-stage grid-connected photovoltaic systems S. Jain and V. Agarwal Abstract: This work presents a comparison of various maximum power point tracking (MPPT) techniques applied to 1-f, single-stage, grid-connected photovoltaic (PV) systems. A representative single-stage grid-connected PV system, based on buck-boost converter topology operating in discontinuous current mode (DCM) with sine-triangle pulse width modulation (SPWM) and feeding sinusoidal power into the grid, is considered for this study. MPPT techniques are compared on the basis of the time taken to reach (track) the MPP, operating point oscillations in the vicinity of MPP and the dependence of the algorithms, if any, on array configuration and parameters. Comparison is also made on the basis of the energy extracted from the PV source during the transient tracking phase. In this context, an energy tracking factor term (ETF) is introduced and defined. It is observed that all the MPPT schemes studied have their own merits and demerits. The ripple correlation and b methods offer an overall good combination of desirable features. All the results of this study are presented.
List of symbols a Vin iin PPV Pavg Pg(t) Vg Ig v iPV vPV VPV (max) VPV (min) Dv˜PV Di˜PV IPV VPV pPV(t)
Tuning parameter used in modified hill climbing method DC input voltage DC input current Average photovoltaic (PV) power Average grid power Instantaneous double sinusoid power fed into the grid Amplitude of the grid voltage Amplitude of the grid current Fundamental angular frequency of the grid voltage Instantaneous value of the PV array current Instantaneous value of the PV array voltage Maximum value of PV array voltage Minimum value of PV array voltage Amplitude of the second harmonic component in PV array voltage Amplitude of the second harmonic component in PV array current Average PV array current Average PV array voltage Instantaneous PV array power
# The Institution of Engineering and Technology 2007 doi:10.1049/iet-epa:20060475 Paper first received 16th May 2006 and in revised form 7th February 2007 The authors are with the Applied Power Electronics Lab, Department of Electrical Engineering, Indian Institute of Technology – Bombay, Powai, Mumbai 400 076, India E-mail:
[email protected] IET Electr. Power Appl., 2007, 1, (5), pp. 753 –762
Vtri(p) M VMPP Voc dri rg dvPV xi ETF tmax
1
Peak amplitude of the carrier waveform Modulation index PV array voltage corresponding to MPP PV array open circuit voltage Reflected Thevenin’s resistance across the PV array terminals PV array’s internal resistance Peak ripple of the PV array voltage State parameters (where ‘i’ ¼ 1, 3, 4, 2p, 2n) Energy tracking factor Time taken by the slowest MPPT scheme to track MPP
Introduction
The need for electrical tracking of the maximum power point in photovoltaic (PV) arrays, on account of their nonlinear i-v characteristics, is well known. Limited life span and high initial cost of the PV arrays make it all the more important to extract as much power from them as possible. Several maximum power point tracking (MPPT) algorithms have been proposed from time-to-time [1–15]. Some of the popular schemes are the hill climbing method [1], incremental conductance method [2], constant voltage method [3, 8], modified hill climbing method [4], b method [5], system oscillation method [6, 9, 11] and the ripple correlation method [7, 12, 13]. Other MPPT methods include those by Solodovnik et al. [10], which uses state space approach with the tracking power converter operating in continuous current mode (CCM) and by Wenkai et al. [15], which is based on a combination of incremental conductance and perturb and observe method. Apart from electrical tracking, mechanical tracking of the sun [16] can also be done to maximise insolation and further increase the PV output power. However, MPPT alone is not sufficient. 753
Energy extracted from the PV source through MPPT should either be utilised by a load or stored in some form (e.g. stored in a battery or used for electrolysis to produce H2 for future use in fuel cells). In view of this, grid-connected PV systems are very popular as they do not have any energy storage requirements as the grid can absorb any amount of PV energy tracked [1]. This paper is concerned only with the electrical tracking schemes for maximum power extraction from a PV array. Typically, the grid-connected PV systems may be required to either buck or boost the voltage levels depending on the available PV array voltage. Usually, grid-connected PV systems involve multiple power stages [17, 18], with a dedicated DC – DC converter stage for MPPT and voltage level transformation. The disadvantage with multi-stage systems is that they have a relatively lower efficiency, larger size and higher cost. Therefore the modern day trend is towards single-stage grid-connected configurations (Fig. 1) because of their small size, low cost, high efficiency and high reliability [19 – 22]. In addition to this, single-stage PV systems readily render themselves for integration into a compact module and ‘plug-and-play’ type applications. Clearly, the single-stage philosophy cannot afford a dedicated DC – DC converter stage for MPPT. Therefore, in single-stage grid-connected (SSGC) PV systems, the sole power stage must achieve MPPT, boosting or bucking (if required) and inversion together [19 – 21]. All the available MPPT schemes, mentioned in the beginning, can be applied to SSGC systems though with the following important differences compared with the DC – DC converter-based MPPT [23 – 25]:
1. In SSGC systems, the MPPT correction to the control signal can only be applied once and only at the beginning of a grid voltage cycle to prevent asymmetry of waveforms and DC current injection into the grid. This slows down the tracking speed. 2. When high quality, unity power factor current is fed into the grid, it results in a power sinusoid of twice the grid frequency, as shown in Fig. 2. This causes second harmonic components to be present either in the current or the voltage on the input side. For example, in case of a rigid DC voltage source (Vin), the current (iin) drawn from the source will contain second harmonic components as per the following equations Vin iin ¼ Vg Ig sin2 vt ¼ )
iin ¼
V g Ig (1 cos 2vt) 2
Vg Ig (1 cos 2vt) 2Vin
(1) (2)
where Vg and Ig are the amplitudes of the grid voltage and current, respectively, and v is the fundamental angular frequency of the grid voltage. At this point, it may be noted that PV is a special source with i-v characteristics as shown in Fig. 3. If the PV fed system supplies double sinusoid power, Pg(t) to the grid, both iPV and vPV will contain second harmonic components. This can be explained using Figs. 2 and 3 as follows. Assuming zero losses in the inverter, the average power drawn from the PV source (PPV) must be equal to the average power (Pavg) fed into the grid. From Fig. 2, it can be observed that Pavg symmetrically divides the power sinusoid into two regions [9], which correspond to the charging and discharging intervals of capacitor Cp (Fig. 1). When Pavg . Pg(t), capacitor Cp is charged in a sinusoidal manner with the excess power drawn from the PV source, as shown in Fig. 2. On the other hand, if Pavg , Pg(t), as in the other region, Cp is discharged sinusoidally, providing the deficit power to the grid. Thus, the capacitor (Cp) voltage, which is same as the PV voltage, oscillates between VPV(max) and VPV(min) around its average value of VPV at twice the grid frequency and can be represented by the following expression vPV (t) ¼ VPV þ D~vPV sin (2vt)
(3)
Fig. 1 A representative single-stage configuration for gridconnected PV system [19, 20] a Power circuit schematic b Block diagram of the control circuit for the discontinuous current mode operation of the converter. The SSGC system block represents the dotted portion shown in a. A similar control circuit can be shown for the CCM operation 754
Fig. 2 Graphical approach to demonstrate the presence of second harmonic components in the current and voltage waveforms of the PV array IET Electr. Power Appl., Vol. 1, No. 5, September 2007
2
Fig. 3 The typical p-v and i-v characteristics of a PV array showing the ‘out-of-phase’ relationship between the current and voltage waveforms at the PV array output
where D~vPV is the amplitude of the second harmonic voltage component. Using the iPV-vPV characteristics shown in Fig. 3, the PV array current can be expressed as iPV (t) ¼ IPV þ D~iPV sin (2vt þ p) ¼ IPV D~iPV sin (2vt)
(4)
where D~iPV is the amplitude of the second harmonic current component. Equations (3) and (4) show that both the PV current and voltage contain second harmonic components. The PV output power is given by pPV (t) ¼ iPV (t) vPV (t) ¼ VPV IPV þ (D~vPV IPV D~iPV VPV )
(5)
sin (2vt) D~iPV D~vPV sin2 (2vt) where IPV is the DC current of the PV array and pPV(t) is the power drawn. Equation (5) shows the presence of fourth-order components in PV power. These higher order components are found to be more pronounced during operation near MPP. Different MPPT schemes perform differently in SSGC systems. The main objective of this paper is to provide a performance comparison between various MPPT schemes applied to SSGC PV systems under similar operating and environmental conditions. With the growing popularity of SSGC PV systems, it is very important to have such a comparison for an optimum utilisation of the available energy. To the best of the author’s knowledge, such a comparison is not available in the literature. As part of this comparative study, all the MPPT schemes are applied to a representative SSGC topology [19 – 21] shown in Fig. 1a. This topology consists of two back-to-back connected buck– boost converters, one each for the two halves (positive and negative) of the grid voltage cycle. Both continuous current mode (CCM) [10, 22] and discontinuous current mode (DCM) [15] operations are possible. However, DCM is preferred because of several advantages such as low grid current THD, high power factor, high stability and stable operation at all operating points of the PV array (i.e. in both the negative and positive slope regions of the P-V characteristics) [17, 19, 20]. In view of the above, only DCM operation is considered in this paper. The topology is operated in sine-triangle pulse width modulation (SPWM) manner to feed sinusoidal power into the grid. IET Electr. Power Appl., Vol. 1, No. 5, September 2007
MPPT techniques applied to SSGC PV system
For an SSGC inverter configuration, operating in DCM, the MPPT can be achieved by suitably adjusting the modulation index (M ) of the sine-triangle PWM. After all, varying ‘M’ amounts to changing the widths of the gating pulses, much in the same manner as a duty cycle variation achieves in DC – DC converters. The modulation index ‘M’ of the SPWM is used to control the operating voltage of the PV array. In principle, all the MPPT algorithms, conventionally implemented in conjunction with DC – DC converters, are applicable to grid-connected configurations, such as the one shown in Fig. 1a. The general control block diagram showing the implementation of MPPT in a grid-connected system is shown in Fig. 1b. The peak of the carrier waveform, Vtri(p) is fixed. Therefore M (¼Vs(p)/Vtri(p)) is varied by changing the peak of reference waveform, Vs(p). However, M 1 is not allowed. 2.1 Working principle and control strategy of the single-stage topology considered Device SWp1 (or SWn1) is switched at high frequency in sine-triangular PWM manner while SWp2 (or SWn2) is kept continuously ON during the positive half cycle (or negative half cycle) of the grid voltage. During turn ON period of the switching cycle buck boost inductor L is charged with the PV source and capacitor Cp , which stores energy in it. During turn OFF, D1 gets forward biased, discharging the stored inductor energy into capacitor Cf which feeds sinusoidal current into the grid. Switches SWn1 and SWn2 are operated in a similar manner during the negative half cycle. Thus, each of the buck – boost converters operates for one half cycle of the grid voltage. The configuration acts as a current source feeding sinusoidal current into the grid. The single-stage configuration aims at feeding a sinusoidal current into the grid. It works on the principle of buck – boost converter operating in DCM. Because of DCM operation there is complete transfer of energy during each switching cycle. Therefore the amplitude of the sinusoidal current fed into the grid is indirectly controlled by the operating voltage of the PV array. The DCM operation also provides stable MPPT operation on both positive [19] and negative slope regions of the p-v characteristics with various algorithms considered in this paper. CCM operation is also possible with the SSGC configuration. Using hysteresis control, the inductor current is made to track a reference current waveform resulting in the feeding of high-quality sinusoidal current into the grid. The amplitude of the reference waveform directly controls the power drawn from the PV array and is modulated as per the MPPT requirements. This requires that the operation of the array be restricted to the negative slope region of the p-v characteristics to avoid instability [22]. No such restriction is required for the DCM operation. 2.2
MPPT algorithms
All the MPPT schemes, considered in this paper, are briefly described here. Fig. 4 shows the flowcharts of all these MPPT schemes. 2.2.1 Hill climbing method: Perhaps, the most popular algorithm is the hill climbing method. It is applied to an SSGC PV system by perturbing the modulation index ‘M’ at regular intervals and by recording the resulting array 755
Fig. 4 Flowcharts of the various MPPT algorithyms compared in this work (C1 –C5 are all constants, as are Kr and Ko ). I(k), V(k) and P(k) correspond to Ipv(k), Vpv(k) and Ppv(k), respectively a Hill Climbing [1] b Incremental conductance method [2] c Constant voltage method [3, 8] d Modified hill climbing [4] e b method [5] f System oscillation method [6, 9, 11] g Ripple correlation method [7, 12, 13]
current and voltage values, thereby obtaining the power. Once the power is known, a check for the slope of the p-v curve or the operating region (current source or voltage 756
source region) is carried out and then the change in ‘M’ is effected in a direction so that the operating point approaches the MPP on the p-v characteristic. The algorithm of this IET Electr. Power Appl., Vol. 1, No. 5, September 2007
scheme is described in the following with the help of mathematical expressions 9 In the voltage source region, > > > > @PPV > > . 0 ) M ¼ M þ DM(i.e. increment M) > > @VPV > = In the current source region, > @PPV > > > , 0 ) M ¼ M DM(i. e. decrement M) > > @VPV > > > ; @PPV At MPP, @V ¼ 0 ) M ¼ M or DM ¼ 0(i.e. retain M) PV
(6) Flowchart for the hill climbing algorithm is given in Fig. 4a.
values) and the previous value of ‘a’. a(k) ¼
cm (PPV (k) PPV (k 1)) a(k 1)
where cm is the constant parameter, PPV(k) and a(k) are the values of power and tuning parameter for the kth iteration. This method requires on-line computation of the tuning parameter ‘a’. The flow chart for the modified hill climbing method is shown in Fig. 4d. 2.2.5 b method: The other method, based on b tracking, has the advantage of both fast and accurate tracking. The analysis of the i-v characteristics of a PV array [5], leads to an intermediate variable ‘b’given by
b ¼ ln (IPV =VPV ) c VPV ¼ ln (Io c) 2.2.2 Incremental conductance method: In the incremental conductance method, the MPP is tracked by matching the PV array impedance with the effective impedance of the converter reflected across the array terminals. The latter is tuned by suitably increasing or decreasing the value of ‘M’. Mathematically, the algorithm can be explained as follows 9 At voltage source region, > > > > @IPV IPV > > . ) M ¼ M þ DM(i. e. increment M) > > > @VPV VPV > > = At current source region, @IPV I > > , PV ) M ¼ M DM(i.e. decrement M) > > > @VPV VPV > > > > @IPV IPV > ¼ ) M ¼ M or DM ¼ 0(i.e. retain M) > At MPP, ; @VPV VPV (7) Complete flowchart of the algorithm is shown in Fig. 4b. Both hill climbing and incremental conductance methods use small (and fixed) incremental changes in the modulation index which results in large transient tracking time (‘t’). ‘t’ is defined as the time taken by an MPPT algorithm to reach with in 95% of the maximum average power available at MPP. In addition to small incremental changes in M, the constraint that the modulation index can be corrected only at the start of a grid voltage cycle further slows down the tracking speed or increases ‘t’. Faster MPPT schemes are described next. 2.2.3 Constant voltage method: Constant voltage method is based on the fact that the ratio of the MPP array voltage (VMPP) to open circuit voltage (Voc) is nearly a constant (’0.78), independent of any external conditions. The sensed PV array voltage is compared with a reference voltage to generate an error signal which, in turn, controls the modulation index, as shown in the flow chart in Fig. 4c. Kobayashi et al. [8] have proposed a method on similar lines, where Voc is determined using a diode mounted at the back of the array (so that it has the same temperature as the array). A constant current is fed into the diode and the resulting voltage across the diode is used as the array’s Voc which is then utilised in tracking VMPP . 2.2.4 Modified hill climbing method: The modified hill climbing method [4] uses a variable step size. Here, a tuning parameter ‘a’, given by (8), decides the step length, whose value depends on the change in power (difference between the present and previous instantaneous power IET Electr. Power Appl., Vol. 1, No. 5, September 2007
(8)
(9)
where ‘Io’ is reverse saturation current and ‘c’ is the diode constant (c ¼ (q/hkTNs)) with q, h, k, T and Ns denoting the electronic charge, ideality factor, Boltzmann constant, temperature in Kelvin and the number of series connected cells, respectively. Thus, b depends on all these parameters. It is observed that the value of b remains within a narrow band as the array operating point approaches the MPP. Therefore by tracking b, the operating point can be quickly driven to close proximity of the MPP using large iterative steps. Subsequently, small steps (i.e. conventional MPPT techniques) can be employed to achieve the exact MPP. Thus, b method approximates the MPP while conventional MPPT technique is used to track the exact MPP. Flow chart for the b method algorithm is given in Fig. 4e. 2.2.6 System oscillation method: System oscillation method [6, 9, 11] works on the principle of maximum power transfer theorem. The MPP is tracked by operating the interfacing power converter in such a manner that the ratio of the peak dynamic resistance, dri (reflected across the PV terminals) to twice the internal resistance (rg) of the array (dri =2rg ) equals a pre-determined constant (ko). At MPP, ko is equal to (dvPV =VPV ), where dvPV is the peak ripple of the PV array voltage [6]. This method requires only the sensing of the array voltage. The array voltage signal is conditioned to extract the dvPV and VPV values, using filters. The block diagram representation of the implementation of this algorithm and the flowchart are shown in Fig. 4 f . 2.2.7 Ripple correlation method: Ripple correlation method was first proposed by Krein [7] and subsequently modified for its implementation in stand-alone or gridconnected PV systems [12, 13]. The scheme requires the sensing of PV array voltage and current and hence computing the power. The high-frequency ripple in power and voltage is then captured using high-frequency filters, which are eventually used to compute dPPV/dVPV . The sign of this derivative is ascertained using a signum function and indicates the region of operation (i.e. constant current or constant voltage region). Subsequently, an integrator is used to generate the reference array voltage, which is then compared with the actual PV voltage to generate the corresponding error, as shown in the implementation block diagram and the flowchart given in Fig. 4g. The error is used to suitably alter the modulation index of the PWM. As per (3) and (4), the PV voltage and current waveforms contain second harmonic components and are out of phase with each other as shown in Fig. 3. If these waveforms are directly used by the MPPT algorithm, convergence to 757
MPP is not possible. Hence, it is necessary to average these waveforms to obtain DC values of Ipv and Vpv to be used by the MPPT algorithm. This problem does not arise in SSGC systems because the MPPT correction can only be applied once, at the beginning of the grid cycle and hence Vpv and Ipv need to be sampled only once during a cycle. Inspite of this, averaged values of Ipv and Vpv only should be preferred in SSGC systems to achieve high-speed tracking of MPP. This point is further elaborated later in Section 3. In DCM operation, the MPPT algorithm decides the modulation index ‘M’ of the SPWM. ‘M’ is multiplied with the grid voltage template to produce a reference sinusoidal waveform for comparison with a high-frequency triangular waveform having fixed amplitude. The comparison results in the generation of control pulses used in the switching of the power devices. The complete control scheme for DCM operation is depicted in Fig. 1b. 3
Simulation and experimental results
MATLAB/SIMULINK-based computer simulations of the various MPPT schemes, described before, were carried out with the SSGC configuration shown in Fig. 1a. Similar environmental conditions were assumed. An accurate PV array model, which takes into account the effect of temperature and insolation was used [5]. During the positive half cycle, the various state equations representing the systems in terms of the state parameters xi (where ‘i’ ¼ 1, 3, 4, 2p, 2n) are as follows: When SWp1 is ON ipv ¼ Cp x01 ; x1 ¼ Lx02p ; Cf x03 þ x4 ¼ 0; x3 ¼ Lf x04 þ vg
(10)
When SWp1 is OFF and D1 is conducting ipv ¼ Cp x01 ; x3 ¼ Lx02p ; Cf x03 þ x4 ¼ x2p ; x3 ¼ Lf x04 þ vg
(11)
Fig. 5 Simulation results showing the power extracted from the PV source using various MPPT methods. Effect of variation of insolation and temperature is also considered. Note that the sudden rise and dip in power at around t ¼ 3.7 s can be attributed to the charging of Cp
parameters in the context of MPPT schemes, such as the tracking time, energy extracted during the tracking phase and energy lost during the tracking phase. Laboratory prototype of a 500 W SSGC PV unit was built with the following specifications: Cp ¼ 2000 mF; L ¼ 310 mH; Cf ¼ 10.2 mF; Lf ¼ 3.25 mH; MOSFET used: IRFP 460; power diodes used: CSD20060; VPV ¼ 0 – 120 V; peak grid voltage, VP ¼ 130 V. DSP
When SWp1 is OFF and D1 is not conducting ipv ¼ Cp x01 ; 0 ¼ Lx02p ; Cf x03 þ x4 ¼ 0; x3 ¼ Lf x04 þ vg
(12)
In a similar manner, state equations can be written for the negative half cycle. Using these state equations, complete PV system was simulated in MATLAB/SIMULINK using switching functions. Values of components used in the simulation for the single-stage topology are: Cp ¼ 3000 mF, L ¼ 400 mH, Lf ¼ 3.25 mH, Cf ¼ 5.85 mF. PV array specifications: Maximum power rating ¼ 670 W; open circuit voltage ¼ 129 V; short-circuit current 7.6 A. The simulation results, comparing the power (energy) extraction and other performance parameters for the various MPPT schemes studied, are shown in Figs. 5 through 8. For comparing the various MPPT schemes, it is convenient to introduce an ‘energy tracking factor (ETF)’ defined as ETF ¼ Energy extracted by a given MPPT scheme duringtmax Maximum energy available duringtmax (13) where tmax is the time taken by the slowest of all the MPPT schemes considered in this work. This is a useful term which reflects on the effects of various performance 758
Fig. 6 Simulation results showing the variation of V power extracted. Also marked is the transient tracking time (t) to reach within 95% of the maximum average power available for extraction at maximum power point IET Electr. Power Appl., Vol. 1, No. 5, September 2007
Fig. 9 Experimental waveforms showing PV array current, voltage and power drawn from the PV source in steady state in the vicinity of maximum power point using hill climbing technique Fig. 7 Simulation results showing the steady-state power ripple (in Watts) around maximum power point (MPP) using different MPP tracking algorithms
TMS320LF2407 was used for implementing the MPPT techniques. Fig. 9 shows the various experimental waveforms on the PV side. Random high current spikes in the experimental waveform of the PV array current are observed because of the measurement noise. Waveforms of the grid current and voltage during steady-state are also shown in Fig. 10. It may be observed that the current fed into the grid is slightly distorted. A slight lack of tuning in the parameters like value of Cf (capacitor across the grid), value of Lf (filter inductor), dead-bands between switching instants and so on will result in distortion of grid current. The distortion also depends on the PWM switching scheme used and the amount of distortion in the grid voltage. While sinusoidal PWM switching scheme has been used to ensure low current THD, the grid voltage distortion cannot be avoided. Typical control gating pulses applied to MOSFET during hill climbing MPPT are shown in Fig. 11.
Fig. 8 Simulation results showing the energy extracted from the PV source during the transient tracking phase with various maximum power point tracking schemes IET Electr. Power Appl., Vol. 1, No. 5, September 2007
4 Comparison of the performance of various MPPT schemes The main points that emerge out of this comparative study are briefly discussed and summarised next with respect to various performance parameters. 1. Transient tracking speed: Hill climbing and incremental conductance methods have the slowest and nearly similar tracking speeds as seen in Figs 5 and 6. This is an expected result as both methods use small and fixed correction steps for tracking the MPP, resulting in large tracking time (t). The modified hill climbing method is slightly faster as it uses variable (but small) correction steps. However, as the operating point approaches MPP, the correction steps become smaller and smaller, lengthening the tracking time. Constant voltage method, b method, system oscillation method and ripple correlation method are clearly ahead of the rest as they employ large and variable correction steps to track the MPP. Out of these four, constant voltage method has minimum tracking speed, which can be attributed to the nonlinear relationship between array voltage and modulation index which results in an un-optimum value of c3 (Fig. 4c). b method and system
Fig. 10 Experimental waveforms showing the current fed into the grid and grid voltage in steady state near maximum power point using hill climbing technique 759
Fig. 11 Experimental waveforms showing control pulses fed to the switching devices in the vicinity of maximum power point using hill climbing technique
Fig. 12 Simulation results showing the effect of using averaged and non-averaged values of PV current and voltage on the power extracted from the PV source a Using hill climbing method b Using b method.
Table 1:
oscillation method have comparable speeds. As explained later, the b method is also more accurate because this algorithm automatically shifts to conventional hill climbing method with fixed small steps as it comes close to MPP and no large oscillations are observed. Ripple correlation method has the fastest tracking speed out of all the schemes considered. 2. Tracking accuracy and ripple in the PV power at MPP: Referring to Fig. 5, 6 and 7, in modified hill climbing method, as the operating point approaches MPP, the correction steps become finer, leading to very accurate tracking of MPP. Power ripple near MPP is very small. Hill climbing, incremental conductance and b methods also track the MPP quite accurately under all environmental conditions, though with slightly larger oscillations than modified hill climbing method because of fixed size correction steps. The constant voltage method assumes that the ratio (VMPP/VOC) is constant irrespective of the existing environmental conditions. Since, this is an approximate assumption, it results in inaccurate tracking under varying environmental conditions. If the system is operating in the negative slope region of the array’s p-v characteristics (which is very steep because of VMPP’s proximity to VOC), this approximation may result in large power loss. Further, the power ripple in steady state with constant voltage method depends on the accuracy of tracking, that is, the farther it is from the MPP, higher is the ripple. It is observed that for fast and wide changes in environmental conditions, the constant voltage method shows large oscillations and vice versa. In system oscillation method, tracking accuracy depends on the constant (ko). As the value ko does not hold good for all environmental conditions, it results in inaccurate tracking and high ripple in power during changing environmental conditions. Ripple correlation method, though fastest, shows large changes in the value of ‘M’ near MPP during low insolation condition, resulting in larger power oscillations. 3. Energy tracking factor: Transient time taken to reach MPP with hill climbing and incremental conductance
Performance comparison of various MPPT schemes for a step change in insolation from 0.0 to 0.9 Suns
MPPT scheme
t (s)
Energy lost
Energy tracking Power ripple (max.)c Remarks
during t (J) factor (ETF) (%)
near MPP in steady state (Watts) Implementation Transient
Accuracy
tracking speed Hill climbing [1]a
0.866 261.87
54.12
616.5– 610
Simple
Slow
Accurate
Incremental
0.866 259.67
54.51
616.5– 610
Complex
Slow
Accurate
0.574 152.86
72.8
614.8– 603
Simple
Fast
Not so accurate
0.645 194.13
65.68
616.5– 614
Complex
Fast
Most accurate
b method [5]b
0.216
55.65
89.89
616.5– 610
Complex
Faster
Accurate
System oscillation
0.233
72.08
86.04
616.0– 606
Simple
Faster
Not so accurate
0.145
40.39
91.5
616.5– 602
Complex
Fastest
Not so accurate
a
conductance [2] Constant voltage [3, 8]b Modified hill climbing [4]
b
method [6, 9, 11]b Ripple correlation method [7, 12, 13]a a
Implementation is independent of PV array parameters Implementation is dependent on PV array parameters The maximum power available for extraction from the PV array under the assumed environmental conditions is 616.5 W
b c
760
IET Electr. Power Appl., Vol. 1, No. 5, September 2007
methods is longest among all the methods. Thus, ETF , given by (13), which reflects the tracking efficiency of an algorithm, is low for these two methods. Modified hill climbing has better tracking efficiency. Though not so accurate, the tracking efficiency of constant voltage method is higher than the modified hill climbing method on account of the former’s higher speed. ETF for b method, system oscillation method and ripple correlation method is comparable. Fig. 8 compares the energy extracted during the tracking phase by different algorithms. 4. Dependency on array parameters: Hill climbing, incremental conductance and ripple correlation methods can be applied to any PV array without the knowledge of its configuration and parameter values. This is not the case with the other methods, which depend on PV array parameters and configuration for their implementation. For example in b method, the range of b (bmin – bmax) of the array operating around MPP is required while in modified hill climbing method, tuning of variable ‘a’ depends on the array configuration. Another important aspect, applicable to grid-connected PV systems, is highlighted with the help of Fig. 12. As mentioned before, because of the reflection of second harmonic components on the PV side, both IPV and VPV oscillate (Fig. 9). As both these quantities are used in MPPT algorithms, these oscillations affect the performance of the MPPT. Fig. 12 shows the performance when averaged and actual (non-averaged) values of IPV and VPV are used for two of the MPPT schemes, the hill climbing method and the b method. It can be seen that when averaged values are used, the tracking time is smaller in both the methods. At the same time, the averaging does not seem to have any effect on the accuracy of tracking, as the steady-state power ripple is almost identical with or without averaging. 5
Conclusions
Comparison of several MPPT techniques, applicable to grid-connected inverter configurations operating in DCM, has been presented. Both dynamic and steady-state performances have been compared. The important issue of the presence of second harmonic components in the PV array voltage and current, in grid-connected systems and its impact on MPPT has been highlighted. The choice of an MPPT scheme is application specific. Overall, the ripple correlation method is the fastest method and will particularly be suitable for fast changing environmental conditions. Further, its application is independent of the array configuration. However, it has a lower tracking capability, particularly at low insolation levels, as it uses large tracking steps near MPP. Hill climbing and incremental conductance methods can track the MPP accurately for all environmental conditions, as small steps are used for tracking. But they require comparatively larger time to track MPP. In this context, the modified hill climbing method is quite attractive as it has a good tracking speed besides having the highest tracking accuracy. The constant voltage and oscillation methods have simple implementation and will perform well in stable environmental conditions, with high tracking speed and reasonable accuracy. Further, these two schemes do not need a current sensor and are relatively more economical. The b method has a tracking speed next only to the ripple correlation method and offers a good combination of speed and accuracy under all environmental conditions. However, the scheme depends on the array configuration parameters. IET Electr. Power Appl., Vol. 1, No. 5, September 2007
The slightly higher power ripple can be reduced further if modified hill climbing is implemented (instead of hill climbing) in the final phase of the tracking. This will, however, decrease the tracking speed. It must be pointed out that only one (representative) single-stage grid-connected topology has been used in this work to test and compare all the MPPT schemes. A different topology may render different values of the performance parameters (e.g. ripple power, tracking time, energy tracking factor and so on), but it is expected that the relative performance of the various schemes will remain the same as established in this work. Table 1 compares and summarises the performance of all the MPPT algorithms studied in this paper.
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