Presentation on theme: "Announcements Be reading Chapters 1 and 2 from the book"— Presentation transcript:
0 ECE 333 Renewable Energy Systems Lecture 3:Basic Circuits, Complex PowerProf. Tom OverbyeDept. of Electrical and Computer EngineeringUniversity of Illinois at Urbana-Champaign
1 Announcements Be reading Chapters 1 and 2 from the book Be reading Chapter 3 from the bookHomework 1 is 1.1, 1.11, 2.6, 2.8, It will be covered by the first in-class quiz on Thursday Jan 29As mentioned in lecture 2, your two lowest quiz/homework scores will be dropped
2 Engineering Insight: Modeling Engineers use models to represent the systems we studyGuiding motto: “All models are wrong but some are useful” George Box, 1979The engineering challenge, which can be quite difficult sometimes, is to know the limits of the underlying models.
3 Basic Electric Circuits Ideal Voltage SourceIdeal Current Source+Load-+Load-
4 Example – Power to Incandescent Lamp Find R if the lamp draws 60W at 12 VFind the current, IWhat is P if vs doubles and R stays the same? 240W+Load-
5 Equivalent Resistance for Resistors in Series and Parallel Resistors in series – voltage divides, current is the same+-+-nodevoltages
6 Equivalent Resistance for Resistors in Series and Parallel Resistors in parallel – current divides, voltage is the samebranch currentsSimplification for 2 resistors+-
7 Voltage and Current Dividers Voltage Divider+-Current Divider+-
8 Wire ResistanceFor dc systems wire resistance is key; for high voltage ac often the inductance (reactance) or capacitance (susceptance) are limitingResistance causes 1) losses (i2R) and 2) voltage drop (vi)Need to consider wire resistance in both directions
9 AC: Phase AnglesAngles need to be measured with respect to a reference - depends on where we define t=0When comparing signals, we define t=0 once and measure every other signal with respect to that referenceChoice of reference is arbitrary – the relative phase shift is what mattersRelative phase shift between signals is independent of where we define t=0
10 Example: Phase Angle Reference Pick the bottom wave as the referenceOr pick the top as the reference- it does not matter!
11 Important Properties: RMS RMS = root of the mean of the squareRMS for a periodic waveformRMS for a sinusoid (derive this for homework)In 333 we are mostly only concerned with sinusoidals
12 Important Properties: Instantaneous Power Instantaneous power into a load“Load sign convention” with current and power into loadpositive+-Identity
13 Important Properties: Average Power Average power is found fromFind the average power into the load (derive this for homework)
14 Important Properties: Real Power P is called the Real Powercos(θV-θI) is called the Power Factor (pf)We’ll review phasors and then come back to these definitions…
15 Review of PhasorsPhasors are used in electrical engineering (power systems) to represent sinusoids of the same frequencyA quick derivation…Ap denotes the peak value of A(t)Identity
16 Review of Phasors Use Euler’s Identity Identity Written in phasor notation asIdentityTilde denotes a phasorNote, a convention- the amplitude used here is the RMS value, not the peak value as used in some other classes!Other, simplified notationRegardless of what notation you use, it helps to be consistent.
17 Why Phasors? Simplifies calculations Turns derivatives and integrals into algebraic equationsMakes it easier to solve AC circuits
18 Why Phasors: RLC Circuit Solve for the current- which circuit do you prefer?++--
20 Complex Power S Q (θV-θI) P Q Reactive Power S Apparent power P Power triangleSQ(θV-θI)Asterisk denotes complex conjugatePQReactive PowerSApparentpowerPReal PowerS = P+jQ
21 Apparent, Real, Reactive Power P = real power (W, kW, MW)Q = reactive power (VAr, kVAr, MVAr)S = apparent power (VA, kVA, MVA)Power factor anglePower factor
22 Apparent, Real, Reactive Power Remember ELI the ICE man“Load sign convention” – current and power into load are assumed positiveSQ(θV-θI)PP(θV-θI)QSQ and θ negative(producing Q)Q and θ positiveELIICEInductive loadsI lags V (or E)Capacitive loadsI leads V (or E)
23 Apparent, Real, Reactive Power Relationships between P, Q, and S can be derived from the power triangle just introducedExample: A load draws 100 kW with leading pf of What are the power factor angle, Q, and S?
24 Conservation of PowerKirchhoff’s voltage and current laws (KVL and KCL)Sum of voltage drops around a loop must be zeroSum of currents into a node must be zeroConservation of power followsSum of real power into every node must equal zeroSum of reactive power into every node must equal zero
25 Conservation of Power Example Resistor, consumed powerInductor, consumed power
26 Power Consumption in Devices Resistors only consume real powerInductors only consume reactive powerCapacitors only produce reactive power
27 ExampleSolve for the total power delivered by the source
28 Reactive Power Compensation Reactive compensation is used extensively by utilitiesCapacitors are used to correct the power factorThis allows reactive power to be supplied locallySupplying reactive power locally leads to decreased line current, which results inDecrease line lossesAbility to use smaller wiresLess voltage drop across the line
29 Power Factor Correction Example Assume we have a 100 kVA load with pf = 0.8 lagging, and would like to correct the pf to 0.95 laggingWe have:We want:SQdes.=?P=80This requires a capacitance of:PQ=60Q=-33.7Qdes=26.3P29
30 Distribution System Capacitors for Power Factor Correction 30