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International Journal of Modern Engineering Research (IJMER)
                  www.ijmer.com         Vol.2, Issue.6, Nov-Dec. 2012 pp-4069-4076       ISSN: 2249-6645

Power Loss Minimization of Permanent Magnet Synchronous Generator
                Using Particle Swarm Optimization
                       Prashant Kumar S. Chinamalli1, Naveen T. S.2, Shankar C. B.3
                           1
                             (Electrical Department,Yashoda Technical Campus/Shivaji University, India)
     2, 3
            (Electrical & Electronics Department, Acharya Institute of Tecnology,Bangalore, Vishweshwaraih Technological
                                                         University, India

ABSTRACT: Interior Permanent-magnet synchronous                   consistently impressive with the main engineering challenge
generators (IPM) are commonly used for variable-speed             to the wind industry to design an efficient wind turbine to
wind turbines to produce high efficiency, high reliability,       harness energy and turn it into electricity.
and low-cost wind power generation. An IPM driven by a                      The use of permanent-magnet synchronous
wind turbine, in which the d-axis and q-axis stator-current       machines (PMSMs) for wind power generation has received
components are optimally controlled to achieve the                increasing attention in recent years [1]โ€“[6]. The PMSMs can
maximum wind power generation and Particle Swarm                  provide high-efficiency and high-reliability power
Optimization (PSO) for loss minimization of the IPMSG.            generation, since there is no need for external excitation and
The effect of magnetic saturation, which causes the highly        no copper losses in the rotor circuits. In addition, the high-
nonlinear characteristics of the IPMSG, has been                  power density PMSMs are small in size, which reduces the
considered in the control scheme design. The optimal d-axis       cost and weight of wind turbines. Furthermore, in the wind
stator-current command is obtained as a function of the           generation system equipped with a PMSM and power-
IPMSG rotor speed by solving a constrained nonlinear-             electronic converters, the wind turbine can be operated to
optimization problem that minimizes the copper and core           extract the maximum power from the wind at various wind
losses of the IPMSG. At any wind speed within the                 speeds by adjusting the shaft speed optimally. Therefore,
operating range, the IPMSG rotor speed is optimally               the PMSMs are commonly used for small variable-speed
controlled to extract maximum wind power. The PSO                 wind turbines to produce high efficiency, high reliability,
technique guides to narrow convergence solution of non-           and low-cost wind power generation.
linearity introduced in the model. The proposed control                     Energy production and utilization, efficiency is
scheme provides the wind generation system with the               always an important issue, so previously the minimization
maximum efficiency and high dynamic performance [1] [2].          of the core losses of a PMSM through a suitable design of
                                                                  magnets and slots and the choice of the number of poles. In
                                                                  fact, the efficiency of an IPMSM can be improved not only
Keywords: Permanent magnet synchronous generator,
                                                                  during the machine design stage but also during the
magnetic saturation, loss minimization.
                                                                  operation stage. By optimally controlling the d-axis
                                                                  component of the stator currents even by optimizing the
                     I. INTRODUCTION                              values with particle swarm optimization, the stator copper
          Resolving the worldโ€™s growing demand for energy,        and core losses of an IPMSM can be minimized.
for minimizing related impacts on the environment and with
increased competition for energy supplies represent some of            II. MODELING OF WIND TURBINE SYSTEM
the greatest technical challenges of the next several decades.              The basic configuration of an IPMSG driven by a
Fossil fuels supply more than 80 percent of the worldโ€™s           wind turbine is as shown in Fig.1. The IPMSG converts the
primary energy but they are finite resources and major            mechanical power from the wind turbine to ac electrical
contributors to global climate change. The ways and means         power, which is then converted to dc power through an
for their ultimate replacement with clean, affordable and         IGBT pulse-width modulation (PWM) converter with a dc
sustainable energy sources at the scale required to power the     link to supply the dc load. Control of the IPMSG is
world are not yet readily available. Turning off the carbon       achieved by controlling the ac-side voltages of this PWM
emissions is the first step and many of the solutions which       power converter. By using an additional power inverter, the
are familiar are windmills, solar panels, nuclear plants etc...   IPMSG can supply the ac electrical power with constant
All three technologies are part of the energy mix, although       voltage and frequency to the power grid or ac load.
each has its issues, including noise from windmills and                     The mechanical power that the wind turbine
radioactive waste from nukes. Moreover, existing energy           extracts from the wind is calculated by
infrastructures around the world are complex and large,
where they require enormous capital investment and have                                  1
operational Life spans of 50 years or more. In windmills (a                        ๐‘ƒ ๐‘š = 2 ๐œŒ๐ด ๐‘Ÿ ๐‘ฃ ๐‘ค ๐ถ ๐‘ƒ ๐œ†, ๐›ฝ                 (1)
much older technology) wind energy is used to turn
mechanical machinery to do physical work; historically,
windmills were used traditionally for grinding grain or
spices, pumping water, sawing wood or hammering seeds.
The evolution of modern turbines is a remarkable success
story of engineering and scientific skill, coupled with a
          Strong entrepreneurial spirit. The progress of wind
energy around the world in recent years has been

                                                         www.ijmer.com                                              4069 | Page
International Journal of Modern Engineering Research (IJMER)
              www.ijmer.com         Vol.2, Issue.6, Nov-Dec. 2012 pp-4069-4076       ISSN: 2249-6645
                                                               Wind speed is in the range of 4โ€“11 m/s. The parameters of
                                                               the wind turbine system as listed in Table. 1.

                                                                       Table. 1: Parameters of the wind turbine system

                                                                            Air density               1.08 kg/m3

                                                                            Rotor diameter            11 m

                                                                            Rated wind speed          10 m/s
     Fig. 1: Wind turbine system using IPMSG [4]                            Rated rotational speed          200 m
where ฯ is the air density in kilograms per cubic meter, Ar
=ฯ€R2 is the area swept by the rotor blades in square meters,
R is the wind-turbine rotor radius in meters, vw is the wind       III. MODELING OF PERMANENT MAGNET
speed in meters per second, and CP is the power coefficient,              SYNCHRONOUS GENERATOR
which is a function of both tip-speed ratio ฮป and the blade              Permanent Magnet Synchronous machines
pitch angle ฮฒ. The mathematical representation of CP is        (PMSMโ€™s) are non-salient pole AC synchronous motors,
given by [4]                                                   these synchronous motor drives are suitable for constant
                                                               speed applications as its speed of operation depends only on
                                          ๐œ‹ ๐œ† + 0.1            the frequency of the stator supply. Synchronous motor with
    ๐ถ ๐‘ƒ ๐œ†, ๐›ฝ = 0.3 โˆ’ 0.00167๐›ฝ ๐‘ ๐‘–๐‘›                              permanent magnet is a choice in kW range for applications
                                          10 โˆ’ 0.3๐›ฝ            like wind turbines, aerospace actuators, electric vehicles etc.
                                                               The advantages of permanent magnet synchronous motor
                                 โˆ’0.000184 ๐œ† โˆ’ 3 ๐›ฝ(2)          over the other motors are of higher efficiency, higher torque
                                                               to inertia ratio and compact in size. The PMSM used here is
         Where ฮป is defined by ฯ‰tR/vwandฯ‰t is the wind-
                                                               an Interior Permanent Magnet Synchronus Generator
turbine rotational speed in radians per second.
                                                               (PMSG).
         The CP โˆ’ ฮป curve described by Eqn (2) for the wind
turbine is as shown in Fig. 2. In terms of Fig.2 and the       3.1 Dynamic Modeling:
definition of ฮป, at any wind speed within the operating                  The stator consists of three phase winding having
range, there is a unique wind-turbine shaft rotational         spatial displacement from each other. The axis of phase-1 is
speed to achieve the maximum power coefficient CPmax. In       taken as reference axis for the stationary co-ordinates fixed
terms of Eqn (1), when CP is controlled at the maximum         to the stator. The currents in the winding can have any
value, the maximum mechanical power is extracted from the      general variation with respect to time. Assuming that the
wind energy.                                                   spatial distribution of mmf produced by each coil is
                                                               sinusoidal in nature, the stator mmf caused by three phase
                                                               currents flowing in the three windings can be represented by
                                                               a single time varying quantity which has got some spatial
                                                               orientation. The stator current space phasor diagram is
                                                               shown in Fig. 4.The space vector of stator current can be
                                                               represented in terms of three phase currents as,
                                                                       ๐‘ 
                                                                   ๐‘–   ๐‘    ๐‘ก = ๐‘– ๐‘ 1 ๐‘ก + ๐‘– ๐‘ 2 ๐‘ก ๐‘’ ๐‘—๐›พ + ๐‘– ๐‘ 3 ๐‘ก ๐‘’ ๐‘—2๐›พ           (3)

                                                               where is1,is2 and is3 are the stator phase currents and ฮณ is the
                                                               advanced current angle.
                                                               The space vector of stator current can also be represented in
         Fig. 2: CP- ฮป curve of the wind turbine.
                                                               terms of equivalent two phase (ฮฑ-ฮฒ) axis currents as,

                                                                                ๐‘– ๐‘ ๐‘  ๐‘ก = ๐‘– ๐‘ ฮฑ ๐‘ก + ๐‘—๐‘– ๐‘ ฮฒ ๐‘ก             (4)
                                                                            0
                                                               As ๐›พ =120 , the ฮฑ axis current and ฮฒ axis currents can be
                                                               written as,

                                                                           ๐‘– ๐‘ ฮฑ ๐‘ก = ๐‘– ๐‘ 1 ๐‘ก cos 0 + ๐‘– ๐‘ 2 ๐‘ก cos 120 +
                                                                                                          ๐‘– ๐‘ 3 ๐‘ก cos 240 (5)

                                                                           ๐‘– ๐‘ ฮฒ ๐‘ก = ๐‘– ๐‘ 1 ๐‘ก sin 0 + ๐‘– ๐‘ 2 ๐‘ก sin 120 +

                                                                                                             ๐‘– ๐‘ 3 ๐‘ก sin 240 (6)
       Fig. 3: Wind velocity input by signal builder.
         The signal builder block is used to give wind speed
as an input to the wind turbine which is as shown in Fig.3.
                                                      www.ijmer.com                                                  4070 | Page
International Journal of Modern Engineering Research (IJMER)
              www.ijmer.com         Vol.2, Issue.6, Nov-Dec. 2012 pp-4069-4076       ISSN: 2249-6645
                                                                          where ฮต is the angle between rotor reference axis and stator
                                                                          reference axis.
                                                                          The above equations are used in the modeling of
                                                                          transformation of co-ordinates and sources as shown in the
                                                                          below Fig. 7, 8 and 9.




     Fig.4: Representations of Co-ordinate Systems

           The above equation can be simplified as,



                                                                                                Fig.7: abc to ฮฑ-ฮฒ transformation




           Fig.5: Stator current space phasor




                                                                                                Fig.8: ฮฑ-ฮฒ to d-q transformation



Fig.6: Stator current transformation from three phase to
                         ฮฑ-ฮฒ axis.
                                 1                 1
           ๐‘– ๐‘ ฮฑ ๐‘ก = ๐‘– ๐‘ 1 ๐‘ก โˆ’ ๐‘– ๐‘ 2 ๐‘ก โˆ’ ๐‘– ๐‘ 3 ๐‘ก                        (7)
                                 2                 2

                     โˆš3              โˆš3
          ๐‘– ๐‘ ฮฒ ๐‘ก =        ๐‘– ๐‘ 2 ๐‘ก โˆ’        ๐‘– ๐‘ 3 ๐‘ก                    (8)
                     2               2
                                                                                          Fig.9: Voltage to Current transformation
For a three phase wire system the condition,
                                                                          3.2       Non-Linearity due to Magnetic Saturation:
           ๐‘– ๐‘ 1 ๐‘ก + ๐‘– ๐‘ 2 ๐‘ก + ๐‘– ๐‘ 3 ๐‘ก = 0                             (9)             Consider a typical Interior PMSG circuit as below
                                                                          in Fig.10. For the IPMSG, burying the magnets inside the
holds good for all instants of time. Using this condition in              rotor introduces saliency into the rotor into the rotor magnet
above and (ฮฑ-ฮฒ) axis currents can be written as,                          circuit. The d-axis flux passes through a wide region of low-
                          3                                               permeability magnets, while the q-axis flux path has a high
              ๐‘– ๐‘ ฮฑ ๐‘ก = 2 ๐‘– ๐‘ 1 ๐‘ก                                    (10)   permeability. Therefore, the IPMSG has a saliency (Lq> Ld)
                          โˆš3               โˆš3                             and the effect of magnetic saturation along the q-axis is
              ๐‘– ๐‘ ฮฒ ๐‘ก =     2
                               ๐‘– ๐‘ 2 ๐‘ก โˆ’     2
                                                ๐‘– ๐‘ 3 ๐‘ก             (11)
                                                                          dominant. Interior PMSG is considered with magnetic
                                                                          saturation, i.e. there is a flux linkage between the q-axis
For the dynamic modeling, first convert the three quantities              inductances so the Lq will be the function of current iq and
to two phase quantities i.e. abc to ฮฑ-ฮฒ transformation. The               d-axis inductance Ld will be considered constant value and
general formula can be given as below,                                    they are represented as Ld, Lq(iq). The dynamic equation of a
                                 3
                            ๐‘‹ฮฑ = ๐‘‹ ๐‘Ž 2
                                                     (12)                 three-phase IPMSG can be written in the rotor reference
                                     โˆš3                                   frame as.
                                ๐‘‹ฮฒ = 2
                                        (๐‘‹ ๐‘       โˆ’ ๐‘‹๐‘)          (13)
                                     3                                               Id               -

                                ๐‘ฃsฮฑ = ๐‘ฃ ๐‘ ๐‘Ž                                                                ฯ‰Lqiq   +
                                                                   (14)                    Rs
                                                                                                                           Iq             +
                                                                                                                                              ฯ‰Lqiod   -

                                     2                                                                                          Rs
                                                                                                                                                            +

                                          โˆš3
                                ๐‘ฃsฮฒ =      2
                                             (๐‘ฃ ๐‘ ๐‘     โˆ’ ๐‘ฃ ๐‘ ๐‘ )
                                                        (15)                    Vd
                                                                                                Rc                    Vq
                                                                                                                                     Rc
                                                                                                                                                           ฯ‰ฯˆm

                                                                                                                                                             -

Similarly the transformation of stator currents and voltages                                               Ld                                   Lq


from ฮฑ-ฮฒ to d-q co-ordinates is done using the angle ฮต.                                   (a) (b)
                 ๐‘ฃ ๐‘ ๐‘‘ = ๐‘ฃ ๐‘ ฮฑ cos ฮต + ๐‘ฃ ๐‘ ฮฒ sin ฮต         (16)                 Fig.10. Equivalent circuits of the IPMSG. (a) d-axis
                 ๐‘ฃ ๐‘ ๐‘ž = ๐‘ฃ ๐‘ ฮฒ cos ฮต โˆ’ ๐‘ฃ ๐‘ ฮฑ sin ฮต         (17)                   equivalent circuit. (b) q-axis equivalent circuit.

                                                                  www.ijmer.com                                                                 4071 | Page
International Journal of Modern Engineering Research (IJMER)
                       www.ijmer.com         Vol.2, Issue.6, Nov-Dec. 2012 pp-4069-4076       ISSN: 2249-6645
                  ๐‘‘๐‘– ๐‘œ๐‘‘                                                                           Rated power                           25 kW
            ๐ฟ๐‘‘     ๐‘‘๐‘ก
                           = โˆ’๐‘… ๐‘  ๐‘– ๐‘‘ + ๐œ”๐ฟ ๐‘ž ๐‘– ๐‘ž ๐‘– ๐‘œ๐‘ž + ๐‘ฃ ๐‘‘               (18)

                       ๐‘‘๐‘– ๐‘œ๐‘ž
                                                                                                Ratedrotor speed                      1200 rpm
          ๐ฟ๐‘ž ๐‘–๐‘ž         ๐‘‘๐‘ก
                               = โˆ’๐‘… ๐‘  ๐‘– ๐‘ž โˆ’ ๐œ”๐ฟ ๐‘‘ ๐‘– ๐‘œ๐‘‘ โˆ’ ๐œ”๐œ“ ๐‘š + ๐‘ฃ ๐‘ž (19)

The electromagnetic torque developed by the machine is
given by,
                       3
      ๐‘‡ ๐‘” = โˆ’ 4 ๐‘ƒ๐‘› [๐œ“ ๐‘š ๐‘– ๐‘œ๐‘ž +                    ๐ฟ๐‘‘ โˆ’ ๐ฟ๐‘ž ๐‘–๐‘ž    ๐‘– ๐‘œ๐‘‘ ๐‘– ๐‘œ๐‘ž ] (20)

The following equations help in complete dynamic
modeling of IPMSG:
                           ๐‘‘๐‘– ๐‘œ๐‘‘
      ๐‘ฃ๐‘‘ = ๐ฟ๐‘‘               ๐‘‘๐‘ก
                                   + ๐‘… ๐‘  ๐‘– ๐‘‘ โˆ’ ๐œ”๐ฟ ๐‘ž ๐‘– ๐‘ž ๐‘– ๐‘œ๐‘ž              (21)                  Fig 11. Simulink model of IPMSG

                                   ๐‘‘๐‘– ๐‘œ๐‘ž                                           3.3      PWM Generator Side Converter:
      ๐‘ฃ๐‘ž = ๐ฟ ๐‘ž ๐‘– ๐‘ž                  ๐‘‘๐‘ก
                                           + ๐‘… ๐‘  ๐‘– ๐‘ž + ๐œ”๐ฟ ๐‘‘ ๐‘– ๐‘œ๐‘‘ + ๐œ”๐œ“ ๐‘š (22)

           ๐‘‘๐œ”
      ๐ฝ         = ๐‘‡ ๐‘š โˆ’ ๐‘‡๐‘”                                                (23)
           ๐‘‘๐‘ก

                   1
       ๐œ”=          ๐ฝ
                           ๐‘‡ ๐‘š โˆ’ ๐‘‡๐‘”          ๐‘‘๐‘ก                           (24)

      ๐‘‘๐œ–           ๐‘ƒ
      ๐‘‘๐‘ก
           =      2
                           ๐œ” = ๐œ”๐‘”                                         (25)
                                                                                            Fig . 12. PWM generator side converter
                                                                                            The pulse width modulation generator side
         where ๐œ“ ๐‘š is the magnet flux linkage, ๐‘… ๐‘  is the                          converter consists of IGBT based 3-phase bridge voltage-
stator resistance, ๐‘ƒ๐‘› is the number of poles, ๐‘‡ ๐‘š is the input                     source converter. The only difference between rectifier and
mechanical torque given by ๐‘‡ ๐‘š = ๐‘ƒ ๐‘š /๐œ” ๐‘” , ๐œ” ๐‘” is the rotor                       inverter is the definition of power sign. The switching
speed, J is the inertia, iod, ioq are initial current values of d-                 frequency of the converter is assumed to be sufficiently high
axis and q-axis respectively, ๐ฟ ๐‘‘ is the d-axis inductance and                     to make an average analysis valid, which means that the
                                                                                   switching ripple should be negligible compared to the
assumed to be constant, and ๐ฟ ๐‘ž is the q-axis inductance
                                                                                   averaged values. The generator side converter is shown in
which varies depending on the value of ๐‘– ๐‘ž .                                       Fig. 12.The system equation for generator side converter
The effect of magnetic saturation is considered by                                 can be written as:
modeling ๐ฟ ๐‘ž as a function of ๐‘– ๐‘ž given by [1],
                                                                                                                  ๐‘‘๐ผ ๐‘Ž               2๐‘† ๐‘Ž โˆ’ ๐‘† ๐‘ โˆ’ ๐‘† ๐‘
                                                                                            ๐‘‰๐‘Ž = ๐‘… ๐‘Ÿ ๐ผ ๐‘Ž + ๐ฟ ๐‘Ÿ           + ๐‘‰ ๐‘‘๐‘ .                          (27)
                                                                                                                   ๐‘‘๐‘ก                      3
                               ๐ฟ ๐‘ž = ๐ฟ ๐‘ž๐‘œ โˆ’ ๐‘˜ ๐‘– ๐‘ž                         (26)
                                                                                                                 ๐‘‘๐ผ ๐‘               โˆ’๐‘† ๐‘Ž +2๐‘† ๐‘ โˆ’ ๐‘† ๐‘
  where k is a positive constant, the parameters of the                                    ๐‘‰๐‘ = ๐‘… ๐‘Ÿ ๐ผ ๐‘ + ๐ฟ ๐‘Ÿ     ๐‘‘๐‘ก
                                                                                                                         + ๐‘‰ ๐‘‘๐‘ .         3
                                                                                                                                                           (28)
IPMSG are given in the Table 2.
                                                                                                                 ๐‘‘๐ผ ๐‘               โˆ’๐‘† ๐‘Ž โˆ’ ๐‘† ๐‘ + 2๐‘† ๐‘
All the above equations along with parameters specified in                                  ๐‘‰๐‘ = ๐‘… ๐‘Ÿ ๐ผ ๐‘ + ๐ฟ ๐‘Ÿ   ๐‘‘๐‘ก
                                                                                                                         + ๐‘‰ ๐‘‘๐‘ .           3
                                                                                                                                                           (29)
Table.2 are used to model interior permanent magnet
synchronous generator considering magnetic saturation as                           where Va,Vb,Vc are the three phase stator voltage; Ia,Ib,Ic are
shown below in Fig.11.                                                             three phase currents; Sa,Sb,Sc are gate pulses to IGBT and
                                                                                   Vdc is DC link voltage.
                    Table 2. Parameters of IPMSG
                                                                                         IV. MODELING FOR MAXIMUM WIND POWER
                                Rs                      0.1764 โ„ฆ
                                                                                             GENERATION WITH LOSS MINIMIZATION
                                Ld                      6.24 mH                    4.1 Maximum Wind Power Generation:
                                                                                            By adjusting the wind-turbine shaft speed
                                Lqo                   20.5822 mH                   optimally, the tip speed ratio ฮป can be controlled at the
                                                                                   optimal value to achieve the maximum power coefficient
                                ฯˆm                      0.246 Wb                   CPmaxregardless of the wind speed. The maximum
                                                                                   mechanical power is therefore extracted from the wind
                                   J                   1.2 kg . m2                 energy. At this optimal condition, the optimal IPMSG rotor
                                                                                   speed is proportional to the wind speed, given by
                                Pn                          6                                          ฯ‰g,opt= kฯ‰vw                      (30)

                                   k                  0.1879 mH/A                  Where kฯ‰ is a constant determined by the wind-turbine
                                                                                   characteristics. The generator rotor speed must be a nearer

                                                                        www.ijmer.com                                                               4072 | Page
International Journal of Modern Engineering Research (IJMER)
               www.ijmer.com         Vol.2, Issue.6, Nov-Dec. 2012 pp-4069-4076       ISSN: 2249-6645
value to the optimal rotor speed which leads to the                    1) Initialize a population of particles with random
extraction of maximum power from wind velocity.                              positions and velocities of M dimensions in the problem
                                                                             space.
4.2 Minimization of the Copper and Core Losses of                      2) Define a fitness-measure function to evaluate the
IPMSG:                                                                       performance of each particle.
         The losses of a PMSG can be decomposed into                   3) Compare each particleโ€™s present position xi with its
four components, namely, stator copper loss, core loss,                      xi,pbestbased on the fitness evaluation. If the current
mechanical loss, and stray-load loss. Only the stator copper                 position xiis better than xi,pbest, then set xi,pbest= xi.
and core losses are explicitly dependent on and can be                 4) If xi,pbest is updated, then compare each particleโ€™s xi,pbest
controlled by the fundamental components of the stator                       with the swarm best position xgbest based on the fitness
currents. Therefore, the maximum efficiency condition of                     evaluation. If xi,pbestis better than xgbest, then set xgbest=
the IPMSG is obtained by solving the following nonlinear-                    xi,pbest.
optimization problem offline to minimize the total copper              5) At iteration k, the velocity of each particle is updated
and core losses of the IPMSG                                                 by
i.e we have                                                                            vi (k + 1) = w ยท vi (k) + c1ฯ†1 (xi,pbest(k) โˆ’ xi (k)) + c2ฯ†2
                                                                                                     (xgbest(k) โˆ’ xi (k)), i= 1, 2, ...,N.     (35)
       ๐‘ƒ๐‘™๐‘œ๐‘ ๐‘  = ๐‘ƒ๐‘๐‘œ๐‘๐‘๐‘’๐‘Ÿ + ๐‘ƒ๐‘๐‘œ๐‘Ÿ๐‘’                                  (31)   6) Based on the updated velocity, each particle then
                                                                             changes its position by
    ๐‘ƒ๐‘๐‘œ๐‘๐‘๐‘’๐‘Ÿ = 1.5 ๐‘… ๐‘  ๐‘– 2 + ๐‘– 2
                        ๐‘‘     ๐‘ž                                 (32)                          xi (k + 1) = xi (k) + vi(k + 1), i= 1, 2, ..,N.(36)
                                                                       7) Repeat steps (3) to (6) until a criterion, usually a
      ๐‘ƒ๐‘๐‘œ๐‘Ÿ๐‘’ = 1.5 ๐‘– 2 + ๐‘– 2 ๐‘… ๐‘ ๐œ” ๐‘”
                    ๐‘๐‘‘    ๐‘๐‘ž                                    (33)         sufficiently good fitness or a maximum number of
                                                                             iterations, is achieved.
                          ๐ฟ ๐‘‘ ๐‘– ๐‘œ๐‘‘ +๐œ“ ๐‘š 2 + ๐ฟ ๐‘ž (๐‘– ๐‘ž )๐‘– ๐‘œ๐‘ž
                                                           2           The final value of xgbest is regarded as the optimal solution
            = 1.5 ๐œ”2                  ๐‘… ๐‘ (๐œ” ๐‘” )
                                                                (34)   of the problem.
                                                                                   In Eqn (35), c1 and c2 are positive constants
Where Pcopper is the copper loss, Pcore is the core loss [6], and      representing the weighting of the acceleration terms that
icd and icq are the currents at the resistant Rc.                      guide each particle toward the individual best and the
                                                                       swarm best positions, xi,pbestand xgbest, respectively; ฯ†1 and ฯ†2
         An optimal IPMSG rotor speed calculated by Eqn
                                                                       are uniformly distributed random numbers in [0, 1]; w is a
(30), the solutions of the nonlinear-optimization problem
                                                                       positive inertia weight developed to provide better control
yield the optimal values of id and iq, which minimize the
                                                                       between exploration and exploitation; N is the number of
total copper and core losses of the IPMSG. Therefore, at
                                                                       particles in the swarm. The last two terms in Eqn (12)
any wind speed, the solutions of Eqn (30) and Eqn (34)
                                                                       enable each particle to perform a local search around its
provide the desired optimal IPMSG rotor speed, optimal
                                                                       individual best position xi,pbestand the swarm best position
currents id and iq to achieve the maximum wind power
                                                                       xgbest. The first term in Eqn (35) enables each particle to
extraction, and loss minimization of the IPMSG. Without
                                                                       perform a global search by exploring a new search space.
considering the effect of magnetic saturation (i.e., Lq is
                                                                                   Because of many attractive features, e.g., multi-
constant) and the variation of Rc, Eqn (34) would be a
                                                                       agent search, simple implementation, small computational
constrained nonlinear quadric optimization problem that can
                                                                       load, and fast convergence, the PSO algorithm can provide a
be solved by conventional nonlinear-optimization methods.
                                                                       fast and efficient search for the optimal solution. These
However, the inclusion of magnetic saturation and variation
                                                                       features provide PSO with superior performance over other
of Rc results in a complex nonlinear-optimization problem
                                                                       evolutionary computation algorithms (e.g., genetic
that requires extensive computation effort when using
                                                                       algorithms) in many applications. In addition, for many
conventional nonlinear optimization methods. In order to
                                                                       complex optimization problems that are difficult to
achieve this stochastic optimization technique called
                                                                       formulate mathematically or to solve by traditional
particle swarm optimization (PSO) [5] is employed to
                                                                       optimization methods, PSO is efficient to find the optimal
obtain the optimal solution of Eqn (34).
                                                                       solution.
                                                                       The values of the PSO parameters are chosen as:
        V. PARTICLE SWARM OPTIMIZATION
                                                                                   c1 = c2 = 2, N = 20 and w= 1.4 โˆ’ (1.4 โˆ’ 0.4)
          Particle Swarm Optimization is a population-based
                                                                       *(k/K), where k is the iteration number and K is the
stochastic optimization technique. It searches for the
                                                                       maximum number of iterations. The PSO algorithm only
optimal solution from a population of moving particles.
                                                                       performs a 1-D search for the optimal value of iq. The
Each particle represents a potential solution and has a
                                                                       optimal value of idis determined by the torque in Eqn (20)
position (vector xi) and a velocity (vector vi ) in the problem
                                                                       and the corresponding optimal value of iq, where the
space. Each particle keeps track of its individual best
                                                                       electrical torque Tgin Eqn (20) is determined by Eqn (30)
position xi,pbest, which is associated with the best fitness it
                                                                       and the constraint equations of Eqn (34). The fitness-
has achieved so far, at any step in the solution. Moreover,
                                                                       measure function is simply the total copper and core losses
the best position among all the particles obtained so far in
                                                                       Ploss of the IPMSG. It is calculated by the first two
the swarm is kept track of as xgbest. This information is
                                                                       constraint equations of Eqn (34). By solving the nonlinear-
shared by all particles.
                                                                       optimization problem in Eqn (34) at various IPMSG rotor
The PSO algorithm is implemented in the following
                                                                       speeds, the optimal values of idand iqare obtained as
iterative procedure to search for the optimal solution.
                                                                       functions of the IPMSG rotor speed ฯ‰g. The relationship
                                                                       between the optimal d-axis and q-axis stator-current
                                                               www.ijmer.com                                                        4073 | Page
International Journal of Modern Engineering Research (IJMER)
              www.ijmer.com         Vol.2, Issue.6, Nov-Dec. 2012 pp-4069-4076       ISSN: 2249-6645
components and the IPMSG rotor speed can be                       6.2 IOL- Based Non-Linear Current Control:
approximated by a fourth-order and a third-order                            Instead of approximating a nonlinear systemโ€™s
polynomial, respectively, given by                                dynamics locally around some operating point via
                                                                  linearization, the IOL technique transforms the nonlinear
๐‘– ๐‘‘,๐‘œ๐‘๐‘ก = ๐พ ๐‘‘4 ๐œ”4 + ๐พ ๐‘‘3 ๐œ”3 + ๐พ ๐‘‘2 ๐œ”2 + ๐พ ๐‘‘1 ๐œ” ๐‘” +
                ๐‘”         ๐‘”         ๐‘”                             system into an equivalent linear system via feedback and
  ๐พ ๐‘‘0 (37)                                                       nonlinear coordinate transformation. This is a systematic
                                                                  way to globally linearize a part of or all the dynamics of the
   ๐‘– ๐‘ž,๐‘œ๐‘๐‘ก = ๐พ ๐‘ž3 ๐œ”3 + ๐พ ๐‘ž2 ๐œ”2 + ๐พ ๐‘ž1 ๐œ” ๐‘” + ๐พ ๐‘ž0
                   ๐‘”         ๐‘”                             (38)   nonlinear system. In such a scheme, the inputโ€“output
                                                                  dynamics are linearized, but the state equations may be only
         The coefficients of both polynomials are listed in       partially linearized. Residual nonlinear dynamics, called
Table 3. However, it should be pointed out that Eqn (37)          internal dynamics, do not depend explicitly on the system
and Eqn (38) only provide the optimal operating conditions        input and, thus, are not controlled. If the internal dynamics
of the IPMSG for the wind speed below the rated value.            are trivial or stable at the equilibrium point, then the entire
When the wind speed exceeds the rated value, the phase            nonlinear system can be stabilized by a standard linear
current and/or the terminal voltage reach their ceiling           feedback control using the linearized inputโ€“output
values, and therefore, the optimal speed tracking control         dynamics.
cannot be applied. Under this condition, the current and
voltage limited maximum output control can be applied to                               VII.     RESULTS
control IPMSG.                                                             The model of Wind turbine system and IPMSG are
                                                                  previously run for the existing condition of initial values.
   Table 3. Coefficients of approximating polynomials             Later, speed control and current control techniques are
                                                                  introduced for the optimization of rotor speed and current
        Coefficients of id,opt   Coefficients of iq,opt           by running Particle Swarm Optimization algorithm. In PSO
                                                                  algorithm the complete model is called through command to
        Kd4    1.291 ร— 10 -11    Kq3   7.528 ร— 10 -9              get the desired output of Maximum generation and Power
                                                                  loss minimization. All results are taken from the simulation
        Kd3    -3.523 ร— 10-8     Kq2   -3.477 ร— 10 -5             of the modeling in MATLAB 2011b.

        Kd2    1.154 ร— 10 -5     Kq1   -1.648 ร— 10 -3

        Kd1    -1.348 ร— 10 -2    Kq0   1.263

        Kd0    -1.589 ร— 10 -2


                VI. CONTROL OF PMSG
                                                                               Fig .14. wind velocity Vs ฯ‰g,opt

                                                                           As per the Eqn(30) the ฯ‰g,opt varies linearly with
                                                                  respect to the wind velocity as shown in Fig .14. From this
                                                                  it can be justified that as the wind velocity varies the rotor
                                                                  speed varies optimally in a linear manner.




        Fig. 13: Control of scheme for the IPMSG

6.1 Optimal IPMSG Rotor-Speed Tracking Control:
         Based on the IPMSG motion Eqn (23), a PI-type
speed controller is designed to track the optimal rotor speed                Fig. 15. Three phase stator current
at any moment, applied for the speed controller, as shown
by the dash-line block in Fig. 22. The gain ka is given by ka
= 1/kp. The output of the speed controller is the optimal
torque command Tโˆ—g,opt for the IPMSG, which corresponds
to the maximum power point for wind power generation. By
using this optimal torque command and the optimal d-axis
current command from Eqn (37), the solution of Eqn (20)
provides the optimal q-axis stator-current command for the
inner loop current regulation. In the real application, the                      Fig .16. Three stator voltage
values of iโˆ—q,opt can be generated offline over the entire
operating range of the IPMSG.

                                                          www.ijmer.com                                             4074 | Page
International Journal of Modern Engineering Research (IJMER)
               www.ijmer.com         Vol.2, Issue.6, Nov-Dec. 2012 pp-4069-4076       ISSN: 2249-6645
          Fig. 15 and Fig. 16 show the three-phase controlled
stator current and voltage of the IPMSG after PSO. As
voltage is 200V and current is 100A so it can be stated that
WTG system generates upto 20 Kw power. The simulated
result for a dc link current, whichis controlled by the
rectifier side controller, is as shown in Fig. 17.
          For maximum wind power tracking the speed
controller is employed, this can be noticed from Fig 18 and                        Fig. 21. Time Vs Iq, after PSO
Fig 19.Because of the relatively slow response of the WTG
mechanical system, during the acceleration of the WTG,the        After the PSO algorithm the optimized results of currents
PI-type speed controller is saturated, and the resulting         are incorporated in Eqn (34), hence there is a minimization
IPMSG electrical-torque command generated by the speed           in the total power loss as shown in Table 5.
controller remains at its limit value of zero.                                    Table .5. Total Ploss minimization
                                                                         Total Ploss        Total Ploss           Total Ploss
                                                                       before PSO         after PSO           minimization

                                                                          3.3 kW               2.57 kW                 22.12%


                                                                                      VIII.      CONCLUSION
                                                                          Modeling and simulation of a 25kW variable speed
                                                                 wind energy conversion system employing a Maximum
                                                                 Torque per Current control and Particle Swarm
                  Fig .17. DC link voltage                       Optimization is presented in the paper. PMSGs are
                                                                 commonly used for small variable speed WTG systems. In
As a result, the electrical output power and the q-axis stator   such systems, by adjusting the shaft speed optimally, the
current of the IPMSG are both regulated at zero during the       maximum wind power can be extracted at various wind
saturation of the speed controller.                              speeds within the operating range. In addition, when using
                                                                 an IPMSG, the stator copper and core losses of the
                                                                 generator can be minimized by optimally controlling the d-
                                                                 axis component of the stator currents. However, to achieve
                                                                 the high performance of the WTG system, magnetic
                                                                 saturation of the IPMSG must be taken into account in the
                                                                 control-system design. Implementation of PSO results in the
                                                                 minimization of total power loss and thus improves the
                                                                 efficiency of the system. This proposed control provides the
                                                                 wind generation system with high dynamic performance and
                                                                 improved power efficiency.
                    Fig .18. Time Vs ฯ‰g
                                                                                             REFERENCES
                                                                 [1]     T. M. Jahns, G. B. Kliman, and T. W. Neumann, โ€œInterior
                                                                         permanentmagnetsynchronous motors for adjustable-speed
                                                                         drives,โ€ IEEE Trans.Ind. Appl., vol. IA-22, no. 4, pp. 738โ€“
                                                                         747, Jul. /Aug. 1986.
                                                                 [2]     E. Muljadi, C. P. Butterfield, and Y. Wang, โ€œAxial-flux
                                                                         modular permanent- magnet generator with a toroidal
                                                                         winding for wind-turbine applications,โ€ IEEE Trans. Ind.
                                                                         Appl., vol. 35, no. 4, pp. 831โ€“836, Jul./Aug. 1999.
                                                                 [3]     S. Grabic, N. Celanovic, and V. A. Katic, โ€œPermanent
                                                                         magnet synchronous generator           for    wind     turbine
                   Fig. 19. Time Vs ฯ‰g,opt                               application,โ€ IEEE Trans. Power Electron., vol. 13, no.3,
                                                                         pp. 1136โ€“1142, May 2008.
  The optimized results of current of d-axis and q-axis are      [4]     S. Morimoto, H. Nakayama, M. Sanada, and Y. Takeda,
shown Fig. 20 and Fig. 21. It can be observed that by the                โ€œSensorless output       maximization control for variable-
optimization the magnetic saturation is nullified.                       speed wind generation system using IPMSG,โ€ IEEE Trans.
                                                                         Ind. Appl., vol. 41, no. 1, pp. 60โ€“67, Jan./Feb. 2005.
                                                                 [5]     Y. Shi and R. C. Eberhart, โ€œEmpirical study of particle
                                                                         swarm optimization,โ€ in            Proc. IEEE Int. Conf.
                                                                         Evol.Comput., May 4โ€“9, 1998, pp. 69โ€“73
                                                                 [6]     H. Li, Z. Chen, Institute of Energy Technology, Aalborg
                                                                         University, Aalborg East DK-9220, Denmark, โ€œOverview of
                                                                         different wind generator systems and their comparisonsโ€.
                                                                         Published in IET Renewable Power Generation Received on
                                                                         24th January 2007, Revised on 23rd August 2007.
              Fig .20. Time Vs Id, after PSO

                                                        www.ijmer.com                                                    4075 | Page
International Journal of Modern Engineering Research (IJMER)
              www.ijmer.com         Vol.2, Issue.6, Nov-Dec. 2012 pp-4069-4076       ISSN: 2249-6645
                      BIOGRAPHY
Prashantkumar.S.Chinamalli         born     in     Shahapur,
Karnataka, India on 10th june 1987,received his B.E. degree
in Electrical & Electronics Engineering department from
Poojya DoddappaEngineering College,Gulbarga in 2010.
M.Tech in Power & Energy System from Basaveshwara
Engineering Department in 2012.His areas of interest
include Power System, Drives and Renewable Energy
Sources. He is presently working as Asst. Prof in the
Department of Electrical Engineering at Yashoda Technical
Campus/Shivaji University, Pune, India.
Naveen T S born in Bangalore, Karnataka, India on 11th Oct
1986, recived his B.E. degree in Electrical & Electronics
Engineering department from Acharya Institute of
Technology, Bangalore in 2008.M.Tech in Power & Energy
System from Basaveshwara Engineering Department in
2012.His areas of interest include Power System, Reactive
Power management. He is presently working as faculty in
the Department of Electrical & Electronics Engineering at
Acharya Institute of technology, Bangalore, India.
Dr. Shankar C B was born in Raichur, Karnataka, India in
1969. He obtained B.E (Electrical & Electronics) and M.E.
(Energy systems) degree from Karnataka University
Dharwad, Karnataka, India in 1991 and Dec 94 respectively.
He got his Ph D from VTU in 2011.His areas of interest
include FACTS controllers, optimization techniques and
intelligent systems.
He has attended National and International Conferences. He
is member of IEEE and presently working as Professor in
the Department of Electrical & Electronics Engineering at
Acharya Institute of technology, Bangalore, India.




                                                      www.ijmer.com                                    4076 | Page

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Power Loss Minimization of Permanent Magnet Synchronous Generator Using Particle Swarm Optimization

  • 1. International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4069-4076 ISSN: 2249-6645 Power Loss Minimization of Permanent Magnet Synchronous Generator Using Particle Swarm Optimization Prashant Kumar S. Chinamalli1, Naveen T. S.2, Shankar C. B.3 1 (Electrical Department,Yashoda Technical Campus/Shivaji University, India) 2, 3 (Electrical & Electronics Department, Acharya Institute of Tecnology,Bangalore, Vishweshwaraih Technological University, India ABSTRACT: Interior Permanent-magnet synchronous consistently impressive with the main engineering challenge generators (IPM) are commonly used for variable-speed to the wind industry to design an efficient wind turbine to wind turbines to produce high efficiency, high reliability, harness energy and turn it into electricity. and low-cost wind power generation. An IPM driven by a The use of permanent-magnet synchronous wind turbine, in which the d-axis and q-axis stator-current machines (PMSMs) for wind power generation has received components are optimally controlled to achieve the increasing attention in recent years [1]โ€“[6]. The PMSMs can maximum wind power generation and Particle Swarm provide high-efficiency and high-reliability power Optimization (PSO) for loss minimization of the IPMSG. generation, since there is no need for external excitation and The effect of magnetic saturation, which causes the highly no copper losses in the rotor circuits. In addition, the high- nonlinear characteristics of the IPMSG, has been power density PMSMs are small in size, which reduces the considered in the control scheme design. The optimal d-axis cost and weight of wind turbines. Furthermore, in the wind stator-current command is obtained as a function of the generation system equipped with a PMSM and power- IPMSG rotor speed by solving a constrained nonlinear- electronic converters, the wind turbine can be operated to optimization problem that minimizes the copper and core extract the maximum power from the wind at various wind losses of the IPMSG. At any wind speed within the speeds by adjusting the shaft speed optimally. Therefore, operating range, the IPMSG rotor speed is optimally the PMSMs are commonly used for small variable-speed controlled to extract maximum wind power. The PSO wind turbines to produce high efficiency, high reliability, technique guides to narrow convergence solution of non- and low-cost wind power generation. linearity introduced in the model. The proposed control Energy production and utilization, efficiency is scheme provides the wind generation system with the always an important issue, so previously the minimization maximum efficiency and high dynamic performance [1] [2]. of the core losses of a PMSM through a suitable design of magnets and slots and the choice of the number of poles. In fact, the efficiency of an IPMSM can be improved not only Keywords: Permanent magnet synchronous generator, during the machine design stage but also during the magnetic saturation, loss minimization. operation stage. By optimally controlling the d-axis component of the stator currents even by optimizing the I. INTRODUCTION values with particle swarm optimization, the stator copper Resolving the worldโ€™s growing demand for energy, and core losses of an IPMSM can be minimized. for minimizing related impacts on the environment and with increased competition for energy supplies represent some of II. MODELING OF WIND TURBINE SYSTEM the greatest technical challenges of the next several decades. The basic configuration of an IPMSG driven by a Fossil fuels supply more than 80 percent of the worldโ€™s wind turbine is as shown in Fig.1. The IPMSG converts the primary energy but they are finite resources and major mechanical power from the wind turbine to ac electrical contributors to global climate change. The ways and means power, which is then converted to dc power through an for their ultimate replacement with clean, affordable and IGBT pulse-width modulation (PWM) converter with a dc sustainable energy sources at the scale required to power the link to supply the dc load. Control of the IPMSG is world are not yet readily available. Turning off the carbon achieved by controlling the ac-side voltages of this PWM emissions is the first step and many of the solutions which power converter. By using an additional power inverter, the are familiar are windmills, solar panels, nuclear plants etc... IPMSG can supply the ac electrical power with constant All three technologies are part of the energy mix, although voltage and frequency to the power grid or ac load. each has its issues, including noise from windmills and The mechanical power that the wind turbine radioactive waste from nukes. Moreover, existing energy extracts from the wind is calculated by infrastructures around the world are complex and large, where they require enormous capital investment and have 1 operational Life spans of 50 years or more. In windmills (a ๐‘ƒ ๐‘š = 2 ๐œŒ๐ด ๐‘Ÿ ๐‘ฃ ๐‘ค ๐ถ ๐‘ƒ ๐œ†, ๐›ฝ (1) much older technology) wind energy is used to turn mechanical machinery to do physical work; historically, windmills were used traditionally for grinding grain or spices, pumping water, sawing wood or hammering seeds. The evolution of modern turbines is a remarkable success story of engineering and scientific skill, coupled with a Strong entrepreneurial spirit. The progress of wind energy around the world in recent years has been www.ijmer.com 4069 | Page
  • 2. International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4069-4076 ISSN: 2249-6645 Wind speed is in the range of 4โ€“11 m/s. The parameters of the wind turbine system as listed in Table. 1. Table. 1: Parameters of the wind turbine system Air density 1.08 kg/m3 Rotor diameter 11 m Rated wind speed 10 m/s Fig. 1: Wind turbine system using IPMSG [4] Rated rotational speed 200 m where ฯ is the air density in kilograms per cubic meter, Ar =ฯ€R2 is the area swept by the rotor blades in square meters, R is the wind-turbine rotor radius in meters, vw is the wind III. MODELING OF PERMANENT MAGNET speed in meters per second, and CP is the power coefficient, SYNCHRONOUS GENERATOR which is a function of both tip-speed ratio ฮป and the blade Permanent Magnet Synchronous machines pitch angle ฮฒ. The mathematical representation of CP is (PMSMโ€™s) are non-salient pole AC synchronous motors, given by [4] these synchronous motor drives are suitable for constant speed applications as its speed of operation depends only on ๐œ‹ ๐œ† + 0.1 the frequency of the stator supply. Synchronous motor with ๐ถ ๐‘ƒ ๐œ†, ๐›ฝ = 0.3 โˆ’ 0.00167๐›ฝ ๐‘ ๐‘–๐‘› permanent magnet is a choice in kW range for applications 10 โˆ’ 0.3๐›ฝ like wind turbines, aerospace actuators, electric vehicles etc. The advantages of permanent magnet synchronous motor โˆ’0.000184 ๐œ† โˆ’ 3 ๐›ฝ(2) over the other motors are of higher efficiency, higher torque to inertia ratio and compact in size. The PMSM used here is Where ฮป is defined by ฯ‰tR/vwandฯ‰t is the wind- an Interior Permanent Magnet Synchronus Generator turbine rotational speed in radians per second. (PMSG). The CP โˆ’ ฮป curve described by Eqn (2) for the wind turbine is as shown in Fig. 2. In terms of Fig.2 and the 3.1 Dynamic Modeling: definition of ฮป, at any wind speed within the operating The stator consists of three phase winding having range, there is a unique wind-turbine shaft rotational spatial displacement from each other. The axis of phase-1 is speed to achieve the maximum power coefficient CPmax. In taken as reference axis for the stationary co-ordinates fixed terms of Eqn (1), when CP is controlled at the maximum to the stator. The currents in the winding can have any value, the maximum mechanical power is extracted from the general variation with respect to time. Assuming that the wind energy. spatial distribution of mmf produced by each coil is sinusoidal in nature, the stator mmf caused by three phase currents flowing in the three windings can be represented by a single time varying quantity which has got some spatial orientation. The stator current space phasor diagram is shown in Fig. 4.The space vector of stator current can be represented in terms of three phase currents as, ๐‘  ๐‘– ๐‘  ๐‘ก = ๐‘– ๐‘ 1 ๐‘ก + ๐‘– ๐‘ 2 ๐‘ก ๐‘’ ๐‘—๐›พ + ๐‘– ๐‘ 3 ๐‘ก ๐‘’ ๐‘—2๐›พ (3) where is1,is2 and is3 are the stator phase currents and ฮณ is the advanced current angle. The space vector of stator current can also be represented in Fig. 2: CP- ฮป curve of the wind turbine. terms of equivalent two phase (ฮฑ-ฮฒ) axis currents as, ๐‘– ๐‘ ๐‘  ๐‘ก = ๐‘– ๐‘ ฮฑ ๐‘ก + ๐‘—๐‘– ๐‘ ฮฒ ๐‘ก (4) 0 As ๐›พ =120 , the ฮฑ axis current and ฮฒ axis currents can be written as, ๐‘– ๐‘ ฮฑ ๐‘ก = ๐‘– ๐‘ 1 ๐‘ก cos 0 + ๐‘– ๐‘ 2 ๐‘ก cos 120 + ๐‘– ๐‘ 3 ๐‘ก cos 240 (5) ๐‘– ๐‘ ฮฒ ๐‘ก = ๐‘– ๐‘ 1 ๐‘ก sin 0 + ๐‘– ๐‘ 2 ๐‘ก sin 120 + ๐‘– ๐‘ 3 ๐‘ก sin 240 (6) Fig. 3: Wind velocity input by signal builder. The signal builder block is used to give wind speed as an input to the wind turbine which is as shown in Fig.3. www.ijmer.com 4070 | Page
  • 3. International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4069-4076 ISSN: 2249-6645 where ฮต is the angle between rotor reference axis and stator reference axis. The above equations are used in the modeling of transformation of co-ordinates and sources as shown in the below Fig. 7, 8 and 9. Fig.4: Representations of Co-ordinate Systems The above equation can be simplified as, Fig.7: abc to ฮฑ-ฮฒ transformation Fig.5: Stator current space phasor Fig.8: ฮฑ-ฮฒ to d-q transformation Fig.6: Stator current transformation from three phase to ฮฑ-ฮฒ axis. 1 1 ๐‘– ๐‘ ฮฑ ๐‘ก = ๐‘– ๐‘ 1 ๐‘ก โˆ’ ๐‘– ๐‘ 2 ๐‘ก โˆ’ ๐‘– ๐‘ 3 ๐‘ก (7) 2 2 โˆš3 โˆš3 ๐‘– ๐‘ ฮฒ ๐‘ก = ๐‘– ๐‘ 2 ๐‘ก โˆ’ ๐‘– ๐‘ 3 ๐‘ก (8) 2 2 Fig.9: Voltage to Current transformation For a three phase wire system the condition, 3.2 Non-Linearity due to Magnetic Saturation: ๐‘– ๐‘ 1 ๐‘ก + ๐‘– ๐‘ 2 ๐‘ก + ๐‘– ๐‘ 3 ๐‘ก = 0 (9) Consider a typical Interior PMSG circuit as below in Fig.10. For the IPMSG, burying the magnets inside the holds good for all instants of time. Using this condition in rotor introduces saliency into the rotor into the rotor magnet above and (ฮฑ-ฮฒ) axis currents can be written as, circuit. The d-axis flux passes through a wide region of low- 3 permeability magnets, while the q-axis flux path has a high ๐‘– ๐‘ ฮฑ ๐‘ก = 2 ๐‘– ๐‘ 1 ๐‘ก (10) permeability. Therefore, the IPMSG has a saliency (Lq> Ld) โˆš3 โˆš3 and the effect of magnetic saturation along the q-axis is ๐‘– ๐‘ ฮฒ ๐‘ก = 2 ๐‘– ๐‘ 2 ๐‘ก โˆ’ 2 ๐‘– ๐‘ 3 ๐‘ก (11) dominant. Interior PMSG is considered with magnetic saturation, i.e. there is a flux linkage between the q-axis For the dynamic modeling, first convert the three quantities inductances so the Lq will be the function of current iq and to two phase quantities i.e. abc to ฮฑ-ฮฒ transformation. The d-axis inductance Ld will be considered constant value and general formula can be given as below, they are represented as Ld, Lq(iq). The dynamic equation of a 3 ๐‘‹ฮฑ = ๐‘‹ ๐‘Ž 2 (12) three-phase IPMSG can be written in the rotor reference โˆš3 frame as. ๐‘‹ฮฒ = 2 (๐‘‹ ๐‘ โˆ’ ๐‘‹๐‘) (13) 3 Id - ๐‘ฃsฮฑ = ๐‘ฃ ๐‘ ๐‘Ž ฯ‰Lqiq + (14) Rs Iq + ฯ‰Lqiod - 2 Rs + โˆš3 ๐‘ฃsฮฒ = 2 (๐‘ฃ ๐‘ ๐‘ โˆ’ ๐‘ฃ ๐‘ ๐‘ ) (15) Vd Rc Vq Rc ฯ‰ฯˆm - Similarly the transformation of stator currents and voltages Ld Lq from ฮฑ-ฮฒ to d-q co-ordinates is done using the angle ฮต. (a) (b) ๐‘ฃ ๐‘ ๐‘‘ = ๐‘ฃ ๐‘ ฮฑ cos ฮต + ๐‘ฃ ๐‘ ฮฒ sin ฮต (16) Fig.10. Equivalent circuits of the IPMSG. (a) d-axis ๐‘ฃ ๐‘ ๐‘ž = ๐‘ฃ ๐‘ ฮฒ cos ฮต โˆ’ ๐‘ฃ ๐‘ ฮฑ sin ฮต (17) equivalent circuit. (b) q-axis equivalent circuit. www.ijmer.com 4071 | Page
  • 4. International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4069-4076 ISSN: 2249-6645 ๐‘‘๐‘– ๐‘œ๐‘‘ Rated power 25 kW ๐ฟ๐‘‘ ๐‘‘๐‘ก = โˆ’๐‘… ๐‘  ๐‘– ๐‘‘ + ๐œ”๐ฟ ๐‘ž ๐‘– ๐‘ž ๐‘– ๐‘œ๐‘ž + ๐‘ฃ ๐‘‘ (18) ๐‘‘๐‘– ๐‘œ๐‘ž Ratedrotor speed 1200 rpm ๐ฟ๐‘ž ๐‘–๐‘ž ๐‘‘๐‘ก = โˆ’๐‘… ๐‘  ๐‘– ๐‘ž โˆ’ ๐œ”๐ฟ ๐‘‘ ๐‘– ๐‘œ๐‘‘ โˆ’ ๐œ”๐œ“ ๐‘š + ๐‘ฃ ๐‘ž (19) The electromagnetic torque developed by the machine is given by, 3 ๐‘‡ ๐‘” = โˆ’ 4 ๐‘ƒ๐‘› [๐œ“ ๐‘š ๐‘– ๐‘œ๐‘ž + ๐ฟ๐‘‘ โˆ’ ๐ฟ๐‘ž ๐‘–๐‘ž ๐‘– ๐‘œ๐‘‘ ๐‘– ๐‘œ๐‘ž ] (20) The following equations help in complete dynamic modeling of IPMSG: ๐‘‘๐‘– ๐‘œ๐‘‘ ๐‘ฃ๐‘‘ = ๐ฟ๐‘‘ ๐‘‘๐‘ก + ๐‘… ๐‘  ๐‘– ๐‘‘ โˆ’ ๐œ”๐ฟ ๐‘ž ๐‘– ๐‘ž ๐‘– ๐‘œ๐‘ž (21) Fig 11. Simulink model of IPMSG ๐‘‘๐‘– ๐‘œ๐‘ž 3.3 PWM Generator Side Converter: ๐‘ฃ๐‘ž = ๐ฟ ๐‘ž ๐‘– ๐‘ž ๐‘‘๐‘ก + ๐‘… ๐‘  ๐‘– ๐‘ž + ๐œ”๐ฟ ๐‘‘ ๐‘– ๐‘œ๐‘‘ + ๐œ”๐œ“ ๐‘š (22) ๐‘‘๐œ” ๐ฝ = ๐‘‡ ๐‘š โˆ’ ๐‘‡๐‘” (23) ๐‘‘๐‘ก 1 ๐œ”= ๐ฝ ๐‘‡ ๐‘š โˆ’ ๐‘‡๐‘” ๐‘‘๐‘ก (24) ๐‘‘๐œ– ๐‘ƒ ๐‘‘๐‘ก = 2 ๐œ” = ๐œ”๐‘” (25) Fig . 12. PWM generator side converter The pulse width modulation generator side where ๐œ“ ๐‘š is the magnet flux linkage, ๐‘… ๐‘  is the converter consists of IGBT based 3-phase bridge voltage- stator resistance, ๐‘ƒ๐‘› is the number of poles, ๐‘‡ ๐‘š is the input source converter. The only difference between rectifier and mechanical torque given by ๐‘‡ ๐‘š = ๐‘ƒ ๐‘š /๐œ” ๐‘” , ๐œ” ๐‘” is the rotor inverter is the definition of power sign. The switching speed, J is the inertia, iod, ioq are initial current values of d- frequency of the converter is assumed to be sufficiently high axis and q-axis respectively, ๐ฟ ๐‘‘ is the d-axis inductance and to make an average analysis valid, which means that the switching ripple should be negligible compared to the assumed to be constant, and ๐ฟ ๐‘ž is the q-axis inductance averaged values. The generator side converter is shown in which varies depending on the value of ๐‘– ๐‘ž . Fig. 12.The system equation for generator side converter The effect of magnetic saturation is considered by can be written as: modeling ๐ฟ ๐‘ž as a function of ๐‘– ๐‘ž given by [1], ๐‘‘๐ผ ๐‘Ž 2๐‘† ๐‘Ž โˆ’ ๐‘† ๐‘ โˆ’ ๐‘† ๐‘ ๐‘‰๐‘Ž = ๐‘… ๐‘Ÿ ๐ผ ๐‘Ž + ๐ฟ ๐‘Ÿ + ๐‘‰ ๐‘‘๐‘ . (27) ๐‘‘๐‘ก 3 ๐ฟ ๐‘ž = ๐ฟ ๐‘ž๐‘œ โˆ’ ๐‘˜ ๐‘– ๐‘ž (26) ๐‘‘๐ผ ๐‘ โˆ’๐‘† ๐‘Ž +2๐‘† ๐‘ โˆ’ ๐‘† ๐‘ where k is a positive constant, the parameters of the ๐‘‰๐‘ = ๐‘… ๐‘Ÿ ๐ผ ๐‘ + ๐ฟ ๐‘Ÿ ๐‘‘๐‘ก + ๐‘‰ ๐‘‘๐‘ . 3 (28) IPMSG are given in the Table 2. ๐‘‘๐ผ ๐‘ โˆ’๐‘† ๐‘Ž โˆ’ ๐‘† ๐‘ + 2๐‘† ๐‘ All the above equations along with parameters specified in ๐‘‰๐‘ = ๐‘… ๐‘Ÿ ๐ผ ๐‘ + ๐ฟ ๐‘Ÿ ๐‘‘๐‘ก + ๐‘‰ ๐‘‘๐‘ . 3 (29) Table.2 are used to model interior permanent magnet synchronous generator considering magnetic saturation as where Va,Vb,Vc are the three phase stator voltage; Ia,Ib,Ic are shown below in Fig.11. three phase currents; Sa,Sb,Sc are gate pulses to IGBT and Vdc is DC link voltage. Table 2. Parameters of IPMSG IV. MODELING FOR MAXIMUM WIND POWER Rs 0.1764 โ„ฆ GENERATION WITH LOSS MINIMIZATION Ld 6.24 mH 4.1 Maximum Wind Power Generation: By adjusting the wind-turbine shaft speed Lqo 20.5822 mH optimally, the tip speed ratio ฮป can be controlled at the optimal value to achieve the maximum power coefficient ฯˆm 0.246 Wb CPmaxregardless of the wind speed. The maximum mechanical power is therefore extracted from the wind J 1.2 kg . m2 energy. At this optimal condition, the optimal IPMSG rotor speed is proportional to the wind speed, given by Pn 6 ฯ‰g,opt= kฯ‰vw (30) k 0.1879 mH/A Where kฯ‰ is a constant determined by the wind-turbine characteristics. The generator rotor speed must be a nearer www.ijmer.com 4072 | Page
  • 5. International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4069-4076 ISSN: 2249-6645 value to the optimal rotor speed which leads to the 1) Initialize a population of particles with random extraction of maximum power from wind velocity. positions and velocities of M dimensions in the problem space. 4.2 Minimization of the Copper and Core Losses of 2) Define a fitness-measure function to evaluate the IPMSG: performance of each particle. The losses of a PMSG can be decomposed into 3) Compare each particleโ€™s present position xi with its four components, namely, stator copper loss, core loss, xi,pbestbased on the fitness evaluation. If the current mechanical loss, and stray-load loss. Only the stator copper position xiis better than xi,pbest, then set xi,pbest= xi. and core losses are explicitly dependent on and can be 4) If xi,pbest is updated, then compare each particleโ€™s xi,pbest controlled by the fundamental components of the stator with the swarm best position xgbest based on the fitness currents. Therefore, the maximum efficiency condition of evaluation. If xi,pbestis better than xgbest, then set xgbest= the IPMSG is obtained by solving the following nonlinear- xi,pbest. optimization problem offline to minimize the total copper 5) At iteration k, the velocity of each particle is updated and core losses of the IPMSG by i.e we have vi (k + 1) = w ยท vi (k) + c1ฯ†1 (xi,pbest(k) โˆ’ xi (k)) + c2ฯ†2 (xgbest(k) โˆ’ xi (k)), i= 1, 2, ...,N. (35) ๐‘ƒ๐‘™๐‘œ๐‘ ๐‘  = ๐‘ƒ๐‘๐‘œ๐‘๐‘๐‘’๐‘Ÿ + ๐‘ƒ๐‘๐‘œ๐‘Ÿ๐‘’ (31) 6) Based on the updated velocity, each particle then changes its position by ๐‘ƒ๐‘๐‘œ๐‘๐‘๐‘’๐‘Ÿ = 1.5 ๐‘… ๐‘  ๐‘– 2 + ๐‘– 2 ๐‘‘ ๐‘ž (32) xi (k + 1) = xi (k) + vi(k + 1), i= 1, 2, ..,N.(36) 7) Repeat steps (3) to (6) until a criterion, usually a ๐‘ƒ๐‘๐‘œ๐‘Ÿ๐‘’ = 1.5 ๐‘– 2 + ๐‘– 2 ๐‘… ๐‘ ๐œ” ๐‘” ๐‘๐‘‘ ๐‘๐‘ž (33) sufficiently good fitness or a maximum number of iterations, is achieved. ๐ฟ ๐‘‘ ๐‘– ๐‘œ๐‘‘ +๐œ“ ๐‘š 2 + ๐ฟ ๐‘ž (๐‘– ๐‘ž )๐‘– ๐‘œ๐‘ž 2 The final value of xgbest is regarded as the optimal solution = 1.5 ๐œ”2 ๐‘… ๐‘ (๐œ” ๐‘” ) (34) of the problem. In Eqn (35), c1 and c2 are positive constants Where Pcopper is the copper loss, Pcore is the core loss [6], and representing the weighting of the acceleration terms that icd and icq are the currents at the resistant Rc. guide each particle toward the individual best and the swarm best positions, xi,pbestand xgbest, respectively; ฯ†1 and ฯ†2 An optimal IPMSG rotor speed calculated by Eqn are uniformly distributed random numbers in [0, 1]; w is a (30), the solutions of the nonlinear-optimization problem positive inertia weight developed to provide better control yield the optimal values of id and iq, which minimize the between exploration and exploitation; N is the number of total copper and core losses of the IPMSG. Therefore, at particles in the swarm. The last two terms in Eqn (12) any wind speed, the solutions of Eqn (30) and Eqn (34) enable each particle to perform a local search around its provide the desired optimal IPMSG rotor speed, optimal individual best position xi,pbestand the swarm best position currents id and iq to achieve the maximum wind power xgbest. The first term in Eqn (35) enables each particle to extraction, and loss minimization of the IPMSG. Without perform a global search by exploring a new search space. considering the effect of magnetic saturation (i.e., Lq is Because of many attractive features, e.g., multi- constant) and the variation of Rc, Eqn (34) would be a agent search, simple implementation, small computational constrained nonlinear quadric optimization problem that can load, and fast convergence, the PSO algorithm can provide a be solved by conventional nonlinear-optimization methods. fast and efficient search for the optimal solution. These However, the inclusion of magnetic saturation and variation features provide PSO with superior performance over other of Rc results in a complex nonlinear-optimization problem evolutionary computation algorithms (e.g., genetic that requires extensive computation effort when using algorithms) in many applications. In addition, for many conventional nonlinear optimization methods. In order to complex optimization problems that are difficult to achieve this stochastic optimization technique called formulate mathematically or to solve by traditional particle swarm optimization (PSO) [5] is employed to optimization methods, PSO is efficient to find the optimal obtain the optimal solution of Eqn (34). solution. The values of the PSO parameters are chosen as: V. PARTICLE SWARM OPTIMIZATION c1 = c2 = 2, N = 20 and w= 1.4 โˆ’ (1.4 โˆ’ 0.4) Particle Swarm Optimization is a population-based *(k/K), where k is the iteration number and K is the stochastic optimization technique. It searches for the maximum number of iterations. The PSO algorithm only optimal solution from a population of moving particles. performs a 1-D search for the optimal value of iq. The Each particle represents a potential solution and has a optimal value of idis determined by the torque in Eqn (20) position (vector xi) and a velocity (vector vi ) in the problem and the corresponding optimal value of iq, where the space. Each particle keeps track of its individual best electrical torque Tgin Eqn (20) is determined by Eqn (30) position xi,pbest, which is associated with the best fitness it and the constraint equations of Eqn (34). The fitness- has achieved so far, at any step in the solution. Moreover, measure function is simply the total copper and core losses the best position among all the particles obtained so far in Ploss of the IPMSG. It is calculated by the first two the swarm is kept track of as xgbest. This information is constraint equations of Eqn (34). By solving the nonlinear- shared by all particles. optimization problem in Eqn (34) at various IPMSG rotor The PSO algorithm is implemented in the following speeds, the optimal values of idand iqare obtained as iterative procedure to search for the optimal solution. functions of the IPMSG rotor speed ฯ‰g. The relationship between the optimal d-axis and q-axis stator-current www.ijmer.com 4073 | Page
  • 6. International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4069-4076 ISSN: 2249-6645 components and the IPMSG rotor speed can be 6.2 IOL- Based Non-Linear Current Control: approximated by a fourth-order and a third-order Instead of approximating a nonlinear systemโ€™s polynomial, respectively, given by dynamics locally around some operating point via linearization, the IOL technique transforms the nonlinear ๐‘– ๐‘‘,๐‘œ๐‘๐‘ก = ๐พ ๐‘‘4 ๐œ”4 + ๐พ ๐‘‘3 ๐œ”3 + ๐พ ๐‘‘2 ๐œ”2 + ๐พ ๐‘‘1 ๐œ” ๐‘” + ๐‘” ๐‘” ๐‘” system into an equivalent linear system via feedback and ๐พ ๐‘‘0 (37) nonlinear coordinate transformation. This is a systematic way to globally linearize a part of or all the dynamics of the ๐‘– ๐‘ž,๐‘œ๐‘๐‘ก = ๐พ ๐‘ž3 ๐œ”3 + ๐พ ๐‘ž2 ๐œ”2 + ๐พ ๐‘ž1 ๐œ” ๐‘” + ๐พ ๐‘ž0 ๐‘” ๐‘” (38) nonlinear system. In such a scheme, the inputโ€“output dynamics are linearized, but the state equations may be only The coefficients of both polynomials are listed in partially linearized. Residual nonlinear dynamics, called Table 3. However, it should be pointed out that Eqn (37) internal dynamics, do not depend explicitly on the system and Eqn (38) only provide the optimal operating conditions input and, thus, are not controlled. If the internal dynamics of the IPMSG for the wind speed below the rated value. are trivial or stable at the equilibrium point, then the entire When the wind speed exceeds the rated value, the phase nonlinear system can be stabilized by a standard linear current and/or the terminal voltage reach their ceiling feedback control using the linearized inputโ€“output values, and therefore, the optimal speed tracking control dynamics. cannot be applied. Under this condition, the current and voltage limited maximum output control can be applied to VII. RESULTS control IPMSG. The model of Wind turbine system and IPMSG are previously run for the existing condition of initial values. Table 3. Coefficients of approximating polynomials Later, speed control and current control techniques are introduced for the optimization of rotor speed and current Coefficients of id,opt Coefficients of iq,opt by running Particle Swarm Optimization algorithm. In PSO algorithm the complete model is called through command to Kd4 1.291 ร— 10 -11 Kq3 7.528 ร— 10 -9 get the desired output of Maximum generation and Power loss minimization. All results are taken from the simulation Kd3 -3.523 ร— 10-8 Kq2 -3.477 ร— 10 -5 of the modeling in MATLAB 2011b. Kd2 1.154 ร— 10 -5 Kq1 -1.648 ร— 10 -3 Kd1 -1.348 ร— 10 -2 Kq0 1.263 Kd0 -1.589 ร— 10 -2 VI. CONTROL OF PMSG Fig .14. wind velocity Vs ฯ‰g,opt As per the Eqn(30) the ฯ‰g,opt varies linearly with respect to the wind velocity as shown in Fig .14. From this it can be justified that as the wind velocity varies the rotor speed varies optimally in a linear manner. Fig. 13: Control of scheme for the IPMSG 6.1 Optimal IPMSG Rotor-Speed Tracking Control: Based on the IPMSG motion Eqn (23), a PI-type speed controller is designed to track the optimal rotor speed Fig. 15. Three phase stator current at any moment, applied for the speed controller, as shown by the dash-line block in Fig. 22. The gain ka is given by ka = 1/kp. The output of the speed controller is the optimal torque command Tโˆ—g,opt for the IPMSG, which corresponds to the maximum power point for wind power generation. By using this optimal torque command and the optimal d-axis current command from Eqn (37), the solution of Eqn (20) provides the optimal q-axis stator-current command for the inner loop current regulation. In the real application, the Fig .16. Three stator voltage values of iโˆ—q,opt can be generated offline over the entire operating range of the IPMSG. www.ijmer.com 4074 | Page
  • 7. International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4069-4076 ISSN: 2249-6645 Fig. 15 and Fig. 16 show the three-phase controlled stator current and voltage of the IPMSG after PSO. As voltage is 200V and current is 100A so it can be stated that WTG system generates upto 20 Kw power. The simulated result for a dc link current, whichis controlled by the rectifier side controller, is as shown in Fig. 17. For maximum wind power tracking the speed controller is employed, this can be noticed from Fig 18 and Fig. 21. Time Vs Iq, after PSO Fig 19.Because of the relatively slow response of the WTG mechanical system, during the acceleration of the WTG,the After the PSO algorithm the optimized results of currents PI-type speed controller is saturated, and the resulting are incorporated in Eqn (34), hence there is a minimization IPMSG electrical-torque command generated by the speed in the total power loss as shown in Table 5. controller remains at its limit value of zero. Table .5. Total Ploss minimization Total Ploss Total Ploss Total Ploss before PSO after PSO minimization 3.3 kW 2.57 kW 22.12% VIII. CONCLUSION Modeling and simulation of a 25kW variable speed wind energy conversion system employing a Maximum Torque per Current control and Particle Swarm Fig .17. DC link voltage Optimization is presented in the paper. PMSGs are commonly used for small variable speed WTG systems. In As a result, the electrical output power and the q-axis stator such systems, by adjusting the shaft speed optimally, the current of the IPMSG are both regulated at zero during the maximum wind power can be extracted at various wind saturation of the speed controller. speeds within the operating range. In addition, when using an IPMSG, the stator copper and core losses of the generator can be minimized by optimally controlling the d- axis component of the stator currents. However, to achieve the high performance of the WTG system, magnetic saturation of the IPMSG must be taken into account in the control-system design. Implementation of PSO results in the minimization of total power loss and thus improves the efficiency of the system. This proposed control provides the wind generation system with high dynamic performance and improved power efficiency. Fig .18. Time Vs ฯ‰g REFERENCES [1] T. M. Jahns, G. B. Kliman, and T. W. Neumann, โ€œInterior permanentmagnetsynchronous motors for adjustable-speed drives,โ€ IEEE Trans.Ind. Appl., vol. IA-22, no. 4, pp. 738โ€“ 747, Jul. /Aug. 1986. [2] E. Muljadi, C. P. Butterfield, and Y. Wang, โ€œAxial-flux modular permanent- magnet generator with a toroidal winding for wind-turbine applications,โ€ IEEE Trans. Ind. Appl., vol. 35, no. 4, pp. 831โ€“836, Jul./Aug. 1999. [3] S. Grabic, N. Celanovic, and V. A. Katic, โ€œPermanent magnet synchronous generator for wind turbine Fig. 19. Time Vs ฯ‰g,opt application,โ€ IEEE Trans. Power Electron., vol. 13, no.3, pp. 1136โ€“1142, May 2008. The optimized results of current of d-axis and q-axis are [4] S. Morimoto, H. Nakayama, M. Sanada, and Y. Takeda, shown Fig. 20 and Fig. 21. It can be observed that by the โ€œSensorless output maximization control for variable- optimization the magnetic saturation is nullified. speed wind generation system using IPMSG,โ€ IEEE Trans. Ind. Appl., vol. 41, no. 1, pp. 60โ€“67, Jan./Feb. 2005. [5] Y. Shi and R. C. Eberhart, โ€œEmpirical study of particle swarm optimization,โ€ in Proc. IEEE Int. Conf. Evol.Comput., May 4โ€“9, 1998, pp. 69โ€“73 [6] H. Li, Z. Chen, Institute of Energy Technology, Aalborg University, Aalborg East DK-9220, Denmark, โ€œOverview of different wind generator systems and their comparisonsโ€. Published in IET Renewable Power Generation Received on 24th January 2007, Revised on 23rd August 2007. Fig .20. Time Vs Id, after PSO www.ijmer.com 4075 | Page
  • 8. International Journal of Modern Engineering Research (IJMER) www.ijmer.com Vol.2, Issue.6, Nov-Dec. 2012 pp-4069-4076 ISSN: 2249-6645 BIOGRAPHY Prashantkumar.S.Chinamalli born in Shahapur, Karnataka, India on 10th june 1987,received his B.E. degree in Electrical & Electronics Engineering department from Poojya DoddappaEngineering College,Gulbarga in 2010. M.Tech in Power & Energy System from Basaveshwara Engineering Department in 2012.His areas of interest include Power System, Drives and Renewable Energy Sources. He is presently working as Asst. Prof in the Department of Electrical Engineering at Yashoda Technical Campus/Shivaji University, Pune, India. Naveen T S born in Bangalore, Karnataka, India on 11th Oct 1986, recived his B.E. degree in Electrical & Electronics Engineering department from Acharya Institute of Technology, Bangalore in 2008.M.Tech in Power & Energy System from Basaveshwara Engineering Department in 2012.His areas of interest include Power System, Reactive Power management. He is presently working as faculty in the Department of Electrical & Electronics Engineering at Acharya Institute of technology, Bangalore, India. Dr. Shankar C B was born in Raichur, Karnataka, India in 1969. He obtained B.E (Electrical & Electronics) and M.E. (Energy systems) degree from Karnataka University Dharwad, Karnataka, India in 1991 and Dec 94 respectively. He got his Ph D from VTU in 2011.His areas of interest include FACTS controllers, optimization techniques and intelligent systems. He has attended National and International Conferences. He is member of IEEE and presently working as Professor in the Department of Electrical & Electronics Engineering at Acharya Institute of technology, Bangalore, India. www.ijmer.com 4076 | Page