Upload
soham-chakraborty
View
217
Download
0
Embed Size (px)
Citation preview
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 1/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 2/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 3/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 4/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 5/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 6/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 7/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 8/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 9/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 10/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 11/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 12/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 13/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 14/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 15/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 16/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 17/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 18/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 19/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 20/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 21/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 22/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 23/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 24/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 25/43
EXP. NO: 4
DATE: 11.04.2016
SMALL-SIGNAL STABILITY ANALYSIS OF SINGLE MACHINE-
INFINITE BUS (SMIB) SYSTEM USING TYPE 1B MACHINE MODEL
EFFECT OF EXCITATION SYSTEM
AIM:
To develop a MATLAB program to study Small-signal stability analysis of single machine-infinite
bus (SMIB) system using Type 1B machine model effect of excitation system.
SOFTWARE REQUIRED:
MATLAB
THEORY:
Small signal (or small disturbance) stability is the ability of the power system to maintain synchronismunder small disturbances. The disturbances are considered sufficiently small for linearization ofsystem equations to be permissible for purpose of analysis. Instability that may result can be of twoforms.
I. Steady increase in rotor angle due to lack of sufficient synchronizing torque.II. II. Rotor oscillations of increasing amplitude due to lack of sufficient damping torque.
Generator Represented by Variable Voltage behind Transient Reactance Effect of Field CircuitDynamics
We consider variation of field flux linkage in this model. We will consider only one winding in therotor, f winding.
The equations for this model are:
Vq=-R aIq + X d Id + Eq
Vd=-R aId + X qIq
pE q =-(1/T d0 )[Eq -(Xd-Xd )Id-EFD]
The system equations in state space form:
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 26/43
EFFECT OF EXCITATION SYSTEM:
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 27/43
The feedback of terminal voltage for purpose of voltage regulation results in negative damping. Thenegative damping is caused by delays in excitation system and synchronous machine field circuit (T d0 )with the latter exerting a predominant influence.
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 28/43
LARGE
SYSTEM
Time Response: Assuming
11 12 12 22 + 13 32
3t
21 12 22 22 + 23 32
3t
PROBLEM:
Single-line-diagram :
System data:Power Pl ant: 3x210 MW. The rating of each unit given below:
Rated kVA = 247,000 kVA; rated power factor = 0.85; rated voltage = 15.75 kV; rated frequency = 50Hz. Machine electrical parameters in per unit on the alternator rating ( i.e., on a base of 247,000 kVAand 15.75 kV) are: X d = 2.225; X d = 0.266; X d = 0.214; X leakage = 0.179; X q = 2.11; X q = 0.2454 pu;
X q (estimated) = 0.25; M af (estimated) = 0.004341= M aD ; R f (estimated) = 0.00106; L ff (estimated) =0.004534; M ag (estimated) = 0.004098= M aQ .
H -constant = 3.0 sec. on machine base.Initial loading conditions: P = 0.85 pu; Q = 0.5268 pu on rated MVA ;V = 1.0 pu.Step-up tr ansformer: 3x 15.75/400 kV, leakage: 9% for each transformer on generator MVA.Tr ansmission li ne: Each line X = 0.3 Ohm/km; length: 300 km.The K-constant values are: K 1 = 0.6821; K 2 = 0.9411; K 3 = 0.3010; K 4 = 1.9702
Neglect the damping due to the other sources [ K D in the acceleration equation equals zero].[p.u. reactance of transmission line=0.1389, base impedance=(kV) 2/kVA*1000]
The K-constant values are: K 1 = 0.6821; K 2 = 0.9411; K 3 = 0.3010; K 4 = 1.9702; K 5 = -0.1102; K 6 =0.5467.The excitation system considered is a simple one consisting of a single transfer function representingthe amplifier block (IEEE Type 1 1968) with typical value of gain and time constant.
G
(a)
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 29/43
PROGRAM:
%power factor=0.85 so base MVA=241 MVA, base voltage=15.75kV %on LT & 400kV on HT clc;k=180/pi; %for converting rad to deg p=0.85;q=0.5268;xd=2.225/3;xdd=0.266/3;xl=0.179/3;xe=0.0994;xq=2.11/3;f=50; v=1.0;kd=0;h=9; %xdd=xd'
k1=0.6821;k2=0.9411;k3=0.3010;k4=1.9702;k5 = -0.1102;k6 = 0.5467;Rf= 0.00106; Lff = 0.004534;ka=200;tr=0.02;tds0=Lff/Rft3=k3*tds0fprintf( 'STATE SPACE MATRIX' );A=[-kd/(2*h) -(k1)/(2*h) -k2/(2*h) 0; %type 1Bmachine with effect of excitation
(2*pi*f) 0 0 0;0 -k4/tds0 -1/(k3*tds0) -ka/tds0;0 k5/tr k6/tr -1/tr ]
B=[1/(2*h); 0; ka/tds0; 0]
fprintf( 'EIGEN VALUES OF A' );lamda=eig(A) %eigen values of matrix A fprintf( 'V--> RIGHT MODAL MATRIX D--> DIAGONAL MATRIX' );[v d]=eig(A) % v is right modal matrix fprintf( 'LEFT MODAL MATRIX' );l=inv(v) % left modal matrix m=l';fprintf( 'PARTICIPATION MATRIX' );p=(v.*m) %participation matrix abs(p)fprintf( 'ANGLE OF P MATRIX (IN RADIAN)' );
angle(p)*kwn=abs(imag(lamda(1,1))) %natural frequencyzita=abs(real(lamda(1,1)))/abs(lamda(1,1))fprintf( 'VALUE OF KA JUST TO COMPENSATE THE DEMAGNETISING EFFECT OFARMATURE REACTION' );-k4/k5s=i*wn;m=(-k3*(k4*(1+(i*wn*tr))+(k5*ka)))/((k3*tds0*tr*i*i*wn*wn)+(((k3*tds0)+tr)*(i*wn))+(1+(k3*k6*ka)));fprintf( 'SYNCHRONIZING & DAMPING TORQUE COEFFICIENT AT ROTOR
OSCILLATION FREQUENCY' );kseq=real(m)ksnet=kseq+k1kdeq=imag(m)fprintf( 'DAMPING TORQUE COEFFICIENT IN P.U.TORQUE/ELEC.RADIAN' );kdeq*((2*pi*f)/wn)fprintf( 'wd=damped frequency zita damping ratio' );zita %damping ratio wd=wn*(sqrt(1-(zita*zita))) %damped frequency wdh=wd/(2*pi)%for plots using zero input response
t=0:0.01:20;dd=(v(2,1)*l(1,2)*5*exp(lamda(1,1)*t))+(v(2,2)*l(2,2)*5*exp(lamda(2,1)*t))+(v(2,3)*l(3,2)*5*exp(lamda(3,1)*t))+(v(2,4)*l(4,2)*5*exp(lamda(4,1)*t)); %assuming initial condition
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 30/43
dw=(v(1,1)*l(1,2)*5*exp(lamda(1,1)*t))+(v(1,2)*l(2,2)*5*exp(lamda(2,1)*t))+(v(1,3)*l(3,2)*5*exp(lamda(3,1)*t))+(v(1,4)*l(4,2)*5*exp(lamda(4,1)*t)); %del=5 deg or 0.0873 rad subplot(3,1,1),plot(t,dd),gridxlabel( 't sec' ),ylabel( 'delta degre' )subplot(3,1,2),plot(t,dw),gridxlabel( 't sec' ),ylabel( 'rotor speed ' )
OUTPUT:
STATOR CURRENT OF ONE GEN.
tds0 =
4.2774
t3 =
1.2875
STATE SPACE MATRIXA =
0 -0.0379 -0.0523 0
314.1593 0 0 0
0 -0.4606 -0.7767 -46.7578
0 -5.5100 27.3350 -50.0000
B =
0.0556
0
46.7578
0
EIGEN VALUES OF A
lamda =
0.0591 + 3.8461i
0.0591 - 3.8461i
-25.4475 +25.9329i
-25.4475 -25.9329i
V--> RIGHT MODAL MATRIX D--> DIAGONAL MATRIX
v =
0.0002 + 0.0121i 0.0002 - 0.0121i 0.0008 + 0.0008i 0.0008 - 0.0008i
0.9843 0.9843 0.0001 - 0.0099i 0.0001 + 0.0099i
0.1728 - 0.0273i 0.1728 + 0.0273i 0.7940 0.7940
-0.0150 - 0.0137i -0.0150 + 0.0137i 0.4190 - 0.4403i 0.4190 + 0.4403i
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 31/43
d =
0.0591 + 3.8461i 0 0 0
0 0.0591 - 3.8461i 0 0
0 0 -25.4475 +25.9329i 0
0 0 0 -25.4475 -25.9329i
LEFT MODAL MATRIX
l =
0.0005 -41.3940i 0.5068 - 0.0078i 0.0059 + 0.0821i -0.0114 - 0.0758i
0.0005 +41.3940i 0.5068 + 0.0078i 0.0059 - 0.0821i -0.0114 + 0.0758i
1.4207 - 0.0612i -0.1100 + 0.1222i 0.6256 - 0.5976i 0.0051 + 1.1327i
1.4207 + 0.0612i -0.1100 - 0.1222i 0.6256 + 0.5976i 0.0051 - 1.1327i
PARTICIPATION MATRIX
p =
-0.4988 + 0.0077i -0.4988 - 0.0077i 0.0011 + 0.0012i 0.0011 - 0.0012i
0.4988 + 0.0077i 0.4988 - 0.0077i -0.0012 + 0.0011i -0.0012 - 0.0011i
-0.0012 - 0.0144i -0.0012 + 0.0144i 0.4967 + 0.4745i 0.4967 - 0.4745i
0.0012 - 0.0010i 0.0012 + 0.0010i -0.4966 - 0.4768i -0.4966 + 0.4768i
ans =
0.4989 0.4989 0.0016 0.00160.4989 0.4989 0.0016 0.0016
0.0144 0.0144 0.6870 0.6870
0.0016 0.0016 0.6885 0.6885
ANGLE OF P MATRIX (IN RADIAN)
ans =
179.1186 -179.1186 47.4918 -47.4918
0.8801 -0.8801 138.5743 -138.5743-94.8268 94.8268 43.6907 -43.6907
-39.0585 39.0585 -136.1656 136.1656
wn =
3.8461
zita =
0.0154
VALUE OF KA JUST TO COMPENSATE THE DEMAGNETISING EFFECT OF ARMATUREREACTION
ans = 17.8784
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 32/43
SYNCHRONIZING & DAMPING TORQUE COEFFICIENT AT ROTOR OSCILLATIONFREQUENCY
kseq =
0.1760
ksnet =
0.8581kdeq =
-0.0278
DAMPING TORQUE COEFFICIENT IN P.U.TORQUE/ELEC.RADIAN
ans =
-2.2672
wd=damped frequency zita damping ratio
zita =
0.0154
wd =
3.8456
wdh =
0.6120
RESULT: E 1 and 2 corresponds to rotor mode. In this mode state variables E q X1 participate very little. E q X1 are associated with modes that decay very rapidly(real part=-25.4475). There is hardly any participation from in this mode. The effect ofAVR is to increase synchronizing torque and decrease damping torque component at the rotoroscillation frequency. The feedback of terminal voltage for purpose of voltage regulation results innegative damping. The negative damping is caused by delays in excitation system and synchronous
machine field circuit (T d0 ) with the latter exerting a predominant influence. A MATLAB programwas written to analyze the small-signal stability of a single-machine-infinite bus (SMIB) system(type1B).
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 33/43
EXP. NO: 5
DATE: 15.04.2016
SMALL-SIGNAL STABILITY ANALYSIS OF SINGLE MACHINE-
INFINITE BUS (SMIB) SYSTEM USING TYPE 1B MACHINE MODEL
WITH A SIMPLE EXCITATION SYSTEM EFFECT OF PSS
AIM:
To develop a MATLAB program to study Small-signal stability analysis of single machine-infinite
bus (SMIB) system using Type 1B machine model with a simple excitation system effect of PSS.
SOFTWARE REQUIRED:
MATLAB
THEORY:
Small signal (or small disturbance) stability is the ability of the power system to maintain synchronismunder small disturbances. The disturbances are considered sufficiently small for linearization ofsystem equations to be permissible for purpose of analysis. Instability that may result can be of twoforms.
I. Steady increase in rotor angle due to lack of sufficient synchronizing torque.II. II. Rotor oscillations of increasing amplitude due to lack of sufficient damping torque.
Generator Represented by Variable Voltage behind Transient Reactance Effect of Field CircuitDynamics
We consider variation of field flux linkage in this model. We will consider only one winding in therotor, f winding.
The equations for this model are:
Vq=-R aIq + X d Id + Eq
Vd=-R aId + X qIq
pE q =-(1/T d0 )[Eq -(Xd-Xd )Id-EFD]
The system equations in state space form:
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 34/43
EFFECT OF EXCITATION SYSTEM AND INCLUSION OF POWER SYSTEM STABILIZER (PSS) :
The feedback of terminal voltage for purpose of voltage regulation results in negative damping. Thenegative damping is caused by delays in excitation system and synchronous machine field circuit (T d0 )with the latter exerting a predominant influence. The negative damping torque component can beneutralized if we can superimpose a sufficient positive damping torque component. The positivedamping torque can be produced by feeding back the speed deviation (from synchronous speed) signalat the excitation system input after providing to it appropriate gain and phase advance for the range ofexpected rotor oscillation frequencies. The basic function of the PSS is to introduce positive dampingtorque to rotor oscillations by controlling the excitation using auxillary stabilizing signal such as thespeed deviation. The PSS consists of three major blocks: (i) Gain (ii) Phase compensation (iii) Signalwashout.
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 35/43
.
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 36/43
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 37/43
In state variable form,
Time Response: Assuming deg.
11 12 12 22 + 13 32
3t
21 12 22 22 + 23 32
3t +
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 38/43
LARGE
SYSTEM
PROBLEM:
Single-line-diagram :
System data:Power Pl ant: 3x210 MW. The rating of each unit given below:
Rated kVA = 247,000 kVA; rated power factor = 0.85; rated voltage = 15.75 kV; rated frequency = 50Hz. Machine electrical parameters in per unit on the alternator rating ( i.e., on a base of 247,000 kVAand 15.75 kV) are: X d = 2.225; X d = 0.266; X d = 0.214; X leakage = 0.179; X q = 2.11; X q = 0.2454 pu;
X q (estimated) = 0.25; M af (estimated) = 0.004341= M aD ; R f (estimated) = 0.00106; L ff (estimated) =0.004534; M ag (estimated) = 0.004098= M aQ .
H -constant = 3.0 sec. on machine base.Initial loading conditions: P = 0.85 pu; Q = 0.5268 pu on rated MVA ;V = 1.0 pu.Step-up tr ansformer: 3x 15.75/400 kV, leakage: 9% for each transformer on generator MVA.Tr ansmission li ne: Each line X = 0.3 Ohm/km; length: 300 km.The K-constant values are: K 1 = 0.6821; K 2 = 0.9411; K 3 = 0.3010; K 4 = 1.9702
Neglect the damping due to the other sources [ K D in the acceleration equation equals zero].[p.u. reactance of transmission line=0.1389, base impedance=(kV) 2/kVA*1000]
The K-constant values are: K 1 = 0.6821; K 2 = 0.9411; K 3 = 0.3010; K 4 = 1.9702; K 5 = -0.1102; K 6 =0.5467.The excitation system considered is a simple one consisting of a single transfer function representing
the amplifier block (IEEE Type 1 1968) with typical value of gain and time constant.The PSS data is as follows: K PSS = 10; T W = 1.4 s; T 1 = 0.1; T 2 = 0.03
PROGRAM:
%power factor=0.85 so base MVA=241 MVA, base voltage=15.75kV %on LT & 400kV on HT clc;k=180/pi; %for converting rad to deg
p=0.85;q=0.5268;xd=2.225/3;xdd=0.266/3;xl=0.179/3;xe=0.0994;xq=2.11/3;f=50;v=1.0;kd=0;h=9; %xdd=xd' k1=0.6821;k2=0.9411;k3=0.3010;k4=1.9702;k5 = -0.1102;k6 = 0.5467;Rf = 0.00106; Lff= 0.004534;ka=200;tr=0.02; KPSS = 10; TW = 1.4 ; T1 = 0.1; T2 = 0.03;a=(-KPSS*kd)/(2*h);b=(-KPSS*k1)/(2*h);c=(-KPSS*k2)/(2*h);d=(-(T1/T2)*(1/TW))+(1/T2); tds0=Lff/Rf t3=k3*tds0 fprintf( 'STATE SPACE MATRIX' ); A=[-kd/(2*h) -(k1)/(2*h) -k2/(2*h) 0 0 0; %type 1Bmachine with effect of excitation
(2*pi*f) 0 0 0 0 0; 0 -k4/tds0 -1/(k3*tds0) -ka/tds0 0 ka/tds0; 0 k5/tr k6/tr -1/tr 0 0; a b c 0 -1/TW 0;
(a*T1)/T2 (b*T1)/T2 (c*T1)/T2 0 d -1/T2] B=[1/(2*h); 0; ka/tds0; 0; KPSS/(2*h); (KPSS/(2*h))*(T1/T2)] fprintf( 'EIGEN VALUES OF A' ); lamda=eig(A) %eigen values of matrix A
G
(a)
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 39/43
fprintf( 'V--> RIGHT MODAL MATRIX D--> DIAGONAL MATRIX' ); [v d]=eig(A) % v is right modal matrix
fprintf( 'LEFT MODAL MATRIX' ); l=inv(v) % left modal matrix m=l'; fprintf( 'PARTICIPATION MATRIX' ); p=(v.*m) %participation matrix abs(p) fprintf( 'ANGLE OF P MATRIX (IN RADIAN)' ); angle(p)*k wn=abs(imag(lamda(1,1))) %natural frequencyzita=abs(real(lamda(1,1)))/abs(lamda(1,1)) s=i*wn; delt=(k2*k3*ka)/(1+(k3*k6*ka)+(k3*tds0*s))abs(delt) fprintf( 'MINIMUM PHASE LEAD THAT SHOULD BE PROVIDED BY THE PSS AT ROTOROSCILLATION FREQUENCY' ); angle(delt)*(-k) m=(-
k3*(k4*(1+(i*wn*tr))+(k5*ka)))/((k3*tds0*tr*i*i*wn*wn)+(((k3*tds0)+tr)*(i*wn))+(1+(k3*k6*ka))); kseq=real(m); kdeq=imag(m)*((2*pi*f)/wn); fprintf( 'GAIN REQUIRED TO NEUTRALISE THE NEGATIVE DAMPING OF AVR AT ROTOROSCILLATION FREQUENCY' ); -kdeq/abs(delt) fprintf( 'wd=damped frequency zita damping ratio' ); zita %damping ratio wd=wn*(sqrt(1-(zita*zita))) %damped frequency wdh=wd/(2*pi) n=delt*KPSS*((s*TW)/(1+(s*TW)))*((1+(s*T1))/(1+(s*T2))); fprintf( 'EFFECT OF PSS AT ROTOR OSCILLATION' );
abs(n) angle(n)*k fprintf( 'VALUES OF KSPSS & KDPSS' ); kdpss=real(n) kspss=imag(n)*(wn/314.159) fprintf( 'NET SYNCHRONIZING AND DAMPING TORQUE COEFFICIENT' ); ksnet=k1+kseq+kspss kdnet=kdeq+kdpss %for plots using zero input response t=0:0.01:20; dd=(v(2,1)*l(1,2)*5*exp(lamda(1,1)*t))+(v(2,2)*l(2,2)*5*exp(lamda(2,1)*t))+(v(2,3)*l(3,2)*5*exp(lamda(3,1)*t))+(v(2,4)*l(4,2)*5*exp(lamda(4,1)*t))+(v(2,5)*l(5,2)*5*exp(lamda(5,1)*t))+(v(2,6)*l(6,2)*5*exp(lamda(6,1)*t)); %assuming initial condition
dw=(v(1,1)*l(1,2)*5*exp(lamda(1,1)*t))+(v(1,2)*l(2,2)*5*exp(lamda(2,1)*t))+(v(1,3)*l(3,2)*5*exp(lamda(3,1)*t))+(v(1,4)*l(4,2)*5*exp(lamda(4,1)*t))+(v(1,5)*l(5,2)*5*exp(lamda(5,1)*t))+(v(1,6)*l(6,2)*5*exp(lamda(6,1)*t)); %del=5 deg or 0.0873 rad subplot(3,1,1),plot(t,dd),grid xlabel( 't sec' ),ylabel( 'delta degre' ) subplot(3,1,2),plot(t,dw),grid xlabel( 't sec' ),ylabel( 'rotor speed ' )
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 40/43
OUTPUT:
tds0 =
4.2774
t3 =
1.2875
STATE SPACE MATRIX
A =
0 -0.0379 -0.0523 0 0 0
314.1593 0 0 0 0 0
0 -0.4606 -0.7767 -46.7578 0 46.7578
0 -5.5100 27.3350 -50.0000 0 0
0 -0.3789 -0.5228 0 -0.7143 0
0 -1.2631 -1.7428 0 30.9524 -33.3333
B =
0.0556
0
46.7578
0
0.55561.8519
EIGEN VALUES OF A
lamda =
-24.4035 +27.2772i
-24.4035 -27.2772i
-0.3725 + 3.6515i
-0.3725 - 3.6515i-0.7463
-34.5260
V--> RIGHT MODAL MATRIX D--> DIAGONAL MATRIX
v = 0.0008 + 0.0009i 0.0008 - 0.0009i -0.0011 + 0.0112i -0.0011 - 0.0112i 0.0015 0.0007
0.0010 - 0.0098i 0.0010 + 0.0098i 0.9645 0.9645 -0.6402 -0.0060
0.8067 0.8067 0.0757 + 0.1597i 0.0757 - 0.1597i 0.4857 0.4369
0.4043 - 0.4288i 0.4043 + 0.4288i -0.0586 + 0.0923i -0.0586 - 0.0923i 0.3412 0.77390.0077 + 0.0088i 0.0077 - 0.0088i -0.0330 + 0.1079i -0.0330 - 0.1079i 0.3541 0.0067
-0.0033 + 0.0417i -0.0033 - 0.0417i -0.0609 + 0.0996i -0.0609 - 0.0996i 0.3352 0.4585
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 41/43
d = -24.4035 +27.2772i 0 0 0 0 0
0 -24.4035 -27.2772i 0 0 0 0
0 0 -0.3725 + 3.6515i 0 0 0
0 0 0 -0.3725 - 3.6515i 0 0
0 0 0 0 -0.7463 0
0 0 0 0 0 -34.5260
LEFT MODAL MATRIX
l =
1.0008 + 0.3091i -0.1046 + 0.0629i 0.6507 - 0.5480i -0.0571 + 1.0618i -0.5400 + 1.0574i -0.5186 - 1.2852i
1.0008 - 0.3091i -0.1046 - 0.0629i 0.6507 + 0.5480i -0.0571 - 1.0618i -0.5400 - 1.0574i -0.5186 + 1.2852i
-9.8334 -45.5794i 0.5414 - 0.0603i 0.0040 + 0.0847i -0.0096 - 0.0791i 1.0070 - 0.0649i 0.0188 + 0.1181i
-9.8334 +45.5794i 0.5414 + 0.0603i 0.0040 - 0.0847i -0.0096 + 0.0791i 1.0070 + 0.0649i 0.0188 - 0.1181i-29.6103 - 0.0000i 0.0703 + 0.0000i -0.0022 + 0.0000i 0.0021 - 0.0000i 3.0822 + 0.0000i -0.0032 + 0.0000i
-0.6931 + 0.0000i 0.0762 + 0.0000i -0.0510 + 0.0000i 0.1540 -1.8294 + 0.0000i 1.9984 - 0.0000i
PARTICIPATION MATRIX
p =
0.0010 + 0.0006i 0.0010 - 0.0006i -0.4997 - 0.1624i -0.4997 + 0.1624i -0.0450 + 0.0000i -0.0005 - 0.0000i
-0.0007 + 0.0010i -0.0007 - 0.0010i 0.5222 + 0.0581i 0.5222 - 0.0581i -0.0450 + 0.0000i -0.0005 + 0.0000i
0.5249 + 0.4420i 0.5249 - 0.4420i 0.0138 - 0.0058i 0.0138 + 0.0058i -0.0011 - 0.0000i -0.0223 - 0.0000i
-0.4784 - 0.4048i -0.4784 + 0.4048i -0.0067 - 0.0055i -0.0067 + 0.0055i 0.0007 + 0.0000i 0.1192
0.0051 - 0.0129i 0.0051 + 0.0129i -0.0402 + 0.1065i -0.0402 - 0.1065i 1.0915 - 0.0000i -0.0122 - 0.0000i
-0.0519 - 0.0258i -0.0519 + 0.0258i 0.0106 + 0.0091i 0.0106 - 0.0091i -0.0011 - 0.0000i 0.9162 + 0.0000i
PARTICIPATION MATRIX
ans = 0.0012 0.0012 0.5255 0.5255 0.0450 0.0005
0.0012 0.0012 0.5255 0.5255 0.0450 0.0005
0.6862 0.6862 0.0150 0.0150 0.0011 0.0223
0.6267 0.6267 0.0087 0.0087 0.0007 0.1192
0.0139 0.0139 0.1138 0.1138 1.0915 0.0122
0.0580 0.0580 0.0140 0.0140 0.0011 0.9162
ANGLE OF P MATRIX (IN RADIAN)
ans = 30.5141 -30.5141 -162.0015 162.0015 180.0000 -180.0000
126.8793 -126.8793 6.3505 -6.3505 180.0000 180.0000
40.1008 -40.1008 -22.6562 22.6562 -180.0000 -180.0000
-139.7581 139.7581 -140.6724 140.6724 0.0000 0
-68.5327 68.5327 110.6851 -110.6851 -0.0000 -180.0000
-153.5428 153.5428 40.4821 -40.4821 -180.0000 0.0000
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 42/43
wn =
27.2772
zita =
0.6668
delt =
0.8061 - 0.8348i
ans =
1.1605
MINIMUM PHASE LEAD THAT SHOULD BE PROVIDED BY THE PSS AT ROTOROSCILLATION FREQUENCY
ans =
46.0022
GAIN REQUIRED TO NEUTRALISE THE NEGATIVE DAMPING OF AVR AT ROTOROSCILLATION FREQUENCY
ans =
1.4672
wd=damped frequency zita damping ratio
zita =
0.6668
wd =20.3290
wdh =
3.2355
EFFECT OF PSS AT ROTOR OSCILLATION
ans =
26.0834
ans =
-13.9295
VALUES OF KSPSS & KDPSS
kdpss =
25.3163
kspss =
-0.5452
NET SYNCHRONIZING AND DAMPING TORQUE COEFFICIENT
ksnet = 0.1890
kdnet = 23.6136
8/18/2019 Lab Record_power System Dynamics
http://slidepdf.com/reader/full/lab-recordpower-system-dynamics 43/43
RESULT: E 3 and 4 corresponds to rotor mode. In this mode state variables E q X1
participate very little. E q X1 are associated with eigen values 1 and 2. There is hardly any
participation from in this mode. X 2 is associated with 5. X s is associated with 6. The
effect of PSS is evident from increase in damping torque component at the rotor oscillation frequency.
A MATLAB program was written to analyze the small-signal stability of a single-machine-infinite bus
(SMIB) system(type 1B) with PSS.