Power System II PSII GTU 3150911 Unit1 Basic

Power System II (PS-II) GTU # 3150911 Unit-1 Basic Principles Prof. Shital Patel Electrical Engineering Department Darshan Institute of Engineering & Technology, Rajkot shital. patel@darshan. ac. in

Power in Single-phase AC Circuits What is electrical power? Electrical power is the rate of change of energy with respect to time Produced at generating station and transmitted to long distance for end use At consumer end converted into various form of energy such as heat, light, sound, motion etc Key element to know heat generated or dissipated in electrical circuit Example : A power consumed by 1 -Φ , 230 V, 5 A heater is Prof. Shital Patel # 3150911 (PS - II) Unit 1 – Basic Principles 2

Power in Single-phase AC Circuits Classification of electrical power Active power § It is the power consumed or dissipated in resistive elements of network § SI unit is watt § Abbreviated as “P” Reactive power § It is the power consumed or dissipated in reactive elements of network § SI unit is reactive volt-ampere § Abbreviated as “Q” Apparent power § It is the actual power supplied to the network i. e. total active and reactive power § SI unit is volt-ampere § Abbreviated as “S” CosΦ is called power factor § Inductive network has lagging power factor i. e. current lags the voltage by angle Φ § Capacitive network has leading power factor i. e. current leads the voltage by angle Φ § Resistive network has unity power factor i. e. current and voltage are in phase Prof. Shital Patel # 3150911 (PS - II) Unit 1 – Basic Principles 3

Power in Single-phase AC Circuits Instantaneous power in 1 -Φ AC circuit It is the power absorbed by load at any instant Instantaneous power consists of two components § A constant power components 0. 5 Vm. Im. CosΦ § A pulsating power components 0. 5 Vm. Im. Cos(2ωt – Φ) Instantaneous power is § Positive when both instantaneous voltage and current are in the same direction § Negative when voltage and current are in opposite direction Prof. Shital Patel # 3150911 (PS - II) Unit 1 – Basic Principles 4

Power in Single-phase AC Circuits Positive power results § Current is flowing in the direction of voltage drop § Rate of transfer of energy to the load from source Negative power results § Current is flowing in the direction of voltage rise § Rate of transfer of energy to the source from load When voltage and current are § In phase i. e. Φ=0 • Load is pure resistive • Instantaneous power of that load is always positive § Out of phase i. e. Φ=90 • Load is pure inductive or capacitive • Average power of that load is always zero Prof. Shital Patel # 3150911 (PS - II) Unit 1 – Basic Principles 5

Power in Single-phase AC Circuits Average power in 1 -Φ AC circuit It is the time average of instantaneous power over one cycle Example : Average power absorbed by R = 50 Ω, L = 20 m. H and C = 20 μF when supplied by v = 100 Sin 200πt Prof. Shital Patel # 3150911 (PS - II) Unit 1 – Basic Principles 6

Complex Power Complex power is the product of voltage across load and conjugate of current flowing through that load. Let, The numeric value of real and imaginary parts of product S = VI* determines, whether P and Q are absorbed or supplied by network. § Current I lags the voltage by an angle Φ (between 0° to 90°) both VICosΦ and VISinΦ are positive § Current I leads the voltage by an angle Φ (between 0° to 90°) both VICosΦ is positive and VISinΦ are negative P > 0, Circuit absorbs real power P < 0, Circuit supplies real power Q > 0, Circuit absorbs reactive power Q < 0, Circuit supplies reactive power Prof. Shital Patel # 3150911 (PS - II) Unit 1 – Basic Principles 7

Complex Power Example : 1 For two identical voltage sources E 1 = 100/0° volt , E 2 = 100/30° volt and Z = 0 + 5 j Ω. Determine (i) whether each machine is generating or consuming real power (ii) whether each machine is receiving or supplying reactive power (iii) P and Q absorbed by the impedance. P 1 = 1000 Watt P 1 > 0, Machine -1 absorbs real power Q 1= -267. 87 VAR Q 1 < 0, Machine -1 supplies reactive power P 2 =-1000 Watt P 2 < 0, Machine -2 supplies real power Q 2= -267. 87 VAR Q 2 < 0, Machine -2 supplies reactive power Prof. Shital Patel Acting as Motor Acting as Generator # 3150911 (PS - II) Unit 1 – Basic Principles 8

Voltage and Current in Balanced Three-phase AC Circuits What is three-phase AC circuits? An electrical power system made up of of three live wire Let, three-phase generators supplies the balanced three-phase star loads Voltages are equal in magnitude and 120° apart in phase, current is also equal in magnitude and 120° apart in phase The condition of same magnitude and displaced 120° apart in phase is called balanced condition. Prof. Shital Patel # 3150911 (PS - II) Unit 1 – Basic Principles 9

Voltage and Current in Balanced Three-phase AC Circuits Algebraic sum of three line currents in balanced condition is zero Algebraic sum of three line currents in unbalanced condition is not zero Example : Current in return conductor for three phase circuit when the line currents are (i) Balanced and (ii) Unbalanced Balanced condition Unbalanced condition Prof. Shital Patel # 3150911 (PS - II) Unit 1 – Basic Principles 10

Voltage and Current in Balanced Three-phase AC Circuits For balance three phase system, phase rotation method is used for analysis Letter α (alpha) is commonly used to designated the phase rotation of 120° in counterclockwise direction Complex number operator of unit magnitude with and angle of 120° Some common identities of α operator are Prof. Shital Patel # 3150911 (PS - II) Unit 1 – Basic Principles 11

Voltage and Current in Balanced Three-phase AC Circuits Example: Line voltages and currents tracing path from a, b and c As a phasor, line values leads the phase values by 30° with √ 3 times greater magnitudes Prof. Shital Patel # 3150911 (PS - II) Unit 1 – Basic Principles 12

Voltage and Current in Balanced Three-phase AC Circuits Example : 1 In a balanced three phase circuit the voltage Vab = 173. 2 /0° volt. Determine all the voltages and currents in star connected load having ZL = 10 /20° Ω. Phase sequence is abc. Prof. Shital Patel # 3150911 (PS - II) Unit 1 – Basic Principles 13

Star/Delta Connected Loads Y- Connected load Starting ends or finishing ends of three coils are connected together Common connection point is called star or neutral point Line current IL and phase current Iph both are same Line voltage VL is vector difference of two of the phase voltages Vph Prof. Shital Patel # 3150911 (PS - II) Unit 1 – Basic Principles 14

Star/Delta Connected Loads Δ- Connected load Starting end of one coil is connected to the finishing end of other phase coil Closed circuit is formed Line voltage VL and phase voltage Vph both are same Line current IL is vector difference of two of the phase current Iph Prof. Shital Patel # 3150911 (PS - II) Unit 1 – Basic Principles 15

Star/Delta Connected Loads Single phase or per phase equivalent circuit is used for calculation Balanced delta connected load is replaced by its equivalent Y connected load for calculation Y – Δ Transformation Δ – Y Transformation Prof. Shital Patel # 3150911 (PS - II) Unit 1 – Basic Principles 16

Power in Balanced Three-phase Circuits For balance load or source, 3 - Φ total power is 1 - Φ power multiply by three Total three phase power Y – Connected load Prof. Shital Patel Δ – Connected load # 3150911 (PS - II) Unit 1 – Basic Principles 17

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