Power oscillation damping control by PSS and DFIG wind ...

Turk J Elec Eng & Comp Sci

(2017) 25: 4354 – 4368

c⃝ TUBITAK

doi:10.3906/elk-1702-190

Turkish Journal of Electrical Engineering & Computer Sciences

http :// journa l s . tub i tak .gov . t r/e lektr ik/

Research Article

Power oscillation damping control by PSS and DFIG wind turbine under multiple

operating conditions

Korakot THANPISIT∗, Issarachai NGAMROODepartment of Electrical Engineering, Faculty of Engineering, King Mongkut’s Institute of Technology Ladkrabang,

Bangkok, Thailand

Received: 15.02.2017 • Accepted/Published Online: 08.06.2017 • Final Version: 05.10.2017

Abstract:Multiple operating conditions in power systems including wind power sources significantly affect the damping

of low frequency oscillation modes due to diverse generating and loading conditions, random wind speeds, line outage

contingencies, etc. To cope with multiple operating conditions, this paper proposes the new parameter optimization

technique of the power system stabilizer (PSS) and the doubly-fed induction generator (DFIG) wind turbine with the

power oscillation damper (POD) based on the probability method. Different operating conditions are randomly generated

by Monte Carlo simulation. Under the generated operating points, the particle swarm optimization of PSS and POD

parameters is carried out to achieve the highest probability that the damping ratios of all oscillation modes are greater

than the desired damping ratio for all operating points. Study results in the IEEE New England 39-bus system indicate

that under the occurrence of faults, the PSS and POD optimized by the proposed method yield better stabilizing

performance than the conventional PSS and POD over a wide range of operating points.

Key words: Doubly-fed induction generator, power oscillation damper, probability method, power system stabilizer,

Monte Carlo simulation

1. Introduction

Generally, the damping of power oscillations with low frequency oscillation between 0.1 and 2.0 Hz, i.e. local and

interarea oscillations, is influenced by several loading and generating conditions, line outage contingencies, etc.

[1]. Without effective countermeasures, undamped power oscillations may lead to an unstable system and result

in a wide-area blackout. To suppress power oscillations, power system stabilizers (PSSs), which are the most

cost-effective devices, have been used for a long time. A PSS is equipped with the automatic voltage regulator

(AVR) of a synchronous generator. By adding a stabilizing signal to the AVR, the PSS can be effectively applied

to solve the problem of local and interarea oscillations in conventional power systems [1].

Nowadays, the penetration of wind power generation widely increases in power systems due to being

abundant, sustainable, and environmentally friendly [2]. By the end of 2015, the global cumulative installed

wind capacity was about 430 GW [3]. Nevertheless, the intermittent power output from wind power sources

makes the power oscillations problem more complicated [4]. Under these situations, the PSS may no longer be

able to suppress power oscillations.

Among wind turbines, the doubly-fed induction generator (DFIG) is popularly adopted in wind energy

conversion systems. The DFIG wind turbine can generate maximum power with variable wind speeds. Further-

∗Correspondence: silver [email protected]

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THANPISIT and NGAMROO/Turk J Elec Eng & Comp Sci

more, it has many advantages such as low power rating of the converter, low loss, and high efficiency [5]. The

salient feature of the DFIG is the ability of active and reactive power output controls. In particular, the active

and reactive power outputs can be controlled to eliminate power oscillations by installing a power oscillation

damper (POD) in the speed and voltage control loops, respectively [6]. The comparison of power oscillation

damping effect between the active and reactive power controls by DFIG wind turbine was studied in [7]. Study

results signified that the active power control may invoke the torsional oscillation of the wind turbine. On

the contrary, the reactive power control is immune to the torsional oscillation and provides satisfying damping

effects.

Previous works used the reactive power control of DFIG wind turbines to damp power oscillations. A POD

with second-order lead/lag compensator structure was designed by the root locus method [7] and particle swarm

optimization [8] so that the damping ratios of oscillation modes could be enhanced. In [9], the optimal tuning of

a POD using mixed H2/H∞ control was presented to obtain the robustness of the POD against various system

operations. In [10], a robust decentralized POD design to improve the system’s robust stability margin by inverse

multiplicative perturbation was proposed. Nevertheless, the design methods in [7–10] were carried out under

set operating conditions. They cannot guarantee the damping performance of the designed PODs under other

operating conditions. In addition, to achieve more stabilizing performance, the coordinated control of the PSS

and DFIG with POD is required. In [11], the design technique for coordination between a PSS and DFIG with a

POD considering random wind power output variation was presented by an extended probabilistic small-signal

stability analysis. Study results indicated that the coordinated PSS and POD yield a higher damping effect

than either the PSS or POD alone. The coordinated damping controller can ensure the damping performance

under diverse operating conditions. To enhance the robustness against system uncertainties, the parameters of

a coordinated PSS and POD in [12] were optimized under several operating points by concurrently and equally

increasing the output power of synchronous generators.

To deal with multiple operating conditions due to various load demands, power generations from syn-

chronous generators, random wind speeds, and line outage contingencies, this paper focuses on the new pa-

rameter optimization of a PSS and DFIG wind turbine with a POD based on the probability method. The

PSS and POD parameters are optimized for the probability that the damping ratios of all oscillation modes

are greater than the desired damping ratios for all random events generated by Monte Carlo simulation (MCS).

The optimization problem is solved by particle swarm optimization (PSO) so that the optimal parameters of

the PSS and POD can be obtained. The damping performance of the proposed PSS and POD in comparison

with the conventional PSS and POD is carried out in the IEEE 39-bus New England system.

The organization of this paper is described as follows. Section 2 presents the study system and modeling.

Next, Section 3 explains the proposed optimization technique. Subsequently, Section 4 provides simulation

results. Finally, the conclusion is given.

2. Study system and modeling

2.1. Study system

Figure 1 displays the modified IEEE 39-bus New England system [13]. All synchronous generators (G1–G10),

which are installed with turbine governor type II and AVR type III, are represented by the fourth-order model

[14]. After the eigenvalue analysis, nine oscillation modes with percent damping ratio (ζ) and oscillation

frequency (f) are given in Table 1. In this study, the acceptable percent damping ratio of each oscillation mode

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is at least 5%. In Table 1, it can be observed that the damping ratios of oscillation modes no. 1, 4, 5, 6, 7, 8,

and 9 are less than 5%.

G10

G1

G8

G2 G3 G4 G5

G7

G6

G9

39

9

8

7

5

6

11

3132

10

13

12

14

4

15

16

2122

35

3433

19

20

3

1

2

30 25

37

26 28

27

29

38

24

23

18 17

36

W3

W2

W1

Figure 1. Modified IEEE 39-bus New England system.

Table 1. Eigenvalue analysis results.

Mode Eigenvalues Damping ratio (ζ) Frequency (f)1st –0.3858 ± j9.4495 4.08% 1.50 Hz2nd –0.6649 ± j9.5230 6.96% 1.52 Hz3rd –0.5154 ± j9.2602 5.56% 1.47 Hz4th –0.3059 ± j8.0050 3.82% 1.27 Hz5th –0.3180 ± j7.6725 4.14% 1.22 Hz6th –0.3038 ± j7.0551 4.30% 1.12 Hz7th –0.2041 ± j6.0972 4.57% 0.97 Hz8th –0.2802 ± j6.0219 4.65% 0.96 Hz9th –0.2023 ± j4.0893 4.94% 0.65 Hz

The selection of proper locations of PSSs is evaluated by the sensitivity of PSS effect (SPE) method [15].

A high value of SPE implies a suitable synchronous generator for installing a PSS. The SPE can be calculated

by:

SPE = φ∆ωψ∆vfKe

Te, (1)

where ϕ∆ω is the right eigenvector corresponding to the speed deviation of the synchronous generator, ψ∆vf is

the left eigenvector corresponding to the field voltage deviation, and Ke and Te are the gain and time constant

of the AVR, respectively. As a result, Table 2 shows that the synchronous generators for suitable installation

of PSSs are at G2, G8, and G9.

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Table 2. SPE analysis results.

G1 G2 G3 G4 G5 G6 G7 G8 G9

SPE 0.0023 0.1134 0.0251 0.0198 0.0340 0.0175 0.0572 0.1067 0.1366

To serve increased load demands, three units of DFIG wind turbines (W1–W3), each with a capacity of

100 MVA, are additionally installed in the study system. The DFIG data are given in the Appendix. A POD

is installed into each DFIG. The aim of the PSS and POD is to ameliorate the damping ratios of all oscillation

modes.

2.2. DFIG model

The structure of the DFIG wind turbine, which is delineated in Figure 2, mainly consists of a grid-side converter

(GSC) and rotor-side converter (RSC). Study results in [16] indicated that damping control using the RSC is

superior to that of the GSC. In this work, the voltage controller in the RSC is used to modulate the reactive

power output of the DFIG to damp out the power oscillations.

Speed

controller

Voltage

controller

PWM

Grid

Induction

machine

Gear boxWind

patterns

Rotor side

converter

Grid side

converter

Figure 2. Structure of DFIG wind turbine and control system.

Here, the reduced fourth-order model of the DFIG [14] is used in the wind turbine-generation system as

the stator and rotor flux dynamics are fast in comparison with grid dynamics and the converter controls. The

steady-state electrical equations of the DFIG are given by

vds = −rsids + ((xs + xµ)iqs + xµiqr)

vqs = −rsiqs − ((xs + xµ)ids + xµidr)

vdr = −rridr + (1− ωm)((xs + xµ)iqr + xµiqs)

vqr = −rriqr − (1− ωm)((xs + xµ)idr + xµids)

, (2)

where vds , vqs , vdr , and vqr are d and q stator and rotor voltages; ids , iqs , idr , and iqr are d and q stator and

rotor currents; rs and rr are stator and rotor resistances; xs is stator reactance; xu is magnetizing reactance;

and ωm is rotor speed.

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The stator voltages are functions of the grid voltage magnitude and phase as

vds = −v sin(θ)vqs = v cos(θ)

, (3)

where v is a magnitude of DFIG terminal voltage and θ is a phase of terminal voltage.

The generator active and reactive powers depend on the stator and converter currents, as follows:

PDFIG = vdsids + vqsiqs + vdcidc + vqciqc

QDFIG = vqsids − vdsiqs + vqcidc − vdciqc, (4)

where PDFIG and QDFIG are active and reactive power outputs, vdc and vqc are d and q converter voltages,

and idc and iqc are d and q converter currents.

Due to the converter operation mode, the converter powers injected in the grid can be written as a

function of stator and rotor currents as

pc = vdcidc + vqciqc

qc = vqcidc − vdciqc, (5)

where pc and qc are converter active and reactive powers on the grid.

On the rotor side we have

pr = vdridr + vqriqr

qr = vqridr − vdriqr, (6)

where pr and qr are rotor-side active and reactive powers.

Assuming a lossless converter model, the active power of the converter coincides with the rotor active

power and thus pc = pr . The reactive power injected into the grid can be approximated neglecting stator

resistance and assuming that the d-axis coincides with the maximum of the stator flux. The flux-based rotating

reference frame is used to model the DFIG. Due to the initial value of θ = 0, Eq. (3) can be written as

vds = vdr = 0

vqs = vqr = v, (7)

and then Eq. (4) can be written as

PDFIG = v(iqs + iqr)

QDFIG = −v(ids + idr). (8)

The relation between stator fluxes and generator currents is

ψds = −((xs + xµ)ids + xµidr)

ψqs = −((xs + xµ)iqs + xµiqr), (9)

where ψds and ψqs are the d and q axis of stator fluxes, respectively.

Substituting Eq. (9) into Eq. (8), the active and reactive power outputs of the DFIG wind turbine are

represented as the function of iqr and idr by

PDFIG = xs

xs+xµviqr

QDFIG = −xµvidrxs+xµ

− v2

xµ

. (10)

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The generator motion equation is expressed by

ωm = (τm − τe)/2Hm

τe = ψdsiqs − ψqsids, (11)

where ωm is the state variable of rotor speed, τm and τe are respectively mechanical and electrical torques,

and Hm is rotor inertia.

Thus, the electrical torque τe can be expressed by

τe = xµ(iqrids − idriqs). (12)

The mechanical power pω extracted from the wind, which is a function of the wind speed vω , the rotor speed

ωm , and the pitch angle θp , can be approximated by

pω =ngρ

2Sncp(λ, θp)Arv

3ω, (13)

where ng is the number of machines in the wind park, ρ is the air density, Sn is the power rating, cp is the

performance coefficient or power coefficient, λ is the tip speed ratio, and Ar is the area swept by the rotor.

The cp(λ , θp) curve is approximated by

cp = 0.22(116

λi− 0.4θp − 5)e−

12.5λt , (14)

With1

λi=

1

λ+ 0.08θp− 0.035

θ3p + 1. (15)

The converter is modeled by an ideal current source, where iqr and idr are state variables and used for the rotor

speed control and the voltage control, respectively, as depicted in Figures 3 and 4. Differential and algebraic

equations for the converter currents are given by

Figure 3. Rotor speed controller.

iqr = (−xs+xµ

xµvp∗ω(ωm)/ωm − iqr)

1Te

idr = KV (v − vref )− v/xµ − idr

0 = v0ref − vref + vs

, (16)

where v0ref is the initial reference voltage, vs is an additional signal of the POD, p∗ω(ωm) is the power-speed

characteristic that roughly optimizes the wind energy capture, Kv is voltage control gain, Te is power control

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Figure 4. Voltage controller.

time constant, and imindr , imax

dr , iminqr , and imax

qr are minimum and maximum rotor currents in the direct axis and

the quadrature axis, respectively. Here, the stabilization of power oscillation is conducted by the voltage control

of idr with the POD signal. Without the risk of torsional oscillation in the wind turbine, the reactive power

output is used to suppress power oscillations.

The pitch angle control is illustrated in Figure 5 and described by

m

ref

p

0

1

p

p

K

T s

Figure 5. Pitch angle controller.

θp = (Kpϕ(ωm − ωref )− θp)/Tp, (17)

where ϕ is a function that allows varying the pitch angle set point only when ωm − ωref exceeds a predefined

value ±∆ω , ωref is the reference speed, Kp is the pitch control gain, and Tp is the pitch control time constant.

Based on Eqs. (11), (16), and (17), the fourth-order model of the DFIG can be represented by state

variables idr , iqr , ωm , and θp .

2.3. PSS and POD model

Figure 6 delineates the model of the PSS and POD as the second-order lead-lag compensator where KSTAB

is the gain, TW is the washout time constant and set at 10 s, and T1 , T2 , T3 , and T4 are time constants of

phase compensators. The input signals vSI of the PSS and POD are the speed deviation of the synchronous

generator and the local power flow signal, respectively. The PSS and POD output signals vS are limited by

±0.2 p.u. The PSS and POD output signals are sent to the AVR and the voltage-control loop of the DFIG,

respectively.

3. Proposed optimization technique

Conventionally, the parameters of the PSS and POD are optimally tuned at an operating point to achieve the

satisfied damping performance. Nevertheless, the resulting PSS and POD cannot confirm the stabilizing effect

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Gain Washout Lead-lag 1 Lead-lag 2

Figure 6. PSS and POD models.

over a wide range of operating points. To ensure the damping performance for diverse operating points, the

new parameter optimization for the PSS and POD by the probability method is described as follows.

The optimization objective is to obtain the damping ratio of all oscillation modes as more than 5% for

all possible operating points. Here, 1000 operating points, which are randomly generated by varying the power

outputs of all synchronous generators and load power between ±20% from a normal operating point, wind

speeds of the DFIG between 9 and 16 m/s, and a line outage contingency, are performed by MCS. The percent

damping ratio of the mth oscillation mode at the evth operating point (ζm,ev) can be calculated by

ζm,ev =−σm,ev√

σ2m,ev + ω2

m,ev

× 100; ev = 1,2,...,1,000, (18)

where σm,ev and ωm,ev are real and imaginary parts of the eigenvalue corresponding to the mth oscillation

mode at the evth operating point, respectively. Under 1000 events, the probability of the events for which the

percent damping ratio of the mth oscillation occurs between ζm and ζm+1% or Pr[ζm ,ζm+1%] is calculated

by

Pr [ζm, ζm + 1%] =N [ζm, ζm + 1%]

NA, (19)

where N [ζm ,ζm+1% ] is the number of events for which the percent damping ratio of the mth oscillation mode

occurs between ζm and ζm + 1%, and NA is the number of total events.

When ζmin and ζmax are the minimum and maximum percent damping ratios of each oscillation mode

for all events, respectively, the histogram of the occurring probability of each percent damping ratio for the

individual oscillation mode from ζmin to ζmax with 1% increasing step can be depicted as in Figure 7. To

make it easy for calculating the area under the histogram, a frequency polygon is established. In this study, the

acceptable percent damping ratio, which is set at 5%, is used to separate the histogram into two areas. Area1m

is the probability area where the percent damping ratio of the mth oscillation mode for all random 1000 events

is less than 5%. On the contrary, Area2m is the probability area where the percent damping ratio of the mth

oscillation mode for all random 1000 events is greater than 5%. The larger Area2m is, the higher damping

ratios of nine oscillation modes can be obtained. By this concept, the objective function for tuning parameters

of the coordinated PSS and POD is formulated by the minimization of the difference between Area1m and

Area2m for nine oscillation modes by

Maximize9∑

m=1

(Area2m −Area1m), (20)

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Area1m Area2m

Histogram

Frequency Polygon

AcceptableDamping ratio

yt ilib

ab

orP

Damping ratio (%). . . 1 2 3 4 5 6 . . .

0.1

0.2

0.3

Figure 7. Histogram of probability of % damping ratio.

Subjectto 0.1 < KSTAB < 50.00.1 < T1,2,3,4 < 1.0

.

PSO [17] is applied to solve optimal parameters in Eq. (20). The optimized PSS and POD are referred to as

PPSS+PPOD. The flowchart of the proposed optimization method can be delineated as in Figure 8.

The damping performance of PPSS+PPOD is compared with that of the PSS coordinated with the POD,

which is tuned at the normal operating point by

Minimize9∑

m=1

|ζspec − ζm|, (21)

Subjectto 0.1 < KSTAB < 50.00.1 < T1,2,3,4 < 1.0

,

where ζspec is the specified damping ratio, which is set at 5%. The PSS and POD optimized by Eq. (21) are

referred to as CPSS+CPOD.

4. Simulation results

The Power System Analysis (PSAT) toolbox [14] is applied for time-domain simulation. In the PSO, the number

of particles and iterations are set at 100 and 50, respectively.

The simulation study is divided into two parts. The first part compares the damping effects among PPSS,

PPOD, and PPSS+PPOD. Note that PPSS and PPOD are individually optimized by Eq. (20). The second

part compares the damping effect between PPSS+PPOD and CPSS+CPOD.

Figure 9 depicts the convergence curves of the objective function of Eq. (20) for PPSS, PPOD, and

PPSS+PPOD. Table 3 shows optimized parameters of CPSS+CPOD while Table 4 shows optimized parameters

of PPSS, PPOD, and PPSS+PPOD.

4.1. Comparison among PPSS, PPOD, and PPSS+PPOD

Figure 10 shows the probability of % damping ratios under 1000 operating points. The damping ratios in the case

of either PPOD or PPSS are higher than those of the system without PPOD and PPSS. Besides, PPSS+PPOD

yields the best damping performance for nine oscillation modes. PPSS+PPOD provides the probability of %

damping ratios that are greater than 5% for all oscillation modes. Figure 11 depicts the eigenvalues plot of all

oscillation modes under 1000 operating points. The result in Figure 11 satisfies that in Figure 10.

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Start End

Iter = 1

Generate the initial particle

Linearize power system

Compute damping ratio of

each oscillation mode by (18)

Evaluate the probability of the

events that the damping ratio of

individual oscillation mode

occurs in each bound by (19)

Use result from (19) to plot

histogram then convert to

frequency polygon.

Calculate objective function

(20) from frequency polygon

Get the optimal parameters

Iter >= Itermax

Itermax = 50

If gold > gnew then gbest = gold.

If gold < gnew then gbest = gnew

Select the maximum value of

objective function as gnew

Iter = Iter+1No

Yes

Update location and velocity in 100 particles

i = number of particles (set at 100)

xi = location for each particle

vi = velocity for each particle

α,β = acceleration constants

ε1,ε2 = random value between 0 to 1

gnew = the best value of objective function at iteration Iter

gold = the old best value of objective function

gbest = the maximum value from comparison between gnew and goldIter = iteration counter

Itermax = number of iterations

Figure 8. Flowchart of the proposed optimization method.

0 5 10 15 20 25 30 35 40 45 50-10

-9

-6

-4

-2

0

2

4

6

8

10

Iteration

no itcn uf e vi tcejbO

PPODPPSSPPSS+PPOD

Figure 9. Convergence curve of the objective function of Eq. (20).

A time-domain simulation is conducted to verify the damping effect of PPSS+PPOD. At the normal

operating point, it is assumed that the temporary three-phase fault occurs at bus 10 at t = 1 s for 100 ms and

is cleared naturally. Figure 12 shows simulation results of power flows between buses 1–2 and buses 9–39. The

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0 2 4 5 6 8 10 12 14 16 18 200

0.10.2

0 2 4 5 6 8 10 12 14 16 18 200

0.10.2

0 2 4 5 6 8 10 12 14 16 18 200

0.10.2

0 2 4 5 6 8 10 12 14 16 18 200

0.10.2

0 2 4 5 6 8 10 12 14 16 18 200

0.20.4

y tiliba

bor

P

0 2 4 5 6 8 10 12 14 16 18 200

0.10.2

0 2 4 5 6 8 10 12 14 16 18 200

0.10.2

0 2 4 5 6 8 10 12 14 16 18 200

0.20.4

0 2 4 5 6 8 10 12 14 16 18 200

0.5

Damping ratio (%)

Without controller PPOD PPSS PPSS+PPOD

MODE 1

MODE 2

MODE 3

MODE 4

MODE 5

MODE 6

MODE 7

MODE 8

MODE 9

Figure 10. Probability of % damping ratios under 1000 events.

Figure 11. Locus plot of all oscillation modes with 1000 events.

0 2 4 6 8 10 12 14 16 18 20-5

0

5Power !ow between buses 1-2

0 2 4 6 8 10 12 14 16 18 20-4

-2

0

2

4

Time (s)Pow

er !

ow (

p.u

.)P

ower

!ow

(p

.u.)

Power !ow between buses 9-39

Without controller PPOD PPSS PPSS+PPOD

Figure 12. Simulation results.

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Table 3. Parameters of CPSS+CPOD.

Parameters of CPSS+CPODKSTAB T1 T2 T3 T4

CPSS of G2 2.94 0.28 0.06 0.44 0.08CPSS of G8 48.66 0.22 0.09 0.91 0.09CPSS of G9 13.81 0.35 0.02 0.32 0.06CPOD of W1 9.22 0.21 0.04 0.21 0.04CPOD of W2 4.43 0.46 0.04 0.21 0.01CPOD of W3 7.15 0.51 0.03 0.37 0.03

Table 4. Parameters of PPSS, PPOD, and PPSS+PPOD.

Parameters of PPSSKSTAB T1 T2 T3 T4

PPSS of G2 38.35 0.79 0.06 0.31 0.04PPSS of G8 3.56 0.84 0.09 0.76 0.01PPSS of G9 8.27 0.24 0.02 0.45 0.05Parameters of PPOD

KSTAB T1 T2 T3 T4PPOD of W1 9.22 0.21 0.04 0.19 0.04PPOD of W2 4.43 0.46 0.04 0.21 0.01PPOD of W3 7.15 0.54 0.03 0.37 0.03Parameters of PPSS+PPOD

KSTAB T1 T2 T3 T4PPSS of G2 26.63 0.67 0.08 0.75 0.03PPSS of G8 31.37 0.54 0.08 0.35 0.09PPSS of G9 27.28 0.82 0.07 0.61 0.08PPOD of W1 10.62 0.43 0.03 0.75 0.01PPOD of W2 21.18 0.13 0.04 0.35 0.04PPOD of W3 5.76 0.14 0.04 0.24 0.03

undamped power oscillation occurs in the case without the controller. On the other hand, the power oscillation

can be suppressed by PPSS, PPOD, and PPSS+PPOD. Nevertheless, PPSS+PPOD provides the best damping

performance. These results confirm that the stabilizing effect of PPSS+PPOD is better than the individual

effect of PPSS or PPOD.

4.2. Comparison between CPSS+CPOD and PPSS+PPOD

Figure 13 shows the probability of % damping ratios of each oscillation mode for 1000 operating points.

PPSS+PPOD provides the damping ratios that are greater than the acceptable value (or ≥5%). On the

contrary, some damping ratios in the case of CPSS+CPOD are less than 5%. Moreover, the damping ratios in

the case of PPSS+PPOD are all higher than those of CPSS+CPOD. To confirm the result in Figure 13, the

scattering of eigenvalues for all oscillation modes under 1000 events is depicted in Figure 14.

Nonlinear simulations for case studies in Table 5 are carried out under various system uncertainties and

faults.

Figure 15 depicts power flows between buses 1–2 and buses 9–39 of each case study. In case 1, as

delineated in Figure 15a, severe power oscillation occurs in the case without the controller. On the other hand,

the power oscillation is completely damped by CPSS+CPOD and PPSS+PPOD. Figure 15b shows case 2,

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0 2 4 5 6 8 10 12 14 16 18 200

0.10.2

0 2 4 5 6 8 10 12 14 16 18 200

0.10.2

0 2 4 5 6 8 10 12 14 16 18 200

0.10.2

0 2 4 5 6 8 10 12 14 16 18 200

0.20.4

0 2 4 5 6 8 10 12 14 16 18 200

0.20.4

yti liba

bor

P

0 2 4 5 6 8 10 12 14 16 18 200

0.10.2

0 2 4 5 6 8 10 12 14 16 18 200

0.10.2

0 2 4 5 6 8 10 12 14 16 18 200

0.20.4

0 2 4 5 6 8 10 12 14 16 18 200

0.5

Damping ratio (%)

Without controller CPSS+CPOD PPSS+PPOD

MODE 1

MODE 2

MODE 3

MODE 4

MODE 5

MODE 6

MODE 7

MODE 8

MODE 9

Figure 13. Probability of % damping ratios under 1000 events.

-2.5 -2 -1.5 -1 -0.5 0

-10

-5

0

5

10

Real part (1/s)

Without controllerCPSS+CPODPPSS+PPOD

Damping ratio = 5%

Imag

inar

y p

art

(rad

/s)

Figure 14. Locus plot of all oscillation modes under 1000 events.

where the system is unstable in the case without a controller. PPSS+PPOD gives a better damping effect than

CPSS+CPOD. In cases 3 and 4, as shown in Figures 15c and 15d, CPSS+CPOD cannot stabilize the power

oscillations. On the contrary, PPSS+PPOD can suppress the power oscillation entirely. These simulation results

guarantee that the damping performance of PPSS+PPOD is superior to that of CPSS+CPOD.

5. Conclusion

This paper deals with the new optimization technique of a PSS and DFIG installed with a POD by the

probability method for stabilization of low-frequency electromechanical oscillations against multiple operating

points. MCS is applied to produce random operating events in the parameter optimization of the PSS and

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Table 5. Case study.

Case

Description

Applied disturbance

% Change

in power

output of all

generators

% Change

in power

output of

all loads

Wind

speed

of

DFIG1

Wind

speed

of

DFIG2

Wind

speed

of

DFIG3

N-1

line outage

contingency

1

Fault occurs at bus 39

for 150 ms and is

cleared naturally

+3% +2% 14 m/s 15 m/s 11 m/s Line 7–8

outage

2


for 150 ms and is

cleared naturally

No change +7% 12 m/s 14.5

m/s 9 m/s

Line 25 –26

outage

3


for 150 ms and is

cleared naturally

–5% No change 11 m/s 11 m/s 13 m/s Line 26 –27

outage

4

Fault occurs at line

16–21 at t = 1 s and is

cleared by tripping this

line at t = 1.10 s

without reclosing

No change +5% 14.5 m/s 10 m/s 15 m/s Line 14 –15

outage

(a) Case 1

(b) Case 2

(c) Case3

0 2 4 6 8 10 12 14 16 18 20-4

-2

0


0 2 4 6 8 10 12 14 16 18 20-4

-2

0

2

Time (s)



0 2 4 6 8 10 12 14 16 18 20-10

-5

0

5


0 2 4 6 8 10 12 14 16 18 20-10

-5

0

5

10

Time (s)



0 2 4 6 8 10 12 14 16 18 20-10

-5

0

5


0 2 4 6 8 10 12 14 16 18 20-10

-5

0

5

10

Time (s)



(d) Case 4

0 2 4 6 8 10 12 14 16 18 20-10

-5

0

5


0 2 4 6 8 10 12 14 16 18 20-10

-5

0

5

10

Time (s)

Po

wer

!o

w (

p.u

.)P

ow

er !

ow

(p

.u.)

Po

wer

!o

w (

p.u

.)P

ow

er !

ow

(p

.u.)

Po

wer

!o

w (

p.u

.)P

ow

er !

ow

(p

.u.)

Po

wer

!o

w (

p.u

.)P

ow

er !

ow

(p

.u.)



Figure 15. Simulation results of case studies 1 to 4: a) case 1, b) case 2, c) case 3, d) case 4.

POD under several generating and loading conditions, random wind speeds, and line outages. The optimization

is conducted by maximizing the probability that the desired damping ratios of all oscillation modes can be

achieved for all random operating points. Solving the optimization problem by PSO, the optimal parameters

4367


of the PSS and POD can be obtained automatically. Small-signal and transient stability results guarantee that

the damping performance of the proposed PSS and POD is much higher than that of the conventional PSS and

POD under multiple operating conditions and faults.

Acknowledgment

This work was supported by the King Mongkut’s Institute of Technology Ladkrabang Research Fund, No.

KREF115901.

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Appendix

DFIG data [18]: blade length: 75 m; blade number: 3; air density: 1.225 kg/m3 ; inertia time constant = 3 s;

gearbox ratio = 1/89; stator resistance = 0.01 p.u.; rotor resistance = 0.01 p.u.; stator reactance = 0.1 p.u.;

rotor reactance = 0.08 p.u.; magnetizing reactance = 3 p.u.; number of poles = 4; voltage control gain = 50;

power control time constant = 0.01; pitch control gain = 50; pitch control time constant = 3.

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