Transmission and Distribution study guide

What this area covers

Transmission and Distribution is about moving power from where it is made to where it is used while keeping voltage in range and the system in step. It covers line models, voltage drop and regulation, how real and reactive power flow, reactive compensation, fault current on networks, and the basics of transient stability. This area accounts for 8–12 questions on the exam. The work is mostly calculation, and it goes faster with a clean per-phase diagram drawn before any numbers go in.

The ideas everything else rests on

Pick the line model by length. A short line is a series impedance and nothing else. A medium line adds shunt capacitance, usually split half at each end in a nominal pi. A long line needs distributed parameters and hyperbolic functions. The model you pick decides whether receiving-end voltage can rise above sending-end voltage at light load, the Ferranti effect, which only appears once shunt capacitance is in the model.

Voltage drop follows the power factor. For a short line, the drop along the line is close to the current times the sum of R times cos θ and X times sin θ. Lagging loads make the reactive term add; leading loads can make the drop negative. Regulation compares no-load and full-load receiving voltage:

$$VR = \frac{V_{NL} - V_{FL}}{V_{FL}} \times 100\%$$

Real power follows angle, reactive power follows voltage. Across a mostly inductive line, real power transfer is

$$P = \frac{V_S V_R}{X} \sin\delta$$

so it peaks at 90 degrees and depends on the angle between the ends. Reactive power, by contrast, flows mostly from the higher-voltage end to the lower. This split is why voltage problems are fixed with reactive devices and loading problems with angle or impedance.

Compensation reshapes the line. Shunt capacitors supply reactive power locally and raise voltage under heavy load. Shunt reactors absorb it and hold voltage down at light load. Series capacitors cancel part of the line's reactance, which raises the transfer limit in the equation above.

Stability is a race between energy in and energy out. After a fault, a generator accelerates while its electrical output is depressed. The equal area criterion compares the accelerating area under the power–angle curve with the decelerating area available after clearing. If the second is at least as large as the first, the machine stays in step; the critical clearing angle is where the two are exactly equal.

How to study it

1. Solve short-line problems first: sending-end voltage, drop and regulation for lagging, unity and leading loads. Check each with the Voltage drop calculator.
2. Move to the nominal pi model. Work ABCD constants for short and medium lines, and compute receiving-end voltage at no load to see the Ferranti rise.
3. Put a network on a common base with the Per-unit converter, then find fault current at several buses and confirm with the Fault current calculator. Note how X/R changes from a generator bus to a distribution feeder.
4. Size shunt capacitors to raise a bus voltage or improve a feeder's power factor, and check the reactive power with the Power-factor correction calculator.
5. Draw power–angle curves for pre-fault, fault-on and post-fault networks, and find the critical clearing angle with the equal area criterion.

Mistakes that cost points

• Using line-to-line voltage in a per-phase drop. Compute drop per phase with line-to-neutral voltage, then convert, or use a formula built for line-to-line values. Never mix the two.
• Losing the sign of sin θ. A leading power factor makes the reactive term negative. Write the angle with its sign before you substitute.
• Doubling the shunt admittance. In a nominal pi, each end gets half of the total. Placing the full value at both ends doubles the charging current.
• Using the wrong curve for each area. The accelerating area uses the fault-on curve; the decelerating area uses the post-fault curve. Swap them and the clearing angle comes out wrong.

References worth having

• Glover, Overbye and Sarma, Power System Analysis and Design: the transmission line and stability chapters
• IEEE Std 141 (Red Book): the voltage considerations chapter
• ANSI C84.1 (service and utilization voltage ranges)