Solving Complex ABCD Equations: 50 Hz, 3-Phase, High-Voltage Line

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In summary, the conversation discusses the calculation of sending-end phase voltage and current for a three-phase high-voltage transmission line. It also mentions the calculation of power lost in the cable and the estimation of primary line coefficients for a 50 km long line. Some participants are struggling to find the solution and are looking for resources for help.
  • #1
topcat123
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FIGURE 3(a) represents a 50 Hz, three-phase, high-voltage, transmission
line. For one phase, the relationships between the sending end voltage
and current and the receiving end voltage are given by the complex
ABCD equations:

Vsp = Vrp(A1 + jA2) + Irp(B1 + jB2)

Isp = Vrp(C1 + jC2) + Irp(D1 + jD2)


where VSP is the sending-end phase voltage, ISP the sending-end phase
current and VRP is the magnitude of the open-circuit receiving end phase
voltage.


(a) Given the parameter values in TABLE A and if the magnitude of the
receiving-end line voltage VRL is measured as 154 kV when feeding
a balanced load of 40 MVA at a power factor of 0.9, calculate the
value of the sending-end phase voltage VSP and sending-end phase
current ISP.

[N.B. VSL = √3 × VSP and the total power in a three-phase load is
given by P = √3VI cos θ.]

(b) Hence or otherwise calculate the sending-end power and thus the
power lost in the cable.

(c) If the line is modeled by the Π-circuit of FIGURE 4(b), see if you
can estimate the primary line coefficients R, L, G and C. The line is
50 km long.


A1= 0.8698
A2= 0.03542
B1= 47.94 Ω
B2= 180.8 Ω
C1= 0 S
C2= 0.001349 S
D1= 0.8698
D2= 0.03542

so

a) P=sqrt(3)VI
I=40000000/(sqrt(3)*154000) = 149.961 A
Vrp=Vrl/sqrt(3) = 88912 V

Using formulas given for ABCD.
Vsp =84524.79 + j30262.16 = 89778.8∠19.70
Isp = 130.44 +j125.252 = 180.83∠43.84

b) p= sqrt(3)VI cos θ = sqrt(3)*154000*149.961*0.9 =36 MW

Vsl = sqrt(3)*89778.8 = 155501.4*149.961*0.9 = 36.3MW

350960.2 W lost in the cable.

c) I don't have a clue?
 

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  • #2
Hi mate, Did you ever find the solution to part (C)? I cannot find for the life of me find any info on how to solve it. I have very similar answers to you for the rest of 4 but (c) has become a road block. Any help would be much appreciated, it almost feels like something is missing from the question!
 
  • #3
I think the OP has come & gone. I'd like to look at this but can't open the .docx with my office 2003. Could you make a pdf file out of it? Or describe fig. 4(b) in words?I do know how to produce the ABCD parameters for a transmission line given R,L,G and C per-unit-length quantities.
 
  • #4
Abcd

Hi mate, I am out of the country at the moment. But basiacally i have a table of values from A1,A2 through to D1, D2 but I can't find the formulas i need to find R,L,G,C.. The values in the table do have the relevant units ie ohms, S, etc with their respective imaginary part. The tranmission line is contructed as a pi circuit with Y being the 2 parallel resistors and z being the top one. It is a 50 hz 3 phase line with a 50 km length..

This probably isn't much use but i didn't want you to think i was ignoring you, I appreciate the offer to help.
 
  • #5

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  • #6
Thanks mate,

I do want to stress however that i am not looking for the answer here. I just need a nudge in the right direction or better still a good resource to look at. I am not finding my books very useful...
 
  • #7
Hello everyone,
I'm struggling with the same here, I don't know how to find R, L, G, C from given data. Has anyone got an idea?
 

FAQ: Solving Complex ABCD Equations: 50 Hz, 3-Phase, High-Voltage Line

1. What are complex ABCD equations and how are they used in the context of high-voltage lines?

Complex ABCD equations are mathematical models used to represent the behavior of electrical circuits, including high-voltage lines. They take into account the complex impedance and admittance of the components in the circuit and can be used to analyze the flow of electricity and voltage across the circuit.

2. How does the frequency of 50 Hz affect the solution of complex ABCD equations?

The frequency of 50 Hz is a standard frequency used in power systems. It affects the solution of complex ABCD equations by determining the reactance of the components in the circuit. At this frequency, the reactance of inductors and capacitors is significant, which can impact the overall impedance and voltage in the circuit.

3. What is the significance of 3-phase in complex ABCD equations for high-voltage lines?

3-phase refers to the three alternating currents that are used in power systems. In the context of complex ABCD equations, 3-phase systems are used to represent the three phases of a high-voltage line. This allows for a more accurate analysis of the flow of electricity and voltage in the system.

4. How do high-voltage lines impact the solution of complex ABCD equations?

High-voltage lines are designed to transmit electricity over long distances with minimal losses. In complex ABCD equations, the high-voltage of the line is represented by the voltage source in the circuit. The voltage of the line can greatly impact the overall impedance and voltage in the system and must be taken into account in the analysis.

5. What are some common techniques for solving complex ABCD equations for high-voltage lines?

There are several techniques for solving complex ABCD equations, including the use of matrices, phasor diagrams, and iterative methods. These techniques involve breaking down the circuit into smaller components and solving for the voltage and current at each point. Computer software programs can also be used to solve complex ABCD equations for high-voltage lines.

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