MPPT control technique for solar powered direct torque control of induction motor drive with a robust speed and parameters adaptation scheme for water pumping
2018; Institution of Engineering and Technology; Volume: 13; Issue: 2 Linguagem: Inglês
10.1049/iet-rpg.2018.5390
ISSN1752-1424
Autores Tópico(s)Solar Radiation and Photovoltaics
ResumoIET Renewable Power GenerationVolume 13, Issue 2 p. 273-284 Research ArticleFree Access MPPT control technique for solar powered direct torque control of induction motor drive with a robust speed and parameters adaptation scheme for water pumping Saurabh Shukla, Corresponding Author Saurabh Shukla saurabh.shukla.ee@gmail.com orcid.org/0000-0002-4882-8769 Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, 110016 IndiaSearch for more papers by this authorBhim Singh, Bhim Singh Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, 110016 IndiaSearch for more papers by this author Saurabh Shukla, Corresponding Author Saurabh Shukla saurabh.shukla.ee@gmail.com orcid.org/0000-0002-4882-8769 Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, 110016 IndiaSearch for more papers by this authorBhim Singh, Bhim Singh Department of Electrical Engineering, Indian Institute of Technology Delhi, New Delhi, 110016 IndiaSearch for more papers by this author First published: 21 November 2018 https://doi.org/10.1049/iet-rpg.2018.5390Citations: 11AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract This paper presents a novel robust model reference adaptive system (MRAS) technique for rotor speed estimation of direct torque control (DTC) of an induction motor drive used for solar PV powered water pumping. The maximum power point tracking (MPPT) of PV array is assured by a proposed P&O algorithm, which has improved tracking time without deviation during insolation change. Moreover, an additional loop is incorporated in the MPPT control, which provides an additional feature of derating the panel, which consequently controls the flow rate. The effect of parameter variation e.g. change in rotor resistance, stator resistance and the rotor time constant on the stability of overall system, is analysed and tested. The MRAS involves fluxes estimation and uses the same machine parameters which are involved in DTC. The elimination of speed sensor and parameters adaptation make the overall induction motor drive (IMD) suitable for such application. The stability of the system is assured by Lyapunov's stability criterion and the stability of parameters adaptation is shown by Bode plot and well-known Popov's stability criterion. Therefore, the reduced sensors (voltage and current sensors) based proposed system with deviation-free MPPT technique and with flow rate controller, is modeled, simulated, and experimentally verified. 1 Introduction Sustainable development is the rising theme of the present generation and a new horizon for researchers. The main benefits of the electrical system based on renewable energy constitute the everlasting stock of the sources and constant pricing regardless of market scenario. Wind farms and solar powered photovoltaic (PV) systems are the fastest growing technologies for power production. Solar PV (SPV) array based power generation, as being clean and noise free [1, 2], is gaining popularity in recent times and the power is being utilised to supply various loads in various sectors. Water pumps in irrigation sector, as well as domestic and industrial sectors, have been benefitted by the introduction of renewable source based power production in these sectors [3]. The advantages of using PV power in water pumps further include low maintenance, ease of installation, high reliability, silent operation, and less wear and tear less due to the absence of moving parts. The maximum power from the solar panel is drawn by using a maximum power point tracking (MPPT) algorithm using a DC–DC converter. These algorithms vary in their speed of response, complexity, and efficiency [4]. A number of DC–DC converters used in MPPT technique have been reported in the literature for water pumping. Amongst them, this study focuses on the use of a boost DC–DC converter for MPPT [5, 6]. A control technique for a successful integration of the wind–PV hybrid system with battery storage is reported in [7, 8]. Recently, a DC motor has been replaced by an induction motor as it is robust, economic easily available and operated in severe conditions [9, 10]. Mechanical sensors, such as tachometers and optical encoders, are used for rotor speed measurement, which increases the cost and size of the system [11]. Ample research has been performed and implemented on sensorless control technique of an induction motor. The estimation of stator and rotor fluxes is the base of all speed estimation techniques [12, 13]. There are few strategies, which are saliency based, e.g. sliding mode observer [14] and extended Kalman filters [15, 16], which are parameters insensitive and robust. However, these strategies are complex and increase the burden on the processor. Another speed estimation technique emerges from the model reference adaptive system (MRAS), where one is an adaptive model and another is a reference model, both depending upon different machine parameters. The error is reduced to zero through a readjustment of parameters affecting one of the models. The MRAS-based models are immune to noise and are simple [17]. Tamai [18] has explained the basic structure of the MRAS scheme based on rotor flux error. Peng et al. and Marwali et al. [19] have proposed another MRAS technique based on back-electromagnetic force. A stator current based MRAS model is dedicated to generation of speed error correction signal from the estimated value to measured value [20]. Various techniques have been proposed in the literature to reduce the number of current sensors. A few techniques are based on the reconstruction of phase currents from the DC link current by proper sampling by simple logics and filters. Some strategies deal with the modification of the modulation index to ensure the reliability of the current measurement from the DC link current under all operating conditions [21]. Here an observer-based algorithm is proposed to estimate the phase currents of induction motor drive (IMD). Direct torque control (DTC) technique is a simpler control technique than vector control and provides quick and robust speed control. It is less parameter dependent. Moreover, the space vector modulation switching technique used in DTC is simpler than the pulse-width modulation used in vector control [22]. Therefore, the novelty of PV array fed direct torque controlled IMD for water pumping is listed here. Proposed deviation-free perturb and observe (P&O) algorithm with a DC–DC boost converter. Proposed rotor flux estimation technique with DC offset removal capability. Proposed current estimation technique, which reduces current sensors. A new speed estimation technique with rotor flux and stator currents in the stationary domain. Stability analysis of stator resistance and rotor time constant (viz. Rs and τr) adaptation technique. The plan of the paper is given as follows. Section 2 includes system structure. Section 3 describes the design of the system and mathematical modelling. The control of the proposed system is given in Section 4. Section 5 describes the current estimation and stability analysis of the system. Simulation results and experimental validation are given in Sections 6 and 7, respectively. Section 8 includes the conclusion of the work. 2 System structure Fig. 1 shows the schematic of the proposed system with MRAS speed adaptation mechanism for DTC of IMD. The details are given in the subsequent sections. Fig. 1Open in figure viewerPowerPoint Block diagrams (a) Schematic of proposed system, (b) Generalised flux estimator, (c) Flow chart: deviation free perturb and observe algorithm, (d) Proposed current estimation method 3 Design of system and mathematical modelling As shown in Fig. 1a, the scheme of a proposed system consisting of a three-phase IMD of a 2.2 kW (3 HP), 230 V powered by a 2.5 kW SPV array, is discussed in subsequent sections. The specifications of the proposed system are given in the Appendix. 3.1 Design of SPV array A SPV array is the combination of different modules connected in series and parallel. The number of series (Nser) and parallel (Npar) modules is estimated by the following expression. The specifications are given in the Appendix (1) 3.2 Design of boost converter The detailed design of the boost converter is used as per the procedure, which is given in [1]. 3.3 Dynamic modelling of motor The stepwise dynamic modelling of the induction motor is used, which is given in [23]. The differential equations of flux and current components in the stationary reference frame, which are required for speed estimation and parameters adaptations, are given as follows: (2) (3) (4) (5) From the above discussion, it can be inferred that (2)–(5) are rotor speed dependent. Therefore, it can be treated as an adaptive model for speed adaptation. The reference model is independent of speed. The reference stationary components of fluxes are estimated by the generalised integrator based flux estimator, as shown in Fig. 1b. The problems associated with pure integral such as the saturation due to the inherent DC offset in flux component is somewhat mitigated by the low pass filter up to a certain extent. Still, it introduces magnitude and phase error in the fundamental flux component. Therefore, a generalised flux integrator is proposed to make the output flux free of all imperfections. In this figure, K is the damping factor, ωg is the tuning frequency, ideally equal to motor frequency, and Γ is the design parameter depending upon the settling time (ts). The conventional second-order integral is used for phase and amplitude extraction of the grid voltage. The control algorithm for fundamental component extraction through the generalised integrator is given is used to eliminate DC offset by calculating the voltage error (ve) and added to grid voltage (vg), as reported in [24]. The controlled quantities at each node are obtained w.r.t. the input given as (6) (7) where ωg = K = loop gain parameter. F(s) is used for filtering and I(s) is for integration. Therefore, the rotor flux observation technique can be considered as (8) When S = jωg(9) where λr(s) is the observed rotor flux in the stationary reference frame. The frequency locked-loop is also required to make ωg = ω1. Γ is a coefficient, which is reported in [24]. Therefore, the rotor flux is a stationary domain is given as (10) where and . As it can be observed from (10), when compared to the pure integral taken for flux observation, the DC-offset is reduced and the saturation problem is removed without phase shift and amplitude. The magnitude of harmonics is also reduced by a factor of . The DC component is reduced by . 4 Control of the proposed system This section deals with the proposed control techniques for the MPPT control of a PV array and the speed control of IMD. The detailed discussion is presented in this section. 4.1 Deviation free P&O algorithm The conventional P&O algorithm technique is a simple and efficient technique but it has some drawbacks associated with the deviation at the time of insolation change. This problem is due to the confusion created for the algorithm to decide the reason for the maximum power point (MPP) change. That is why there is a deviation for two–three steps, which associates with the small power loss. This problem can be avoided by taking the change in MPP current into the loop. Killi et al. [25] have explained this deviation problem during an incremental change in insolation. Fig. 1c shows a modified deviation free MPPT, where an additional loop is introduced for insolation decrease in order to avoid the step deviation during this case too. Moreover, an additional loop is incorporated to control the flow rate by assigning the value to a fixed duty ratio corresponding to the desired power output for flow rate control. The duty ratio generated above is used to switch the boost converter, which is responsible for MPPT control. The DC link voltage control is achieved by three-phase voltage source inverter (VSI) (11) The error signal Vdcl(k) is driven to zero by using a proportional–integral controller and the resultant is reference speed at the kth sampling instant. (12) The second component of reference speed is obtained from the affinity law of pump explained as (13) where K1 is the proportionality constant. The reference speed is estimated as (14) 4.2 DTC of IMD The DTC method is used to control the torque and flux. It can be explained as follows. The flux error is fed to flux comparator, which is a hysteresis band comparator by the following logic: (15) (16) where λs* is the rated flux of the machine and λs is the resultant rotor flux component in the stationary reference frame. The reference torque (Te*) is estimated from the speed controller output of reference speed (ωref) and estimated motor speed (ωm). This torque is compared with the estimated torque (Te) and an error signal is controlled by a hysteresis controller as (17) (18) The torque error (dTe) is the input of torque comparator with the help of the following logic: (19) (20) (21) where . The torque error (dTe) and flux error (dψs) are utilised for voltage vector generation, which is utilised for sectors selection. The signal computation also involves the sectors selection, S(k) in which the flux vectors lie. Each sector is π/3 radian apart from each other and the error signals HBψ and HBTe and sectors S(k) are the input used to develop the switching logic according to Table 1. Table 1. Voltage vector selection for switching dψ dTe S1 S2 S3 S4 S5 S6 1 1 V2 (110) V3 (010) V4 (011) V5 (001) V6 (101) V1 (100) 0 V0 (000) V7 (111) V0 (000) V7 (111) V0 (000) V7 (111) −1 V6 (101) V1 (100) V2 (110) V3 (010) V4 (011) V5 (001) −1 1 V3 (010) V4 (011) V5 (001) V6 (101) V1 (100) V2 (110) 0 V7 (111) V0 (000) V7 (111) V0 (000) V7 (111) V0 (000) −1 V5 (001) V6 (101) V1 (100) V2 (110) V3 (010) V4 (011) 5 Current estimation and stability analysis of the proposed system This section includes the stability analysis of the system in terms of speed estimation, stator resistance adaptation and rotor time constant adaptation. The elaborated discussion is given as follows. 5.1 Current adaptive approach Fig. 1d shows a block diagram of current adaptation technique to construct phase currents. Sinusoidal unit templates in the α–β domain are used as the oscillator, which is used to construct the phase currents from the error signal. The differential equation in a form of state space matrix is given as (22) where ω is the speed of IMD, [A] is the system matrix, [G] is the input matrix required to obtain the gains or Eigen vectors of the proposed system and are expressed as The differential equation for the error signal in a state space matrix form is given as follows: (23) The matrix '' is the error signal in the a–b–c phase, which is expressed as, (24) The frequency of the saw-tooth waveform is selected as 4 kHz for 20 kHz analogue-to-digital converter sampling frequency. However, the optimum values of two Eigen values are obtained at (λ = −4ω) for the stability of the feedback system. The characteristic equation is given as (25) (26) By substituting the Eigen values, λ1 = λ2 = −4ω, in (26) the Eigen vectors are obtained as (27) Similarly, other Eigen vectors are calculated as (28) These adaptive gains are used for current estimation. 5.2 Adaptive scheme for ωm adaptation The improved model used here is based upon the speed adaptation by the flux observer method. The observer is like an estimator that depends upon a definite model and measured variables in the feedback loop. Here, the adaptation loop relies on the state variables viz. idss, iqss, λdrs, and λqrs. By using these quantities, a new MRAS model expression is gleaned for speed estimation. If the rotor speed signal (ωm) is already known, the parameters can be easily estimated. However, if there is a deviation in ωm from the actual value, there is a deviation in the actual model from the estimated model. In this rotor flux observer model, rotor fluxes (λ′sdr and λ′sqr) are estimated and compared with actual machine rotor fluxes. A corrective signal Keλ is introduced by eλ so that eλ becomes zero as time t tends to infinity. Hence the final observer equation becomes (29) In general, the estimation error in terms of current and fluxes is interpreted by (30) (31) (32) where (33) (34) (35) Therefore (36) (37) 5.3 Stability analysis of MRAS scheme for speed adaptation The stability of the system with a small perturbation in speed (Δωm) can be checked by Lyapunov's stability function. Recently, to design the stable MRAS, Lyapunov's stability criterion and theory of hyper stability are successfully implemented for the nonlinear system. There are different design equations for both the theories. However, the adaptive laws are basically similar. The positive definite Lyapunov's function is defined as (38) The derivative of the above function can be written as (39) (40) where Putting (40) in (39), the final expression becomes as (41) [(A + KC)T + (A + KC)] is made negative semi-definite. Therefore, the equation becomes (42) From (42), only first and second terms are considered with rotor flux vector error. The reason for this selection is that the errors in idss and iqss can be readily obtained since the stator currents are measured quantities, the same cannot happen for fluxes as they are estimated quantities. The final expression can be assessed as (43) 5.4 Stability of MRAS based stator resistance (Rs) adaptation The equations required to construct the state variables matrices for stator resistance estimation are as follows. In a similar way as before, the error matrix w.r.t change in stator resistance (ΔRs) i.e. [W] is given as (44) The state space representation of the machine in the stationary reference frame with stator current and rotor flux is given as (45) (46) The state error equations after linearising (45) and (46) are given as (47) (48) where and By taking Laplace transform of (47) and (48), the final equation is given as (49) The stator resistance equation from the machine dynamic equation is given as Fig. 2a represents the block diagram of Rs estimation. It is clear from the figure that (50) where Δɛ are d–q axes stator current error equations. Fig. 2Open in figure viewerPowerPoint Model reference adaptation of parameters with proposed MPPT technique (a) Closed-loop control system for Rs estimation, (b) Schematic of proposed parameters adaptation, (c) Tracking time elapsed by proposed MPPT algorithm during insolation change from 1000 to 500 W/m2 and vice-versa Considering only the d-axis component, the final equation becomes (51) Therefore, the transfer function of the stator resistance estimator for the single input single output control system is given below. The final closed loop transfer function is given as (52) where where The stability of the estimated parameter is proved by Bode plot and discussed in the preceding section. 5.5 MRAS-based rotor time constant (τr) adaptation scheme As per the previous discussion, the error matrix [W] can be represented as (53) (54) where, and . The system is hyperstable if forward path matrix has all poles on the left half of the s-plane. Moreover, the [F(jω) + FT(−jω)] is strictly positive Hermitian. Therefore, the system has a forward path matrix with strictly positive real. Now, to check the stability of the nonlinear feedback path matrix, Popov's inequality criterion has to be satisfied. By Popov's inequality (55) Popov's inequality can be satisfied and the solution can be derived as (56) Therefore, the following inequality satisfies Popov's theorem. The adaptive rotor-time constant can be identified as (57) Fig. 2b presents a schematic of the proposed adaptation mechanism. 6 Simulated results This section presents the simulated results of the proposed topology along with test results in a subsequent section. 6.1 Performance of deviation free P&O technique Fig. 2c shows the simulation results of the deviation free P&O algorithm. As it can be seen from the result that the tracking time of this particular algorithm is lesser than the conventional P&O technique both during insolation increment and decrement because it does not suffer from deviation problem as discussed earlier. 6.2 Starting performance of the drive Fig. 3a shows the smooth starting of the system. The PV array quickly tracks the maximum power and operates at rated condition. The DC link voltage (Vdc) can be seen to be settled at 400 V and Ppv at 2500 W. It can be seen from the graph that the reference speed (ωref) reaches a rated speed of 150 rad/s as soon as the MPP is tracked. Three-phase currents (iabc), the electromagnetic torque (Te) and the pump torque (Tp) reach their rated steady state value. Fig. 3b shows a similar observation, which is made when the system is operated at 500 W/m2. Fig. 3Open in figure viewerPowerPoint Performance of the system during insolation change (a) 1000 W/m2, (b) 500 W/m2 It is observed in Fig. 4a that the frequency plot of flux estimation through pure integral lacks DC offset rejection capability, while with the proposed flux observer DC offset is not integrated in fact it is reduced with a damping factor. Although it introduces 90° phase shift in the lower frequency region, it can be mitigated by adding the reference flux term. Fig. 4Open in figure viewerPowerPoint Performance indices (a) Bode plot of improved flux observer, (b) 1000 W/m2, (c) Boost performance indices at 1000 W/m2, (d) Simulation results at rated insolation and 60% of rated flow-rate Fig. 4b manifests the estimation of rotor speed (ωm) through the adaptation mechanism at 1000 W/m2. These waveforms show the nature of stationary components of the rotor fluxes utilised for rotor speed adaptation. The intermediate signals in terms of boost inductor voltage (VL), inductor current (IL), diode voltage (VD), diode current (ID), switch voltage (Vsw) and switch current (Isw) are shown in Fig. 4c. Fig. 4d demonstrates the operation of the system at 1000 W/m2 insolation, however, at reduced power output (60% of rated power output). The first waveform in these figures shows the insolation set at 1000 W/m2. The second waveform exhibits the PV power curve, which settles at the reduced value required to adjust the desired flow rate. The motor speed (ωm) is regulated by the speed controller at its reference speed (ωref). 6.3 Dynamic performance of drive at insolation change Figs. 5a and b demonstrate the drive performance when the insolation (S) undergoes a sudden step change. These are the extreme conditions, which generally do not occur. Therefore, it is inferred that if the proposed system can withhold with these atmospheric variations then its suitability of this system is unquestionable. Fig. 5Open in figure viewerPowerPoint System performance during a change in insolation (a) 1000–500 W/m2, (b) 500–1000 W/m2, (c) Rs as per reference stator resistance, (d) τr as per reference value 6.4 Stator resistance (Rs) and rotor time constant (τr) adaptation Figs. 5c and d display the simulation results of stator resistance and rotor time constant (τr) adaptation when the machine resistance is varied from its rated value of 0.603–1.8 Ω and τr varies to double its value, respectively. This is an extreme case, which generally does not occur. However, it is shown here just to verify the robustness of the system under any condition of parameter variation. 7 Hardware results Fig. 6a shows the control architecture of the system and Fig. 6b shows a prototype developed in the laboratory, which constitutes a PV array simulator (ETS600 × 17DPVF Terra SAS) used as the SPV array. A Hall-effect voltage sensor (LV-25P) is used for DC-link voltage and two current sensors (LA-55P) are used for DC-link current and PV array current, respectively. A VSI (SEMIKRON MD B6CI 600/415–35F) and a real-time digital signal processing controller (dSPACE 1104) are used. For recording purpose, a four-channel digital storage oscilloscope (Agilent make DSO) is used. The transistor (2N2222) and opto-couplers (6N136) circuitry are used. The characteristic of the water pump is realised by a separately excited DC generator coupled to a resistive load coupled with the induction motor. Fig. 6Open in figure viewerPowerPoint Experimental validation of proposed system (a) Control architecture of the proposed system, (b) Photograph of a prototype for test prototype 7.1 Efficiency of MPPT algorithm Figs. 7a–d verify the MPPT at 500–1000 W/m2. The tracking efficiency under the rated condition is found to be 99.99%, whereas, at 500 W/m2, it is found to be 99.61%. This means that under all operating conditions, the tracking efficiency is nearly 100%. This implies that the maximum power is drawn from the PV array for a wide range of insolation change. Fig. 7Open in figure viewerPowerPoint MPPT performance of PV array (a) 500 W/m2 (b)600 W/m2, (c) 800 W/m2 (d) 1000 W/m2 7.2 Behaviour of the proposed system during starting and steady state Figs. 8a–d deal with the starting and steady state performance of the proposed system. It can be seen that at the time of starting, the DC link capacitor (Cdc) is charged to its initial voltage that is fixed at open circuit voltage (Voc). As the SPV array achieves its MPP, the drive with rated load achieves its rated speed. Fig. 8Open in figure viewerPowerPoint Starting of proposed system (a) System indices at 1000 W/m2, (b) Intermediate flux signals, (c) System indices at 1000 W/m2, (d) Boost converter indices Fig. 8a shows the MPPT with Voc finally reaching Vmp (=Vpv). It is worth mentioning here that the DC–DC boost converter is responsible for MPP tracking and the three-phase inverter is used for DC link voltage regulation. The other waveforms show the drive performance in terms of motor phase current (isa) and the rated speed (ωm). Fig. 8b shows the intermediate signals in terms of λdrs, λqrs and rotor speed (ωm) estimated by adaptation mechanism. The reference speed (ωref) is shown in the figure to be closely followed by ωm. Fig. 8c deals with the proposed system subjected to reduced insolation of 500 W/m2. It can be observed that the performance of the drive is satisfactory in terms of Vpv, Ipv, isa, and ωm. Fig. 8d exhibits the intermediate signals associated with the boost converter in terms of IL, VL, VD, and Vsw. The response is quite satisfactory during the steady state condition. Figs. 9a and b present the steady state behaviour of the drive in terms of three phase currents isa, isb, isc and rotor speed (ωm) at 1000 and 500 W/m2, respectively. It can be observed that the motor currents are sinusoidal in nature with 8.2 and 6.4 A (rms), respectively. Fig. 9Open in figure viewerPowerPoint Drive during steady state (a) 1000 W/m2, (b) 500 W/m2, (c) Bode plot of Rs estimation at ωm = 150 rad/s, Rs = 0.603 Ω and S = 1000 W/m2, (d) Bode plot of Rs estimation at ωm = 150 rad/s, Rs = 3.0 Ω and S = 1000 W/m2 7.3 Stability analysis of Rs adaptation The stability of the system is obtained by creating a perturbation in the stator resistance. It is assumed that the actual resistance value is constant. If the estimated value after perturbation comes back to the rated value, then the system is stable. Fig. 9c shows the Bode plot at the rated condition and the stability is judged by observing the gain margin (GM) and phase margin (PM) of the plot. It is observed that GM and PM are positive, which justifies that the system is stable. Moreover, the GM is at infinity, which demonstrates the robustness of the parameter estimation method. The adaptability of the system is verified for one more operating condition in which the motor resistance is fixed at five times the rated resistance. Fig. 9d demonstrates the stability of the system for this given operating condition. GM is infinite in this case, which again validates the robustness of the system. 7.4 Performance indices during insolation change Fig. 10a displays the performance of the system step change in insolation from 1000–500 W/m2. As the DC link voltage (Vdc) is constant by virtue of the two-stage control technique, the change in Ipv is observed on the PV array side. This effect is well-abided by the drive and the phase current (isa) and rotor speed (ωm). Fig. 10b exhibits the satisfactory current construction at rated condition. Figs. 10c and d exhibit the phase voltage and current waveforms and their respective harmonic contents. It is seen that the total harmonic distortion (THD) of the motor phase current is 6.82%. Fig. 10Open in figure viewerPowerPoint Performance of the proposed system during insolation change (a) 1000–500 W/m2, (b) Reconstructed currents, (c) Phase current waveforms, (d) Total harmonic distortion (THDi) 7.5 Stator resistance (Rs) estimation and its variation during insolation change Figs. 11a and b exhibit the estimated resistance and its variation with the insolation change. It can be observed from the waveforms that the estimated resistance is reference and adaptive rotor flux dependent and remain unaltered with the changing insolation. The stator resistance only changes when the actual resistance of the machine changes. This case occurs when the machine is allowed to operate for a long time. This has been discussed in the earlier section. Fig. 11Open in figure viewerPowerPoint Performance of the proposed system during insolation change (a) Variation of estimated resistance during insolation change 1000–500 W/m2, (b) Variation of estimated resistance during insolation change 500–1000 W/m2 8 Conclusion The proposed system constituting of the proposed MPPT control algorithm for PV array fed to drive the operating water pump has been realised by induction motor coupled with separately excited DC generator. The proposed system performance is simulated and its suitability is checked on a test prototype in the laboratory. The MPPT has been controlled by a proposed algorithm, which has improved tracking time with an additional loop incorporated for flow rate control. A successful flow rate control has been shown at rate insolation. A technique, based on second-order generalised integration, has been proposed to estimate the rotor flux in a stationary domain with a proposed flux integrator, which not only avoids saturation, but it also avoids phase difference in fundamental flux estimation, with DC offset mitigation. Moreover, a motor phase current estimation technique has been used, which has reduced number of current sensors and therefore, reduces the cost of the overall system. In conventional speed estimation technique, the speed is estimated considering all the motor parameters to be constant. However, this is not a practical case as these parameters are temperature dependent. Therefore, an adaptive mechanism has been adopted for parameters estimation. The parameters adaptation has been analysed through detailed mathematical modelling of the proposed adaptive method and it has been justified by increasing the value of parameters such as stator resistance (Rs) has been increased to thrice its rated value (i.e. 1.8 Ω) and the estimated value has been successfully tracked it. Likewise, rated rotor time constant is also changed stepwise and the suitability of the adaptation technique has once again been justified. The flux-error and stator currents in a stationary frame of reference are used for speed adaptation, while only stationary components of current are used for Rs adaptation. Therefore, a cost-effective, mechanical sensorless, robust and parameters insensitive system with improved MPPT, flux and phase current estimation techniques has been proposed, simulated in MATLAB/Simulink platform and tested on a prototype developed in the laboratory. 9 Acknowledgment The authors are thankful for all the support and encouragement from MHRD and Shakti Pumps (India) Ltd, industry partner for supporting the work carried under the project grant number: RP03222G, under the ambit of Uchhatar Avishkar Yojana. 11 Appendix 11.1 SPV array Voc = 370 V, Vmp = 317 V, Isc = 7.23 A, Imp = 6.85 A, DC link inductor (L1) = 3.2 mH, DC link capacitor (Cdc) = 800 μF, duty ratio (D) = 0.15, switching frequency (fs) = 10 kHz. 11.2 Specification of IMD 2200 W, three-phase, 230 V, four poles, Rs = 0.603 Ω, Lls = 0.00293 H, Rr = 0.7 Ω, Llr = 0.00293 H, M = 0.07503 H, J = 0.011 kg m2, Voltage controller gains Kpd = 0.19, Kid = 0.1, speed controller gain Kpω = 0.4, Kiω = 1.8. 10 References 1Saxena, N., Singh, B., Vyas, A.L.: 'Single-phase solar PV system with battery and exchange of power in grid-connected and standalone modes', IET Renew. 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Electron., 2015, 62, (9), pp. 5549– 5559 Citing Literature Volume13, Issue2February 2019Pages 273-284 FiguresReferencesRelatedInformation
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