代做ELEC4617 Power System Protection Laboratory 2: Implementation of Digital Relaying in Simulink代做Mat
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Laboratory 2: Implementation of Digital Relaying in Simulink
A transmission line could be protected by differential protection, distance protection or even overcurrent protection. In this laboratory session, a distance protection based on impedance relay is to be developed in Simulink to study the basic concepts of distance protection.
Trip
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Filter and relay algorithm |
Figure 1 Distance and over current protection
The operating region of an impedance relay is formed by a circle with its radius equal to the impedance setting. An impedance relay operates whenever the detected impedance falls within its operation region. When the detected impedance is outside the circle, the distance relay does not operate.
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Operating |
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Figure 2 Impedance relay operating region
Assume that current transformer (CT) ratio is CTR and phase-voltage voltage transformer (VT) is VTR, the phase-voltage at the primary side of VT is Vph and phase-current at the primary side of CT is Iph.
Impedance relay setting is the value seen at secondary sides of CT and VT. Here it is assumed as Zset. For an impedance relay, Zset is a positive value. For other distance relays, it could a complex number.
The line impedance is proportional to its length. When a bolted three-phase fault occurs on the line, the impedance detected by the relay is the impedance of line segment between relay location and faulty point.
Assume that a bolted three-phase fault occurs at a point which is l meters away from relay. The line per-unit-length positive-sequence impedance is zl . Then the impedance detected by the relay is
If a distance relay needs to reach 100% of a line with length of Len or to protect the whole length of the transmission line, then the impedance relay setting should be equal to
When the bolted fault occurs on the line, ZDetectByRelay < Zset and the relay trips.
Modern distance protection is implemented by using more advantageous distance relays.
Objectives
This laboratory session targets at implementation of a digital distance protection in Simulink based on impedance relay. Three basic methods for computing magnitudes of voltage, current and impedance and the argument or angle of impedance are adopted.
Methods for processing voltage and current signals include:
1) Sample and first-order derivative method;
2) Frist-order and second-order derivative method;
3) Two-sample-point technique.
Policy for doing this laboratory
No copying any files to PC and no email or internet retrieval of files. Plagiarism is not allowed.
Fundamentals of the methods to compute voltage, current and impedance
1. Sample and first-order derivative method
Peak values of voltage and current are computed by
The magnitude of the impedance is
The argument of the impedance is
θZ = θV -θI = tan-1(v①0 / v ') - tan-1(i①0 / i ')
Approximation of derivatives in discrete form.: Two-sample-point approximation:
Three-sample-point approximation:
where f could be i or v, Δt is the sampling interval, and k, k-1 and k-2 are subscripts referring to a series of consecutive samples.
2. Frist-order and second-order derivative method
The magnitude of the impedance is
Z = V / I = v '(t)2 + (v" (t) / ①0 )2 i '(t)2 + (i" (t) / ①0 )2 (9)
The argument of the impedance is
θZ = θV -θI = tan-1 i "(①0 i ') - tan-1 v "(①0 v ') (10) For this method, the following expressions are used to compute first- and second-order derivatives:
(11)
(12)
where f could be i or v, Δt is the sampling interval, and k+1, k and k-1 are subscripts referring to a series of consecutive samples.
3. Two-sample-point technique
Peak value of voltage is (13a)
Peak value of current is computed by
(13b)
Z = V / I (14)
Impedance angle is given by
Procedures
Step 1
The program using method 1 is given as an example. It is based on equations (1) through (6). Open files named Laboratory2Method1main.m and Laboratory2Method1.mdl under the directory of Laboratory2 on the desktop. Below are some fundamental variables settings and their explanations. There is a accompanying subroutine named as ZTrajectory.m. There is no need to change it. Other parts in the program of Laboratory2Method1main.m are for drawing. You may not change them as well. Laboratory2Method1.mdl is called by Laboratory2Method1main.m. So you only need to run Laboratory2Method1main.m.
Ts=5E-04; % Sampling time in second.
VsLL=2.2E03; %Line-line voltage of source.
Rsource=1E-05; % Source resistance.
Lsource=2e-5; % Source inductance.
Duration=0.4; % Simulation time in seconds.
R_Line=5E-01; % Transmission line resistance in ohm.
L_Line=1E-02; % Transmission line inductance in Henry.
Zline=sqrt(R_Line^2+(2*pi*50*L_Line)^2); CTR=50; % CT ratio.
VTR=50; % VT ratio
% IfVTR/CTR=1, no adjustment required to calculated impedance. RLoad=50; % Per-phase load resistance in ohm.
ImpedanceRelaySetting=1.2* Zline; % Radius = Relay impedance setting. FaultOccurMoment=0.15; % It must be less than Duration.
% BreakerControlInAction=0: Breaker is controlled by digital relay;
% BreakerControlInAction=1: Breaker is always closed for testing V,I,Z algorithm. BreakerControlInAction=1;
sim('Laboratory2Method1.mdl');% To run the Simulink program.
Laboratory2Method1.mdl is a Simulink program for implementing overcurrent and distance protection for the power system as shown in Fig.1. Each of the three different methods as described above can be implemented to compute magnitudes of voltage, current and impedance
and the angle of impedance. In the given program, Method 1 is adopted.
Figure 3 Overall system in Simulink for distance protection study Content in BLOCK “V & I sensing” in Fig. 3 is shown in Fig. 4.
Figure 4 Voltage and current sensing Content in BLOCK “Relay” in Fig. 3 is shown in Fig. 5.
Figure 5 Relay model
Content in BLOCK “ImpedanceCalculator” in Fig. 5 is shown in Fig. 6.
Figure 6 Impedance computation block
Content in BLOCK “ComplexImpedance_U1” in Fig. 6 is shown in Fig. 7.
Figure 7 Block for computing magnitudes of voltage, current and impedance and angle of impedance
The codes in BLOCK “Magnitude and Angle Computation” in Fig. 7 is shown below, where Method 1 is adopted.
function [iout,vout,VMag,thetaV,IMag,thetaI,ZMag,ZAngle,co,deltaT1,IDeritive1,VDeritive1] = fcn(i,v,time,iold,vold,counter,deltaT)
iout=iold; vout=vold; deltaT1=deltaT; IDeritive1=0;
VDeritive1=0;
VMag=0; thetaV=0; IMag=0; thetaI=0; ZMag=0; ZAngle=0; co=counter+1;
mega=2*pi*50; if counter==1
iout(1)=i; vout(1)=v;
else
if counter==2
deltaT1=time;
iout(2)=i;
vout(2)=v;
iout(1)=iold(2); vout(1)=vold(2);
else
iout(3)=i;
iout(2)=iold(3); iout(1)=iold(2); vout(3)=v;
vout(2)=vold(3); vout(1)=vold(2);
VDeritive1=(3*vout(3)-4*vout(2)+vout(1))/(2*deltaT); IDeritive1=(3*iout(3)-4*iout(2)+iout(1))/(2*deltaT);
thetaV=atan(v*omega/VDeritive1);
thetaI=atan(i*omega/IDeritive1); ZAngle=thetaV-thetaI;
if ZAngle<-1.0
ZAngle=ZAngle+pi;
end
VMag=sqrt(v^2+(VDeritive1/omega)^2); IMag=sqrt(i^2+(IDeritive1/omega)^2);
ZMag=VMag/IMag;
end end
Content in BLOCK “ImpedanceRelay” in Fig. 5 is shown in Fig. 8.
Figure 8 Block for implementing digital relay logic
The code for relay logic in Fig. 8 is given below.
Function [BK_Command,InterLock2,counter1]=
fcn(Impedance,ImpedanceRelaySetting,counter,InterLock1)
InterLock2=InterLock1; InterLock1=0;
Z1=Impedance(1); Z1Ang=Impedance(2); R1=Z1*cos(Z1Ang); X1=Z1*sin(Z1Ang);
BK_Command=1; % Breaker is in closed-position.
if sqrt(R1^2+X1^2)<ImpedanceRelaySetting && counter>50 && InterLock1==0
BK_Command=0; % When the impedance falls in the trip region, open the breaker. InterLock2=1; % set Interlock to 1.
end
if InterLock2==1 && counter>150
BK_Command=0; end
counter1=counter+1;
BK_Command=double(BK_Command); return;
Study both programs Laboratory2Method1main.m and Laboratory2Method1.mdl. Then run the program Laboratory2Method1main.musing MATLAB under two cases:
1) BreakerControlInAction=1; 2) BreakerControlInAction=0.
Record steady-state magnitudes of voltage, current and impedance and angle of impedance
before and after faults from graphs. Compare them with theoretical values. Comment the results for both cases.
Step 2
Modify the code in the BLOCK as shown in Fig. 7 using Method 2 to compute the magnitudes of voltage, current and impedance and angle of impedance. Save the file using L2Method2_YourNameM.m and L2Method2_YourNameMDL.mdl.
Record steady-state magnitudes of voltage, current and impedance and angle of impedance before and after faults from graphs. Compare them with theoretical values.
Step 3
Modify the code in the BLOCK as shown as in Fig. 7 using Method 3 to compute the magnitudes of voltage, current and impedance and angle of impedance. Save the file using L2Method3_YourNameM.m and L2Method3_YourNameMDL.mdl.
Record steady-state magnitudes of voltage, current and impedance and angle of impedance before and after faults from graphs. Compare them with theoretical values.
Step 4
Compare the results from three methods and comment on the results.
Submission
Submit all four files from steps 2 and 3. Prepare a word file with comparison between calculated and theoretical magnitudes of voltage, current and impedance and angle of impedance for each of the three methods. The word file should include your comments from Step 4. Submit this file using filename of L2_YourName_Comments.doc.