Solar PV Array-Fed Water Pumping System Using Zeta Converter based Closed-Loop Control of BLDC Motor Drive

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Solar PV Array-Fed Water Pumping System Using Zeta Converter based Closed-Loop Control of BLDC Motor Drive

R. Durgaprasad Department of Electrical & Electronics Engineering, AITAM, Srkakulam, India.

P. Guruvulunaidu Department of Electrical & Electronics Engineering, AITAM, Srikakulam, India.

Ch. Prasad Department of Electrical & Electronics Engineering, AITAM, Srikakulam, India.

Abstract: This paper proposes a solar photovoltaic (SPV) array fed water pumping system utilizing a zeta converter as an intermediate DC-DC converter in order to extract the maximum available power from the SPV array. Controlling the zeta converter in an intelligent manner through the incremental conductance maximum power point tracking (INC-MPPT) algorithm offers the soft starting of the brushless DC (BLDC) motor employed to drive a centrifugal water pump coupled to its shaft. Soft starting i.e. the reduced current starting inhibits the harmful effect of the high starting current on the windings of the BLDC motor. A fundamental frequency switching of the voltage source inverter (VSI) is accomplished by the electronic commutation of the BLDC motor, thereby avoiding the VSI losses occurred owing to the high frequency switching. A new design approach for the low valued DC link capacitor of VSI is proposed. The proposed water pumping system is designed and modeled such that the performance is not affected even under the dynamic conditions. Suitability of the proposed system under dynamic conditions is demonstrated by the simulation results using MATLAB/Simulink software.

Key words: Brushless dc (BLDC) motor, incremental conductance maximum power point tracking (INC-MPPT), solar photovoltaic (SPV) array, voltage-source inverter (VSI), water pump, zeta converter


Severe environmental protection regulations, shortage of fossil fuels and eternal energy from the sun have motivated the researchers towards the solar photovoltaic (SPV) array generated electrical power for various applications [1]. Water pumping is receiving wide attention now a days amongst all the applications of SPV array. To enhance the efficiency of SPV array and hence the whole system regardless of the operating conditions, it becomes essential to operate SPV array at its maximum power point by means of a maximum power point tracking (MPPT)algorithm [2-4]. Various DC-DC converters have been already employed to accomplish this action of MPPT. Nevertheless, a Zeta converter [5-9] based MPPT is still unexplored in any kind of SPV array based applications. An incremental conductance (INC) MPPT algorithm [2] is used in this work in order to generate an optimum value of duty cycle for the IGBT(Insulated Gate Bipolar Transistor) switch of Zeta converter such that the SPV array is constrained to operate at its MPP. Various configuration of

Zeta converters such as self-lift circuit, re-lift circuit, triple- lift circuit and quadruple-lift circuit using voltage lift (VL) technique have been reported in aforementioned topologies have high voltage transfer gain but at the cost of increased number of components and switching devices. Therefore, these topologies of Zeta converter do not suit the proposed water pumping system.

The PV inverters dedicated to the small PV plants must be characterized by a large range for the input voltage in order to accept different configurations of the PV field. This capability is assured by adopting inverters based on a double stage architecture where the first stage, which usually is a dc/dc converter, can be used to adapt the PV array voltage in order to meet the requirements of the dc/ac second stage, which is used to supply an ac load or to inject the produced power into the grid. This configuration is effective also in terms of controllability because the first stage can be devoted to track the maximum power from the PV array, while the second stage is used to produce ac current with low Total Harmonic Distortion (THD).

BLDC motors are preferred over DC motors and induction motors due to their advantages like long operating life, higher efficiency, low maintenance and better speed torque characteristics. Stator windings of BLDC motors are energized in a sequence from an inverter. A bulkier DC link capacitor is connected in between the dc-dc converter and inverter to get a constant voltage at the input of inverter, thus to make the voltage ripple free. But the DC link capacitor is bulkier in size and its life time is affected by operating temperature. Moreover the cost is about 5-15% of overall cost of BLDC motor drive. As an attempt to reduce the cost of motor, DC link capacitor can be eliminated at the expense of torque ripple. Thus a new torque ripple compensation technique is proposed to compensate for the torque ripple associated with the elimination of the DC link capacitor. In this method, torque ripple compensation technique is proposed to a solar PV array fed DC link capacitor free BLDC motor.

The permanent magnet brushless DC (BLDC) motor is employed to drive a centrifugal water pump coupled to its shaft. The BLDC motor is selected because of its merits [7,9] useful for the development of suitable water pumping system. This electronically commutated BLDC motor [9-11] is supplied by a voltage source inverter (VSI) which is operated by fundamental frequency switching resulting in

low switching losses [12-15]. Suitability of the proposed SPV array fed water pumping system subjected to various operating and environmental conditions is demonstrated by satisfactory simulated results using MATLAB/Simulink environment.

The existing literature exploring SPV array-based BLDC motor-driven water pump is based on a configuration shown in Fig.1. A dcdc converter is used for MPPT of an SPV array as usual. Two phase currents are sensed along with Hall signals feedback for control of BLDC motor, resulting in an increased cost. The additional control scheme causes increased cost and complexity, which is required to control the speed of BLDC motor. Moreover, usually a voltage-source inverter (VSI) is operated with high- frequency PWM pulses, resulting in an increased switching loss and hence the reduced efficiency.

Fig.1. Conventional SPV-fed BLDC motor-driven water pumping system


    Equivalent circuit model of a PV string is indicated in fig. 2(a). In this model, ISc is the generated current of a PV string and RS and RP are the series and parallel resistances of a string. Also, equivalent circuit model of multiple strings are shown in fig. 2(b). In this figure, bypass diode is considered for each string. To obtain the V-I characteristic of a PV, below equation is used:

    Fig.2. Equivalent circuit model of (a) a PV string model, (b) multiple PV strings model.


    The proposed converter is based on DC-DC converter to maintain the constant output voltage. The sixth DC-DC converter that we will study now was developed at the end of the 1980s, separately by Kazimierczuk, under the name of Dual SEPIC, and Barbi, under the name of Zeta converter (from the sixth letter of the Greek alphabet, to correspond to the sixth converter). Zeta is a fourth order DC-DC converter. Zeta converter will vary above or below the input voltage without change in output polarity. A Zeta is similar to a BUCK BOOST converter but has advantages of having non-inverted output (the output voltage is of the same polarity as the input voltage). The inductors and the capacitors can also have large effects on the converter efficiency and ripple voltage. This converter transfers the energy between the inductance nd the capacitance in order to change from the voltage to another. The transferred energy is controlled by switching device S (MOSFET).

    q(v Rs I )

    v R I


    I I

    • I e KT

    1 s

    SC 0


    Where T, q, k and I0 are the temperature (K), the electron charge (C), q=1.602×10-19 C, Boltzmanns constant (k=1.381×10-23 J/K) and the reverse saturation current (A), respectively. In a PV panel, the generated maximum power is the point that the product (V×I) is maximum which is called maximum power point (MPP). It is obvious that the irradiation and temperature are two important factors in the value of generated electricity by a PV panel which affect the point of generated maximum power.

    Fig.3.Schematic Diagram of Zeta Converter

    A. Operating Modes Of Zeta Converter

    The converter circuit is divided into two parts as shown in fig.4 and fig.5. In mode 1 the switch will be closed as shown in fig.4. When S is turning on (ON-state), the diode is off. This is shown as an open circuit (for diode) and short circuit (for S). In this time interval diode D1 is OFF with a reverse voltage equal to – (VS +VO). During this state, inductor L1 and L2 are in charge phase. These mean that the inductor current iL1 and iL2 increase linearly.

    dVC1 iL1

    dt C1

    The relation between input and output voltages of the zeta converter is given by

    The duty cycle D for zeta converter in CCM is given

    Fig.4.Zeta Converter when switch is ON

    The capacitor C1 will discharge and the energy will charged to VO and it is connected in series with L2. The sum of the charging inductor current flows through S.

    Applying the Kirchhoff's voltage law to the circuit in Fig.4 and writing the voltage equations


    D V0 V0 VS

    D V0 iS

    (1 D) VS i0

    diL1 VS dt L1

    diL2 VS VC1 VC 2

    dt L2 L2 L2

    By applying Kirchhoffs current law the rate of voltage through the capacitors will be,

    dVC1 iL 2

    dt C1


    A three-phase brushless DC motor has three induction coils with equivalent circuit of BLDC motors as described in the following section.

    A. Mathematical Model of the BLDC Motor:

    The equivalent circuit of BLDC motor is shown in Fig.6. The dynamic equations of BLDC motor may be expressed in matrix form:

    dVC 2

    iL 2

    • VC 2


    1 0


    L M 0

    0 Ia



    dt C R C

    2 L 2

    Vb R0 1

    0Ib 0

    L M 0 dt Ib Eb The

    In mode 2 the switch will be open as shown in fig.4. When S is turning off (OFF-state), the diode is on. Opposite

    Vc 0 0

    1Ic 0

    0 L M Ic


    to previous ON-state, the equivalent circuit shows that the diode is short circuit and S is open circuit. Inductor L1, that was previously charged will now have to be in a discharging. At this state, inductor L1 and L2 are in discharge phase. Since the voltage polarity of the inductor changes the diode will get forward biased and it will conduct.

    electromagnetic torque developed by the motor is given by

    T Ea I a Eb Ib Ec Ic e

    The moment of inertia includes all inertia connected to the motor shaft, and damping constant includes the air friction and the bearing friction. Therefore, the torque equation is

    J d B T T

    dt e l

    Fig.5. Zeta Converter when switch is OFF

    Energy in L1 and L2 are discharged to capacitor C1 and output part, respectively. As a result, inductor current iL1 and iL2 are decreasing linearly.

    By applying Kirchoffs voltage law, voltage across

    inductor L1 is expressed as,

    Fig.6. The Equivalent Circuit Of BLDC Motor

    1. The BLDC Motor Control:

      BLDC motors are driven by a three-phase inverter with

      diL1 dt diL2 dt



      VC 2


      six-step commutation sequence. The inverter is commutated every 60 degree electrical when Ha, Hb and Hc are Hall effect sensor signal of each phase as shown in Fig.7.

      By applying Kirchoffs current law, current flows through the capacitor C1 is expressed as,

      Fig.7. Six Step Commutation Sequence

    2. BLDC Motors Back EMF:

    The 2 coils are induced to rotate through a magnetic field; the induced voltage is created in this coils, call that Back Electromotive force or Back-EMF. The relation between Back-EMF signal and Hall effect sensor of each phase is shown in Fig.8.


    The structure of proposed SPV array-fed BLDC motor driven water pumping system employing a zeta converter is shown in Fig.9. The proposed system consists of (left to right) an SPV array, a zeta converter, a VSI, a BLDC motor, and a water pump. The BLDC motor has an inbuilt encoder. The pulse generator is used to operate the zeta converter. A step-by-step operation of proposed system is elaborated in Section III in detail.

    Fig.8. Back EMF signal and Hall Effect sensor


    The SPV array generates the electrical power demanded by the motor-pump. This electrical power is fed to the motor pump via a zeta converter and a VSI. The SPV array appears as a power source for the zeta converter as shown in Fig.9. Ideally, the same amount of power is transferred at the output of zeta converter which appears as an input source for the VSI. In practice, due to the various losses associated with a dcdc converter, slightly less amount of power is transferred to feed the VSI. The pulse generator generates, through INCMPPT algorithm, switching pulses for insulated

    gate bipolar transistor (IGBT) switch of the zeta converter. The INC-MPPT algorithm uses voltage and current as feedback from SPV array and generates an optimum value of duty cycle. Further, it generates actual switching pulse by comparing the duty cycle with a high-frequency carrier wave. In this way, the maximum power extraction and hence the efficiency optimization of the SPV array is accomplished.

    The VSI, converting dc output from a zeta converter into ac, feeds the BLDC motor to drive a water pump coupled to its shaft. The VSI is operated in fundamental frequency switching through an electronic commutation of BLDC motor assisted by its built-in encoder. The high frequency switching losses are thereby eliminated, contributing in an increased efficiency of proposed water pumping system.

    Fig.9. Proposed SPV-zeta converter-fed BLDC motor drive for water


  6. DESIGN OF PROPOSEDSYSTEM Various operating stages shown in Fig.9 are properly

    designed to develop an effective water pumping system, capable of operating under uncertain conditions. A BLDC motor of2.89-kW power rating and an SPV array of 3.4-kW peak power capacity under standard test conditions (STC) are selected to design the proposed system. The detailed designs of various stages such as SPV array, zeta converter, and water pump are described as follows.

    1. Design of SPV Array

      As per above discussion, the practical converters are associated with various power losses. In addition, the performance of BLDC motor-pump is influenced by associated mechanical and electrical losses. To compensate these losses, the size of SPV array is selected with slightly more peak power capacity to ensure the satisfactory operation regardless of power losses. Therefore, the SPV array of peak power capacity of Pmpp=3.4 kW under STC (STC: 1000 W/m2, 25oC, AM 1.5), slightly more than demanded by the motor-pump is selected and its parameters are designed accordingly. Solar World make Sun module Plus SW 280 mono SPV module is selected to design the SPV array of an appropriate size. Electrical specifications of this module are listed in Table1 and numbers of modules required to connect n series/parallel are estimated by selecting the voltage of SPV array at MPP under STC as Vmpp= 187.2V.



      2 Nrated P 2 3000 6 942rad / s

      Specifications of Sun module plus SW 280mono SPV






      Peak power, Pm (W)


      Open circuit voltage, Vo (V)


      Voltage at MPP, Vm (V)


      Short circuit current, Is (A)


      Current at MPP, Im (A)


      Number of cells connected in series, Nss


      The fundamental output frequency of the VSI corresponding to the minimum speed of the BLDC motor essentially required to pump the water (N= 1100r/min) min is estimated as


      2 NP 2 1100 6 345.57rad / s

      The current of SPV array at MPP Impp is estimated as






      Pmpp Vmpp

      3400 18.16A


      Where frated and fmin are fundamental frequencies of output voltage of VSI corresponding to a rated speed and a

      minimum speed of BLDC motor essentially required to

      The numbers of modules required to connect in series are as follows:

      pump the water, respectively, in Hz; Nrated is rated speed of the BLDC motor; P is a number of poles in the BLDC






      187.2 6



      The value of dc link capacitor of VSI at rated is as follows:

      The numbers of modules required to connect in parallel

      are as follows:

      I dc 17

      N I mpp

      p I

      18.16 2


      C2,rated 6


      • Vdc


        6 942 200 0.1


        Connecting six modules in series, having two strings in

        Similarly, a value of dc link capacitor of VSI at min is as follows:

        parallel, an SPV array of required size is designed for the

        proposed system.



        I dc

        min Vdc


        6 345.57 200 0.1


    2. Design of Zeta Converter

    To achieve the high performance and efficiency of the dc-dc converter the values of passive elements (Inductor and Capacitor) have significant impact. Here designing equations are used to design zeta converter.

    Zeta converter designing equations are as follows:

    Where Vdc is an amount of permitted ripple in voltage across dc-link capacitorC2.Finally, C2= 410µF is selected to design the dc-link capacitor.

    D. Design of Water Pump

    To estimate the proportionality constant K for the selected water pump, its powerspeed characteristics is used

    D Vdc

    Vmpp Vdc

    200 0.52

    200 187.2



    K P

    2.89 103

    9.32 105



    0.52 187.2


    r 2

    3000 3

    fsw I L1

    20000 18.16 0.06





    L (1 D)Vdc

    sw L2

    (1 0.52) 200 20000 17 0.06


    Where P=2.89 kW is rated power developed by the BLDC motor and r is rated mechanical speed of the rotor (3000r/min) in rad/s.


    DI dc

    f V

    0.52 17

    20000 200 0.1


    A water pump with these data is selected for proposed system.

    sw C1

    Where fsw is the switching frequency of IGBT switch of the zeta converter; IL1 is the amount of permitted ripple in the current flowing throughL1, same as IL1=Impp; IL2is the amount of permitted ripple in the current flowing throughL2, same as IL2=Idc; VC1 is permitted ripple in the voltageacrossC1, same asVC1=Vdc.

    C. Estimation of DC-Link Capacitor of VSI

    The fundamental output frequency of VSI corresponding to the rated speed of BLDC motor rated is estimated as


The proposed system is controlled in two stages. These two control techniques, viz., MPPT and electronic commutation, are discussed as follows.

  1. INC-MPPT Algorithm

    An efficient and commonly used INC-MPPT technique [8],[13] in various SPV array based applications is utilized in order to optimize the power available from a SPV array and to facilitate a soft starting of BLDC motor. This technique allows perturbation in either the SPV array voltage or the duty cycle. The former calls for a proportional integral (PI) controller to generate a duty cycle [8] for the zeta converter, which increases the complexity. Hence, the direct duty cycle control is adapted in this work. The INC-

    MPPT algorithm determines the direction of perturbation based on the slope of PpvVpv curve, shown in Fig.10. As shown in Fig.10, the slope is zero at MPP, positive on the left, and negative on the right of MPP, i.e.,

    commutating the currents flowing through its windings in a predefined sequence using decoder logic. It symmetrically places the dc input current at the center of each phase voltage for 120o. Six switching pulses are generated as per the various possible combinations of three Hall-effect

    signals. These three Hall-effect signals are produced by an

    = 0; at mpp

    > 0; left of mpp

    inbuilt encoder according to the rotor position.


    Switching States for Electronic Commutation of BLDC

    Rotor Position (°)

    Hall Signals

    Switching States





























































































    < 0; right of mpp

    dPpv dv pv

    d(vpv ipv ) i dv pv

    • vpv

      • dipv

        dv pv


    • vpv

    • ipv


    Therefore, (14) is rewritten as

    = ; at mpp



    ; left of mpp

    ; right of mpp

    A particular combination of Hall-effect signals is produced for each specific range of rotor position at an interval of60o [5],[6]. The generation of six switching states with the estimation of rotor position is tabularized in Table

    Thus, based on the relation between INC and instantaneous conductance, the controller decides the direction of perturbation as shown in Fig.10, and increases/decreases the duty cycle accordingly. For instance, on the right of MPP, the duty cycle is increased with a fixed perturbation size until the direction reverses. Ideally, the perturbation stops once the operating point reaches the MPP. However, in practice, operating point oscillates around the MPP.

    As the perturbation size reduces, the controller takes more time to track the MPP of SPV array. An intellectual agreement between the tracking time and the perturbation size is held to fulfill the objectives of MPPT and soft starting of BLDC motor. In order to achieve soft starting, the initial value of duty cycle is set as zero. In addition, an optimum value of perturbation size (D=0.001) is selected, which contributes to soft starting and also minimizes oscillations around the MPP.

    Fig.10. Illustration of INC-MPPT with SPV array PpvVpv characteristics.

  2. Electronic Commutation of BLDC Motor

The BLDC motor is controlled using a VSI operated through an electronic commutation of BLDC motor. An electronic commutation of BLDC motor stands for

  1. It is perceptible that only two switches conduct at a time, resulting in 120oconduction mode of operation of VSI and hence the reduced conduction losses. Besides this, the electronic commutation provides fundamental frequency switching of the VSI; hence, losses associated with high- frequency PWM switching are eliminated. A motor power company makes BLDC motor with inbuilt encoder is selected for proposed system and its detailed specifications are given in the Appendixes.



      In the sensored BLDC drive, hall sensors or a shaft encoder is used to obtain the rotor position information. The drive control system consists of an outer speed loop for speed control and an inner current loop for current control. Conventionally three separate current sensors are used to measure the phase currents. But here only one current sensor is used, which is placed on the DC link.

      A. Speed control

      The speed control block uses a Proportional Integral (PI) controller. A PI controller attempts to correct the error between a measured process variable and desired set point by calculating and then outputting a corrective action that can adjust the process accordingly. The PI controller calculation involves two separate modes the proportional mode and the integral mode. The proportional mode determine the reaction to the current error, integral mode determines the reaction based recent error. The weighted sum of the two mode output as corrective action for the control element. The PI controller is widely used in the industry due to its ease in design and simple structure. The PI controller algorithm can be implemented as


      output(t) K p e(t) KI e( )d


      Here the input to speed controller is the speed error. The output of the controller is considered as a reference torque. A limit is put on the speed controller output depending on permissible maximum winding currents.


      Fig. 11 Matlab/Simulink circuit of Starting and steady-state performances of the proposed SPV array based zeta converter-fed BLDC

      motor drive for water pump




      Fig.12 Starting and steady-state performances of the proposed SPV array based zeta converter-fed BLDC motor drive for water pump. (a) SPV

      array variables. (b) Zeta converter variables. (c) BLDC motor-pump variables.

      Fig.13 Matlab/Simulink circuit for Dynamic performance of SPV array-based zeta converter-fed BLDC motor drive for water pump




      Fig.14 Dynamic performances of the proposed SPV array-based zeta converter-fed BLDC motor drive for water pump. (a) SPV array variables.

      (b) Zeta converter variables. (c) BLDC motor-pump variables.

      Fig.15 Matlab/Simulink circuit of SPV array-based zeta converter-fed BLDC motor drive Closed loop control for water pumping system.

      Fig.16. Speed.

      Fig.17. Torque.

      Fig.18. Stator current and emf.


A solar photovoltaic array fed Zeta converter based BLDC motor has been proposed to drive water-pumping system. The proposed system has been designed, modeled and simulated using MATLAB along with its Simulink and simpower system toolboxes. Simulated results have demonstrated the suitability of proposed water pumping system. SPV array has been properly sized such that system performance is not influenced by the variation in atmospheric conditions and the associated losses and maximum switch utilization of Zeta converter is achieved. Zeta converter has been operated in CCM in order to reduce the stress on power devices. Operating the VSI in conduction mode with fundamental frequency switching eliminates the losses caused by high frequency switching operation. Stable operations of motor-pump system and safe starting of BLDC motor are other important features of the proposed system.


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Ragolu Durgaprasad was born in srikakulam, India in 1992. He received the B.Tech. degree in Electrical and Electronics Engineering from Aditya Institute of Technology and Management, Srikakulam, India in 2013, and pursuing M.Tech. in Power electronics and Electrical Drives in

Aditya Institute of Technology and Management, Srikakulam, India.

P Guruvulunaidu received B.Tech. Degree in Electrical and Electronics Engineering from JNTU Hyderabad, India in 2006 and M.Tech. degree in Electrical Engineering from JNTU Ananthapur, India in 2008. He is pursuing Ph.D. degree in Electrical Engineering in JNTU Kakinada, India.

Currently he is working as Senior Assistant Professor in Aditya Institute of Technology and Management, Srikakulam, India.

Ch Prasad received B.E. degree in Electrical and Electronics Engineering from AU, Visakhapatnam, India in 2009 and M.E degree in Electrical Engineering from AU Visakhapatnam, India. Currently he is working as Assistant Professor in Aditya Institute of Technology and Management, Srikakulam, India.

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