' Question: Calculate the line current flowing through the…

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Fathima Shifana SK · Accepted Answer

Given Data: Sending end voltage (line-to-line), V s V_s V s ​ = 110 kV Receiving end voltage (line-to-line), V r V_r V r ​ = 100 kV Transmission line impedance per phase, Z = 5 + j 20 Z = 5 + j20 Z = 5 + j 20 ohms Load power, P = 50 P = 50 P = 50 MW Power factor (lagging), p f = 0.9 pf = 0.9 p f = 0.9 1. Calculate the line current flowing through the transmission line. First, let's calculate the phase voltage and the current drawn by the load. The line-to-line voltage at the receiving end V r V_r V r ​ is 100 kV, which translates to a phase voltage V r ϕ V_{r\phi} V r ϕ ​ : V r ϕ = V r 3 = 100 × 1 0 3 3  V V_{r\phi} = \frac{V_r}{\sqrt{3}} = \frac{100 	imes 10^3}{\sqrt{3}} 	ext{ V} V r ϕ ​ = 3 ​ V r ​ ​ = 3 ​ 100 × 1 0 3 ​  V The load power P P P and power factor p f pf p f are used to calculate the apparent power S S S and the current I r ϕ I_{r\phi} I r ϕ ​ : S = P p f = 50 × 1 0 6 0.9  VA S = \frac{P}{pf} = \frac{50 	imes 10^6}{0.9} 	ext{ VA} S = p f P ​ = 0.9 50 × 1 0 6 ​  VA I r ϕ = S 3 ⋅ V r = 50 × 1 0 6 3 × 100 × 1 0 3 × 0.9 I_{r\phi} = \frac{S}{\sqrt{3} \cdot V_{r}} = \frac{50 	imes 10^6}{\sqrt{3} 	imes 100 	imes 10^3 	imes 0.9} I r ϕ ​ = 3 ​ ⋅ V r ​ S ​ = 3 ​ × 100 × 1 0 3 × 0.9 50 × 1 0 6 ​ Now, let's compute these values. The phase voltage at the receiving end is approximately 57,735.03 V (or 57.735 kV ). The apparent power S S S is approximately 55.56 MVA . The line current I r I_r I r ​ flowing through the transmission line is approximately 320.75 A . 2. Determine the voltage regulation of the transmission line. Voltage regulation is calculated as: Voltage Regulation = V s ϕ − V r ϕ V r ϕ × 100 % 	ext{Voltage Regulation} = \frac{V_{s\phi} - V_{r\phi}}{V_{r\phi}} 	imes 100\% Voltage Regulation = V r ϕ ​ V s ϕ ​ − V r ϕ ​ ​ × 100% To find V s ϕ V_{s\phi} V s ϕ ​ (sending end phase voltage), we use the voltage drop across the transmission line: V s ϕ = V r ϕ + I r ϕ ⋅ Z V_{s\phi} = V_{r\phi} + I_{r\phi} \cdot Z V s ϕ ​ = V r ϕ ​ + I r ϕ ​ ⋅ Z Where: V s ϕ V_{s\phi} V s ϕ ​ is the sending end phase voltage, I r ϕ I_{r\phi} I r ϕ ​ is the current per phase. Now, let's calculate the sending end voltage V s ϕ V_{s\phi} V s ϕ ​ and the voltage regulation. ​ The sending end phase voltage V s ϕ V_{s\phi} V s ϕ ​ is approximately 59,338.78 V with an imaginary component, indicating a phase angle (about 6,415.00j V ), but the magnitude is the relevant value for voltage regulation. The voltage regulation of the transmission line is approximately 3.38% . 3. Find the real power losses in the transmission line. Real power losses in the transmission line P l o s s P_{loss} P  l oss ​ are given by: P l o s s = 3 × I r ϕ 2 × R P_{loss} = 3 	imes I_{r\phi}^2 	imes R P  l oss ​ = 3 × I r ϕ 2 ​ × R where R = Re ( Z ) R = 	ext{Re}(Z) R = Re ( Z ) is the resistance per phase. Let's calculate the real power losses. ​ The real power losses in the transmission line are approximately 1.54 MW . Summary of Results: Line current flowing through the transmission line : 320.75 A . Voltage regulation of the transmission line : 3.38% . Real power losses in the transmission line : 1.54 MW . ​

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Fathima Shifana SK

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