Assessment of a fuzzy logic based MRAS observer used in a photovoltaic array supplied AC drive

Abstract

In this paper a fuzzy logic (FL) based model reference adaptive system (MRAS) speed observer for high performance AC drives is proposed. The error vector computation is made based on the rotor-flux derived from the reference and the adaptive model of the induction motor. The error signal is processed in the proposed fuzzy logic controller (FLC) for speed adaptation. The drive employs an indirect vector control scheme for achieving a good closed loop speed control. For powering the drive system, a standalone photovoltaic (PV) energy source is used. To extract the maximum power from the PV source, a constant voltage controller (CVC) is also proposed. The complete drive system is modeled in MATLAB/Simulink and the performance is analyzed for different operating conditions.

Keywords

induction motor drive / fuzzy logic (FL) control / model reference adaptive system (MRAS) / photovoltaic (PV) array / vector control

Introduction

Photovoltaic (PV) energy in recent years has shown promising capabilities for the inclusion in the list of conventional energy sources. The main advantageous features of the PV energy generation include the abundant, free of cost and non-polluting fuel. Furthermore, the reduction in price of PV energy generation per peak watt over the years has encouraged the exploration into the solar technology. The PV energy generation is more appropriate for low power distributed generation systems, particularly in the areas where agriculture is one of the main occupations and grid supply is not easily available. Nevertheless, PV application areas are seamless and can also be used with high performance AC drives for electric vehicles applications [1,2].

The two challenges still persisting in using a PV array are its nonlinear output and low energy conversion efficiency. The solutions to the first challenge in the form of maximum power point (MPP) tracking technique are available in the literature. Most of the MPP tracking techniques use the information of PV array current and/or voltage. The constant voltage controller (CVC) is simple in scheme and uses only voltage level information to track the MPP in comparison to the other techniques [3,4].

Being an important part of an electric drive, different types of electric motors are tested for high performance drive applications by different researchers. Perhaps, in the literature, induction motor is the first choice for these applications due to its low-cost construction and robustness. However, induction motors are designed to impart high efficiency at the rated conditions of load and supply. So, for achieving high performance, an indirect vector control scheme is used as suggested by various researchers [5-7]. The implementation of the vector control scheme requires the measurement of speed, forcing to mount a speed sensor on the motor shaft. Due to the well-known drawbacks of speed sensors in a drive, it is preferable to use a speed observer in the applications requiring high performance [8].

Among the various speed estimation techniques, the model reference adaptive system (MRAS) scheme is most extensively employed for induction motor drives. The popularity of the MRAS scheme lies in its various advantageous features such as simple structure, easy implementation and low computational effort. Generally, MRAS scheme is realized by forming an error vector required to update the speed. Depending upon the variable used for the formation of error vector, the MRAS scheme can be classified as rotor flux error based MRAS scheme [9,10], stator current error based MRAS scheme [11], back electromotive force (EMF) error based MRAS scheme [12], and reactive power error based MRAS scheme [13].

Usually, the accuracy of control scheme is influenced by the variations in motor parameters and the operating conditions. Proportional- integral (PI) controllers are widely used for a long time for control system applications. But despite their simple structure and wide range applicability, fixed-gain PI controllers are not supposed to be used in the systems with varying parameters, nonlinearities and changing operating conditions. Among the artificially intelligent controllers available, the fuzzy logic controller (FLC) has gained significant attention, particularly in the field of control system. But, it has not yet been comprehensively applied to speed estimation solutions [14-17].

In this paper an attempt has been made to assess the performance of an AC drive employing a fuzzy logic based MRAS speed observer. To explore the advantages of technologies available, the drive uses an indirect vector control scheme and is supplied from a photovoltaic energy source. Simulation model of each component of the system is designed separately and then assembled in the MATLAB/Simulink environment. The performances of the drive for different operating conditions are presented.

System description and modeling

The system mainly consists of a PV array, a CVC, a power modulator, a vector control, an induction motor and load. The block diagram of the system is shown in Fig. 1. The drive is solely supplied by a PV array by means of power modulator. Here, the main function of the power modulator is to change the DC input into a controlled AC to be used by the induction motor. The brief description of each component is given below under their respective headings.

PV array

Interconnected solar cells in series and/or parallel connection are known as PV array. For imitating the electrical behavior of the PV array, different equivalent models have been proposed by researchers. Each equivalent model differs in the number of parameters involved in calculating the voltage and current of the PV array. A diode DC equivalent model demonstrated in Fig. 2 is the simplest and is used in Ref [2]. The output voltage of the equivalent model of the solar cell used can be calculated by

(1)V_C={\displaystyle \frac{nAk{T}_{\mathrm{C}}}{q}}\ln \left({\displaystyle \frac{I_{\mathrm{p}\mathrm{h}}+I_{\mathrm{r}}-I_{\mathrm{C}}}{I_{\mathrm{r}}}}\right)-I_{\mathrm{C}}{R}_{\mathrm{s}},

where V_C and I_C are the voltage and current of the array respectively, R_sis the cell resistance, I_{ph} is the photocurrent, I_r is the reverse saturation current of the diode, q is the electron charge, k is Boltzmann constant, and T_r is the reference operating temperature of the cell.

As the cell output depends upon the operating temperature and insolation level, the changes in any of them will affect the output of the cell. The effects are incorporated in the designed cell with the help of the coefficients explained in more detail in Ref [2].

For this work, the constants of the associated equations are so adjusted that the curves of a single cell can be in proximity to the model CS6P-250P of Canadian solar. To fulfil the voltage requirement of the drive, 12 such cells are connected in series.

Induction motor

Although an additional stage of power conversion is required while using an induction motor with a PV array, it is still very attractive due to its advantageous features. In this analysis, the following dynamic d-q equivalent machine model of a three phase squirrel cage induction motor expressed in Eqs. (2) to (7) is used.

(2)v_{\mathrm{s}dq}^{\mathrm{e}}=R_{\mathrm{s}}{i}_{\mathrm{s}dq}^{\mathrm{e}}+p{\mathit{\psi }}_{\mathrm{s}dq}^{\mathrm{e}}+\mathrm{j}{\omega }_{\mathrm{e}}{\mathit{\psi }}_{sdq}^{\mathrm{e}},

(3){\mathit{v}}_{rdq}^e=\mathbf{0}=R_r{\mathit{i}}_{rdq}^e+p{\mathit{\psi }}_{rdq}^e+j({\omega }_e-{\omega }_r){\mathit{\psi }}_{rdq}^e,

(4){\mathit{\psi }}_{sdq}^e=L_s{\mathit{i}}_{sdq}^e+L_m{\mathit{i}}_{rdq}^e,

(5){\mathit{\psi }}_{rdq}^e=L_r{\mathit{i}}_{rdq}^e+L_m{\mathit{i}}_{sdq}^e,

(6)T_e=P{\displaystyle \frac{L_m}{L_r}}({\mathit{\psi }}_{dr}^e{\mathit{i}}_{qs}^e-{\mathit{\psi }}_{qr}^e{\mathit{i}}_{ds}^e),

(7)p{\omega }_r={\displaystyle \frac{P}{J}}(T_e-T_L)-{\displaystyle \frac{F}{J}}{\omega }_r,

where the suffix ‘e’ signifies that the electrical variables are considered in synchronously rotating reference frame. R_r, L_r, {\mathit{i}}_{rdq}^e, {\mathit{v}}_{rdq}^e, and{\mathit{\psi }}_{rdq}^e are the resistance, the inductance, d-q axis current vectors, d-q axis voltage vectors, and d-q-axis flux vectors of rotor respectively. R_s, L_s, {\mathit{i}}_{sdq}^e, {\mathit{v}}_{sdq}^e, and {\mathit{\psi }}_{sdq}^e are the resistance, the inductance, d-q axis current vectors, d-q axis voltage vectors, and d-q-axis flux vectors of stator respectively. {\omega }_e, {\omega }_r, T_e, and T_L are the angular synchronous speed, the angular rotor speed, the electromagnetic torque, and the load torque respectively. L_m, pJ, F, and Pare the mutual inductance, the differential operator, the moment of inertia, the friction coefficient, and the pole pairs respectively.

Vector control

Vector control techniques are now mature techniques for high performance induction motor control. Ideally, a vector controlled induction motor drive operates like a separately excited DC motor drive. Essentially there are two general methods for vector control: direct and indirect method, as explained in detail in Ref [6]. The indirect vector control technique is more popular in industrial applications. The angular position {\theta }_e for unit vector signals is generated using

(8){\theta }_e={\displaystyle \int {\omega }_{e}dt={\displaystyle \int ({\omega }_r+{\omega }_{sl})dt}},

where {\omega }_{sl} is the angular slip frequency calculated using

(9){\omega }_{sl}={\displaystyle \frac{L_m{R}_r}{{\psi }_r{L}_r}}{i}_{qs}^e.

Power modulator

The power modulator stage for this work consists of a boost converter and an inverter. The duty cycle of the DC-DC boost converter is controlled using a CVC to track the MPP of the PV array. A fixed-gain PI controller is used to generate the corresponding duty cycle for the boost converter with respect to the operating condition of the PV array. The gains of the PI controller are optimized using the trial and error method. In designing the boost converter, the value of the inductor and capacitor must be chosen with outmost care.

The DC output from the converter is given to the three-phase voltage source inverter (VSI) composed of a set of six IGBT switches connected in a bridge configuration. The switches are commutated from the firing pulse generated by a fixed band hysteresis current controller.

FL based MRAS speed observer

The FL technique has been applied in many control applications. In this work, the MRAS scheme consisting of voltage model, current model and FL based adaptation mechanism are used for the rotor speed estimation and adaptation. The block diagram of the FL based MRAS speed observer is depicted in Fig. 3. It is generally opted to have a smaller rule matrix dimension, so a 25 rule-based matrix is formulated for this work. The FL control generally consists of fuzzification, inference engine, and defuzzification. Equations (10) to (13) have been used for generating the rotor flux values for error vector formation.

(10){\psi }_{rd}={\displaystyle \frac{L_r}{L_m}}\left[{\displaystyle \int (v_{sd}-R_s{i}_{sd})dt}-\sigma L_{\mathrm{s}}p{i}_{sd}\right],

(11){\psi }_{rq}={\displaystyle \frac{L_r}{L_m}}\left[{\displaystyle \int (v_{sq}-R_s{i}_{sq})dt}-\sigma L_{s}p{i}_{sq}\right],

(12){\psi }_{rd}^{*}={\displaystyle \int \left({\displaystyle \frac{L_m}{T_r}}{i}_{sd}-{\displaystyle \frac{\mathrm{1}}{T_r}}{\psi }_{rd}-{\omega }_r{\psi }_{rq}\right)}dt,

(13){\psi }_{rq}^{*}={\displaystyle \int \left({\displaystyle \frac{L_m}{T_r}}{i}_{sq}-{\displaystyle \frac{\mathrm{1}}{T_r}}{\psi }_{rq}+{\omega }_r{\psi }_{rd}\right)}dt,

where \sigma =\mathrm{1}-L_m^{\mathrm{2}}/(L_s{L}_r) is a leakage coefficient.

The two inputs chosen for the FLC are speed adjustment signalE_{\omega } and its change which can be given as

(14)E_{\omega }=G_e({\psi }_{rq}{\psi }_{rd}^{*}-{\psi }_{rd}{\psi }_{rq}^{*}),

(15)\mathrm{\Delta }{E}_{\omega }=G_{ce}(E_{\omega }(k)-E_{\omega }(k-\mathrm{1})),

where G_e,G_{ce} are the scaling factors used for the normalization of the inputs to the FLC. Based on the implication of rules summarized in the rule matrix table for FLC (Table 1), the corresponding output {\omega }_{re} is generated. In Table 1, PB= positive big, PS= positive small, ZE= zero, NB= negative big, and NS= negative small. The triangular and trapezoidal membership functions illustrated in Fig. 4 are used in the simulation. The universe of discourse for all variables is from 1 to - 1.

The inference engine used is the Mamdani type with the if-then rule base used. The input/output variables have five membership functions. The output {\omega }_{re} is normalized by scaling factor (G_o). The scaling factors are optimized by the trial and error method.

Simulation results and discussion

In this work, the analysis is conducted with the help of the Simulink model of an indirect vector control drive consisting of a 2 kW, 400 V, 50 Hz induction motor with parameters given in Appendix A. The drive is powered by a PV array (Appendix B) designed with a standard testing condition (STC). As the drive is fed by the PV array, to get maximum power from the PV array, its output voltage is forced at a reference value of 320 V by varying the duty ratio of boost converter. For the speed control loop, the estimated speed from the fuzzy MRAS speed observer is used in the drive. Various operating conditions generally experienced in practical cases are considered for assessment of the performance of the sensorless induction drive with the proposed speed observer. The results obtained and their discussions at considered operating conditions are as follows:

PV array curves

The current-voltage (I-V) curves of the designed PV array are presented in Fig. 5. The I-V curves of different insolation level of 1000, 850, 700 and 550 W/m² and a constant operating temperature of 40°C are displayed in Fig. 5(a). The dependency of the PV array current on the variations in the insolation level is clearly observed from Fig. 5(a), however the variation in array voltage in the narrow band is observed for the same operating condition.

Figure 5(b) shows the I-V curves of the PV array for different operating temperatures of 20 °C, 30 °C, 40 °C and 50 °C with a constant insolation of 1000 W/m². It is evidently seen from Fig. 5(b) that the cell current is minutely affected by the variation in the operating temperature; however the cell voltage is affected accountably.

Drive performance with constant normal operating condition of PV array

With motor under no load condition

The normal operating condition (NOC) of the PV array refers to the insolation level of 1000 W/m² at a temperature of 40°C. In this case, the motor is started and run without any load to track the command speed. To keep the PV array voltage in the region on MPP the duty ratio is controlled using a CVC. The variation in the duty ratio is presented in Fig. 6(a). The PV array output/converter input voltage and the converter output voltage obtained are presented in Fig. 6(b). It is evidently observed from Fig. 6(b) that the converter input voltage is constant at 320 V and when the duty ratio is 0.5 the converter output voltage is approximately 640 V. A disturbance at time t = 2 s can be noticed in the duty cycle, input voltage and output voltage due to the change in the operating condition of the drive. At this time the direction of the drive motion is reversed.

Initially the drive is started and run to track the command speed of 120 rad/s which is suddenly changed to - 120 rad/s for investigating its robustness. Figure 7(a) shows the response of the estimated rotor speed and the command speed. Figure 7(a) clearly indicates that the drive effectively tracks the command speed even during the reversal of speed. Under the above stated operating condition, Fig. 7(b) exhibits the response of motor stator current while Fig. 7(c) the torque response. Transients in the motor current and torque are observed at the reversal of speed. The transients are of high magnitude but vanish in a very short period of time. However, a limiter is recommended to limit the values within the permissible range.

With motor loaded by rated load

Under the NOC stated above, the drive is again started at no load and suddenly loaded with a step rated load at time t = 1 s. As the load is applied, the operating point of the motor shifts from its previous value, forcing the CVC to change the duty cycle for maintaining the PV array voltage at 320 V. The variation in the duty cycle is sketched in Fig. 8(a), while the input and output voltage of the boost converter for stated operating condition are depicted in Fig. 8(b). It is evidently noticed from Fig. 8(b) that the input voltage is maintained constant at 320 V, but the output voltage is decreased to 480 V. The decrease in the output voltage is caused by the increase in the duty cycle of the converter.

The rotor speed response of the induction motor drive is shown in Fig. 9(a) when it is running to trace the command speed of 120 rad/s. A slight deviation in the speed from command speed is observed at the time of application of the rated load. The drive shows the robustness to the load disturbance by rejecting it and again tracking the command speed. Figure 9(b) shows the response of motor torque from which it can be observed that the motor torque is increased at time t = 1 s in order to balance the load torque.

During quickly varying insolation level

To test the drive in difficult operating conditions, the insolation level is varied quickly in a wide range of 500-1000 W/m² as shown in Fig. 10. The operating temperature is kept constant at 40 °C. The drive is loaded with 1/4 of the rated load at time t = 1 s and then run continuously with the same load. As the insolation level is varying, so it is the duty ratio generated by the CVC to keep the PV array output/DC-DC converter input voltage constant at 320 V. The response from the CVC in the form of duty cycle is depicted in Fig. 11(a), while the variation in the output voltage of the boost converter resulted from the variation in duty ratio is depicted in Fig. 11 (b). The response of the rotor speed estimated with the help of the fuzzy MRAS speed observer corresponding to the command speed is shown in Fig. 12(a). A step change in command speed from 120 rad/s to - 120 rad/s is introduced at time t = 2 s. The response of motor torque showing a minute increment with the application of load at time t = 1 s and a transient at time t = 2 s with speed reversal is shown in Fig. 12(b).

Conclusions

In this paper, a simpler FLC for adaptation mechanism of MRAS speed observer has been proposed. The proposed observer is used with a sensorless induction motor drive supplied by a standalone PV array system. The conventional approach for error vector formation in MRAS is adopted. Furthermore, a CVC is designed for effective tracking of the voltage point corresponding to the maximum power region of the PV array. A complete simulation model of the system has been developed in the MATLAB/Simulink environment. The steady-state and dynamical performance of the drive is assessed for different operating conditions. The results show that the proposed FL based MRAS works satisfactorily for sensorless operation of the AC drive system.

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