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MMME2104 Design & Selection of Mining Equipment Electrical Component Three-Phase AC Systems Lecture 2 6 August 2003 Lecture Outline • Polyphase systems • 3-phase systems – 3-phase power flow – 3-phase circuit arrangements – Star and Delta connections – Active, reactive and apparent power in 3phase systems – Analysing 3-phase circuits Poly-Phase Systems • “many phases” • Multiple phases produces a smoother electrical power input/output • Piston-engine analogy • Trade-offs in the number of phases – Simplicity – Cost – Efficiency Three-Phase Systems Electrical power is generated, transmitted and distributed as 3-phase power. Why? Three-phase systems are generally considered to be the best trade-off: • 3-phase motors, generators and transformers are simpler, cheaper and more efficient • 3-phase transmission lines can deliver more power for a given weight and cost • The voltage regulation of 3-phase transmission lines is inherently better Single-Phase System a N 400 S 1 Voltage (V), Current (A) 300 200 100 0 0.000 -100 Va1 0.005 0.010 -200 -300 -400 time (s) Va1 0.015 0.020 Single-Phase System a R S 300 Voltage (V), Current (A) N 400 200 100 0 0.000 -100 Va1 0.005 0.010 0.015 0.020 Ia1 -200 -300 -400 1 time (s) 60000 50000 Ia1 Va1 Power (W) 40000 Pow er 30000 20000 10000 0 0.000 0.005 0.010 time (s) 0.015 0.020 Three-Phase System a R N S c 1 3 2 b R R Three-Phase System 3-Phase Voltages and Currents 400 voltage (V), current (A) 300 200 Va1 100 Ia1 0 0.000 -100 Vb2 0.005 0.010 0.015 0.020 Ib2 Vc3 Ic3 -200 -300 -400 time (s) Three-Phase System Vb2 Phasor Diagram Ib2 120º 120º 120º Ic3 Vc3 Ia1 Va1 Three-Phase System 3 Phase Pow ers 80000 70000 power (W) 60000 Phase a1 50000 Phase b2 40000 Phase c3 30000 Total 20000 10000 0 0.000 0.005 0.010 time (s) 0.015 0.020 Three-Phase System • The power flow in an ideal 3-phase system is constant • This has inherent advantages for an electrical power system: – – – – Components are not oversized or under-utilised Losses are minimised Vibration is minimised Mechanical components connected to the electrical system (motors or generators) have smooth input/output Three-Phase System: 6-wire a Z 1 3 c 2 b Z Z • Each phase is electrically independent • Therefore, the 3 return conductors can be combined into 1 to create a 3-phase, 4-wire system Three-Phase System: 4-wire a Z n c neutral conductor b Z Z • Neutral conductor carries the sum of the 3 phase currents (ideally zero) • If balanced, we can remove the neutral conductor to get a 3-phase, 3-wire system Three-Phase System: 3-wire a Z n c b Z Z • Loads (impedances) must be identical • Otherwise unbalanced voltages are produced across the 3 loads Balanced Three-Phase System a Z n c b Z Z • A 3-phase system is said to be balanced when the impedances (Z) of each phase are equal. • (Under these circumstances, all voltages, currents and powers “balance” each other.) Three-Phase Systems • 3-phase, 4-wire systems are widely used to supply electric power to commercial and industrial users • 3-phase, 3-wire systems most commonly occur in motor/generator drives Star (Wye) and Delta Connections a a n c b c • For balanced loads (3-wire system) • Most applicable to transformers and machines • Different voltage/current relationships b Star (Wye) Connection -Van Vca 30º Vab Vcn 30º Van Vbn -Vbn Line-to-neutral voltages: VLn: Van, Vbn, Vcn Line-to-line (line) voltages: VL: Vab, Vbc, Vca 30º Vbc -Vcn |VL| = 2 x |VLn| cos30º = √3 |VLn| Delta Connection -Ibc Ica Branch currents: IB: Iab, Ibc, Ica Ic 30º Line currents: IL: Ia, Ib, Ic Iab Ib -Iab 30º 30º Ibc Ia -Ica |IL| = 2 x |IB| cos30º = √3 |IB| Three Phase Power: Star (Wye) and Delta Connections Star… Power in each branch: PB = VLn x IL = 1/√3 x VL x IL Delta… Power in each branch: PB = VL x IB = 1/√3 x VL x IL Total power: Ptot = 3PB = √3VLIL Total power: Ptot = 3PB = √3VLIL The same! Three-Phase Systems: active, reactive and apparent power The relationship between active power P, reactive power Q, and apparent power S is the same for balanced 3-phase circuits as for single-phase circuits. Three-Phase Systems: active, reactive and apparent power S2 = P2 + Q2 cosφ = P / S Where: S = total 3-phase apparent power (VA) P = total 3-phase active power (W) Q = total 3-phase reactive power (VAr) cosφ = power factor φ = phase angle between line current and lineto-neutral voltage Three-Phase Systems: active, reactive and apparent power Q. But how do we find φ for delta connections where there is no line-to-neutral voltage? A. For analysis purposes, we simply assume that our circuit is star-connected. The maths still works! Analysing 3-Phase Circuits A balanced 3-phase load may be considered to be composed of three identical single-phase loads. Consequently, the easiest way to analyse such circuits is to consider only one phase.