EKT103 ELECTRICAL ENGINEERING Chapter 1 Three-Phase System by Dr Rosemizi Abd Rahim

COURSE OUTCOME (CO) CO1: Ability to define and explain the concept of single-phase and three-phase system.

Revision A sinusoid is a signal that has the form of the sine or cosine function. A general expression for the sinusoid, where Vm = the amplitude of the sinusoid ω = the angular frequency in radians/s Ф = the phase

Revision A periodic function is one that satisfies v(t) = v(t + nT), for all t and for all integers n. Only two sinusoidal values with the same frequency can be compared by their amplitude and phase difference. If phase difference is zero, they are in phase; if phase difference is not zero, they are out of phase.

Revision Example 1 Given a sinusoid, , calculate its amplitude, phase, angular frequency, period, and frequency.

Revision Example 1 Given a sinusoid, , calculate its amplitude, phase, angular frequency, period, and frequency. Solution: Amplitude = 5, phase = –60o, angular frequency = 4p rad/s, Period = 0.5 s, frequency = 2 Hz.

Revision Find the phase angle between and , does i1 lead or lag i2? Example 2 Find the phase angle between and , does i1 lead or lag i2?

Revision Find the phase angle between and , does i1 lead or lag i2? Example 2 Find the phase angle between and , does i1 lead or lag i2? Solution: Since sin(ωt+90o) = cos ωt therefore, i1 leads i2 155o.

Revision Impedance transformation

Single-Phase Circuit A single phase circuit consists of a generator connected through a pair of wires to a load Three wired system same magnitude same phase Two wire system

Second source with 90° out Two-Phase Circuit A a Three wired system Second source with 90° out of phase Three wired system same magnitude different phase

What is a Three-Phase Circuit? It is a system produced by a generator consisting of three sources having the same amplitude and frequency but out of phase with each other by 120°. Three sources with 120° out of phase Four wired system

Balance Three-Phase Voltages A three-phase generator consists of a rotating magnet (rotor) surrounded by a stationary winding (stator). A three-phase generator The generated voltages

Balance Three-Phase Voltages Two possible configurations: Three-phase voltage sources: (a) Y-connected ; (b) Δ-connected

Balance Three-Phase Voltages Phase sequences a) abc or positive sequence b) acb or negative sequence

Balance Three-Phase Voltages If the voltage source have the same amplitude and frequency ω and are out of phase with each other by 120o, the voltage are said to be balanced. Balanced phase voltages are equal in magnitude and out of phase with each other by 120o

Balance Three-Phase Voltages abc sequence or positive sequence: is the effective or rms value acb sequence or negative sequence:

Balance Three-Phase Voltages Example 1 Determine the phase sequence of the set of voltages.

Balance Three-Phase Voltages Solution: The voltages can be expressed in phasor form as We notice that Van leads Vcn by 120° and Vcn in turn leads Vbn by 120°. Hence, we have an acb sequence.

Balance Three-Phase Voltages Two possible three-phase load configurations: a) a wye-connected load b) a delta-connected load

Balance Three-Phase Voltages A balanced load is one in which the phase impedances are equal in magnitude and in phase. For a balanced wye connected load: For a balanced delta connected load:

Balance Three-Phase Connection Four possible connections Y-Y connection (Y-connected source with a Y-connected load) Y-Δ connection (Y-connected source with a Δ-connected load) Δ-Δ connection Δ-Y connection

Balance Y-Y Connection A balanced Y-Y system is a three-phase system with a balanced y-connected source and a balanced y-connected load.

Balance Y-Y Connection Source impedance Line impedance Load impedance Total impedance per phase Since all impedance are in series, Thus

Balance Y-Y Connection ale29559_12010.jpg

Balance Y-Y Connection Applying KVL to each phase:

Balance Y-Y Connection Line to line voltages or line voltages: Magnitude of line voltages: ale29559_12011.jpg

Balance Y-Y Connection Example 2 Calculate the line currents in the three-wire Y-Y system shown below:

Balance Y-Y Connection Example 2 Calculate the line currents in the three-wire Y-Y system shown below:

Balance Y-Δ Connection A balanced Y-Δ system is a three-phase system with a balanced y-connected source and a balanced Δ-connected load.

Balance Y-Δ Connection A single phase equivalent circuit ale29559_12016.jpg

Balance Y-Δ Connection A single phase equivalent circuit Line voltages: ale29559_12016.jpg

Balance Y-Δ Connection A single-phase equivalent circuit of a balanced Y- circuit Line currents: Phase currents: ale29559_12015.jpg

Balance Y-Δ Connection A single-phase equivalent circuit of a balanced Y- circuit Magnitude line currents: ale29559_12015.jpg

Balance Y-Δ Connection Example 3 A balanced abc-sequence Y-connected source with ( ) is connected to a Δ-connected load (8+j4) per phase. Calculate the phase and line currents. Solution Using single-phase analysis, Other line currents are obtained using the abc phase sequence

Balance Δ-Δ Connection A balanced Δ-Δ system is a three-phase system with a balanced Δ -connected source and a balanced Δ -connected load.

Balance Δ-Δ Connection Phase currents: Line voltages: Line currents: Magnitude line currents: Total impedance:

Balance Δ-Δ Connection Example 4 A balanced Δ-connected load having an impedance 20-j15  is connected to a Δ-connected positive-sequence generator having ( ). Calculate the phase currents of the load and the line currents. Ans: The phase currents The line currents

Balance Δ-Y Connection A balanced Δ-Y system is a three-phase system with a balanced y-connected source and a balanced y-connected load.

Balance Δ-Y Connection Applying KVL to loop aANBba: From: Line currents:

Balance Δ-Y Connection Replace Δ connected source to equivalent Y connected source. Phase voltages:

Balance Δ-Y Connection A single phase equivalent circuit

Balance Δ-Y Connection Example 5 A balanced Y-connected load with a phase impedance 40+j25  is supplied by a balanced, positive-sequence Δ-connected source with a line voltage of 210V. Calculate the phase currents. Use Vab as reference. Answer The phase currents

Power in a Balanced System Comparing the power loss in (a) a single-phase system, and (b) a three-phase system If same power loss is tolerated in both system, three-phase system use only 75% of materials of a single-phase system

Power in a Balanced System For Y connected load, the phase voltage:

Power in a Balanced System Phase current lag phase voltage by θ. If The phase current:

Power in a Balanced System Total instantaneous power: Average power per phase: Reactive power per phase: Apparent power per phase: Complex power per phase:

Power in a Balanced System Total average power: Total reactive power: Total complex power:

Power in a Balanced System Power loss in two wires: Power loss in three wires: PL : power absorbed by the load IL : magnitude of line current VL : line voltage R : line resistance

Example 6 A three-phase motor can be regarded as a balanced Y-load. A three-phase motor draws 5.6 kW when the line voltage is 220 V and the line current is 18.2 A. Determine the power factor of the motor.

Example 6 A three-phase motor can be regarded as a balanced Y-load. A three-phase motor draws 5.6 kW when the line voltage is 220 V and the line current is 18.2 A. Determine the power factor of the motor. The apparent power is The real power is The power factor is

Exercise 6 Calculate the line current required for a 30-kW three-phase motor having a power factor of 0.85 lagging if it is connected to a balanced source with a line voltage of 440 V.

Exercise 6 Calculate the line current required for a 30-kW three-phase motor having a power factor of 0.85 lagging if it is connected to a balanced source with a line voltage of 440 V. Answer :

Exercise 7 For the Y-Y circuit in Exercise 2, calculate the complex power at the source and at the load.