two-level inter-area oscillation dampers design by …

Rev. Roum. Sci. Techn.– Électrotechn. et Énerg. Vol. 64, 3, pp. 211–216, Bucarest, 2019

1 Faculty of Engineering, King Mongkut’s Institute of Technology Ladkrabang, Bangkok 10520, Thailand, Email: [email protected]

TWO-LEVEL INTER-AREA OSCILLATION DAMPERS DESIGN BY MONTE CARLO SIMULATION

ISSARACHAI NGAMROO1

Key words: Doubly-fed induction generator (DFIG), Monte Carlo simulation (MCS), Power system stabilizer, Inter-area oscillation, Probability, Wind turbine (WT).

Various system operations such as load changes, time delays, communication failure, and line outages have an influence on the stabilizing effect of inter-area damping controllers. Moreover, the penetration of large wind farms makes power oscillations problem more complicated. This paper proposes the two-level control design of power system stabilizers and power oscillation dampers of wind turbines with doubly fed induction generator by Monte Carlo simulation (MCS) and probability. In the two-level damping control, the centralized damper acts as the main control while the local damper works as the backup control when the communication failure occurs. Using the MCS to produce random operating points, the parameters tuning of centralized and local dampers is independently performed by the particle swarm optimization so that the probability of expected damping ratio is maximized. Study results in the modified IEEE New England 39 bus system guarantee the damping effect and robustness of the proposed control.

1. INTRODUCTION

The growing of interconnection among power systems not only makes the power oscillations problem more complicated, but also weakens the damping of the low frequency oscillations between 0.2 and 2.0 Hz [1]. To enhance the oscillation damping, as the most promising device, the power system stabilizers (PSSs) have been successfully used. Nevertheless, the inevitable problem of the PSS is how to optimally tune the PSS parameters so that the PSS can handle the oscillation problem against various system conditions.

Currently, the installation of wind generators in power systems extensively increases due to sustainable and environment friendly. Among wind turbines, the doubly fed induction generator (DFIG) currently occupies close to 50 % of wind energy market due to low installation cost, small power converter rating, and high power generation at various wind speeds [2]. Furthermore, the ability of independent output power control of the DFIG is widely used to eradicate the power oscillations by installing the power oscillations damper (POD) [3]. However, the study result in [4] indicates that only DFIG wind turbines with PODs may no longer be able to give adequate stabilizing effect. The coordination between PODs and other devices is required.

In [5], the decentralized control between DFIG wind turbines with PODs and PSSs has been presented to stabilize power oscillations. Nevertheless, the local input signals of the decentralized control is not suitable for the observability of inter-area oscillation modes. Recently, the phasor measurement unit (PMU) technology enables the damping controller to capture the dynamic information of wide area power systems. The input signals with high observability of the inter-area modes can be achieved. In [6], the inter-area oscillation is suppressed by the centralized controller based on the wide area input signal taking into account the variable communication time delay. Nonetheless, the centralized controller may fail to operate when the communication failure takes place. To tackle this obstacle, the two-level control consisting of centralized and local controls have been presented. In [7] and [8], the

control parameters are designed at an initial operating point by H∞ optimization and root locus method, respectively. The resulted controllers may not ensure the stabilizing effect over diverse operating conditions.

To cope with possible operating conditions, this work deals with the new design using the combination of Monte Carlo simulation (MCS) and probability for the two-level coordinated control. The PSS and POD parameters of centralized and local controllers are independently and optimally tuned under wide operating points in order to get the maximum probability of the desired damping ratios. Small signal and transient stability studies in the modified IEEE New England 39 bus system are conducted to evaluate the damping ability of the proposed two-level control in comparison with that of the conventional control.

2. PROPOSED TWO-LEVEL CONTROL

The two-level coordinated control which mainly consists of centralized and local levels, is illustrated in Fig. 1.

Power SystemLocal input

signalStabilizing signal from Local PSS

Synchronous generator DFIG wind turbine

PSS signal POD signal

Wide area input signal

Transmitted time delay

Received time delay

Control center

PMU

First-level control

Delay

Received time delay

Centralized POD

Stabilizing signal from Centralized PSS

Stabilizing signal from Centralized POD

Centralized PSS

Local POD

Local PSS

Delay

Delay

Two-way switch

Two-way switch

Stabilizing signal from Local POD

Second-level control

Fig. 1 – Two-level coordinated control.

In each level, the PSSs of synchronous generators and the

PODs of DFIG wind turbines are used to attenuate the power oscillations. The centralized PSS and POD which are operated as the primary controller, are employed for solving the power oscillations. The input signals of centralized PSS and POD are obtained from PMUs considering the

212 Two-level inter-area oscillation dampers design 2

transmitted time delay. By including the receiving time delay, the output signals of centralized PSS and POD are sent to the automatic voltage regulator (AVR) of the synchronous generator and the voltage control loop of the DFIG, respectively. When the communication failure occurs, the local PSS and POD are operated as the backup control by using the two-way switch to handle the power oscillations.

3. SYSTEM MODELING AND ANALYSIS

In Fig. 2, the modified IEEE New England 39 bus system consisting of ten synchronous generators (G1–G10) and three DFIG wind turbine (W1, W2, and W3), with each, power capacity of 100 MVA is used in this study. A fourth order model is used to represent synchronous generators. A turbine governor type II and AVR type III are equipped with synchronous generators.

G10

11 13

12

10

39

5

4

6

7

8

931

32

14

1

2

G1

G2

G3

30

3

2537

G8

18 17

27

26

16

15

28 29

38

24 G9

G6

2122

23

19

20

G4 G5

3334

G7

36

35

W1

W2

W3

Fig. 2 – Modified IEEE New England 39 bus system.

Figure 3 shows the DFIG wind turbine structure which is

mainly formed by the rotor side converter (RSC) and grid side converter (GSC). The fourth order model is used to represent the DFIG wind turbine [9].

,DFIG DFIGP Q

w

Fig 3 – DFIG wind turbine structure.

Study result in [10] shows that the better damping capability can be contributed by the RSC. The RSC consists of voltage and rotor speed controllers. In this work, the voltage controller of RSC is applied to damp the power oscillations by the additional POD signal (vsPOD). Based on the vector control method [9], the active power output is controlled by the quadrature axis rotor current (iqr) via the rotor speed control, while the reactive power output is regulated by the direct axis rotor current (idr) through the voltage control. The active and reactive power outputs of the DFIG are represented by the functions of iqr and idr as

qrus

sDFIG vi

xx

xP

,

,2

udr

us

uDFIG x

vvi

xx

xQ

(1)

where PDFIG and QDFIG are active and reactive power outputs, respectively. Here, the reactive power output is modulated by the voltage control loop to eliminate the power oscillations. The linearized system state equation is given by

.UDXCY

UBXAX

(2)

where Δ is a small deviation, is the derivative with time, X is a state vector, Y is an output vector, U is an input vector, A, B, C, and D are state, input, output, and feed-forward matrices, respectively. To perform the small signal analysis, the MCS is adopted here. MCS is the best alternative to observe the risk analysis of power systems based on statistics and probability [11]. Under various random samplings affecting any operating points, the MCS can be conducted to simulate the variable risks. The basic concept of MCS is to achieve the probability of the occurrence of the possible scenarios by simulating the frequency that such events occur. This method relies on a variety of simulated test with high precision. With increasing simulation time, the precision of MCS will be improved. Among the large number of repeated samplings, the computational method and procedure structure of MCS are not complicated. Moreover, the convergent probabilistic and computation speed do not depend on the system dimension. Accordingly, the MCS can be used to generate all possible operating points by various inputs, i.e. power generations etc., in order to get the target variables such as damping ratios of inter-area oscillation modes etc. Here, the MCS is used to randomly generate 1000 different operating conditions under the variation of output power of synchronous generators and all load powers between –20 % and 20 % from the normal operation, wind speeds of DFIG wind turbines from 9 to 12 m/s, and a line outage. The percent damping ratio of mth oscillation mode at the evth operating point (ζm,ev) can be expressed as the function of real part (σm,ev) and imaginary part (ωm,ev) of the eigenvalue corresponding to the oscillation mode by

.1000,...,2,1;1002

,2

,

,,

ev

evmevm

evmevm (3)

Next, the probability of the number of events that percent damping ratios of the mth oscillation mode occur for each one percent increasing step from the minimum damping ratio (min ) to the maximum damping ratio (max), or (Pr[m ,m+1%]) is computed by

.

%1,%1,Pr

A

mmmm N

N (4)

},%,1,

,...%2%,1,%1,{%1,

max

m

mmmmmm

where N[m,m+1 % ] is the number of events that the percent damping ratios of the mth oscillation mode occur

3 Issarachai Ngamroo 213

between m and m + 1 %, and NA is the number of total events, i.e. 1000 events.

In this system, there are nine inter-area oscillation modes [5]. Figure 4 shows the probability of % damping ratios under 1000 events of nine inter-area oscillation modes. The probability of percent damping ratios of the oscillation modes no.1, 4, 5, 7, 8, and 9 may be less than the desired value or 5 %. To augment the damping ratios of these target modes, PSSs and PODs are used.

2 4 5 6 8 10 120

0.05

0.1

0.15

0.2

Pro

babi

lity

2 4 5 6 8 10 120

0.05

0.1

0.15

0.2

2 4 5 6 8 10 120

0.1

0.2

0.3

0.4

2 4 5 6 8 10 120

0.05

0.1

0.15

0.2

Pro

babi

lity

2 4 5 6 8 10 120

0.1

0.2

0.3

0.4

2 4 5 6 8 10 120

0.05

0.1

0.15

0.2

2 4 5 6 8 10 120

0.05

0.1

0.15

0.2

Pro

babi

lity

Damping ratio (%)2 4 5 6 8 10 12

0

0.1

0.2

0.3

0.4

Damping ratio (%)2 4 5 6 8 10 12

0

0.1

0.2

0.3

0.4

Damping ratio (%)

MODE 1 MODE 2 MODE 3

MODE 4 MODE 5


MODE 6

Fig. 4 – Probability of % damping ratios under 1000 events.

Figure 5 delineates the 2nd-order lead-lag compensator of

centralized/local PSS and POD, where KC and KL are the stabilizing gains, TW is the washout time constant and equal to 10 s, TC1, TC2, TC3 TC4, TL1, TL2, TL3, and TL4 are time constants, S1 and S2 are the two-way switch for selecting the stabilizing signal, vsPSS

and vsPOD are the stabilizing signals

of PSS and POD, respectively. In scenario of the communication failure, the S1 is immediately switched to S2 so that the stabilizing signals can be achieved from local PSS and POD.

1 3

2 4

(1 )(1 )

(1 )(1 )L L

L L

sT sT

sT sT

1

WL

W

sTK

T

1 3

2 4

(1 )(1 )

(1 )(1 )C C

C C

sT sT

sT sT

1

WC

W

sTK

T

1 ( / 2)

1 ( / 2)D

D

s T

s T

1 ( / 2)

1 ( / 2)D

D

s T

s T

1S

2S

Fig. 5 – PSS and POD models.

The transmitted and received time delays which are

assumed to be equal to TD/2, are integrated into the centralized controller. The time delay effect which is

modeled by DsTe , can be approximated by the Padé approximation as

.1

2

12e

sT

sT

D

D

sTD (5)

The speed deviations of synchronous generators and the local power flows are taken as the input signals of local PSS and POD, respectively. The selection of suitable input signals for the centralized PSS and POD is explained as follows.

The suitable synchronous generators and DFIG wind turbines are selected for installing the PSS and POD,

respectively. To obtain the suitable synchronous generators and DFIGs as well as the proper input signals for the centralized PSS and POD, the geometric measure of controllability and observability [12] is used as given by

,

,T

T

hm

mhob

gm

mgcon

C

Cmg

mg

B

B

(6)

where gcon(m) and gob(m) are the controllability and observability corresponding to the mth oscillation mode, respectively, Bg is the gth

column of B, Ch is the hth row of C, ϕm is right eigenvectors of the mth oscillation mode, ψm is left eigenvectors of the mth oscillation mode, | | and || || are the Modulus and Euclidean norm of matrix, respectively. The superscript T is the matrix transpose. The high value of controllability implies the suitable synchronous generators and DFIGs for equipping PSS and POD, respectively. The high value of observability signifies the proper input signals of PSS and POD. As a result, the PMUs can be appropriately located.

Figure 6 shows the results of geometric measure of observability of active power flows in all transmission lines. Table 1 provides the results of geometric measure of controllability of all generators for the target oscillation modes. As a result, the proper generators and the suitable input signals can be summarized in Table 2. The locations of PMUs for measuring suitable power flows are buses 2, 10, 17, and 5.

0 5 10 15 20 25 30 350

0.1

0.2

0.3

0.4

Obs

evab

ilit

y

Mode 1

0 5 10 15 20 25 30 350

0.1

0.2

Mode 4

0 5 10 15 20 25 30 350

0.1

0.2

0.3

0.4

Obs

evab

ilit

y

Mode 5

0 5 10 15 20 25 30 350

0.05

0.1

0.15

0.2Mode 7

0 5 10 15 20 25 30 350

0.05

0.1

0.15

Obs

evab

ilit

y

Line number

Mode 8

0 5 10 15 20 25 30 350

0.05

0.1

Line number

Mode 9Active power in the line between

bus 17 and bus 27

Active power in the line between bus 2 and bus 3




Active power in the line betweenbus 10 and bus 11

Fig. 6. – Geometric measure of observability.

Table 1

Geometric measure of controllability

Generator mode no.

1 4 5 7 8 9

G1 0.0015 0.0035 0.0023 0.0036 0.0033 0.0037 G2 0.0022 0.0056 0.0357 0.0518 0.0132 0.0122 G3 0.0116 0.1061 0.0095 0.0494 0.0366 0.0487 G4 0.0476 0.0128 0.0074 0.0406 0.0740 0.0635 G5 0.0006 0.0009 0.0011 0.0103 0.0157 0.0044 G6 0.0057 0.0223 0.0224 0.0082 0.0080 0.0167 G7 0.0041 0.0094 0.0090 0.0033 0.0034 0.0089 G8 0.0251 0.0198 0.0044 0.0015 0.0055 0.0037 G9 0.0028 0.0311 0.2323 0.0651 0.0383 0.0294 G10 0.0461 0.0477 0.0184 0.0135 0.0402 0.0413 W1 0.0333 0.0803 0.0747 0.0527 0.1014 0.0579 W2 0.0392 0.0749 0.0276 0.1217 0.0380 0.0626 W3 0.0431 0.0677 0.0284 0.0551 0.0547 0.0657


Table 2

Suitable generators for damping the target modes and proper input signals of centralized PSS and POD

Suitable generators Target oscillation modes Proper input signals G3 4th P2-3

G4 1st P2-25 G9 5th P10-11 W1 8th P17-27 W2 7th P5-6 W3 9th P5-8

4. PROPOSED DESIGN METHOD

Conventionally, the PSS and POD which are designed at a single operating point, cannot assure the stabilizing capability under different operating conditions. To counteract this problem, the new design method using MCS and probability is proposed for two-level coordinated control. By the MCS, 1000 different operating points are randomly generated under several uncertainties as follows.

1) The variation of output power of each synchronous generator between ±20 % from the normal operating point.

2) The variation of all load bus powers between ±20 % from the normal operating point.

3) The variation of wind speeds of DFIG wind turbines from 9 to 12 m/s.

4) A single line outage contingency. 5) The variation of time delay of centralized PSS and

POD between 100 and 500 ms. The percent damping ratio of each operating point

generated by MCS can be computed by (3). Subsequently, the probability of events that damping ratios occur in each one percent increasing step from min to max can be calculated by (4). As a result, the histogram of the probability of percent damping ratio in each one percent interval for any oscillation mode can be established as shown in Fig. 7.

Area1m Area2m

HistogramFrequency Polygon

Damping ratio 5%

Prob

abili

ty

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

0.1

0.2

0.3

max

ζmin

ζ

min

ζ+2

%

min

ζ+1

%

max

ζ-1

%

max

ζ-2

%

Fig. 7. – Histogram of probability of % damping ratio of oscillation mode.

To simplify the calculation, the frequency polygon is

built from the histogram. In this work, the desired damping ratio is set at 5 %. Therefore, the area of frequency polygon is divided into two areas. Area1m and Aream are the probability areas of events that the percent damping ratios of mth oscillation mode are less and greater than 5 %, respectively. To achieve at least 5 % damping ratio of the target oscillation modes, the optimization problem based on the maximization of the difference between Area2m and Area1m for all oscillation modes is formulated by

Maximize ,121 1

,,

OS

m

N

evevmevm

A

AreaArea (7)

subject to 50,1.0 LC KK

0.1,,,1.0 4321 CCCC TTTT

0.1,,,1.0 4321 LLLL TTTT ,

where OS is the number of oscillation modes, Area1m,ev, and Area2m,ev are areas 1 and 2 of the mth oscillation mode at the evth event. The centralized/local POD and PSS are individually tuned by the particle swarm optimization (PSO) [11]. The proposed controllers optimized by (7) are referred to as Centralized PPSS and PPOD, and Local PPSS and PPOD. The flow chart of the proposed design can be depicted in Fig.8.

The effect of the proposed two-level controller is compared with that of the conventional two-level controller. The optimized parameters of centralized/local PSS and POD are separately tuned at a normal operating condition to attain 5 % damping ratio by the following optimization.

Initialize parameters of Centralized or Local PPSS and PPOD

Compute ζm,ev of 1,000 different scenarios generated by MCS under several uncertainties from (3)

(TD is only considered for optimal tuning of Centralized PPSS and PPOD)

Calculate the Pr[ζm,ζm+1%] by (4)

All damping ratios ≥ 5%

Use result from (4) to draw the histogram and convert to

the frequency polygon

Evaluate the objective function (7) from the frequency polygon

End

Start

Update control parameters by PSO

Get the optimal parameters

No

Yes

Fig. 8. – Proposed design for centralized/local PPOD and PPSS.

Minimize

OS

imspec

1

. (8)

Subject to 50,1.0 LC KK

0.1,,,1.0 4321 CCCC TTTT

0.1,,,1.0 4321 LLLL TTTT .

where ζspec is the desired damping ratio which is equal to 5 %, ζm is the damping ratio of the mth oscillation mode. The conventional controllers tuned by (8) are referred to as Centralized CPSS and CPOD and Local CPSS and CPOD. In the case of Centralized CPSS and CPOD, TD is set at 300 ms.

5 Issarachai Ngamroo 215

5. STUDY RESULTS

The simulation study is carried out by Power System Analysis toolbox (PSAT) [9]. The MATLAB programming is used to solve the optimization problem. The PSO is performed with 100 particles and 50 iterations.

First, the comparsion of stabilizing performance between the proposed centralized/local PPSS and PPOD is conducted. Note that the local PPSS and PPOD are operated when the communication failure occurs. Figure 9 depicts the probability of percent damping ratios under 1000 different operating conditions. Some damping ratios in case of without controller are lower than 5 %. The probablity that the damping ratio is greater than 5 % in case of centralized PPSS and PPOD is much greater than that in case of local PPSS and PPOD.

Next, the comparsion of stabilizing effect between the proposed Centralized PPSS and PPOD, and Centralized CPSS and CPOD is carried out. Fig. 10 shows the probability of percent damping ratios under 1000 different operating conditions, and the plot of eigenvalues. The probability that the damping ratios of target modes of Centralized PPSS and PPOD are always higher than 5 % is much higher than that of Centralized CPSS and CPOD. Some damping ratios in case of Centralized CPSS and CPOD are less than 5 %.

2 4 5 6 8 10 12 14 16 18 200

0.05

0.1

0.15

0.2

Pro

babi

lity

2 4 5 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

2 4 5 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

2 4 5 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

Pro

babi

lity

2 4 5 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

2 4 5 6 8 10 12 14 16 18 200

0.05

0.1

0.15

0.2

2 4 5 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

Pro

babi

lity

Damping ratio (%)2 4 5 6 8 10 12 14 16 18 20

0

0.1

0.2

0.3

0.4

Damping ratio (%)2 4 5 6 8 10 12 14 16 18 20

0

0.1

0.2

0.3

0.4

Damping ratio (%)

Without controller Local PPSS and PPOD Centralized PPSS and PPOD

MODE 1

MODE 4

MODE 7 MODE 8

MODE 5

MODE 2 MODE 3

MODE 6

MODE 9


2 4 5 6 8 10 12 14 16 18 200

0.05

0.1

0.15

0.2

Pro

babi

lity

2 4 5 6 8 10 12 14 16 18 200

0.05

0.1

0.15

0.2

2 4 5 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

2 4 5 6 8 10 12 14 16 18 200

0.05

0.1

0.15

0.2

Pro

babi

lity

2 4 5 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

2 4 5 6 8 10 12 14 16 18 200

0.05

0.1

0.15

0.2

2 4 5 6 8 10 12 14 16 18 200

0.05

0.1

0.15

0.2

Pro

babi

lity

Damping ratio (%)2 4 5 6 8 10 12 14 16 18 20

0

0.1

0.2

0.3

0.4

Damping ratio (%)2 4 5 6 8 10 12 14 16 18 20

0

0.1

0.2

0.3

0.4

Damping ratio (%)

Without controller Centralized CPSS and CPOD Centralized PPSS and PPOD

MODE 5 MODE 6

MODE 3MODE 2MODE 1

MODE 4



Under the occurrence of communication failure, Figs. 11 and 12 depict the probability of percent damping ratios under 1000 different operating points, and the eigenvalues plot, respectively. The damping ratios in case of local PPSS and PPOD are much greater than local CPSS and CPOD. The scattering of eigenvalues in Fig.12 matches the probability in Fig. 11.

2 4 5 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

Pro

babi

lity

2 4 5 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

2 4 5 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

2 4 5 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

Pro

babi

lity

2 4 5 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

2 4 5 6 8 10 12 14 16 18 200

0.05

0.1

0.15

0.2

2 4 5 6 8 10 12 14 16 18 200

0.1

0.2

0.3

0.4

Pro

babi

lity

Damping ratio (%)2 4 5 6 8 10 12 14 16 18 20

0

0.1

0.2

0.3

0.4

Damping ratio (%)2 4 5 6 8 10 12 14 16 18 20

0

0.1

0.2

0.3

0.4

Damping ratio (%)

Without controller Local CPSS and CPOD Local PPSS and PPOD

MODE 4

MODE 1 MODE 2

MODE 5 MODE 6

MODE 3

MODE 9MODE 8MODE 7


-1.2 -1 -0.8 -0.6 -0.4 -0.2 0

-10

-5

0

5

10

Real part (1/s)

Imag

inar

y pa

rt (ra

d/s)

Damping ratio = 5%

Fig. 12. – Locus plot; without controller: gray star, local CPSS and CPOD:

brown star, local PPSS and PPOD: green star.

Table 3

Case studies Details

Case

Applied

disturbance

% Change in power output of

all generators

% Change in load power

Average wind

speeds of W1,

W2, W3

Line outage

Time delay

TD (ms)

a

Temporary 3 phase fault occurs at bus 27 for 100 ms and is cleared naturally.

No change No change

12.0 m/s, 12.0 m/s, 12.0 m/s

- 300

b

Temporary 3 phase fault occurs at bus 21 for 150 ms and is cleared naturally.

No change + 4.5% 10.7 m/s, 12.0 m/s, 11.4 m/s

Line 23-24

400

c

Under the communication failure, temporary 3 phase fault occurs at bus 21 for 150 ms and is cleared naturally.

No change + 4.5% 10.7 m/s, 12.0 m/s, 11.4 m/s

Line 23-24

-

d

Under the communication failure, 3 phase fault occurs at line 4-5 at t = 1 s and is cleared by tripping this line at t = 1.15 s without reclosing.

+ 7.0% + 4.0% 12.0 m/s, 12.0 m/s, 12.0 m/s

Line 21-16

-


The stabilizing effect of proposed and conventional two-level controllers is compared by the nonlinear simulation under various case studies as described in Table 3. Nonlinear simulation results are delineated in Fig. 13. At normal operating condition in case a, without controller, the power oscillations are undamped. On the contrary, centralized CPSS and CPOD and centralized PPSS and PPOD are able to suppress the power oscillations. Nevertheless, centralized CPSS and CPOD yield higher damping ability than centralized PPSS and PPOD. In case b, centralized CPSS and CPOD cannot tolerate system uncertainties and fail to remove the power oscillations. On the other hand, the centralized PPSS and PPOD are able to alleviate the power oscillations. With the communication failure in cases c and d, the local control is activated. Local PPSS and PPOD still effectively eliminate the power oscillations, while local CPSS and CPOD cannot damp out the oscillations.

6. CONCLUSIONS

In this paper, the new design method of two-level coordinated damping controllers based on MCS and probability is presented. Small signal stability analysis and nonlinear simulation confirm that the stabilizing capability of the proposed two-level control is much superior to that of the conventional control under severe short circuits and the high robustness to various system operations.

ACKNOWLEDGMENT

This work was supported by King Mongkut’s Institute of Technology Ladkrabang Research Fund no. KREF 115901.

Received February 28, 2018

REFERENCES 1. P. Kundur, Power System Stability and Control, McGraw-Hill, Inc.,

New York, 1994. 2. I. Ngamroo, Review of DFIG wind turbine impact on power system

dynamic performances, IEEJ Trans. Elect. Electron. Eng., 12, 3, pp. 301–311 (2017).

3. T. Surinkaew, I. Ngamroo, Robust power oscillation damper design for DFIG-based wind turbine on specified structure mixed H2/H∞ control, Renewable Energy, 66, pp. 15–24 (2014).

4. F. M. Hughes, O. Anaya-Lara, N. Jenkins, G. Strbac, A power system stabilizer for DFIG-based wind generation, IEEE Trans. Power Syst., 21, 2, pp. 763–772 (2006).

5. T. Surinkaew, I. Ngamroo, Coordinated robust control of DFIG wind turbine and PSS for stabilization of power oscillations considering system uncertainties, IEEE Trans. Sustainable Energy, 5, 3, pp. 823–833 (2014).

6. M. Mokhtari, F. Aminifar, Toward wide-area oscillation control through doubly-fed induction generator wind farms,” IEEE Trans. Power Syst., 29, 6, pp. 2985-2992 (2014).

7. S. Zhang, V. Vittal, Design of wide-area power system damping controllers resilient to communication failures, IEEE Trans. Power Syst., 28, 4, pp. 4292-4300 (2013).

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

-2

0

2

Pow

er flo

w (p.

u.)

0 2 4 6 8 10 12 14 16 18 20

-2

0

2

Time (s)

Pow

er flo

w (p.

u.)


Power flow between buses 1-2


Case (a)

0 2 4 6 8 10 12 14 16 18 20

-10

0

10

20

Pow

er flo

w (p.

u.)

0 2 4 6 8 10 12 14 16 18 20

-10

0

10

Time (s)

Pow

er flo

w (p.

u.)



Power flow between buses 1-2Unstable

Unstable

Case (b)

0 2 4 6 8 10 12 14 16 18 20

-10

-5

0

5

10

15

Pow

er flo

w (p.

u.)

0 2 4 6 8 10 12 14 16 18 20

-10

-5

0

5

10

Time (s)

Pow

er flo

w (p.

u.)




Unstable

Unstable

Unstable

Case (c)

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

-5

0

5

10

Pow

er flo

w (p.

u.)

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

-5

0

5

10

Time (s)

Pow

er flo

w (p.

u.)


Unstable

Unstable



Unstable

Case (d) Fig. 13 – Nonlinear simulation results.

8. L. Fan, H. Yin and Z. Miao, On active/reactive power modulation of

DFIG-based wind generation for interarea oscillation damping, IEEE Trans. Energy Conv., 26, 2, pp. 513-521 (2011).

9. F. Milano, Power system analysis toolbox version 2.1.8. 2013. 10. A. Rahim, I.O. Habiballah, DFIG rotor voltage control for system

dynamic performance enhancement, Elect. Power Syst. Res., 81, 2, pp. 503-509 (2011).

11. X.S. Yang, Engineering Optimization, John Willey & Sons, Sep. 2010. 12. Y. Zang, A. Bose, Design of wide-area damping controllers for

interarea oscillations, IEEE Trans. Power Syst., 23, 3, pp. 1136-1143 (2008).

two-level inter-area oscillation dampers design by …

Documents