Optimization & Control of PMSM Based Wind Energy Using...

International Journal of Science, Engineering and Technology Research (IJSETR), Volume 4, Issue 5, May 2015

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ISSN: 2278 – 7798 All Rights Reserved © 2015 IJSETR

Abstract— In recent years, the increasing concerns to the

environmental issues and the limited availability of conventional

fossil fuels lead to rapid research and development for more

sustainable and alternative electrical sources. Wind energy, as

one of the most prominent renewable energy sources, is gaining

increasing significance throughout the world.

In this paper, a design fuzzy logic controller for a variable

speed permanent magnet wind generator connected to a grid

system is proposed. A new current control method of grid side

conversion is developed by integrating the fuzzy controller, in

which both active and reactive power, delivered to a power grid

system, is controlled effectively. The fuzzy logic controller is

designed to adjust the gain parameters of the PI controllers

under any operating conditions, so that the dynamic stability is

enhanced. The simulations have been performed using Matlab.

Simulation results prove the excellent performance of fuzzy

control unit as improving power quality and stability of wind

turbine.

Index Terms— PMSM; Fuzzy Logic Controller; PI

Controller; Wind Energy; Renewable Energy.

I. INTRODUCTION

The global demand for electrical energy and fossil fuel is

increasing at breath taking pace worldwide. Whilst demand is

increasing, the days of overcapacity in electricity production

are coming to an end. Many older power plants will soon

reach to the end of their working lives. About half of the

estimated capacity will be required to replace the existing

aging power plants. The world may have to face a severe

energy crisis in future in the absence of suitable precautionary

measures, especially when there is already shortage of the

fossil fuels widely used for power generation. The fossil fuels

provides about three quarters of the world’s energy. The

burning of fossil fuels produces lot of carbon dioxide, one of

the main greenhouse gases, which is also considered as the

main culprit for global warming and other environmental

hazards like melting of the polar ice caps, flooding of

low-lying land, storms, droughts and violent changes in

weather patterns. Considering all these problems associated

with fossil fuels, there is sudden need of the more efficient

ways the world produces and consumes energy. Alongside the

more efficient generation and use of energy, renewable

sources of energy offer the great potential for deep cuts in

carbon dioxide emissions. Despite the global abundance of

renewable energy resources, renewable energy generation

capacity represents merely 3% of the world’s installed power

capacity. Since the past decade, however, there has been a

renewed interest in many countries on renewable energy for

power generation.

The wind power generation is rapidly becoming competitive

with conventional fossil fuel sources and already today is at

par with new coal or gas fired power stations. The wind

turbine design objectives have changed over the past decade

from being convention-driven to being optimized driven

within the operating regime and market environment. The

wind turbines are growing in size, designs are progressing

from fixed speed, stall-controlled having drive trains with

gearboxes, to become pitch controlled, variable speed and

with or without gearboxes. The advancement in power

electronics devices further supports the trend toward variable

speed turbines. Today, the wind turbines in the market have a

variety of innovative concepts, with proven technology for

both generators and power electronics interface. However, the

increasing penetration of large wind farms into electrical

power systems also poses different kind of challenges due to

their intermittent nature. This inspires the designers to

develop both custom generators and power electronics

devices with sophisticated modern control system strategies.

Recently, variable-speed permanent magnet synchronous

generator (PMSG) based wind energy systems are becoming

more attractive in comparison to fixed-speed wind energy

system. In the variable-speed generation system, the wind

turbine can be operated at maximum power operating points

over a wide speed range by adjusting the shaft speed

optimally. Moreover, the use of Permanent Magnet reduces

size, and weight of overall wind energy system, as there is no

need of field winding and its excitation system. The absence

of rotor winding also reduces heat dissipation in the rotor and

hence improves the overall efficiency. This kind of

configuration also find special favour for off-shore wind

application, where the geared doubly fed induction generator

requires regular maintenance due to tearing-wearing in

brushes and gear box.

To perform maximum power point tracking at different wind

speeds, the variable speed operation of PMSG is required. For

the variable speed operation of PMSG, generally vector

control is preferred as it allows the independent torque and

field control just like a simple DC motor control. The vector

control of PMSG essentially requires the rotor position and

speed information. For this purpose, usually shaft mounted

speed and position sensors are used, resulting into additional

cost and complexity of the system. In order to eliminate the

sensors and their associated problems, a fuzzy logic controller

(FLC) is proposed for rotor position and speed estimation

over wide range of speed operation.

In the proposed work a PMSG based Wind energy system is

modelled for grid connected system. In grid connected

system, the fault ride through capability of wind energy

Optimization & Control of PMSM Based Wind

Energy Using PI and Fuzzy Logic Controller

Munendra Pratap Singh, Er. Vinay Kumar Tripathi


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system is demonstrated under grid voltage sag/swell

conditions.

Another objective is to develop an advance controller for grid

side inverter. Since the inverter works under highly

fluctuating operating conditions, it is not possible to set the

optimal value of gains for the conventional

proportional-integral (PI) regulator. This may lead to false

operation of inverter.

The main objective is to achieve smooth operation of grid side

inverter, where the conventional PI controller may fail due to

the rapid change in the dynamics of the overall system. The

combined capability of PI-fuzzy controller in handling the

uncertainties and learning from the processes is proved to be

advantageous while controlling the inverter under fluctuating

operating conditions.

II. MODEL OF WIND TURBINE

The static characteristic of the turbine (output as a function of

wind speed) can be described by the relationship between the

total power and mechanical energy of the wind:

where ρ is the air density (1,225 kg/m3), Rturbine is then rotor

radius (m), vwind is the wind speed (m/s). It is impossible to

extract all the kinetic energy of wind, so it extracts a fraction

of the power of wind as shown in (2) as the power coefficient

Cp.

Pm is the mechanical power of the wind (Nm/s). The

maximum power coefficient CpM is 0.59. This coefficient is

also known as Betz limit. It can be expressed in terms of

reduced velocity λ and angle of light θ: Cp = Cp (λ, θ).

If W is the rotor speed, the reduced speed λ is defined:

Assuming a constant wind speed vwind, the reduced speed λ

varies proportionally to the rotor speed [10]. The maximum

value of Cp is generally obtained for values of λ around 8 to 9

(when the tip of the movements of blade is 8 to 9 times faster

than the wind). On modern wind turbines, it is possible to

adjust the angle of the blades through a control mechanism

[11]. If Cp-λ curve is known for a specific wind with a radius

of turbine rotor Rturbine, it is easy to construct the curve of Cp as

a function of rotational speed Ω for a wind speed vwind. The

output torque of the turbine is calculated :

If the speed ratio λ is maintained at its optimal value λopt, the

power coefficient is at its maximum value CpM=Cp(λopt), the

maximum power of the wind turbine will be:

On the other hand, the speed ratio assumed to be maintained at

the optimum value, we obtain the optimum speed rotor:

Thus, the wind power turbine characteristics is shown in

figure 1.

Figure 1: Wind Turbine Power Characteristics

In this paper, a wind turbine is simulated by using a look-up

table, where inputs are wind speed and rotor speed and output

is the mechanical torque.

III. MODELLING OF PMSM

The mathematical model for the vector control of the PMSM

can be derived from its dynamic d-q model which can be

obtained from well-known model of the induction machine

with the equation of damper winding and field current

dynamics removed. The synchronously rotating rotor

reference frame is chosen so the stator winding quantities are

transformed to the synchronously rotating reference frame

that is revolving at rotor speed.

The model of PMSM without damper winding has been

developed on rotor reference frame using the following

assumptions:

1) Saturation is neglected.

2) The induced EMF is sinusoidal.

3) Core losses are negligible.

4) There are no field current dynamics.

It is also be assumed that rotor flux is constant at a given

operating point and concentrated along the d axis while there

is zero flux along the q axis, an assumption similarly made in

the derivation of indirect vector controlled induction motor

drives [15]. The rotor reference frame is chosen because the

position of the rotor magnets determine independently of the

stator voltages and currents, the instantaneous induced emf

and subsequently the stator currents and torque of the

machine. When rotor references frame are considered, it

means the equivalent q and d axis stator windings are

transformed to the reference frames that are revolving at rotor

speed. The consequences is that there is zero speed

differential between the rotor and stator magnetic fields and

the stator q and d axis windings have a fixed phase

relationship with the rotor magnet axis which is the d axis in

the modelling. The stator equations of the induction machine


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in the rotor reference frames using flux linkages are taken to

derive the model of the PMSM as shown in Fig.2:

Fig.2: PM machine synchronously rotating d-q reference

frame.

So an PM machine is described by the following set of general

equations:

Voltage equations are given by:

Vd = Rsid – ωrλq + (1)

Vq = Rsiq – ωrλd + (2)

Flux linkages are given by

λq = Lqiq (3)

λd = Ldid + λf (4)

Substituting (3) & (4) into (1) & (2), we get

Vq = Rsiq + ωr(Ldid + λf ) + (Lqiq) (5)

Vd = Rsid - ωrLqiq + (Ldid + λf ) (6)

Arranging equations (5) and (6) in matrix

form

The developed torque motor is being given by

Te = 3/2 (P/2) (λdiq – λqid) (8)

Te = 3/4 P[λfiq + (Ld - Lq) iqid] (9)

The mechanical torque equation is

Te = TL + Bωm + J (10)

Solving for rotor mechanical speed from (10), we get

ωm = ( Te – TL- Bωm / J ) dt (11)

and rotor electrical speed is ωr = ωm(P/2). (12)

3.1. Park Transformation and Dynamic d-q Modelling:

The dynamic d-q modelling is used for the study of motor

during transient and steady state. It is done by converting the

three phase voltages and currents to dqo variables by using

Parks transformation [16]. Converting the phase voltages

variables Vabc to Vdqo variables in rotor reference frame the

following equations are obtained:

In contrast, Vdqo can be converted to Vabc as:

3.2. Equivalent circuit of PMSM:

For analysis purpose equivalent circuits of the motors are

used for study and simulation of motors. From the d-q

modelling of the motor using the stator voltage equations the

equivalent circuit of the motor can be derived. Assuming rotor

d axis flux from the permanent magnets is represented by a

constant current source as described in the following equation

λf= Ldmif , following figure can be obtained from [15] shown

as fig 3 and fig.4.

The equivalent circuits are

1. Dynamic stator q-axis equivalent circuit

2. Dynamic stator d-axis equivalent circuit

Fig.3: Stator q-axis equivalent circuit


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Fig.4: Stator d-axis equivalent circuit.

IV. FUZZY LOGIC CONTROLLER

A fuzzy logic controller may consist of three basic blocks,

namely, Fuzzification, Inference system and Defuzification

[7]

Fig-5: Fuzzy control arrangement

4.1 Fuzzification: Fuzzification is the procedures to process

the input variables with membership functions and determine

the degree to which the input variables are belong to each of

the appropriate fuzzy sets via membership functions.

Membership functions (MF) are used to convert each value of

input variables into a membership value between 0 and 1.

Membership functions may take any Arbitrary shape or form,

such as Gaussian distribution curves, Sigmoid curves, bell

shape curves, triangular functions or tables. The selection of

membership functions is very important as it means a kind of

controller tuning. Once the membership function shape has

been chosen, the values they are centered about and the width

of the functions have to be set. Overlapping of membership

functions is required as it means that more than one rule is

fired at any time, which is a key feature of fuzzy systems.

Triangular membership function are used as they are easier to

implement and quicker to process. In the proposed fuzzy

system, seven fuzzy sets have been considered for each input:

Large Negative (LN), Medium Negative (MN), Small

Negative (SN), Very Small (VS), Small Positive (SP),

Medium Positive (MP), and Large Positive (LP). Before

fuzzification, the input variables are normalized using base

values.

4.2 Fuzzy Inference System The fuzzy inference includes

the process of fuzzy logic operation, fizzy rule implication

and aggregation. In the fuzzy inference system, the fuzzified

input variables are processed with fuzzy operators and the

IF-THEN rule implementation. The output fuzzy sets for each

rule are then aggregated into a single output fuzzy set.

Aggregation is the process by which the fuzzy sets that

represent the outputs of each rule are combined into a single

fuzzy set. The input of the aggregation process is the list of

output fuzzy sets and the output of the aggregation process is

one fuzzy set for each output variable.

4.3 Defuzzification The input for the defuzzification process

is a fuzzy set (the aggregate output fuzzy set) and the output is

a single value. The centroid method is used for

defuzzification; it returns the centre of the area under the

curve representing the aggregated output fuzzy set.

Figure 6: Membership Function dpout

Figure 7: Membership Function dwr

Figure 8: Membership Function Ldwr


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Fig-9: Rule view of the next fuzzy control system

Fig-10 surface view of the next fuzzy control system

V. MODELLING & RESULT

In this proposed model, a 3-phase permanent magnet

synchronous machine with sinusoidal back EMF is

implemented. The sinusoidal machine is modelled in the dq

rotor reference frame. Stator windings are connected in wye

to an internal neutral point. The rest system parameter values

are tabulated in appendix A.

Figure 11: Complete model of wind energy with PI and

Fuzzy Controller

In wind turbine block implements a variable pitch wind

turbine model. The performance coefficient Cp of the turbine

is the mechanical output power of the turbine divided by wind

power and a function of wind speed, rotational speed, and

pitch angle (beta). Cp reaches its maximum value at zero beta.

The base generator speed is the 1.2 p.u. For a synchronous

generator, the base speed is the synchronous speed. For a

permanent-magnet generator, the base speed is defined as the

speed producing nominal voltage at no load.

The blade pitch angle is zero degree and the wind speed is

12m/s. the nominal output mechanical power is 150 x 103 W.

In this model a PLL is also implemented. The Phase Locked

Loop (PLL) system can be used to synchronize on a set of

variable frequency, three-phase sinusoidal signals. If the

Automatic Gain Control is enabled, the input (phase error) of

the PLL regulator is scaled according to the input signal

magnitude.

PMSG Values

Rated Speed 4250 rpm

Stator Resistence 1.6 ohm

Magnetic flux Linkage 0.1852 wb

Stator inductance (Ld, Lq) 0.006365, 0.006365 mH

Rated Torque 3.2 Nm

Torque Constant 0.5556 Nm

Friction Factor 5.369 * 10-005

Appendix : A

The output results are


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Figure 12: Waveform of Permanent Magnet synchronous

machine : (i) Electromagnetic Torque Te, (ii) Rotor Speed

rad/sec and (iii) waveform of Stator Current in Ampere.

Figure 13: Waveform of active and reactive power at

sending end.

Figure 14: Waveform of active and reactive power at

receiving end

Figure 15: Waveform of current at sending end

Figure 16: Waveform of current at receiving end

Figure 17: waveform of voltage at sending end


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Figure 18: waveform of voltage at receiving end.

VI. CONCLUSION

In this paper, a new Fuzzy-PI controller for variable speed

permanent magnet wind generators connected to a power grid

is proposed and investigated in order to enhance its dynamic

performances. The controller combines fuzzy logic with a

classical PI controller in order to adjust the PI gains online.

The stabilizing effect of the proposed PMSG system on the

fixed speed wind generators is also investigated. The results

show that the proposed Fuzzy-PI controller is very effective in

improving the transient stability of overall wind farm systems

during temporary and permanent fault conditions. The steady

state performance of the proposed system is analyzed using

variable wind speed data, and it is demonstrated that the

terminal voltage of wind farm under randomly varying wind

speed can be controlled constantly.

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BIOGRAPHY

.

Munendra Pratap Singh Belongs to UP received

his Bachelor of Technology degree from Ideal

Institute of technology, Ghaziabad in 2013. He is

pursuing his M.Tech in Electrical Engg. (Power

System) from SHIATS, Allahabad, UP-India. His

field of interest includes power quality,

embedded system, programmable logic controller

and electric drives.

Er. Vinay kumar tripathi belongs to district

Allahabad of uttar pradesh. He received his bachelor

of technology degree from UCER, allahabad in

2003. He obtained his M. Tech. in electrical eng.

(control & instrumentation) from MNNIT,

allahabad, Uttar pradesh in 2006 and pusuing Phd.

from sam higginbottom institute of agriculture

technology and sciences university (SHIATS),

allahabad, up, india. He is having 10 years’

experience in teaching and presently working as

asst. prof. in electrical engineering department,

SSET, SHIATS, allahabad. His field of interest

includes control and instrumentation, multiphase

system, power quality and electric drive

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