Consider the simple power system shown in Figure 2 with generator internal and terminal buses and a load fed through a t

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Consider the simple power system shown in Figure 2 with
generator internal and terminal buses and a load fed through a
transmission line.

Consider The Simple Power System Shown In Figure 2 With Generator Internal And Terminal Buses And A Load Fed Through A T 1 (249.59 KiB) Viewed 54 times

E, Z8 VzZo X, Xc V ZO 11 I PL I2 Bc Figure 2. a. If the network is assumed to be lossless and the load has unity power factor, write the power flow equations of the system and further show that the load voltage is given by Eg cos V = 1 – B2X where X= Xg+Xe;

b. According to part (a), calculate V as a function of P, i.e., V(P); show that in the graph of V-P, for a given constant power load of P Po > 0 there are two voltage solutions Vi (higher voltage) and V2 (lower voltage); and calculate the value of P at which bifurcation happens; c. c. Now assume the load is voltage sensitive and there is a control mechanism (using OLTC or voltage regulator) to restore the load, which can be modelled by the equation V 7. P(V) – Po] IP where Po is the nominal load power that is to be maintained at all voltages. Use the Lypunov indirect method to show that stability of the two solutions depends on the sensitivity dPldV sign and give precise stability statements for the two solutions found in Part (b); d. Show how to compute dP/dV from the power flow Jacobian; and derive the region of attraction as an interval of voltages for any stable solution found by the stability criterion in (c).