Problem 1 - 20 Points

A 150-km, 230-kV, 60-Hz, three-phase overhead transmission line has a series impedance   =

0.6∠87° Ω/km and series admittance̅(y)  = 4 × 10−6∠90° S/km. At full load, the line delivers

250 MW at 0.9 pflagging and 220-kV. Calculate

a)   The ABCD parameters for this line

b)  The sending end voltage and current

c)   The percent voltage regulation

Problem 2 - 15 Points

a)   The fuel-cost curves of two generators are given as follows:

C1 (P1) = 800 + 18P1  + 0.015(P1)2

C2 (P2) = 400 + 15P2  + 0.025(P2)2

For a load of 600 MW, what three equations are used to solve the ED problem?

b)   A 280-km, three-phase overhead transmission line has a series impedance ̅(z)  =

0.55∠80° Ω/km and series admittance̅(y)  = 4.2 × 10−6∠90° S/km. Calculate ZC  andyℓ .

c)   What is the surge impedance loading (SIL) of a 500 kV line with   =   0.03 + j0.4 Ω/km

andy  = j4.5 × 10−6  S/km?

Problem 3 - 10 Points

Two points each. Circle T if statement is true, F if statement is False.

T         F           1.         When there are constrained lines, the ED and OPF solutions are identical.

T         F          2.         From the power flow perspective, the addition of load to a bus is represented as a negative power injection.

T         F          3.         A power system with one slack bus, two PV buses, and a PQ bushas 5 unknown state variables in the power flow formulation.

T         F          4.         By default, PowerWorld uses the Newton-Raphson method for the power flow solution.

T         F          5.          In an electricity market, the Independent System Operator (ISO) solves the OPF.

Problem 4 - 20 Points

A generator (slack) bus at voltageV1(̅)  =  1∠0° supplies another bus with loads(̅) =  1 + j0.5 pu

through a lossless short transmission line model with per-unit impedance z   =  j0.15. Also

assume there is also a capacitor with admittance̅(y)C   = −j4 pu connected to the load bus.

a)  Determine the bus admittance matrix (ybus ) for the system

b)  Calculate 21  via Gauss-Seidel

c)  Using a flat start, help initialize (do NOT solve) the Decoupled Newton-Raphson method by calculating 0 , F(0), and J(0 )