Power Flow Analysis

Question 1

3 Phase voltage’s phases are how many degrees apart?

Answer 1

120°

Question 2

Any 3 phase voltage can be said to have a frequency and ‘overall phase’, explain what is meant by this.

Answer 2

Consider two 3 phase voltage sources (eg the grid and a connected generator).
If they have the same frequency then the period between peaks of eachof their three phases will be the same.
But unless their phases rise and fall at the same time they’re ‘overall phase’ wont be in sync.

Question 3

What happens if a generator connected to the grid is running with a different frequency than the grid?

Answer 3

Efficiency is lost. Windings in the generator will heat up.
Prevent this by controlling the rotor using electronics or convert the voltage befor it connects to the grid.

Question 4

What is a load or delay angle?

Answer 4

The load angle tells us how far away from the grids nominal angle a voltage is.

Question 5

A lagging or leading load angle provides what kind of power?

Answer 5

Reactive Power

Question 6

Define a Resistive Load

Answer 6

A load which consumes only active power (therefor PF is 1).
Voltage and current waveforms are in phase.
Examples:
* Lights
* Heaters

Question 7

Define an Inductive Load

Answer 7

An inductive load consumes only reactive power.
Current lags behind voltage by 90°
Power factor is lagging in nature
Examples:
* Motors!

Question 8

Define a Capacitive Load

Answer 8

A capacitive load consumes only reactive power.
Current leads voltage by 90°
Power factor is leading in nature.
Capacitor banks improve the power factor of a system.

Question 9

What is the unit of Active Power?

Answer 9

Watts

Question 10

What is the unit of Reactive Power?

Answer 10

VAR (Volt-Ampere Reactive)

Question 11

What is apparent power?

Answer 11

The product of Active (P) and Reactive (Q) power, unit VA.
S² = P² + Q²

Question 12

Define Power Factor

Answer 12

The ratio of Active Power (P) to Apparent Power (S).
PF = P/S

Question 13

What happens if a Grid cannot provide enough Reactive Power to meet demand?

Answer 13

The connected machines will use Active Power causeing grid voltgae to drop.
Managers of the grid will tell producers when to provide lagging/leading Reactive Power to prevent this.

Question 14

Given Apparent Power (S) and Phase Angle (θ) find Active Power (P)

Answer 14

COS(θ) = P / S
P = S COS (θ)

COS = Ajacent / Hypot

Question 15

Given Apparent Power (S) and Phase Angle (θ) find Reactive Power (Q)

Answer 15

SIN(θ) = Q / S
Q = S SIN (θ)

SIN = Oposite / Hypot.

Question 16

Given Apparent Power (S) and Reactive Power (Q) find Phase Angle (θ)

Answer 16

SIN(θ) = Q / S

Question 17

Recall and define the formula describing the effects of Active/Reactive Power Imbalance

Answer 17

ΔV = (RP + XQ) / V
Change in Voltage = Resistance∘Active Power + Reactance∘Reactive Power / Voltage

Change in voltage between two nodes

Question 18

Decribe the steps to solve a Transmission Diagram question

Answer 18

1. Convert values to per unit values (100MVA reference)
2. Working backwards find the total active and reactive power drain at each stage

Question 19

Define Slack/Swing Bus

Answer 19

Taken as reference where the magnitude and phase angle of the voltage are specifed and constant. The effective generator at this node supplies the losses to the network.

Question 20

Define Load/QP Bus

Answer 20

The real and reactive powers are specified.
Voltage magnitude and phase are unknown.

Question 21

Define Voltage Controlled Bus
AKA: Generator Bus or PV Bus

Answer 21

The real power and voltage magnitude are specifed.
Reactive power and voltage phase are unknown.
The limits on the value of reactive power are also specified.

Question 22

Define admitance in terms of Impedance Z

Answer 22

Admidance Y = 1/Z

Allows I = VxY

Question 23

List the steps to analyse a bus system

Answer 23

1) Each transmission line has impedance and therefore admitance. Redraw the bus system as a network of admitances labelled with their connections. Each bus will be a node. Each generator will be a current source. Drains will be addmitances connected to ground.
2) Apply Kirchhoff’s current law at each node (bus)
3) Arrange in matrix form
4) Further solution depends on the requirements of the question

Question 24

What is the modified Real/Active power equation used in a Bus System Load Flow Study

Answer 24

Pi = |Vi|SUM(j=1 to n)[|Vj||Yij|(di-dj)]

Question 25

What is the modified Reactive power equation used in a Bus System Load Flow Study

Answer 25

Qj = -|Vi|SUM(j=1 to n, j\=i)[|Vj||Vij|cos(di-dj) + |Vi|^2 |Yii|]

Question 26

Define the total n-bus system's reactive power losses (due to the transmision lines)

Answer 26

Qloss = SUM[Qgen] - SUM[Qdemand] ## Footnote Lazy notation.

Question 27

What is the formula for Active Power Transfer between two nodes?

Answer 27

Pij = (|Vi||Vj|/|Xij|)sin(di-dj)

Question 28

What is the formula for Reactive Power transfer between nodes i and j?

Answer 28

Qij = (|Vi|^2/|Xij|)-(|Vi||Vj|/|Xij|)cos(di-dj)

Question 29

Describe the bus classifications applicable to power networks and explain why explicit solutions of power flow analysis are complicated.

Answer 29

In power networks, buses are classified into three main types based on the quantities specified and those that need to be determined: **Generation Bus (P-V Bus):** Specified Quantities: Active power (P) and voltage magnitude (|V|). Unknown Quantities: Reactive power (Q) and voltage phase angle (δ). Function: This bus maintains a constant voltage magnitude by injecting reactive power. **Load Bus (P-Q Bus):** Specified Quantities: Active power (P) and reactive power (Q). Unknown Quantities: Voltage magnitude (|V|) and voltage phase angle (δ). Function: This bus injects active and reactive power into the network. The voltage magnitude can vary within a permissible range. **Slack Bus (Reference Bus):** Specified Quantities: Voltage magnitude (|V|) and voltage phase angle (δ). Unknown Quantities: Active power (P) and reactive power (Q). Function: This bus absorbs or emits active and reactive power to balance the system. It serves as a reference point for the phase angle. Explicit solutions of power flow analysis are complicated due to several factors: Non-linear Equations: Power flow equations are inherently non-linear, involving complex relationships between voltage magnitudes, phase angles, active power, and reactive power. Network Complexity: The interconnected nature of power networks, with numerous buses and transmission lines, leads to a large system of equations that must be solved simultaneously. Convergence Issues: Traditional methods like Newton-Raphson and Gauss-Seidel can face convergence problems, especially in systems with high R/X ratios or ill-conditioned Jacobian matrices. Computational Load: Solving these equations requires significant computational resources, particularly for large-scale networks. High-performance computing methods are often needed to handle the load

Question 30

How do you convert Radians to Degrees?

Answer 30

Degrees = Radians⋅(180/π)

Question 31

How do you convert Degrees to Radians?

Answer 31

Radians = Degrees⋅(π/180)

Question 32

List the assumptions which have to be made in order to obtain the DC load flow equations. | Used to find a nodes Pi and Qi

Answer 32

1. Line resistances are neglected. Active power loss is zero. 2. Angle δi - δj is small. This makes the equations linear and makes an analytic solution possible. 3. Busses other than the Slack bus are PV/Voltage controlled busses.

Question 33

Outline the steps to solve a bus network when a PV bus is present.

Answer 33

1) Find Q(k+1) usingG-S iteration 2) Find a fake V(k+1) using a flat V start with the new Q value 2b) Find δ using the fake V(k+1) 2c) Use δ with the PV Voltage magnitude to find the complex form of V 3) if asked to show the effect on other nodes now the G-S iteration of other nodes can be updated with thr new V

Question 34

What effect does a poor power factor have?

Answer 34

Drop in efficiency. For a given power and voltage, the current flowing through the line is inversely proportional to the power factor. This means that a poor power factor i.e. low power factor will result in higher load current and hence higher losses. ## Footnote High loss = more power used hence environmental impact