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Energy Procedía 74 (2015) 760 - 771

Fuzzy Logic Space Vector Direct Torque Control of PMSM for Photovoltaic Water Pumping System

H. Bouzeriaa*, C. Fethaa, T. Bahib, I. Abadliab, Z. Layateb, S. Lekhchinec

a Electrical Engineering Department, LEB, Hadj Lakhdar University, Batna 05000, Algeria b Electrical Engineering Department, Badji Mokhtar University, Box 12, Annaba 23000, Algeria c Electrical Engineering Department, 20 August 1955 University, Skikda 21000, Algeria

Abstract

This paper presents an intelligent artificial speed control approach of permanent magnet synchronous motor which leads photovoltaic water pumping system. The photovoltaic solar energy source is connected to boost converter, then it will be controlled using fuzzy logic technical, in order to ensure the maximum power point whatever the climatically conditions and load variation, when their characterises is non-linear. However, an effective solution must ensure that the photovoltaic generator operated at the maximum power and that the motor runs at a high efficiency level. The three-phase inverter and two levels that supplies permanent magnet synchronous motor when was controlled by a space vector pulse weigh modulation. The space vector direct torque control is also studied. So, to analyze the performance of speed control between the fuzzy logic controller and proportional integrator controlled. The performance index based on speed error is assigned to provide a numerical comparison among different controllers. When compared with other methods, the torque ripples are reduced remarkably with the proposed method. The topology of these speed controllers is developed and the simulations with Matlab/Simulink according to the speed and load variation tests are shown and discussed.

© 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.Org/licenses/by-nc-nd/4.0/).

Peer-reviewunderresponsibility ofthe Euro-MediterraneanInstituteforSustainable Development(EUMISD) Keywords: Photovoltaic; Water pumping; MPPT; Fuzzy logic; Direct torque Control; Simulation.

* Corresponding author. Tel.: +213-771-247-853. E-mail address: bhamza23000@gmail.com

1876-6102 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativec0mm0ns.0rg/licenses/by-nc-nd/4 .0/).

Peer-review under responsibility of the Euro-Mediterranean Institute for Sustainable Development (EUMISD) doi:10.1016/j.egypro.2015.07.812

1. Introduction

Nowadays, there are many forms of renewable energy, the most commonly used are: solar, wind and hydraulic. The sun is in the form of heat that is transmitted by infrared radiation, these exhibits under effect of photovoltaic (PV).

The speed control of AC drive supplied by PV is one of the most important applications in PV systems, it has become a favorable solution for many applications, because of gaining more acceptance and market share, particularly in rural: areas that have a substantial amount of insolation and have no access to an electric grid. So, photovoltaic systems are used to pump water for livestock, plants or humans. Since the need for water is greatest on hot sunny days, the technology is an obvious choice for this application. Agricultural watering needs are usually greatest during sunnier periods when more water can be pumped with a solar system [1, 2].

In the North Mediterranean countries like Algeria has one of the fastest growing surfaces in this continent. However, it is remotely isolated rural areas posed problems to rural energy management and development of renewable energy sources. The average annual daily solar radiation is within the range of 5:7 kWh/m2/day [3]. The major problem of Photovoltaic Generator (PVG) is their nonlinear elements[4], where its optimum operating point depends on climatic conditions such as the temperature, the solar radiation and also the load variations. Indeed, an effective solution must ensure that the PVG runs at the maximum power point (MPP) and that the motor runs at a high efficiency level. The latter's role is to pursue maximum power, it is mounted up stream of a converter. The objective is to control the DC-DC converter type boost, on the one hand by acting on the duty cycle (d) by using the maximum power point tracking (MPPT) based on fuzzy logic controller (FLC)[5]. The inverter on the other control by using the vector mode by FLC direction of rotor flux in order to control the torque and speed. Generally, the DTC is insensitive to the motor parameters variations [6, 7], however, in renewable energy application, it is interesting to verify that quality is checked under the constraint of the variation of the load torque and the DC bus voltage of the inverter which varied inevitably.

In this work, the speed control of permanent magnet synchronous motor (PMSM) is considered in the aim to achieve high accuracy and a fast dynamic response. In this way, the direct torque control-space vector modulation (DTC-SVM) technic is used for to optimize the switching selection table and offer more voltage space vector than traditional DTC [8, 9].The paper is organized as follows: in section II the proposed and study system is presented. Section III we illustrate the design of fuzzy logic methodology. In section IV the speed control and the direct torque control-space vector modulation are developed. Finally, section V presents the simulation and results obtained with the proposed techniques.

Nomenclature

a p-n junction ideality factor

d Duty cycle

de(k) derivate variable of error

e(k) Error input variable of fuzzy logic

Eg Band Gap

G,Gr Real and reference solar radiation

h',h Height and total height

Io Cell reverses saturation current

I0r Reverse saturation current

Id Diode Current

id, iq Current components in d-q system

Iph Generated photocurrent

Isc Short-circuit current

Iscr Reference short-circuit current

K Boltzmann's constant

ki Temperature coefficient

NB Negative big

NM Negative medium

NS Negative small

ns Number cell series

P Number of pole pairs

P',P Power and nominal power

Ppv(k) PV array output power

PB Positive Big

PS Positive small

q Electron charge

Q', Q Flow and the nominal flow pump

Rp, Rse Parallel and serie resistances

Rs, Ls Resistance and the inductance stator

Te,Tref Real and reference electromagnetic torque

Tl Load torque

T,Tr Real and reference temperator

Ti:3 Sector number

Ta:c Action time of three phase

ud,uq Stator voltage in the d-q axis

Vpv PV panel output voltage

Vdc Output voltage of boost converter

ZE Zero

®ref ,0 Reference speed and position of rotor

®r Real speed

Of Flux of permanent magnet

Yd,q flux of permanent magnet in d, q coordinate system

2. Structure of system

The photovoltaic water pumping system consists at the PVG, power converters (Boost converter and DC-AC converter), permanent magnet synchronous motor and centrifugal pump, see Fig. 1.

* □□

Fig. 1. Synoptic bloc of photovoltaic water pumping.

2.1. Modeling ofphotovoltaic generator

The PV panel is composed of many cells, placed in series Ns or in shunt Nsh. Where it can be modelled by current source connected in parallel with diode according with shunt and series resistor noted by Rsh and Rse as illustrated in Fig. 2.

Fig. 2. Photovoltaic array circuit.

The output current is given by the following equation [10]:

Ipv = Nsh Iph - NshI0|exp

qrpv+N^'pvRseJ

akTn«

Vpv+Njh'pvRse fj:rRsh

Where, the cell reverse saturation current is related to the temperature (T) as follows [11]:

I0 = Iorg) exp-g^-i]}

Similarly, the photocurrent Iph depends on the solar radiation (G) and the cell temperature (T) [12]: Iph = Oscr + kiCT - 298)} f

2.2. Modeling of power converters

The PVG is fed the DC voltage converter, see Fig. 3, where the optimum value of duty cycle d is decided from the MPPT controller who depends of climatic conditions but the inverter (DC/AC converter) is controlled by space vector pulse width modulation (SVPWM).

Fig. 3. Boost converter circuit.

The output voltage (Vdc) is expressed by following relation [13]:

pv 1-d

The SVPWM has object to provide motor with circular magnetic field [14]. So, according to ideal flux circle generated by three-phase symmetric sinusoidal voltage, we defined the following expressions of the voltage and the conducting time of each inverter switch is shown in Table 1:

Urefb = Ua(1.73) - Up [Urefc = -Ua(1.73)-Uß

Table 1. Ti and T2 in Different Sectors.

N 1 2 3 4 5 6

Ti -Z Y X Z -Y -X

T2 X Z -Y -X -Z Y

X=Up.T(1.73)/Vdc Y = (3Ua + Up(1.73))T/2Vdc = (-3Ua + Up(1.73))T/2Vdc So, the action time are defined as following: (Ta = (T - Ti - T2)/4 j Tb = 0,51! + Ta I Tc = 0,5T2 + Tb

Assign T1, T2 and T3 according to Table 2, where are defined as the conducting time of phase a, b and c, respectively.

Table 2. Calculation of Switch Point.

N 1 2 3 4 5 6

Ti Tc Ta Tb Tc Ta Tb

T2 Ta Tc Tb Ta Ta Tc

T3 Tb Tb Ta Tb Tc Ta

2.3. Modeling of Permanent Magnet Synchronous Motor

Suppose to ignore the core saturation, eddy current, and hysteresis loss of the motor and there is no damper winding in rotor, the following equations describe the mathematical model of PMSM in the d-q coordinate system [15]:

(ud = Rsid + kËd_ WrofSine (uq = Rsiq + i^ä + cos 0

^d = /(ud - Rsid) dt

^q = /(uq - Rsiq)dt = fpC^dlq - ®qid)

2.4. Modeling of Centrifugal Pump

The centrifugal pump applies a load torque proportional to the square of the rotational speed of the motor. Centrifugal pump is the most commonly employed type of pumps [16], it has a relatively high efficiency and capable of pumping a high volume of water. The performances Q, h and P are given in terms of the speed using the following relationships:

i Q' = Q-Z

jh' = h.z2 (11)

= P.Z3 Where, Z= ror'/ro r.

3. Direct torque space vector control

The basic principle in conventional DTC for induction motors is to directly select stator voltage vectors by means of a hysteresis stator flux and torque control. As it is seen in Fig. 4 [17].

Switch Table Table. 3

Sector number

Fig. 4. The diagram block of traditional DTC.

According to Fig. 4 stator flux (^ref) and torque references (Tref) can be obtained and then compared with the corresponding real values. Both stator flux and torque errors (A9), and (ATe), are processed by means of a hysteresis band comparators. In particular, stator flux is controlled by the two-level hysteresis comparator. On the basis of the hysteresis comparators and stator flux sector a proper VSI voltage vector is selected by means of the switching table given in Table 3.

Table 3. Basic DTC Switching table.

Sector number 1 2 3 4 5 6

<p = l Te = 1 V5 V6 V1 V2 V3 V4

Te = 0 V0 V7 V0 V7 V0 V7

Te = -1 V3 V4 V5 V6 V1 V2

y = 0 Te = 1 V6 V1 V2 V3 V4 V5

Te = 0 V7 V0 V7 V0 V7 V0

Te = -1 V2 V3 V4 V5 V6 V1

In direct torque control with space vector pulse width modulation (DTC-SVM) with close loop flux control, with close loop torque control and with close loop flux and torque control, the calculation of reference voltage vector is based on demanded.

This differentiation algorithm is very sensitive to disturbances. In case of errors in the feedback signals, the differentiation algorithm may not be stable .and this is very serious drawback of these methods that causes torque and flux ripple with deteriorate the performance of system. The proposed method DTC-SVM based on amplitude stator voltage and stator flux angle is used to modify the control system. The stator flux angle is controlled by rotor angular frequency and slip angular frequency. Figure. 5 shows the block diagram of sensor DTC -SVM based on amplitude voltage and stator flux angle. This control system is consist of PI controller for slip angular frequency, PI torque controller, PI flux controller and Cartesian to polar transformation block to calculate amplitude of stator voltage, while polar to Cartesian block is used to calculate stator voltages in direct and quadrature reference frame at next sampling time. Ziglar nicals method is used to tune Kp and Ki gains of PI where in this method the damping ratio is fixed at 1 and the rise time tr = 0.5 s . In this method, the PI speed controller is used to optimize the reference torque (7Vef) of the motor from the error between reference speed and the rotor speed (ro,-ef, ro) respectively.

4. Maximum power point tracking

The maximum power that can be delivered by a PV panel depends greatly on the insulation level and the operating temperature. Therefore, it is necessary to track the MPP all the time. They have the advantage to be robust and relatively simple to design as they do not require the knowledge of the exact model. They do require on the other hand the complete knowledge of the operation of the PV system. The FLC input variables are the error (e) and derivate of error (de) at sampled times k defined by [18]:

( n PpvOO-Ppv(k-l)

j Vpv(k)-Vpv(k-1) (12)

(de(k) = e(k) - e(k - 1)

The FLC tracks the MPP based on master rule of "If X and Y, Then Z" [19, 20]. To determine the output of the positive, negative and zero sequence voltages, currents, and impedances fuzzy logic, the inference is used. There are many methods for inference but the popular one is Memdani. Other methods include compositional rule of inference, generalized modus ponens and Sugeno inference method. The fuzzy inference is carried out by using Memdani's method and the defuzzification uses the centre of gravity to compute the output of this FLC which is the optimum duty cycle. The control rules are indicated in Table 4 with (e) and (de) as inputs and d as the output, where d is associated fuzzy sets involved in the fuzzy control rules .

Table 4. Fuzzy rules.

de|e NB NM NS ZE PS PM PB

NB NB NB NB NB NM NS ZE

NM NB NB NB NM NS ZE PS

NS NB NB NM NS ZE PS PM

ZE NB NM NS ZE PS PM PB

PS NM NS ZE PS PM PB PB

PM NS ZE PS PM PB PB PB

PB ZE PS PM PB PB PB PB

4. Simulation results

The diagram bloc of the PV water pumping system with Matlab is seen in Fig.6

Fig. 6. The simulation bloc of system.

In order to establish a good test of the proposed system (fuzzy logic space vector direct torque control of PMSM for photovoltaic water pumping system), two simulation conditions operation are applied:

• Two speed references (- 120 rad/s and +120 rad/ s) are considered are explained by Fig. 9.

• Twice negative, twice positive and fours nulls reference torque are illustrated in Fig. 10.

According to figure 9 it shown that the speed with PI and FLC shows their reference, it note that with using PI controller there are a short speed response time accompanying with a heaver oscillations. Comparing to PI controller, the FLC design improve the more soupless response, not speed oscillations but more speed response time.

Figure.10 demonstrates the variation reference of the torque with the two controllers design, the torque present a good pursuit, it's observed with using FLC mains overshoots and oscillations, a grave pics with conventional controller at instants during to start and speed inversion.

Concerning the electrical characteristics Fig. 7 and Fig. 8 presents respectively the response currents with FLC and PI. It's observed that the currents are sinusoidal forms while the PI controller design present a grave pics under realistic speed conditions compared to FLC design.

Fig. 7. Response stator current of motor with FLC.

Fig. 8. Response stator current of motor with PI controller.

Fig. 9. Speed response PMSM.

Fig. 10. Torque response of PMSM.

According to Fig.11, the trajectory of flax in a b farm is a cercal form. It's prove that the sinusoidal flux form. It's shown in Fig.12 a good flux reference follows with not any overshoot or oscillates, these improved the DTC-SVM potential. It shows the behavior of the greatness flows.

Fig. 12. Flux Response with FLC and PI.

5. Conclusions

The study of performances speed control photovoltaic system with fuzzy logic has been tested. The performances are analyzed in the response time and overflow are analysed and comprised between traditional DTC and DTC-SVM. It is concluded that the propeller torque is proportional to its square of the speed approximately by analyzing the propeller's characteristic.

The simulation results show clearly that the proposed DTC-SVM proposed for torque ripple reduction is very appropriate for electric propulsion ship. The DTC system based on SVPWM manifests for continuous output of voltage vector from the converter, making the periodical pulsation of the flux and torque decrease greatly. So, it can meet the requirement of the constant output of torque in real time for propulsion motor.

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