Consider a radial transmission power system shown in Fig.1 with the nominal bus voltage Vo =...

 

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Consider a radial transmission power system shown in Fig.1 with the nominal bus voltage Vo = Vozdo before the transformer, the sending bus voltage V, V.Zd, after transformer and the receiving bus voltage V = Vr 20 at the load end. The load located at the receiving bus consumes P = 1 MW and Q = 0.2 MVAr. The combined impedance of the line and transformer between bus Vo and bus V, has resistance Ro = 5 Ohms and reactance Xo 15 Ohms. The transmission line between bus Vs and bus Vr has resistance R₁ = 5 Ohms and reactance X₁ = 10 Ohms. Voltage regulation standards require the load-side or receiving voltage to be within 10.45 kV- 11.55 KV. Vo Ro+ jXo You can prove that: t: 1 V₂ FIG. 1: A radial power network assuming the following relation is given: R₁ + jX₁ V² — V² = 2(RP + XQ) + (R² + X²) P² +Q² V² VV₁ + V₂V = 2 (RP+XQ) +2V2², (V-Vr)(V-Vr) R² + X² (0.2) We show the above relationship as the following. The current flowing from the sending bus to the receiving bus is calculated as I = (V-Vr)/(R+jX). Thus, squared magnitude of the current can be computed as 1² = 1² = V₂ P + jQ p² +Q² V2 (0.1) where ()* denotes conjugate operator. On the other hand, squared magnitude of the current can also be computed based on the load apparent power as (0.3) (0.4) By equating (0.3) and (0.4), you can arrive at (0.1). (a) Assume that the high order term (R² + X²) P²+² in (0.1) is small enough to be ignored. You have the following approximation V²-V²2(RP+XQ), (0.5) which will be used hereafter. You can also use p.u. system with Sbase = 10 MVA and Vbase = 11 kV. In this problem, all quantities are that of one phase. i. Find the corresponding base impedance and the per unit value for Zo and Z₁. ii. Without voltage regulation such as that with tap facilities, the sending voltage is fixed at a nominal value of V 11 kV. Find the receiving voltage magnitude V. Check if such receiving voltage magnitude lies within the acceptance voltage limits, i.e., from 10.45 kV to 11.55 kV. (b) With voltage regulation by using a transformer with tap t, the nominal bus voltage magnitude Vo = 11 kV and the sending bus voltage V, is unknown. i. Given the receiving bus voltage magnitude V, 10.45 kV, find the sending bus voltage magnitude V.. ii. Calculate the value of transformer tap t. Consider a radial transmission power system shown in Fig.1 with the nominal bus voltage Vo = Vozdo before the transformer, the sending bus voltage V, V.Zd, after transformer and the receiving bus voltage V = Vr 20 at the load end. The load located at the receiving bus consumes P = 1 MW and Q = 0.2 MVAr. The combined impedance of the line and transformer between bus Vo and bus V, has resistance Ro = 5 Ohms and reactance Xo 15 Ohms. The transmission line between bus Vs and bus Vr has resistance R₁ = 5 Ohms and reactance X₁ = 10 Ohms. Voltage regulation standards require the load-side or receiving voltage to be within 10.45 kV- 11.55 KV. Vo Ro+ jXo You can prove that: t: 1 V₂ FIG. 1: A radial power network assuming the following relation is given: R₁ + jX₁ V² — V² = 2(RP + XQ) + (R² + X²) P² +Q² V² VV₁ + V₂V = 2 (RP+XQ) +2V2², (V-Vr)(V-Vr) R² + X² (0.2) We show the above relationship as the following. The current flowing from the sending bus to the receiving bus is calculated as I = (V-Vr)/(R+jX). Thus, squared magnitude of the current can be computed as 1² = 1² = V₂ P + jQ p² +Q² V2 (0.1) where ()* denotes conjugate operator. On the other hand, squared magnitude of the current can also be computed based on the load apparent power as (0.3) (0.4) By equating (0.3) and (0.4), you can arrive at (0.1). (a) Assume that the high order term (R² + X²) P²+² in (0.1) is small enough to be ignored. You have the following approximation V²-V²2(RP+XQ), (0.5) which will be used hereafter. You can also use p.u. system with Sbase = 10 MVA and Vbase = 11 kV. In this problem, all quantities are that of one phase. i. Find the corresponding base impedance and the per unit value for Zo and Z₁. ii. Without voltage regulation such as that with tap facilities, the sending voltage is fixed at a nominal value of V 11 kV. Find the receiving voltage magnitude V. Check if such receiving voltage magnitude lies within the acceptance voltage limits, i.e., from 10.45 kV to 11.55 kV. (b) With voltage regulation by using a transformer with tap t, the nominal bus voltage magnitude Vo = 11 kV and the sending bus voltage V, is unknown. i. Given the receiving bus voltage magnitude V, 10.45 kV, find the sending bus voltage magnitude V.. ii. Calculate the value of transformer tap t.

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