A New Method for Analyzing Frequency and Voltage Fluctuations of Power System with Wind

Generators Installed

Junji Tamura, Marwan Rosyadi, Rion Takahashi, Atsushi Umemura

Kitami Institute of Technology Kitami-Hokkaido, Japan

Tomoyuki Fukushima, Akira Kuwayama Kazuki Yoshioka, Tomohisa Kaiso Hokkaido Electric Power Co., Inc.

Sapporo, Hokkaido, Japan

Abstract—This paper proposes a new method for evaluating characteristics of frequency and voltage fluctuations of power system in which wind generators are installed. In this paper, a new method based on the transfer function models for frequency response and voltage responses of the power system is developed, from which voltage response of each node in the power system as well as the frequency response can be obtained easily and quickly. Its accuracy is investigated by comparing the results between the proposed method and PSCAD/EMTDC simulations.

Keywords—wind generators, power system, frequency fluctuation, node voltage fluctuation.

I. INTRODUCTION In recent years, renewable energy sources, like wind power

generation, are widely being introduced in the world. However, wind turbine generator output, in general, fluctuates due to wind speed variations. Hence, if a large number of wind turbine generators are connected to a power system, wind farm output can have a serious influence on the power system characteristics, that is, frequency fluctuation and node voltage fluctuation. Therefore smoothing control of wind generator output fluctuations is very important. Simulation analysis of the power system is needed in order to analyze the characteristics of the power system. However, it is difficult to perform simulation analyses of large and complicated power system including various types of wind generators and energy storage systems by using instantaneous value based simulation tool like PSCAD/EMTDC. The new method proposed in this paper is based on transfer function block models of each component in the power system and can easily be applied to a large and complicated power system model.

II. POWER SYSTEM MODEL Power system model considered in this paper is shown in Fig. 1, which is composed of 9-bus main system and two wind farms. Hydro turbine and two steam turbine driven synchronous generators are connected with the main system as SG1, SG2 and SG3, respectively. Two wind farms (WF 1 and WF2) with Variable Speed Wind Turbine-Permanent Magnet Synchronous Generator (VSWT-PMSG) rated at 50 MW are considered to be connected to the main system through Bus 6

Fig. 1. Power system model

TABLE I. SYNCHRONOUS GENERATOR PARAMETERS

Parameters Synchrounous Generators

SG1 (Hydro)

SG2 (Steam)

SG3 (Steam)

Rated MVA 150 200 250 Ra 0.002 pu 0.004 pu 0.003 pu Xa 0.130 pu 0.107 pu 0.102 pu Xd 1.200 pu 1.220 pu 1.651 pu Xq 0.700 pu 1.160 pu 1.590 pu X`d 0.3 pu 0.258 pu 0.273 pu X`q - 0.365 pu 0.380 pu X``d 0.22 pu 0.207 pu 0.215 pu X``q 0.29 pu 0.207 pu 0.215 pu T`do 5.2 sec 8.710 sec 8.970 sec T`qo - 1.500 sec 0.535 sec T``do 0.029 sec 0.033 sec 0.033 sec T``qo 0.034 sec 0.141 sec 0.078 sec

H 3.0 sec 5.4 sec 6.0 sec

SG1

SG2 SG3

Load BLoad A

Load C

P = 1.75 puV = 1.012 pu

P = 1.25 puV = 1.015 pu

P = 0.90 puQ = 0.30 pu

P = 1.25 puQ = 0.50 pu

P = 2.00 puQ = 0.35 pu

j0.065 j0.0576

j0.0

586

18kV/230kV 230kV/16.5kV

13.8

kV/2

30kV

P = 0.45 puV = 1.027 pu

j0.045

1

2 3

4

5

6

7 8

9 12 13

230kV/66kV

0.0085+j0.072 0.0119+j0.1008

0.03

2+j0

.16

0.03

9+j0

.17

0.0075+j0.052

50 Hz, 100 MVA Base

WF2

B/2 = j0.0745 B/2 = j0.1045

B/2

= j0

.153

B/2

= j0

.179

B/2 = j0.054

10

11

j0.0

45

66kV

/230

kV

WF 1

0.0075+j0.052 B/2 = j0.054

P = 0.30 pu

PMSG P = 0.48 pu

PMSG

978-1-4799-0224-8/13/$31.00 ©2013 IEEE 1466

TABLE II. WIND GENERATOR PARAMETERS

Permanent Magnet Synchrounous Generator Parameters WF1 and WF2 Rated MVA 50

Rs 0.02 pu Ls 0.06 pu Lsd 0.90 pu Lsq 0.70 pu

Flux 1.40 pu Frequency 20 Hz

H 6.0 s and 9, respectively. The grid system frequency is 50Hz and the system base power is 100 MVA. The parameters of synchronous generators and PMSG are presented in Table I and Table II, respectively.

III. WIND TURBINE MODEL The mechanical power output of wind turbine captured

from the wind power can be calculated as follows [1]:

),(5.0 32 βλρπ pww CVRP = (1)

where Pw is the captured wind power (W), ρ is the air density (Kg/m3), R is the radius of rotor blade (m), Vw is wind speed (m/s), and Cp is the power coefficient. The value of Cp is dependent on tip speed ratio (λ) and blade pitch angle (β) based on the turbine characteristics as follows [1]:

λβλ

βλ λ643

21

5

),( ceccccC i

c

ip +⎟⎟

⎠

⎞⎜⎜⎝

⎛−−=

−

(2)

with

w

r

VRωλ = (3)

1

035.008.0

113 +

−−

=ββλλi

(4)

where c1 to c6 denote characteristic coefficients of wind turbine (c1=0.5176, c2=116, c3=0.4, c4=5, c5=21 and c6=0.0068) [2], and ωr is rotational speed of turbine in rad/sec.

The Cp-λ characteristics for different values of the pitch angle β are illustrated in Fig. 2. The maximum value of Cp (Cp_opt = 0.48) is achieved for β = 00 and λ= 8.1. This particular value of λ is defined as the optimal value (λopt). Fig. 3 depicts the characteristic between the turbine power output and the rotor speed for different wind speeds where the blade pitch angle is set at 0 deg. The maximum power output (1 pu) of wind turbine is obtained at 11.5 m/sec of wind speed and 1 pu of rotational speed.

Fig. 4 shows the model of the blade pitch controller of wind turbine. The control loop of the pitch actuator is represented by a first-order transfer function with the pitch rate limiter. A PI controller is used to manage tracking error.

optλ

00=β

05=β

010=β

015=β

020=β

Fig. 2. Cp - λ characteristic for different pitch angle

Fig. 3. Wind Turbine Characteristic

β

Fig. 4. Pitch Controller

In variable speed wind turbine the pitch controller is used to regulate rotational speed of PMSG under its rated value (1pu).

The mechanical torque (Tm) is obtained by the ratio between the mechanical power output and rotor speed of the wind turbine as follows:

r

wm

PTω

= (5)

The drive train model of turbine, shaft, and generator is modeled using the single rotating mass model:

dtd

JTT r

tem

ω1=− (6)

where Te and Jt are electrical torque and the total moment of inertia of entire mechanical system, respectively.

The Maximum Power Point Tracking (Pmppt) is calculated without measuring the wind speed as expressed in eq. (7) [3].

optopt

rmppt CpRRP

325.0 ⎟

⎟⎠

⎞⎜⎜⎝

⎛=

λωρπ (7)

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IV. EXCITER AND GOVERNING SYSTEM MODEL OF SYNCHRONOUS GENERATOR

Automatic Voltage Regulator (AVR) model in PSCAD/ EMTDC package [4] are used in this paper. Fig. 5 shows the exciter model considered for all synchronous generator. The field voltage (Ef) is controlled by the AVR system to maintain the terminal voltage (Vt) at reference voltage (Vref).

The schematic diagram of hydro turbine and its governing system used in SG1 are shown in Fig. 6. The hydraulic turbine model equipped with governor system including transient drop compensator, where Rp = 0.05, Tg = 0.2s, TR = 5.0s, RT = 0.38 Tw =1[5], is considered in the simulations.

Fig. 7 shows the block diagram of reheat type steam turbine and its governing system used in SG2 and SG3, where Rp = 0.05, Tg = 0.2s, FHP = 0.3, TRH = 7.0s, and TCH = 0.3s [5], typical values of the turbine system, are used in the analyses.

Fig. 5. Exciter model

Fig. 6. Hydro turbine governing system

Fig. 7. Steam turbine governing system

V. BASIC CONCEPT OF THE NEW METHOD The model system depicted in Fig. 1 is constructed on

PSCAD/EMTDC software to calculate instantaneous (exact) responses of the model system in order to perform comparative analyses between the exact responses and approximated responses obtained from the new method. It is needless to say that such a detailed instantaneous model requires very long computation time.

Fig. 8. Transfer function block model for frequency deviation

As a simple method to calculate frequency responses of the power system quickly and easily, the transfer function block model was developed and proposed in [6], where it is shown that the transfer function block model has very high accuracy.

In Fig.8, conventional synchronous generators in the power system are expressed by using the governor models, in which the total deviation in the active power, PΔ , is used to calculate the frequency deviation, ωΔ . The total active power deviation is calculated by summing the output from conventional generators and wind generators, and then subtracting the consumed power in loads and transmission lines. Output from each conventional generator is controlled by the governor systems according to the frequency deviation. Output from each wind generator is calculated by using eq.(1) for varying wind speed. The transmission line loss is assumed constant here.

Motion equation for all of the conventional generators in the system can be expressed approximately by using the difference between the total supplied power and the demand as follows. This equation also represents the system frequency dynamics.

PePm

dtdM Δ−Δ=Δω

(8)

ωΔ+Δ=Δ DPPe L

(9)

1+1.5s1+1.0s

1001+0.02s

Efmax

Efmin

Ef

Vt

Vref+

- Control Exciter

11+sTg

Δω 1Rp

1+sTR

1+s(RT/RP)TR

Governor

Load reference

+-

Turbine

Pm1-sTw

1+s0.5Tw

Transient Droop Compensator

11+sTg

Δω 1Rp

1+sFHPTRH

(1+sTCH)(1+sTRH)

Governor

Load reference

+-

Turbine

Pm

Wind Farm 1 (WF1)

Wind Farm 2 (WF2)

Hydro Power Plant(SG1)

Thermal Power Plant(SG2)

Thermal Power Plant(SG3)

Load A, B and C

Transmission Loss

+

+

+

+

+

-

-

1Ms+D

Equivalent modelOf generators

ΔPΔω

Pm1

Pm2

Pm3

Pw1

Pw2

PL

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where, M = Equivalent inertia constant (sec) Δω = Angular velocity deviation (pu) ΔPm = Generator mechanical input deviation (pu) ΔPe = Generator electrical output deviation (pu) ΔPL = Load change (pu) D = Frequency characteristic coefficient of load (%/%Hz)

Eqs.(8) and (9) can be represented as a block diagram shown in Fig. 9.

On the other hand, Fig.10 shows a block model for node voltage calculation. It should be noted that the frequency and voltage analyses are calculated separately. The frequency of power system analysis is performed in Simulink/Matlab. The power output of synchronous generators, wind farms and loads are exported to work space of Matlab with 0.1 sec of step time.

Fig. 9. Equivalent model of generator

Fig. 10. Block model for voltage deviation

Fig. 11. Equivalent circuit of conventional generator

In Fig. 10, internal voltage of each conventional generator, Ef, can be obtained from AVR system. Then, using the equivalent circuit of conventional generators shown in Fig.11, output current from each generator can be calculated as follows. XS denotes a synchronous reactance and it is assumed here that Xd=Xq=XS for simplicity.

( ) ( ) ⎪

⎭

⎪⎬

⎫

−=

≈

Gf

S

Gfm

VargEarg

sinX

VEP

δ

δ3

(10)

⎟⎟⎠

⎞⎜⎜⎝

⎛= −

Gf

Sm

VEXP

sin3

1δ (11)

( )δjexpVV

EEG

Gff = (12)

( )N,,,,,nZ

VEI

Gn

GnfnGn 21=

−= (13)

where N denotes the total number of conventional generators. For wind generators and loads, their reactive power can be,

in general, determined as a function of active power and terminal voltage as follows.

( )LnLnLnLn V,PFQ = (14)

Therefore, output current from each of them can be expressed as follows.

( )M,,,,,nV

jQPI

*

Ln

LnLnLn 21=⎟

⎟⎠

⎞⎜⎜⎝

⎛ += (15)

where M denotes the total number of these components. Then, terminal voltage at each node in the power system can be obtained as follows.

[ ]

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

=

⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢

⎣

⎡

−

0

0

1

1

1

1

1

1

LM

L

GN

G

SYS

FK

F

LM

L

GN

G

I

II

I

Y

V

VV

VV

V

(16)

where [YSYS] is the system admittance matrix of the power system and VFn denotes floating node voltage. As each node voltage is included also in the right hand side of the above equation, iterative calculation is needed to solve it. In order to determine the initial node voltages of the system the Newton Raphson method [7] can be adopted, in which the SG1 is selected as slack generator bus.

VI. SIMULATION AND RESULTS Simulation analyses have been carried out to investigate

the performance of the approximate method by using MATLAB with 0.1 sec of time step scenario. Comparison with detailed method performed by PSCAD/EMTDC simulation is also demonstrated to show the effectiveness of the new method.

1Ms+DΔPm Δω

+

-

ΔPL

Pm IGNConventional Generator

Eqs. (1０) ~ (13)

LoadsEq. (15)

Wind GeneratorEq. (15)

PL

PW

ILN

Eq. (16)

VG , VL, VF

AVR SystemEf

GI

mP

fE GV

SaG jXrZ +=

1469

Fig. 12. Wind speed data

Fig. 13. Active power output of wind farms

Fig. 14. Active power output of conventional synchronous generators

Fig. 15. Power system frequency

Fig. 16. Terminal volatge of synchronous generators

Fig. 17. Terminal voltage at load bus

Fig. 18. Terminal voltage of Wind Farm

In order to investigate frequency and voltage fluctuations of the power system, wind speed data for 600 sec shown in Fig. 12 are applied to each wind generator. Fig.13 shows the active power output of wind farms. It is seen that the power output of wind farms obtained by the approximated method is slightly larger than those obtained by the PSCAD/EMTDC simulation. This is because the generator and converter losses are not considered in the approximate approach. Responses of active power output of conventional generators are shown in Fig. 14. Fig. 15 shows the power system frequency response. Node voltage responses of the generators, loads and wind farms are shown in Figs. 16, 17 and 18, respectively. From these results, it can be seen that responses of the frequency and node voltages of power system including wind farms can be calculated by the proposed method with sufficient accuracy.

Table III shows computation times of the simulation of 600sec for the approximate method and the PSCAD/EMTDC simulation (PC spec is Intel (R) Core(TM)i7 CPU 870 @2.93GHz). It can be noted that the computation time of the approximate method is much shorter than that of the PSCAD/EMTDC simulation.

TABLE III. COMPUTATION TIME OF EACH METHOD

Simulation Duration

Computation TimePSCAD/EMTDC

simulation Approximate

method600 sec 63720 sec 19.8 sec

Time step 10 μ sec 100 msec

VII. CONCLUSION In this paper, a new method for calculating frequency and

voltage deviations of power system in which wind generators are installed. The new method is based on the transfer function block models for frequency response and voltage responses of

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the power system, from which voltage response of each node in the power system as well as the frequency response can be obtained easily and quickly with sufficient accuracy. In addition, the proposed method can be used to analyze dynamic responses of a large power system model.

Acknowledgements This study was supported by a Grant-in-Aid for scientific

Research (B) from The Ministry of Education, Science, Sports and Culture of Japan.

REFERENCES [1] Siegfried Heier, Grid integration of wind energy conversion systems,

John Wiley & Sons Ltd 1998, pp. 34-36

[2] MATLAB documentation center [online] on http://www.mathworks. co.jp/jp/help/. (Accessed on 3 November 2012).

[3] S. M. Muyeen, J. Tamura, and T. Murata, Stability augmentation of a grid connected wind farm, Green Energy and Technology, London, Springer-Verlag, 2009. Ch. 2.

[4] PSCAD/EMTDC User’s Manual, Manitoba HVDC Research Center, Canada (1994)

[5] Prabha Kundur, Power System Stability and Control, McGraw-Hill: New York, 1994, pp. 581-600

[6] Norifumi Kurose, Rion Takahashi, Junji Tamura, Tomoyuki Fukushima, Eiichi Sasano, Koji Shinya : A Consideration on the Determination of Power Rating of Energy Storage System for Smoothing Wind Generator Output, International Conference on Electrical Machines and Systems 2010, PS-SRE-28(6 pages), 2010/10.

[7] J. D. Glover, M. S. Sarma, T. J. Overbye, Power System Analysis and Design, Thomson Learning Inc,2008, Ch. 6

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