12.47 kv to 480v transformer

Distribution System And Power Quality

Cal Poly Pomona ECE 5750 Distribution System and Power Quality – Instructor Dr. Ha Thu Le

1

California State Polytechnic University Pomona Department of Electrical and Computer Engineering

ECE 5750 Distribution system and power quality – Spring 2020

Homework 5 Voltage sag – Harmonics analysis and control

Problem 1 Consider a simple distribution feeder shown in Fig. 1. Laterals L1 and L4 are of single phase with taps on phases A and B, and with the maximum load currents of 60A and 54A, respectively. Laterals L2 and L3 are of 3-phase with maximum load currents of 84A and 90A. Three-phase (if any) and single line to ground fault currents are shown in the one-line diagram. The fast tripping feature of the substation circuit breaker B is disabled. A mid-line recloser with minimum trip ratings of 560A (phase) and 280A (ground) is used. The reclosing sequence would be two fast and two delayed if the fast-tripping feature of the recloser is enabled. The first reclose interval is 15 cycles, and the subsequent reclose interval is 2 seconds. The recloser operating mode is three-phase trip and three-phase lockout. Time-current characteristics of the recloser and fuses (65T and 100T) are shown in Fig. 2.

Fig. 1 Simple distribution feeder with 3-phase and single-phase fault currents. Laterals L1 and L4 are

single phase, while laterals L2 and L3 are three-phase.

Consider the following cases: C1. Suppose the utility employs a fuse-saving scheme and a three-phase to ground permanent fault occurs on lateral L2. Assume that voltages on laterals L2, L3, and L4 during the fault are below 0.1 pu C2. Same as Case C1. However, the utility does not employ the fuse-saving scheme. Determine the appropriate closing sequence and intervals for this scheme.

Cal Poly Pomona ECE 5750 Distribution System and Power Quality – Instructor Dr. Ha Thu Le

2

For each case, assume that the load current are at maximum when a short circuit condition occurs. Determine the following:

a) Sketch the current profiles during the fault clearing operation as seen by 100T fuse on lateral L2 and the mid-line recloser.

b) The number and duration of interruptions seen by customers downstream (customers in L2 and L3+L4) from the recloser.

c) What type of disturbances do customers on Lateral L1 experience? How many and how long are these disturbances?

d) Based on your analysis, argue advantages and disadvantages of employing a fuse saving scheme in the above situation.

Fig. 2 Time-current characteristics of overcurrent protective devices used in the distribution feeder shown in Fig. 1

Cal Poly Pomona ECE 5750 Distribution System and Power Quality – Instructor Dr. Ha Thu Le

3

Problem 2 The following instantaneous voltage and current are measured at the load terminal:

v(t) = 24 cos (2  60t) + 8 cos (2  60  3t)

i(t) = 10 cos (2  60t  100) + 5 cos (2  60  3t  500)

Compute the following: a) The RMS values of v(t) and i(t) b) The apparent power S c) The total active power d) The fundamental active power P1 e) The fundamental reactive power Q1 f) Show numerically S2 > (P1)2 + (Q1)2 g) The distortion power SDP h) The harmonic apparent power SHA i) True and displacement power factor

Problem 3 A nonlinear load is fed by a 10MVA 12.47/4.16kV delta-grounded wye transformer with a leakage impedance of 10%. The harmonic spectrum of the load current is shown in Fig. 3.

a) Write time-domain expression for load currents ia(t), ib(t) and ic(t) using a cosine function. Use odd order harmonics up to the 15th order.

b) Plot ia(t), ib(t) and ic(t) for two cycles of the fundamental frequency with 1024 sample points/cycle. You can use any software for this task.

c) Compute the current flowing in the neutral of the transformer analytically. d) Sum ia(t), ib(t) and ic(t) and plot the neutral current. Compare this result to that in part c. e) What is the neutral loading in percentage of the fundamental current? f) Compute the TDD of the load. g) Compute the harmonic voltage at the secondary of the transformer.

Cal Poly Pomona ECE 5750 Distribution System and Power Quality – Instructor Dr. Ha Thu Le

4

Fig. 3 Current spectrum of Phase A of the nonlinear load

Problem 4 An equivalent source at 69kV has a three-phase short circuit capacity of 1180 MVA with X/R = 10. It feeds a dedicated feeder through as 30 MVA, 69kV/12.47kV transformer with a leakage impedance of 5%. A data hotel whose loads primarily consist of computers and network servers is fed by a 1500 kVA, 12.47kV/480V service transformer. Its leakage impedance is 4%. A capacitor bank is configured wye-grounded and installed at the secondary of the 69kV/12.47kV transformer. The capacitor bank has an adjusted rating of 3.287 MVAR at 12.47kV (line-line voltage). The nonlinear load has the fundamental current of 450A and it produces 11th order harmonic current of 5.3% of the fundamental. The feeder with the harmonic problem is shown in Fig. 4.

Fig. 4 One-line diagram of a feeder having harmonic issues

Cal Poly Pomona ECE 5750 Distribution System and Power Quality – Instructor Dr. Ha Thu Le

5

a) Drawn an equivalent circuit at the fundamental frequency of the 12.47-kV system. The equivalent circuit must show values of impedances and the harmonic current magnitude at the 12.47-kV feeder.

b) Determine the system parallel resonant frequency at the 12.47-kV system and repeat part (a) at the resonance frequency.

c) Find the harmonic voltage across the capacitor bank at the resonance frequency. d) Find the magnitude of the harmonic current flowing in the capacitor back at the resonance

frequency. e) Find the voltage THD at the capacitor bus assuming that the fundamental voltage is at nominal.

Problem 5 Single-tuned harmonic filters for industrial applications can be configured from a delta-connected low- voltage capacitor bank and in-line reactors. This configuration is shown in Fig. 5. The short-circuit reactance, filter and capacitive reactances are XS, XF, and XC.

a) Derive the system impedance Z() from the perspective of nonlinear loads. Write Z() as a function of Lf, LS, and Cf.

b) Show that

𝑓 𝑓

𝑋 3𝑋

Fig. 5 A single-tuned harmonic filter