Power System Fundamentals EE-317 Lecture 3 06 October 2010.
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Transcript of Power System Fundamentals EE-317 Lecture 3 06 October 2010.
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Power System Power System FundamentalsFundamentalsPower System Power System FundamentalsFundamentals
EE-317EE-317Lecture 3Lecture 3
06 October 2010
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AimsAims
Finish Chapter 1 – Real and Reactive PowerReal and Reactive LoadsPower Triangle
Chapter 2 – Three Phase Circuits Chapter 3 – Transformers
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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.
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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.
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Resistive and Reactive LoadsResistive and Reactive Loads
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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
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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)
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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
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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
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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
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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.
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The Power TriangleThe Power Triangle
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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
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Read Chapters 2 & 3Read Chapters 2 & 3
HW Assignment 2: Problems 1-9, 1-15, 1-18, 1-19, 2-4
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Example ProblemExample Problem
HW 1-19 (a)
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Chapter 2Chapter 2
Three-Phase (3-) CircuitsWhat are they? Benefits of 3- SystemsGenerating 3- Voltages and CurrentsWye (Y) and delta () connectionsBalanced systemsOne-Line Diagrams
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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
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Multiple poles….Multiple poles….
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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)
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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?
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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)
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Wye (Y) and delta () connectionWye (Y) and delta () connection
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Delta () Delta ()
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Y and Y and
Y-connectionIL = IVLL = 3 V
-connectionVLL = V
IL = 3 I
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Balanced systemsBalanced systems
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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])
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Chapter 3Chapter 3
TransformersBenefits of TransformersTypes and Construction, The Ideal TransformerTransformer Efficiency and Voltage RegulationTransformer TapsAutotransformers3- Transformer connections– Y-Y, Y-, -Y, -
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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