Chapter 6, Problem 6.46P

Discuss the role of FACTS (Flexible Alternating Current Transmission Systems) devices in power system control and optimization.

400Ω A k=0.9 600Ω B k=0.8 66Ω 600Ω

The 6-bus power system network of an electric utility company is shown in the Figure below. The line and transformer data containing the subtransient series resistance and reactance in per unit, and one-half of the total capacitance in per unit susceptance on a 100-MVA base, is tabulated below. The prefault voltage profile of the power system as obtained from four iterations of the newton Raphson power flow method are provided below as well.

The one-line diagram of a simple power system is shown in Figure below. The neutral of each generator is grounded through a current-limiting reactor of 0.25/3 per unit on a 100-MVA base. The system data expressed in per unit on a common 100-MVA base is tabulated below. The generators are running on no-load at their rated voltage and rated frequency with their emfs in phase. G Stark Item Base MVA Voltage Rating X' x² 20 kV 20 kV 20/220 kV 20/220 kV 100 0.05 0.15 0.15 0.10 0.10 220 kV 0.125 0.125 0.30 0.15 0.25 025 0.7125 0.15 100 100 0.15 0.05 0.10 0.10 0.10 100 0.10 100 100 Lu La 220 kV 0.15 220 kV 0.35 100 A balanced three-phase fault at bus 3 through a fault impedance Zf= jo.I per unit. The magnitude of the fault current in amperes in phase b for this fault is: Select one: A. 345.3 B. 820.1 C. 312500 3888888 产产

For the system in Figure 4 with given generation and load dispatch determine the voltages after two itterations of Gauss-Seidel method. Assume the initial voltage to be 1.01 at angle of 0◦ pu at bus 1, 1.015 at angle of 0◦ pu at bus 2, and 1.0 at angle of 0◦ pu at bus 3. All line impedances are in per unit on a common base, and charging is neglected. Take base power of 100 MVA.

The figure below shows the one-line diagram of a four- bus power system. The voltages, the scheduled real power and reactive powers, and the reactances of transmission lines are marked at this one line diagram (The voltages and reactances are in PU referred to 100 MW base. The active power P2 in MW is the last three digits (from right) of your registration number (i.e for the student that has a registration number 202112396, P2 =396). [10] Starting from an estimated voltage at bus 2, bus 3, and bus 4 equals V2 (0) = 1.15<0°, V3 = 1.15 < 0°, V4 1.1< 0°. 1- Specify the type of each bus and known & unknown quantities at each bus. 2- Find the elements of the second row of the admittance matrix (i.e. [Y21 Y22 Y23 Y24]). 3- Using Gauss-Siedal fınd the voltage at bus 2 after the first iteration. 4- Using Newton-Raphson, calculate: |- The value of real power (P2), at bus 2 after the first iteration. Il- The second element in the first row of the Jacobian matrix after the first iteration. 2 P2…

please solve for nodal stress method. (if it is possible to apply supernodes)

6. For a three bus power system assume bus 1 is the swing with a per unit voltage of 1.020 , bus 2 is a PQ bus with a per unit load of 2.0 + j0:5, and bus 3 is a PV bus with 1.0 per unit generation and a 1.0 voltage setpoint. The per unit line impedances are j0.1 between buses 1 and 2, j0.4 between buses 1 and 3, and j0.2 between buses 2 and 3. Using a flat start, use the Newton-Raphson approach to determine the first iteration phasor voltages at buses 2 and 3.

Problem 6.10: A 2-MVA, 4160/480 V transformer has series impedance of R = 2% and X = 6%. Determine the (i) full load voltage regulation of the trans- former at 0.85 pf lagging, and (ii) secondary output voltage on unloading the transformer completely.