Fuzzy Algorithm for Supervisory Voltage / Frequency Control of a Self Excited Induction Generator

Many publications in the field of SEIG have been dealt with solutions to a range of problems (e.g. enhancing performance, loading, interfacing with the grid, etc). El Sousy et al [1] discuss a method for controlling a 3 phase induction generator using indirect field orientation control, while Mashaly at al [2] introduce an FLC controller for a wind energy utilization scheme. We have found no studies concentrating on a wind energy scheme system for supplying an isolated load. The primary advantages of SEIG are less maintenance costs, better transient performance, no need for dc power supply for field excitation, brushless construction (squirrel-cage rotor), etc. In addition, induction generators have been widely employed to operate as wind-turbine generators and small hydroelectric generators for isolated power systems [3, 4]. Induction generators can be connected to large power systems, in order to inject electric power, when the rotor speed of the induction generator is greater than the synchronous speed of the air-gap-revolving field. In this paper the dynamic performance is studied for SEIG driven by WECS to feed an isolated load. The d-q axes equivalent circuit model based on different reference frames extracted from fundamental machine theory can be employed to analyze the response of the machine transient in dynamic performance [3,4]. The voltage controller, for SEIG, is conducted to adapt the terminal voltage, via a semiconductor switching system. The semiconductor switch regulates the duty cycle, which adjusts the value of the capacitor bank connected to the SEIG [5, 6]. The SEIG is equipped with a frequency controller to regulate the mechanical input power. In addition, the stator frequency is regulated. This is achieved by adjusting the pitch angle of the wind turbine. In this paper, the integral gain (Ki) of the PI controller is supervised using the FLC to enhance the overall dynamics response. The simulation results of the proposed technique are compared with the results obtained for the PI with fixed and variable Ki.


Introduction
Many publications in the field of SEIG have been dealt with solutions to a range of problems (e.g.enhancing performance, loading, interfacing with the grid, etc).El Sousy et al [1] discuss a method for controlling a 3 phase induction generator using indirect field orientation control, while Mashaly at al [2] introduce an FLC controller for a wind energy utilization scheme.We have found no studies concentrating on a wind energy scheme system for supplying an isolated load.The primary advantages of SEIG are less maintenance costs, better transient performance, no need for dc power supply for field excitation, brushless construction (squirrel-cage rotor), etc.In addition, induction generators have been widely employed to operate as wind-turbine generators and small hydroelectric generators for isolated power systems [3,4].
Induction generators can be connected to large power systems, in order to inject electric power, when the rotor speed of the induction generator is greater than the synchronous speed of the air-gap-revolving field.In this paper the dynamic performance is studied for SEIG driven by WECS to feed an isolated load.The d-q axes equivalent circuit model based on different reference frames extracted from fundamental machine theory can be employed to analyze the response of the machine transient in dynamic performance [3,4].The voltage controller, for SEIG, is conducted to adapt the terminal voltage, via a semiconductor switching system.The semiconductor switch regulates the duty cycle, which adjusts the value of the capacitor bank connected to the SEIG [5,6].The SEIG is equipped with a frequency controller to regulate the mechanical input power.In addition, the stator frequency is regulated.This is achieved by adjusting the pitch angle of the wind turbine.In this paper, the integral gain (K i ) of the PI controller is supervised using the FLC to enhance the overall dynamics response.The simulation results of the proposed technique are compared with the results obtained for the PI with fixed and variable K i .

The system under study
Fig. 1 shows the block diagram for the study system, which consists of SEIGs driven by WECS connected to an isolated Fig. 1: System under study load.Two control loops for terminal voltage and pitch angle using FLC to tune K i of the PI controller are shown in the same figure.The mathematical model of SEIG driven by WECS is simulated using the MATLAB/SIMULINK package to solve the differential equations.Meanwhile, two controllers have been developed for this system.The first is the voltage controller to adjust the terminal voltage at the rated value.This is done by varying the switching capacitor bank, for changing the duty cycle, to adjust the self excitation.The second controller is the frequency controller to regulate the input power to the generator and thus to keep the stator frequency constant.This is achieved by changing the value of the pitch angle for the blade of the wind turbine.First, the system under study is tested when equipped with a PI controller for both voltage and frequency controllers at different fixed values K I .Then the technique is developed to drive the PI controller by a variable K I to enhance the dynamic performance of the SEIG.K I is then tuned by using two different algorithms.
The simulation is carried out when the PI controller is driven by variable K I using a linear function, with limitors, between K I and voltage error for voltage control.The simulation also includes variable K I based on the mechanical power error for the frequency controller.Meanwhile, variable K I has lower and upper limits.Then, the simulation is conducted when the PI controller is driven by a variable K I through FLC technique.The simulation results depict the variation of the different variables of the system under study, such as terminal voltage, load current, frequency, duty cycles of the switching capacitor bank, variable K I in voltage controller K IV and variable K I in frequency controller K IF .

Electrical equation of the SEIG
The stator and rotor voltage equations using the Krause transformation [3,4], based on a stationary reference frame, are given in the appendix [7].

Mechanical equations of the WECS
The mechanical equations relating the power coefficient of the wind turbine, the tip speed ratio (m) and the pitch angle (b) are given in [7,8,9].The analysis of an SEIG in this research is performed taking the following assumptions into account [3]: l All parameters of the machine can be considered constant except X m .
l Per-unit values of the stator and rotor leakage reactance are equal.
l Core loss in the excitation branch is neglected.l Space and time harmonic effects are ignored.

Switching
Switching of capacitors has been discarded in the past because of the practical difficulties involved [5,6], i.e. the occurrence of voltage and current transients.It has been argued, and justly so, that current 'spikes', for example, would inevitably exceed the maximum current rating as well as the (di/dt) value of a particular semiconductor switch.The only way out of this dilemma would be to design the semiconductor switch to withstand the transient value at the switching instant.
The equivalent circuit in Fig. 2 is added to explain this situation of the switching capacitor bank due to the duty cycle.The details of this circuit are given in [6].For the circuit of Fig. 2, the switches are operated in anti-phase, i.e. the switching function fs2 which controls switch S 2 is the inverse function of f s1 which controls switch S 1 .In other words, switch S 2 is closed during the time when switch S 1 is open, and vice versa.This means that S 1 and S 2 of branch 1 and 2 are operated in such a manner that one switch is closed while the other is open.

Voltage control
As shown in Fig. 1, the input to the controllers is the voltage error, while the output of the controllers is used to execute the duty cycle (l).The value of calculated l is used as an input to the semiconductor switches to change the value of the capacitor bank according to the need for the effective value of the excitation.Accordingly, the terminal voltage is controlled by adjusting the self-excitation through automatic switching of the capacitor bank.

Frequency control
Frequency control is applied to the system by adjusting the pitch angle of the wind turbine blades.This is used to keep the SEIG operating at a constant stator frequency and to counteract the speed disturbance effect.The pitch angle is a function of the power coefficient C p of the wind turbine WECS.The value of C p is calculated using the pitch angle value according to the equation mentioned in [7,8,9].Consequently, the best adjustment for the value of the pitch angle improves the mechanical power regulation, which, in turn, achieves a better adaptation for the frequency of the overall system.Accordingly, the frequency control regulates the mechanical power of the wind turbine.Two different types of controller strategies have been conducted.First, the conventional PI controller with fixed and variable gains is applied.Second, FLC is applied to adjust the value of K I for both frequency and voltage controllers.

Conventional PI controller
The simulation program is carried out for different values of K I while the value of the proportional gain is kept constant, as shown in Fig. 3.It is observed from the simulation results that the value of the percentage overshoot (P.O.S), rising time and settling time change as K I is changed.Then the technique of having variable KI depending on the voltage error, for voltage control, is introduced to obtain the advantage of high and low value of the integral gain of voltage loop K IV .

PI-Controller with variable gain
A program has been developed to compute the value of the variable integral gain K IV , using the following rule: if (e V <e Vmin ), where, e V = voltage error, e Vmin = minimum value of the voltage error, e Vmax = maximum value of the voltage error, K IVmin = minimum value of K IV , K IVmax = maximum value of K IV , C is a constant and M is the slope value.Fig. 4 shows the rule for calculating K IV of K IV against the terminal voltage error e V .The value of e Vmin and e Vmax is obtained by trail and error to give the best dynamic performance.
The proportional gains (K PV and K PF ) are also kept constant for the voltage and frequency controllers, respectively.Various characteristics are tested to study the effect of changing the value of (K IV ) to update the voltage control.The simulation results cover the starting period and the period when the system is subjected to a sudden increase in the load, at instant 8 sec.Fig. 3 shows the simulation results for the variable K IV .Figs. 5, 6 show the effect of variable voltage integral gain K IV and frequency K IF controllers versus time, respectively.

A Fuzzy Logic Controller (FLC)
To design the fuzzy logic controller, FLC, the control engineer must gather information on how the artificial decision maker should act in the closed-loop system, and this would be done from the knowledge base [10].The fuzzy system is constructed from input fuzzy sets, fuzzy rules and output fuzzy sets, based on the prior knowledge base of the system.Fig. 7 shows the basic construction of the FLC.There are rules to govern and execute the relations between inputs and outputs for the system.Every input and output parameter has a membership function which could be introduced between the limits of these parameters through a universe of discourse.The better the adaptation of the fuzzy set parameters is, the better the tuning of the fuzzy output is conducted.The proposed FLC is used to compute and adapt the variable integral gain K I of PI controller.

Global input and output variables
For voltage control the fuzzy input vector consists of two variables; the terminal voltage deviation e V , and the change of the terminal voltage deviation De V .Five linguistic variables are used for each of the input variables, as shown in Fig. 8a and Fig. 8b, respectively.The output variable fuzzy set is shown in Fig. 8c and Fig. 8d, while shows the fuzzy surface.For frequency control, the fuzzy input vector also consists of two variables; the mechanical power deviation e F , and the change of the mechanical power deviation De F .Five linguistic variables are used for each of the input variables, as shown in Fig. 9a and Fig. 9b, respectively.The output variable fuzzy set is shown in Fig. 9c, and Fig. 9d shows the fuzzy surface.In Figs. 8,   and output variables, it is required to develop the set of rules, the so-called Look-up table, which defines the relation between the input variables, e V , e F , De V and De F and the output variable of the fuzzy logic controller.The output from the fuzzy controller is the integral gain value of K I used in the PI controller.The look-up table is given in Table 1.

The defuzzification method
The Minimum of maximum method has been used to find the output fuzzy rules representing a polyhedron map, as shown in Fig. 10.First, the minimum membership grade, which is calculated from the minimum value for the intersection of the two input variables (x 1 and x 2 ) with the related fuzzy set in that rule.This minimum membership grade is calculated to rescale the output rule, then the maximum is taken, as shown in Fig. 11.Finally, the centroid or center of area has been used to compute the fuzzy output, which represents the defuzzification stage, as follows: More details about the variables of the above equation are given in [10].

Dynamic performance due to sudden load variation
The FLC utilizes the terminal voltage error (e V ) and its rate of change (De V ) as input variables to represent the voltage control.The output of FLC is used to tune up K I of the PI controller.Another FLC is used to regulate the mechanical power via the blade angle adaptation of the wind turbine.Figs.8a, b, c and d   ).The output of FLC is KIV, which changes between (5e-003 and 5.5e-003).Table 1 shows the lookup table of fuzzy set rules for voltage control.The same technique is applied for the frequency controller, where the two inputs for FLC are the mechanical power error (e F ), which varies between (-1 and 1) and its change (De F ), which varies between (-0.1 and 0.1).The output of FLC is K IF , which changes between (4e-006 and 5e-006).The output of the PI-FLC in the frequency controller adapts the pitch angle value to enhance the stator frequency.14 shows the stator frequency.The system is equipped with a conventional controller having fixed and variable integral gain and the FLC algorithm.The proposed FLC is used to adapt K I to give a better dynamic performance for the overall system, as shown in Figs.11, 12, 13, regarding P.O.S and settling time compared with fixed PI and PI with variable K I for different loads.Figs. 15, 16 depict the simulation results for the load current and controller's duty cycle.The same conclusion is achieved as explained for Fig. 11.

Dynamic performance due to sudden wind speed variation
There are different simulation results when the overall system is subjected to a suddenly disturbance the wind speed from 7 m/s to 15 m/s in Figs.17, 18 show the simulation results of the wind speed variation and the stator frequency, respectively.The simulation given in Fig. 18

Conclusion
This paper presents an application of FLC to a self-excited induction generator driven by wind energy.The proposed FLC is applied to frequency and voltage controls of the system to enhance its dynamic performance.FLC is used to regulate the duty cycle of the switched capacitor bank to adjust the ter-minal voltage of the induction generator.FLC is also applied to regulate the blade angle of the wind energy turbine to control the stator frequency of the overall system.The simulation results show better dynamic performance of the overall system using the FLC controller than for the variable PI type.Another simulation was conducted to study the dynamic performance to this system with a suddenly disturbance for wind speed variation.A comparison was conducted for the stator frequency in dynamic performance with variable and fixed K I .
where j ds is the stator flux linkage (Wb) at direct axis, i dr the rotor current (A) at direct axis, i ds the stator current (A) at direct axis.j qs ls qs m qr qs where j qs is the stator flux linkage at quadrant axis, i qr the rotor current at quadrant axis, i qs the stator current at the quadrant axis.j dr lr dr m dr ds j qr lr qr m qr qs where j dr , j qr is the rotor flux linkage at the direct and quadrant axis, respectively, w b the base speed.

Fig. 3 :Fig. 4 :
Fig. 3: Dynamic response of the terminal voltage with different values of integral gain for voltage control

Fig. 9 :
Fig. 9: a) membership function of mech.power error, b) membership function of change on mech.power error, c) membership function of variable K IF , d) fuzzy surface Fig. 10: Schematic diagram of the defuzzification method using the center of area Fig. 14: Dynamic response of stator frequency for PI with and without FLC

Acta
Fig. 16: Dynamic response of duty cycle for PI with and without FLC Lds is the load current in the direct axis, i Lqs the load current in quadrant axis, R L the load resistance (W), L L the load inductance (H). the effective capacitor bank value (mF), C max is the maximum capacitor value, C min is the minimum capacitor value, s = (C max /Cmin), and l is the duty cycle value.the mechanical speed (rad/sec), P m the mechanical power (kW), T m the mechanical torque (Nm), n the rotor revolution per minute (rpm), C p the power coefficient of the wind turbine, b the blade pitch angle ( °), m the tip speed ratio, v w the wind speed (m/s), R the rotor radius of the wind turbine (m), D the rotor diameter of the wind turbine (m), B a the friction factor, T e the electrical torque (Nm), p = 3.14, r air density (kg/m 9 linguistic variables have been used for the input variables, P for Positive, N for Negative, AV for Average, B for Big and S for Small.For example, PB is Positive Big and NS is Negative Small, etc.After constructing the fuzzy sets for input http://ctn.cvut.cz/ap/Acta Polytechnica Vol.46 No. 6/2006

Table 1 :
depict the fuzzy sets of e V , De V , K IV and the Look up table of fuzzy set rules for voltage control