A control scheme with performance prediction for a PV fed water pumping system

Abstract

This paper focuses on modeling and performance predetermination of a photovoltaic (PV) system with a boost converter fed permanent magnet direct current (PMDC) motor-centrifugal pump load, taking the converter losses into account. Sizing is done based on the maximum power generated by the PV array at the average irradiation. Hence optimum sizing of the PV array for the given irradiation at the geographical location of interest is obtained using the predetermined values. The analysis presented here involves systems employing maximum power point tracking (MPPT) as they are more efficient than directly coupled systems. However, the voltage and power of the motor might rise above rated values for irradiations greater than the average when employing MPPT, hence a control scheme has been proposed to protect the PMDC motor from being damaged during these conditions. This control scheme appropriately chooses the optimum operating point of the system, ensuring long-term sustained operation. The numerical simulation of the system is performed in Matlab/Simulink and is validated with experimental results obtained from a 180 V, 0.5 hp PMDC motor coupled to a centrifugal pump. The operation of the system with the proposed control scheme is verified by varying the irradiation levels and the relevant results are presented.

Graphical abstract

Keywords

photovoltaic system / boost converter / maximum power point tracking (MPPT) / DC permanent-magnet motor / centrifugal pump

1 Introduction

Solar energy is widely used in many domestic applications, especially in developing countries where there is a considerable power deficit [1]. Water pumping is one of the typical applications particularly in rural areas where solar energy is used [2]. DC motors are extensively used as the prime mover for the pump as the power obtained from the photovoltaic (PV) source is DC in nature [3]. Though induction motors have lesser maintenance and are compact, they demand an additional DC-AC conversion stage which may further reduce the efficiency [4]. Permanent magnet direct current (PMDC) motors are a much preferred choice for PV pumping systems because it avoids unnecessary energizing of the field coil [5].

Directly coupled PV fed PMDC motor-centrifugal pump systems are widely used due to their low installation cost and excellent matching characteristics [6,7]. However a directly coupled system does not work at the maximum power point (MPP) at all times and results in very low operating efficiencies [8]. It has been found that the systems which employ MPP tracking (MPPT) are 30% more efficient than directly coupled systems [9]. A PV source is generally operated in conjunction with a DC-DC power converter in order to track the instantaneous MPP [10]. Boost converters are usually used to achieve greater output voltage and reduce the number of panels in series string [11]. They also have a higher operating efficiency than the buck or buck-boost configurations [12]. Hence a boost converter is used in this paper to interface the PV array to the motor-pump load and to implement MPPT. There are various MPPT techniques available to extract maximum power from the PV panels [13−16]. In this paper, the P&O algorithm has been employed to implement MPPT due to its ease of implementation.

In a PV system with battery storage, the battery limits the output voltage and hence only the output current will change based on the power variations at the input. However in a standalone solar PV water pumping system without batteries, output voltage of the boost converter will change according to the power variations at the input [17]. If the PV system is over-sized, employing MPPT will cause the output voltage or the output power to exceed the rated values of the motor. Hence proper sizing of the PV array is one of the main design considerations for PV pumping systems. Sizing is done based on the maximum power generated by the PV array at the average irradiation at the geographical location of interest [18]. However the irradiation continuously varies during the course of the day and the values higher than the average irradiation are attained. When the irradiation increases above the average irradiation value, the MPPT controller will still track the MPP at that higher irradiation, resulting in more power output. When the PV array power output exceeds the power rating of the motor, the array and system efficiencies will decrease [19]. Exceeding the rated values will also damage the motor and degrade the system performance in the long run. Hence proper care must be taken during design so that the system is optimized and its performance is not affected by the irradiation levels greater than the design irradiation [20].

With a proper modeling of the designed system, simulations can be done with the help of the irradiation data in a region and its performance can be completely predetermined before its installation at the site. This paper presents an accurate modeling of the PV fed motor-pump system including the losses in the DC-DC converter. The relevant analytical expressions for the speed of the PMDC motor, output power, output voltage of the boost converter and the discharge of the pump are formulated and their values are predetermined. The parameters are predetermined using the Newton-Raphson technique with PV array voltage (U_PV) and array current (I_PV) as the input variables. Case studies for three different number of set of panels subjected to the average and maximum peak irradiation have been conducted to evaluate the performance of the system.

Analysis has been performed for choosing the optimal number of PV panels. It is done by equating the predetermined power generated at average irradiation and power rating of the PMDC motor. This is done because the PMDC motor has peak efficiency at rated values [21]. The case studies also involve analysis of the system during peak irradiation when the predetermined output voltage and output power at MPP exceed the rated values. Hence, a control scheme has been proposed to prevent the motor from damage during higher irradiations by restricting the output voltage to rated value. The proposed control logic performs MPPT for output voltage lesser than the rated value and voltage control mode for output voltages greater than the rated value. This ensures long-term sustained operation without hampering motors’ performance.

2 System description

The array of PV panels and the PMDC motor-centrifugal pump load are interfaced with the boost converter. This DC-DC converter is used in conjunction with PV panels to extract the maximum power and transfer it to the loads. A system level block diagram is given in Fig. 1.

2.1 Modeling of a PV module

A PV cell is modeled as a current source in parallel with a diode. Figure 2 shows the equivalent circuit of a PV cell.

A relatively common approximation done is neglecting R_SH [22]. The total current of a photovoltaic cell is expressed in Eq. (1).

(1)I=I_{PH}-I_o\left[\exp \left({\displaystyle \frac{q(V/N_S+I{R}_S)}{n{k}_{B}T}}\right)-\mathrm{1}\right],

where I_PH is the photo current, I_o is the reverse saturation current, q is the charge of an electron, R_S is the series resistance, k_B is the Boltzman constant, n is the ideality factor, and T is the cell temperature. Many numbers of such PV cells are connected in series to obtain a PV module. The current-voltage characteristics of a PV panel depend on the solar irradiation and cell temperature. The specifications of the PV panels used in this paper are listed in Table 1.

2.2 DC-DC converter

A boost converter is used to interface the PV panels with the PMDC motor-centrifugal pump system. The boost converter matches the load with the PV array and performs MPPT. The boost converter consists of an inductor, a switch (IGBT), a diode and a capacitor. The energy stored by the inductor during the ON period of the switch is pumped back to the load along with the input during the OFF period, resulting in boosted output voltage [23].

The losses in the inductor can be equivalently represented by its resistance R_L. The IGBT is modeled as the voltage drop V_SW in series with the on-state resistance R_ON while the diode can be represented by the series combination of the forward resistance R_D and the voltage drop V_D.

The total time period for one cycle is T_s. The equivalent circuit when the switch (IGBT) is ON for duration DT_s is given in Fig. 3(a), where D is the duty cycle. The equivalent circuit for a duration D'T_s when the switch is OFF is presented in Fig. 3(b), where D' = 1–D. The boost converter can be represented by the non-ideal components and an ideal DC-DC transformer [24]. The load is represented with respect to the primary side of the D':1 ideal transformer.

The average voltage v_L across the inductor over a cycle of duration T_s is zero and the average current i_C through the capacitor over a cycle of duration T_s is zero. Therefore, v_L and i_C is expressed as,

(2)v_L=D(V_{DC}-I_{DC}{R}_L-V_{SW}-I_{DC}{R}_{ON})+D^{\prime }(V_{DC}-I_{DC}{R}_L-V_D-I_{DC}{R}_{ON}-D^{\prime }{V}_o)=\mathrm{0},

(3)i_C=D\left(-{\displaystyle \frac{V_o}{R_{EFF}}}\right)+D^{\prime }\left(I_{DC}-{\displaystyle \frac{V_o}{R_{EFF}}}\right)=\mathrm{0},

R_EFF is the effective load resistance seen at the output of the boost converter. I_DC is evaluated from Eq. (3). Therefore, V_o can be evaluated by substituting D + D' = 1 and I_DC in Eq. (2),

(4)V_o=\left({\displaystyle \frac{\mathrm{1}}{D^{\prime }}}\right)(V_{DC}-D^{\prime }{V}_D-D{V}_{SW}){\displaystyle \frac{R_{EFF}{D}^{\prime \mathrm{2}}}{D^{\prime \mathrm{2}}{R}_{EFF}+R_L+D{R}_{ON}+D^{\prime }{V}_D}}.

2.3 PMDC motor and centrifugal pump

The PMDC motor is represented by the series combination of the armature resistance R_A and the Back-emf E_B. At steady-state, the terminal voltage is given by

(5)V_o=I{R}_A+E_B,

Since the flux Φ is constant for a PMDC motor, the Back-emf can be expressed as

(6)E_B=c\omega ,

where \omega is the speed in rad/s and c is the motor constant.

The dynamic equation for electrical torque T_E of a PMDC motor is given by

(7)T_E-T_L=J{\displaystyle \frac{d\omega }{dt}}+C\omega +D,

where T_L is the load torque, J is the inertia constant, C is the viscous torque constant for rotational losses, and D is the torque constant for rotational losses.

For a centrifugal pump load, the load torque T_L increases with speed and is given by the relation

(8)T_L=T_{FL}+B_L{\omega }^{\mathrm{2}},

where T_FL is the coulomb friction torque and B_L is the load constant.

Combining Eqs. (6) and (7) and substituting d\omega /dt=\mathrm{0}, the steady-state torque equation of a PMDC motor-centrifugal pump can be represented as

(9)T_E=P+Q\omega +R{\omega }^{\mathrm{2}},

where P, Q and R are arbitrary constants.

The discharge Q is the measure of water output from the pump. It is directly proportional to the speed and is given by the relation

(10)Q=A\omega +B.

The constants A and B decrease with increasing head of the centrifugal pump [5].

3 Steady-state analysis of the system

Performance parameters of the system are determined using steady-state analysis. The input of the boost converter is connected to the PV array and the output is connected to a PMDC motor coupled to a centrifugal pump. The electrical equivalent circuit of the overall system is given in Fig. 3(c).

The KVL equation for this circuit is given by

(11)V_{PV}=I_{PV}{R}_L+D{V}_{SW}+I_{PV}D{R}_{ON}+D^{\prime }{V}_D+I_{PV}{D}^{\prime }{R}_D+I_{PV}{R}_A{D}^{\prime \mathrm{2}}+E_B{D}^{\prime }.

For a PMDC motor, the electrical torque is given by

(12)T_E=c{l}_L=c{l}_{PV},

Equating the expressions for T_E from Eqs. (8) and (12),

(13)c{l}_{PV}{D}^{\prime }=P+Q\omega +R{\omega }^{\mathrm{2}}.

Solving the quadratic Eq. (13) for ω and considering only the positive root, the expression for speed is derived as

(14)\omega ={\displaystyle \frac{\sqrt{Q-\mathrm{4}R(P-c{I}_{PV}{D}^{\prime })}-Q}{\mathrm{2}R}}.

Substituting the expression ω from Eq. (14) and E_B from Eq. (6) in Eq. (11), the overall equation becomes

(15)V_{PV}=I_{PV}{R}_L+D{V}_{SW}+I_{PV}D{R}_{ON}+D^{\prime }{V}_D+I_{PV}{D}^{\prime }{R}_D+I_{PV}{R}_A{D}^{\prime \mathrm{2}}+c{D}^{\prime }{\displaystyle \frac{\sqrt{Q-\mathrm{4}R(P-c{I}_{PV}{D}^{\prime })}-Q}{\mathrm{2}R}}.

Equation (15) is a function of the duty cycle and is expressed as

(16)$$\begin{gathered} f(D)=I_{PV}{R}_L+D{V}_{SW}+I_{PV}D{R}_{ON}+D^{\prime }{V}_D+I_{PV}{D}^{\prime }{R}_D+ \\ {I}_{PV}{R}_A{D}^{\prime \mathrm{2}}+c{D}^{\prime }{\displaystyle \frac{\sqrt{Q-\mathrm{4}R(P-c{I}_{PV}{D}^{\prime })}-Q}{\mathrm{2}R}}-V_{PV}. \end{gathered}$$

The duty cycle is assigned with an initial value and Newton-Raphson’s method is used to solve for the duty cycle

(17)D_{n+\mathrm{1}}^{\prime }=D_n^{\prime }-{\displaystyle \frac{f(D_n^{\prime })}{f^{\prime }(D_n^{\prime })}}.

The iterations are conducted until the duty cycle converges. The flowchart is demonstrated in Fig. 4. The duty cycle D (1–D') at which the boost converter operates can be accurately predicted and is used in predetermination of the performance parameters such as speed, discharge and efficiency.

The output power of the boost converter is given by

(18)P_o=(V_{PV}-I_{PV}{R}_L-D{V}_{SW}-I_{PV}D{R}_{ON}-D^{\prime }{V}_D-I_{PV}{D}^{\prime }{R}_D)I_{PV}.

The expression for net output power considering losses in the motor is

(19)P_{OUT}=(V_{PV}-I_{PV}{R}_L-D{V}_{SW}-I_{PV}D{R}_{ON}-D^{\prime }{V}_D-I_{PV}{D}^{\prime }{R}_D-I_{PV}{R}_A{D}^{\prime \mathrm{2}})I_{PV}.

The overall efficiency η of the system can be computed as

(20)\eta ={\displaystyle \frac{P_{OUT}}{V_{PV}{I}_{PV}}}.

The efficiency can be compared at different operating points in the PV characteristics to determine the optimal operating point.

4 Sizing of the PV array

Sizing of the PV system is done based on the average solar irradiation. The average irradiation in India is found to be approximately 700 W/m² for a panel that is tilted at an angle of latitude degrees toward south [25]. This average irradiation may vary from country to country and it may be taken into consideration according to the geographical location of interest. The average irradiation is taken to be 700 W/m² throughout this paper. Hence while designing the system, the power taken into consideration is the maximum power available for the given set of panels at an average irradiation of 700 W/m².

The motor considered for analysis has a rating of 0.5 hp, 180 V. Each PV module has an output of 80 W for an irradiation of 1000 W/m² at the MPP. The I-V curve is simulated and all the set of V_PV, I_PV values are generated for a particular irradiation. These values are fed to the model developed in this paper. Using the model, parameters such as output voltage, output power are predetermined. To determine the optimum sizing of the PV array, a case study has been conducted with three different PV array configurations.

4.1 Average power less than rated power

The PV array consists of six panels connected in series subjected to uniform irradiation conditions. All the PV panels are subjected to the solar irradiation of 700 W/m². The output P-V characteristics for this case are displayed in Fig. 5(a). The output power at the MPP is predetermined to be 299.58 W and the corresponding output voltage at the MPP is 168.51 V. These values are lesser than the rated power of 373 W (0.5 hp) of the motor. The efficiency at MPP is calculated to be 91.7%. Hence if the configuration of six panels in series is used, the motor will be underutilized even at the MPP. So it can be concluded that the size of the PV array has to be increased to improve the motor utilization and achieve better system performance.

4.2 Average power nearly equal to rated power

In this case, the PV array consists of seven panels connected in series subjected to uniform irradiation of 700 W/m². The output P-V characteristics are exhibited in Fig. 5(b). The maximum output power is predetermined to be 350.25 W and the corresponding output voltage is 179.07 V. These values obtained are very close to the motor ratings and effectively improves motor utilization. This configuration is found to have a higher efficiency of 92.1% which is 0.4% more than the previous case. Hence for the given motor-pump system, the array configuration of seven PV modules in series has very good performance. Further analysis is required to determine if this configuration has the best performance and output.

4.3 Average power greater than rated power

The PV array configuration consists of a string of eight PV panels connected in series. The output P-V characteristics for this configuration are shown in Fig. 5(c). The maximum output power for this case is predetermined to be 400.76 W and the maximum output voltage is 188.74 V. These are greater than the rated values of the motor and will lead to over-utilization of the motor thereby hampering its performance. It will lead to performance degradation in a long run.

If eight or more modules are used, over-sizing of the PV array occurs and the maximum output power exceeds the rated values at the average irradiation. Hence for the given motor-pump load, optimum sizing of the PV array is achieved when the series string contains seven PV modules. This configuration will have the best performance and is best suited for a long-term sustained operation.

5 Effect of irradiation variation

Figure 6 shows the variation of irradiation with time on a clear summer day in Chennai, India. The peak irradiation comes out to be 903 W/m² though the average irradiation is approximately 700 W/m². The peak irradiation at noon will have adverse effects on the motor as the voltage and power go beyond the rated values. In summer, the peak irradiation may go as high as 1000 W/m² to 1200 W/m². However it rarely exceeds the STC conditions of 1000 W/m². Hence the peak irradiation value considered for the subsequent analysis is 1000 W/m².

Figure 7 (a), (b), and (c) depicts the output power and output voltage characteristics (V_o, P_o) with respect to input voltage (V_PV). As seen in all cases, at peak irradiation of 1000 W/m², the motor is over utilized with the boost converter output voltage and power exceeding rated values. Hence the array sizing with 6, 7 and 8 panels will affect the motor and degrade its performance in a long run. Hence a control scheme has been proposed to ensure a long-term sustained operation irrespective of the irradiation variation above the rated value.

6 Proposed control scheme

The control scheme proposed here requires the PV voltage, PV current and the motor voltage as the input to the controller. Based on these values, the controller selects appropriate duty ratio that is to be fed to the boost converter.

Figure 8 shows the proposed control logic. The control input is either 0 or 1 based on the motor voltage V_o. If the motor voltage is less than the reference voltage (rated voltage), the control input becomes 0, thereby executing MPPT algorithm. The P&O algorithm has been employed to implement MPPT [13]. The output voltage is not regulated while executing MPPT. If the motor voltage is higher than the reference voltage, the control input becomes 1, thereby switching to voltage control mode. Voltage control mode is achieved using a PI controller. The boost converter is modeled as a second order system and symmetrical optimum method is used to obtain the PI control parameters. The values so obtained are K_P = 12 and K_i = 0.54.

The rated motor voltage is given as the reference and the instantaneous motor voltage is given as the feedback. The PI controller varies the duty cycle of the boost converter based on the error value and maintains the output voltage at the rated value. This mode restricts the motor voltage, thereby preventing it from being damaged. Since the motor voltage is limited, the speed does not exceed the rated value. Consequently, the torque is also retained within rated limits.

As it is seen in Fig. 7 (a), (b), and (c), there is only one peak point but two potential operating points to maintain the output voltage at 180 V (Points A and B). For the PV array configuration of 7 modules in series, it has been observed from the simulation that the converter has an efficiency of 92.52% at B while it is only 89.53% at the operating point A. The analysis shows that in the 3 cases, the operating point B has a higher efficiency. Table 3 shows that the efficiency is 2% to 4% more than operating point A. The higher efficiency implies lesser converter losses and therefore improves the lifetime of the converter. Hence the PI controller should be properly tuned to make the PV panels operate at the higher efficiency operating point. Table 3 lists the duty cycles and the corresponding efficiencies of the two operating points where the motor voltage is 180 V

It can be seen from Table 3 that the operating point A predominantly operates at a duty cycle of approximately 0.54 and operating point B operates at a duty cycle of less than 0.40. As discussed in Section 4, if the number of panels chosen is 7, it can be safely assumed that the duty cycle of operating point B will be less than 0.40. Hence, in the voltage control mode the range of duty cycle is limited between 0 and 0.40 for the PI controller using a duty limiter. This will enable the controller to track operating point B which has a higher efficiency, thereby improving the lifetime of the converter.

7 Results

A PV system consisting of a PV array, a boost converter and the motor-pump load is considered in order to verify and validate the simulation results. The PV array consists of 7 PV panels (rated 80 W) connected in series and the load is a PMDC motor (Rated at 180 V, 0.5 hp) coupled to a centrifugal pump. The boost converter is used to implement MPPT/voltage control mode depending on the control input received from a Microcontroller. The converter input and output voltages and input current are sensed using Hall Effect voltage transducers LV25 P and a current transducer LA55P respectively. These signals are fed to the microcontroller. The proposed control scheme is implemented using Texas instruments MSP430F5438 experimenter board and the configuration of the system set up is shown in Fig. 9.

The performance evaluation of the system has been done by keeping the PV array at a fixed tilt of 15° with the horizontal and also by changing the orientation of PV panels periodically to face the sun.

For steady-state operation of the PMDC motor, d\omega /dt=\mathrm{0} and the electromagnetic torque is given by

T_E=\mathrm{0.068}+\mathrm{0.001}\omega +\mathrm{0.9455}\times {\mathrm{10}}^{-\mathrm{5}}{\omega }^{\mathrm{2}}.

Substituting the values of constants A and B in Eq. (10), the centrifugal pump discharge is given by

Q=\mathrm{0.19}\omega +\mathrm{9.97.}

By tilting the panels, the irradiation is fixed around 700 W/m² and the PV system is allowed to power the motor. Table 4 shows the comparison of the predetermined output parameters and the experimental values obtained at the irradiation of 693 W/m² for a series string of 7 PV modules operating at the MPP. The experimental values obtained are found to be close to the predetermined simulation values.

The controller works in MPPT mode when the output voltage is less than the rated voltage of 180 V. Figure 10(a) shows the controller operating in MPPT mode to extract maximum power at the irradiation of 693 W/m². As the P&O algorithm is used to implement MPPT, the output power oscillates about the MPP.

When the irradiation is increased to 1000 W/m², the output voltage starts increasing rapidly. When the output voltage exceeds 180 V, the control input changes from 0 to 1 and the controller switches to voltage control mode. Further rise in voltage is prevented and the PI controller maintains the output voltage constant at 180 V.

Figure 10 (b) and (c) show the variation of output voltage of the boost converter with time. Figure 10 (b) shows the response of the controller in moving from MPPT to voltage control mode when the irradiation is increased from 700 W/m² to 1000 W/m² for a series string of 7 panels. The voltage here is restricted around the rated voltage (180 V). Figure 10(c) shows the response of the controller in moving from voltage control mode to MPPT when the irradiation is decreased back to 700 W/m².

Thus the control algorithm restricts the voltage at 180 V and prevents from the motor to be over utilized. Besides, it ensures maximum power transfer from the PV source if the motor voltage is less than the rated value.

8 Conclusions

This paper presents the complete modeling and performance predetermination of a PV fed PMDC motor-centrifugal pump system considering converter losses. Performance parameters such as output power, motor voltage, speed of the motor and discharge of the pump were predetermined with V_PV and I_PV as input variables using the Newton-Raphson method. The number of PV modules for optimum performance was designed using the predetermined values for average irradiation. A control scheme was proposed to prevent the motor from being damaged during peak irradiation above the average value. The predetermined values were compared with the practical value and were found to be in close accordance. The proposed control scheme was implemented in the system and their relevant waveforms were presented.

References

[1] Ramakumar R, Hughes W L. Renewable energy sources and rural development in developing countries. IEEE Transactions on Education, 1981, 24(3): 242–251

[2] Surendra T S, Subbaraman S V V. Solar PV water pumping comes of age in India. In: Conference Record of the 29th IEEE Photovoltaic Specialists Conference. New Orleans, 2002, 1485–1488

[3] Taufik A O, Anwari M, Taufik M. Modeling and Simulation of Photovoltaic Water Pumping System. In: Proceedings of the 3rd Asia International Conference on Modelling and Simulation, Bandung/Bali, 2009, 497–502

[4] Ministry Of New and Renewable Energy, Government of India. Solar photovoltaic water pumping systems. 2014-02-07

[5] Chandrasekaran N, Ganeshprabu G, Thyagarajah K. Comparative study of photovoltaic pumping system using a DC motor and PMDC motor. In: Proceedings of 2012 International Conference on Advances in Engineering, Science and Management, Nagapattinam. 2012, 129–132

[6] Minai A F, Tariq A. Alam Q. Theoretical and experimental analysis of photovoltaic water pumping system. In: Proceedings of India International Conference on Power Electronics, Delhi, 2011, 1–8

[7] Kolhe M, Joshi J C, Kothari D P. Performance analysis of a directly coupled photovoltaic water-pumping system. IEEE Transactions on Energy Conversion, 2004, 19(3): 613–618

[8] Dunlop J P. Analysis and design optimization of photovoltaic water pumping systems. In: Conference Record of the Twentieth IEEE Photovoltaic Specialists Conference. Las Vegas, 1988, 1182–1187

[9] Elgendy M A, Zahawi B, Atkinson D J. Comparison of directly connected and constant voltage controlled photovoltaic pumping systems. IEEE Transactions on Sustainable Energy, 2010, 1(3): 184–192

[10] Patel H, Agarwal V. Maximum power point tracking scheme for PV systems operating under partially shaded conditions. IEEE Transactions on Industrial Electronics, 2008, 55(4): 1689–1698

[11] Walker G R, Sernia P C. Cascaded DC–DC converter connection of photovoltaic modules. IEEE Transactions on Power Electronics, 2004, 19(4): 1130–1139

[12] Graditi G, Colonnese D, Femia N. Efficiency and reliability comparison of DC-DC converters for single phase grid connected photovoltaic inverters. In: Proceedings of International Symposium Power Electronics, Electrical Drives, Automation and Motion, Pisa, 2010, 140–147

[13] Hua C, Lin J, Shen C. Implementation of a DSP-controlled photovoltaic system with peak power tracking. IEEE Transactions on Industrial Electronics, 1998, 45(1): 99–107

[14] Femia N, Petrone G, Spagnuolo G, Vitelli M. Optimization of perturb and observe maximum power point tracking method. IEEE Transactions on Power Electronics, 2005, 20(4): 963–973

[15] Safari A, Mekhilef S. Simulation and hardware implementation of incremental conductance MPPT with direct control method using cuk converter. IEEE Transactions on Industrial Electronics, 2011, 58(4): 1154–1161

[16] Mei Q, Shan M, Liu L, Guerrero J M. A novel improved variable step-size incremental-resistance MPPT method for PV systems. IEEE Transactions on Industrial Electronics, 2011, 58(6): 2427–2434

[17] Kappali M, Uday Kumar R Y, Sheelavant V R. Solar photo voltaic water pumping: harnessing maximum power. ACEEE International Journal on Electrical and Power Engineering, 2013, 4(1): 1–8

[18] Wolete J N. An interactive menu-driven design tool for stand-alone photovoltaic systems. Dissertation for the Master’s Degree. Virginia: Virginia Polytechnic Institute and State University, 1998

[19] Odeh I, Yohanis Y G, Norton B. Simulation procedure for the co-optimization of photovoltaic water pumping systems. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 2010, 629–640

[20] Sandia National Laboratories. Stand-Alone Photovoltaic Systems: A Handbook of Recommended Design Practices. NTIS, 1995

[21] Odeh I, Yohanis Y G, Norton B. Influence of pumping head, insolation and PV array size on PV water pumping system performance. Solar Energy, 2006, 80(1): 51–64

[22] González-Longatt F M. Model of photovoltaic module in Matlab^TM. 2nd Iberoamerican Student Congress on Electrical, Electronics and Computer Engineering (II CIBELEC 2005). 2005

[23] Rashid M H. Power Electronics Handbook. Academic Press, 2011

[24] Erickson R W, Maksimovic D. Fundamentals of Power Electronics. Springer, 2000

[25] Joshi A B. The Energy Equation: Requirements, Resources, and Projections. CreateSpace Independent Publishing, 2013

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg