Fuzzy

based Controller for rectifiers of a Direct-Drive

Permanent-Magnet Wind

Power Generator

P.Kaseem1, M.Ramasekhara Reddy2

PG Scholar, Power and Industrial Drives,

Dept. of EEE, JNTUA college of Engg., Ananthapuramu, AndhraPradesh, India1

Assistant Professor, Dept. of EEE, JNTUA College of Engg.,

Ananthapuramu, Andhra Pradesh, India2

Abstract

This

paper proposes a detailed control strategy for multiple parallel connected

converter units integrated with wind turbine driving PMSG. A model of multiple

rectifiers in parallel with common dc link and zero sequence current dynamics

are derived and analyzed. The structure of parallel back to back pulse width

modulation converters are adopted for multi megawatt high power generation

system. The fuzzy based controller is developed to restrain circulating currents

flows between the power modules caused by power device discrepancy and asynchronous

operation of the parallel units. The control driving signals are generated by individual

current control and produced by carrier phase shifting synchronously. The effectiveness of the proposed control

strategy is verified through MATLAB simulations.

KEYWORDS: PMSG, Zero sequence

current, parallel operating controllers, Fuzzy logic controller

Introduction

Wind

is one of the most abundant renewable sources of energy in nature. Wind energy

can be harnessed by a wind energy conversion system (WECS) 4-5 composed of

a wind turbine, an electric generator, a power electronic converter and the

corresponding control system. Based on the types of components used, different

WECS structures can be realized to convert the wind energy at varying wind

speeds to electric power at the grid frequency. The most advanced generator

type is perhaps the permanent magnet synchronous generator (PMSG). This machine

offers, compared at the same power level and machine size, the best efficiency

among all types of machines with high robustness and easy maintenance due to

slip ring?less

and exciter?less

features. The inherent benefit of permanent magnet which supplies rotor flux in

synchronous machines without excitation loss supports the wind power generation

development. This thus results in the increasing use of PMSG 3.

The

rectifiers in parallel connected to the PMSG have the advantage of higher

reliability, high efficiency, and lower grid side harmonics The parallel

configurations 2–9 can be classified as parallel voltage source converters(VSC)

with separate direct voltage links and parallel VS converters(VSC) with a common direct voltage link. For

multiple converters in parallel with a common dc bus, when discontinuous Space-Vector

Modulation (SVM)7 is used, due to different switching characteristics and

impedance discrepancy of individual converter, even if synchronized control of

each converter is applied, the switching status of the converters in parallel

will differ from each other. This creates currents that flow among power

switching devices and will flow in a circular loop between the power converters

and not affect the net current in either the generator or the power grid. The

circulating currents load switching devices and other components heavily,

distort waveforms, and might damage converters. Further, these currents may

cause a direct error in the measurement of ground fault currents of that loop,

thereby making fault detection more difficult. Large common mode inductors are

required to limit the amount of circulating currents between the converters.

The particular discontinuous SVM modulation scheme was proposed without using

zero vectors. However, since it was not attempted to reject zero sequence

disturbance, any mismatches between the parallel converters can still cause

zero sequence current even without using zero vectors. New modulation schemes

8 introduce a new control variable to adjust the duration of zero vectors

instead of eliminating the zero vectors. This method can effectively inhibit

the zero sequence circulation.

As

shown in Fig.1, The structure of parallel back to back PWM converters is adopted

for multi megawatt high-power

generation system

Fig.1.

High-power direct-drive variable-speed PMSG wind generator system connected to

the power grid.

Fig.2.

Multiple three-phase PWM rectifiers with parallel connection.

This

model provides separate control of the generator side converter and grid-side

converter. The interconnection of the power converters in this manner can

accommodate not only multiphase but also three phase generators for WTs. In

this paper, zero-sequence circulation mathematical model is derived and

analyzed. An improved space vector SVPWM parallel control strategy is presented

to repress the zero-sequence circulating current. Independent current

regulation is implemented for each branch power module.

II. CIRCULATING CURRENT CONTROLLER

The

term circulating current has been generally used to depict streams that stream

among the converter units in parallel 1. In rehearse; a circling current is

thought to be a present that goes amiss from the sought burden current level

just as shared by the paralleled units.

A.

Expression of the Circulating Current at Generator Side

Fig.

2 shows n rectifiers in parallel; all the active switches are assumed to be ideal

switches, and the equivalent series resistances of inductors are also

considered.

Fig.

3. Circulating current among multi converters.

Applying

Kirchhoff’s voltage law, the following equations can be obtained corresponding to

a-phase, respectively:

(1)

is the voltage between the negative end of

and neutral point. Where Zj =

d/dt + Rj,j?{1, 2, . . . , n}, the

general phase current expression for any individual branch unit in parallel

connection.

(2)

Where

k ?{a, b, c};

is the k-phase line current of the jth

converter,

is the source voltage. The circulating

currents for n paralleled three-phase converters in Fig. 3 can be

defined as follows. Considering the circulating current for the first

branch unit B1 as displayed in the Fig.3,

denotes the circulating current between

B1 and B2.

denotes the circulating current between B1

and B3. Similarly, the circulating current between B1 and Bn

is denoted as CCk1n. Therefore, the k-phase

circulating current of the first converter CCk1 consists of n circulating-current

components as follows:

(3)

The

expression for the k-phase circulating current of the jth

converter can be derived 9 as follows

(4)

Where

i ? j and

and

are the k-phase line current of the jth and

ith converter respectively. The general expression of the circling current of

the jth converter is determined as

(5) It is shows that both the output dc voltage

and the three ac phase voltages contribute to the generation of the circulating

currents. The impedance of the kth converter in a particular circulating

path also influences the magnitude of its circulating current.

B. Circulating-Current Model of Three-Phase

Parallel Converters in abc Coordinate

A

phase-leg-averaged model for a single two-level three phase rectifier is shown

in Fig. 4 8.

Fig.

4. Phase-leg-averaged model of a single two-level three-phase rectifier.

Applying

Kirchhoff’s voltage law and the current law to node n ( at

) results in a set of differential

and algebraic equations

(6)

The

system equation can be written as

(7)

Applying

Kirchhoff’s voltage law to loops that are formed among the converters results

in 3n ? 1 algebraic equations

(8)

Where

k ? (a, b, c) and Rs and Ls are the equivalent

resistance and inductance of the PMSG, respectively

Applying

Kirchhoff’s current law to node n (at

) results in one algebraic equation

(9)

Differentiating

(9), we get,

(10)

Assuming

=

= · · · = Ln and

=

= · · · =

Further

arranges the set of equations as the state-space form

(11)

Where

T

Is the State vector

U=

,

,

,

,

,

, . . . . ,

,

,

T

I

is the input vector. Y is the output vector. The state matrix is

A=

And

the input matrix is

B=

The

output matrix C is the identity matrix with the dimensions of 3n × 3n

T

=

I is the identity matrix

with the dimensions of 3× 3. The transfer function matrix is calculated

in the Laplace domain based on the state-space model.

G(s)

= C(sI-A)-1B

=

(12)

Where

the first terms represent the circulating-current part and the second terms

represent the currents that flow from the PMSG to the converters

C.

Model of Three-Phase Parallel Converters in d?q?0 Rotating Coordinate

Assuming

that the voltage udc and current are continuous and with small ripples,

the phase voltage expression is ukj = dkjudc. Compared with the

inductance, the resistance of each power module is small. Neglecting

resistance, the state-space equations for the two converters in parallel

connection are

(13)

(14)

By

transforming (13) and (14) from the stationary reference frame into the

synchronous d?q?0 rotating reference frame 6

(15)

(16)

(17)

Where

? is the ac line frequency. Ud?uq?u0 is the d?q?0 axis

components of the ac voltage in the d?q?0 reference frame, respectively.

id1?iq1?i01 and id2?iq2?i02 are the d?q?0

components for the first converter and second converter, respectively. dd1?dq1?d01

and dd2?dq2?d02 are the d?q?0 components of the

duty cycles for the first converter and second converter, respectively.

u0 = usa + usb + usc and

d0 = da +db + dc. The equivalent circuit of

three-phase parallel rectifiers in the d?q?0 rotating reference frame is

shown in Fig. 5. It is noted that a zero-sequence current occurs in the 0-axis

and plays a significant role in the paralleled multiple rectifiers.

D. Zero-Sequence Current

Control Scheme

Fig. 6. Shows the designed control scheme for zero

sequence dynamics developed according to the equivalent circuits of three phase

parallel Converters in d-q-o rotating reference

frame.

.

Fig.

5. Equivalent circuit of three-phase parallel rectifiers in d?q?0

rotating Reference frame.

Fig.6.

Zero-sequence current control scheme.

A modified SVPWM control strategy is proposed

for parallel converters. Individual branch unit uses a separate current

regulator. The controlling algorithm can be summarized as follows: First, the

zero sequence current is suppressed by using a fuzzy controller on the 0-axis

which produces the output zero-sequence voltage

. The reference voltage vectors

and

are transformed

into the stator coordinate by coordinate transformation, according to the

sector in which the reference vector stays by using SVPWM modulation, and duty

cycles are calculated. Second, the zero sequence output voltage is normalized

and superposed with modulation duty cycles. Finally, the resulting duty cycle

will be compared with the modulating carrier wave, and the switching function

is obtained.

From

the Fig. 5, the two parallel rectifiers contain a zero sequence current path in

d?q?0 reference frame due to the discrepancy of 0-axis duty cycle components. From

(15) and (16), The dynamics of zero-sequence current

are expressed The second term on the right can

be expected as a disturbance.

The

fuzzy controller can be cascaded with the plant to achieve closed-loop current

regulation. The bandwidth of the

control can be designed to be high, and a

strong current regulation that suppresses the zero sequence current can be

achieved. For n number of rectifiers in parallel, the sum of zero

sequence currents is equal to zero, i.e.,

+

+ · · · +

= 0. Due to the

interaction among the n currents, the number of independent

zero-sequence currents is n ? 1. The number of zero sequence current

controllers should be n ? 1 for n parallel rectifiers.

III. FUZZY LOGIC CONTROLLER

Fuzzy

logic controller, approaching the human reasoning that makes use of the

tolerance, uncertainty, imprecision and fuzziness in the decision making

process and manage to propose a very satisfactory operation, without the need

of a detailed mathematical model of the system, just by integrating the expert’s

knowledge into fuzzy rules. In addition, it has essential abilities to deal

with noisy date or inaccurate, thus it has able to develop control capability

even to those operating conditions where linear control techniques fails i.e.,

large parameters variations.

Rule

Base: It consists of a number of If-Then rules. Then side of rules is called

the consequence and If side is called antecedent. These rules are very similar

to the human thoughts and then the computer uses the linguistic variables. Rule

base of FLC is listed in table 1

TABLE 1.MEMBRSHIP FUNCTI0N TABLE

FUZZY RULES

E(n)

NB

NS

ZE

PS

PB

NB

NS

ZE

PS

PB

ZE

PB

PB

PS

PS

PS

PS

PS

ZE

ZE

PS

ZE

ZE

ZE

NS

ZE

ZE

NS

NS

NS

NS

NS

NB

NB

ZE

IV.

CONTROL OF PMSG WITH MULTIPLE RECTIFIERS

In

wind turbine PMSG systems, three system variables need to be strictly

controlled 6: (1) the optimal power generated by the PMSG at different wind

speed levels; (2) the active and reactive power injected into the grid; (3) the

DC bus voltage of the back to back converter. The proposed system contains a

direct-drive wind turbine PMSG fed by a back-to-back converter. The use of

parallel converters compared with a solution with only one converter is higher

reliability, higher efficiency, and the possibility of extremely low grid

harmonics.

In

parallel connection, one converter unit functions as a master and the others

function as slaves. A serial communication bus is arranged between the

converter units in which each unit has its own modulation cycle counter and it

is synchronized with each other on the basis of serial communication messages.

In this manner, the modulation counters operate as simultaneously as possible.

Fig.

7. Overall structure for the control of parallel multi converters on the

machine side

Carrier

phase-shifting modulation technique 10 has a great advantage for power

converters in parallel. When a module fails to operate, the master controller

just changes the corresponding carrier phase angle and limits the capacity of

the system, other modules can continue to work, standby unit can also be

activated, and full-power operation can still be achieved. The PMSG is

controlled by two 750-kW generator-side converters connected in parallel in a

rotor rotating d?q axis frame, with the d-axis oriented along the

rotor-flux vector position. In this way, the d-axis current is held to

zero to obtain maximum electromagnetic torque with minimum current. The optimum

active power setting or torque reference can be calculated according to maximum

power point tracking strategies. The two sets of PWM driving signals are

generated by using separate current regulators and produced by

carrier

phase-shifting synchronously. The rotor position is fed by the rotor position

observer without any position sensor. Each converter module is independent of

each other identifying the rotor flux position. The currents of each module are

balanced and synchronized with respect to each other producing the optimal

total generator torque. This arrangement will reduce the requirements for large

impedance needed to equalize the current sharing and allow increasing the power

handling capability for a converter with parallel connection. The zero-sequence

current fuzzy controllers have been integrated with the control of parallel

converters.

V. Simulation Results

Fig8.Ten

kilowatt generator side circulating current with PI controller

Fig.9.

Ten kilowatt grid side circulating current with PI controller

Fig.10.Generator

currents of individual

converter when generator operated at 1.5KW with PI controller.

Fig.11.

Three phase Generator currents of individual converter when generator operated

at 1.5KW with PI controller.

Fig.12.Ten

kilowatt generator side circulating current with Fuzzy controller

Fig.13.

Ten kilowatt grid side circulating current with Fuzzy controller

Fig.14.

Three phase Generator currents of individual converter when generator operated

at 1.5KW with Fuzzy controller.

Fig.15.Generator

currents of individual

converter when generator operated at 1.5KW with Fuzzy controller

OBSERVATION TABLE

Circulating

currents

Total

harmonic distortion (THD)

With

PI controller

Fuzzy

Logic Controller

Generator(10KW)side

circulating current

29.20%

17.52%

Grid

side circulating current

33.14%

28.16%

Generator(1.5MW)

currents of individual converter

35.86%

25.26%

Three

Phase Generator(1.5MW) currents of individual converter

34.13%

20.20%

V. CONCLUSION

This

paper has described the control schemes of a permanent magnet wind power

generator connected to parallel converters with common dc link. A dynamic model

of zero-sequence currents has been derived and analyzed for a number of n three-phase

PWM rectifiers in parallel connection.

The

zero sequence currents are effectively controlled and suppressed by using the

model technique SVPWM with fuzzy logic controller.

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