0 ∠ I 18 7 22 24 L oad MW 2 4 1 3 16 22

Smart Grid: Assignment 1
Q1)
A single phase load draws 10 kW from a 416-V line at a power factor of 0.85 lagging.
1. Find S = P + jQ.
2. Find |I|.
3. Assume that I0 , find the instantaneous power p(t).
Q2) Convert the following instantaneous currents to phasors, using cos(wt) as the reference.
1. i(t)=300cos(wt-30)
2. i(t)=400sin(wt-30)
3. i(t)=100sin(wt-15)+200cos(wt-20)
Q3) Two balanced Y-connected loads, one drawing 10 kW at 0.8 power factor lagging and
the other 15 kW at 0.9 power factor leading, are connected in parallel and supplied by a
balanced three-phase Y-connected, 480-V source (line to line). Determine the source
current.
Q4) The fuel-cost curves for two generators are given as follows:
C1(P1)= 600 + 15 P1 + 0.05 P12
C2(P2) =700 +20P2 + 0.04 P22
Constraints
200 ≤P1 ≤ 800 MW
100 ≤P2 ≤500 MW
Assuming the system is lossless; calculate the optimal dispatch values of P1 and P2 for a
total load of 1000 MW, the incremental operating cost, and the total operating cost. Repeat
the calculations for a total load of 400 MW.
( Active and Reactive power).
(1)Using the electricity price at EEX
Load MW
Q5) The figure shows A load during a day
4
3
2
1
Calculate the cost to run this load
22
7
EEX (www.eex.com) on 20.10.2014,
7
11
16
18
22
For simplicity assume the company pays only for the active power. Furthermore, multiply the
electricity price on the EEX website by 3 (to reflect power transmission costs, EEG-Umlage,
taxes…). (2) Then assume that it is possible to reallocate 1MWh. How much would be the
savings?
(3) What is the power factor at time 16:00? (4) Assume that the load is supplied by a 13.8 kV
and the transmission line has an impedance of Z=1+2j, Determine the reactive power
required from a parallel capacitor to bring the power factor of the parallel combination up to
0.9.
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