Power System Power System FundamentalsFundamentalsPower System Power System FundamentalsFundamentals

EE-317EE-317Lecture 3Lecture 3

06 October 2010

AimsAims

Finish Chapter 1 – Real and Reactive PowerReal and Reactive LoadsPower Triangle

Chapter 2 – Three Phase Circuits Chapter 3 – Transformers

Sine Wave Basics (Review)Sine Wave Basics (Review) RMS – a method for computing the effective value of a time-varying e-m

wave, equivalent to the energy under the area of the voltage waveform.

Real, Reactive and Apparent Power in AC Circuits

Real, Reactive and Apparent Power in AC Circuits in DC circuits: P=VI but…= in AC circuits: average power

supplied to the load will be affected by the phase angle between the voltage and the current.

If load is inductive the phase angle (also called impedance angle) is positive; (i.e, phase angle of current will lag the phase angle of the voltage) and the load will consume both real and positive reactive power

If the load is capacitive the impedance angle will be negative (the phase angle of the current will lead the phase angle of the voltage) and the load will consume real power and supply reactive power.

Resistive and Reactive LoadsResistive and Reactive Loads

Impedance Angle, Current Angle & PowerImpedance Angle, Current Angle & Power Inductive loads positive impedance angle

current angle lags voltage angle Capacitive loads negative impedance angle

current angle leads voltage angle

Both types of loads consume real power One (inductive) consumes reactive as well while

the other (capacitive) supplies reactive power

Useful EquationsUseful Equations

First term is average or Real power (P) Second term is power transferred back and forth

between source and load (Reactive power- Q)

More equationsMore equations

Real term averages to P = VI cos (+) Reactive term averages to Q = VI sin (+/-)

Reactive power is the power that is first stored and then released

in the magnetic field of an inductor or in the electric field of a capacitor

Apparent Power (S) is just = VI

Loads with Constant ImpedanceLoads with Constant Impedance V = IZ

Substituting… P = I2Z cos Q = I2Z sin S= I2Z

Since… Z = R + jX = Z cos + jZ sin P = I2R and Q = I2X

Complex Power and Key Relationship of Phase Angle to V&I

Complex Power and Key Relationship of Phase Angle to V&I

S = P + jQ S = VI(complex conjugate operator) If V = V30o and I = I15o

THEN….. COMPLEX POWER SUPPLIED TO LOAD = S = (V30o)(I-15o) = VI (30o-15o )= VI cos(15o ) + jVI sin(15o )

NOTE: Since Phase Angle = V - IS = VI cos() + jVI sin() = P + jQ

Review V, I, ZReview V, I, Z

If load is inductive then the Phase Angle (Impedance Angle Z) is positive, If phase angle is positive, the phase angle of the current flowing through the load will lag the voltage phase angle across the load by the impedance angle Z.

The Power TriangleThe Power Triangle

ExampleExample

V = 2400o V Z = 40-30o

Calculate current I, Power Factor (is it leading or lagging), real, reactive, apparent and complex power supplied to the load

Read Chapters 2 & 3Read Chapters 2 & 3

HW Assignment 2: Problems 1-9, 1-15, 1-18, 1-19, 2-4

Example ProblemExample Problem

HW 1-19 (a)

Chapter 2Chapter 2

Three-Phase (3-) CircuitsWhat are they? Benefits of 3- SystemsGenerating 3- Voltages and CurrentsWye (Y) and delta () connectionsBalanced systemsOne-Line Diagrams

What does Three-Phase mean?What does Three-Phase mean?

A 3- circuit is a 3- AC-generation system serving a 3- AC load

3 - 1- AC generators with equal voltage but phase angle differing from the others by 120o

Multiple poles….Multiple poles….

Benefits of 3- circuitsBenefits of 3- circuits

GENERATION SIDE: More power per kilogram Constant power out (vs. pulsating sinusoidal)

LOAD SIDE: Induction Motors (no starters required)

Common NeutralCommon Neutral

A 3- circuit can have the negative ends of the 3- generators connected to the negative ends of the 3- AC loads and one common neutral wire can complete the system

If the three loads are equal (or balanced) what will the return current be in the common neutral?

If loads are equal….If loads are equal….

the return current can be calculated to be… ZERO! (see trig on p. 59 for more detail) Neutral is actually unnecessary in a balanced

three-phase system (but is provided since circumstances may change)

Wye (Y) and delta () connectionWye (Y) and delta () connection

Delta () Delta ()

Y and Y and

Y-connectionIL = IVLL = 3 V

-connectionVLL = V

IL = 3 I

Balanced systemsBalanced systems

One-Line DiagramsOne-Line Diagrams

since all phases are same (except for phase angle) and loads are typically balanced only one of the phases is usually shown on an electrical diagram… it is called a one-line diagram

Typically include all major components of the system (generators, transformers, transmission lines, loads, other [regulators, swithes])

Chapter 3Chapter 3

TransformersBenefits of TransformersTypes and Construction, The Ideal TransformerTransformer Efficiency and Voltage RegulationTransformer TapsAutotransformers3- Transformer connections– Y-Y, Y-, -Y, -

BenefitsBenefits

Range of Power Systems Power Levels Seamless Converter of Power (Voltage) Reduced Transmission Losses Efficient Converter Low Maintenance (min. moving parts) Enables Utilization of Power at nearly all levels