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EE1 PEEE Refresher Class Power Part 1 notes by T. Ernst
EE1 – Power Part 1 Notes Fall 2011, Page 1
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Vectors, phasors & phasing 1-phase & 3-phase Per Unit System
Power System Review Vectors, phasors & phasing 1-phase & 3-phase Per Unit System Bases (VA, V, amp & ohm) Convert between different bases EE1 – Power Part 1 Notes Fall 2011, Page 2
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Static (don’t change over time) Map Coordinates
Vectors Static (don’t change over time) Map Coordinates EE1 – Power Part 1 Notes Fall 2011, Page 3
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Static (don’t change over time) X-Y Plots
Vectors Static (don’t change over time) X-Y Plots EE1 – Power Part 1 Notes Fall 2011, Page 4
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Static (don’t change over time) Impedance
Vectors Static (don’t change over time) Impedance EE1 – Power Part 1 Notes Fall 2011, Page 5
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Polar versus Rectangular Coordinate System
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Polar versus Rectangular Coordinate System
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Polar versus Rectangular Coordinate System
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Vectors that rotate: ω = 2πf (radians/sec)
Phasors Vectors that rotate: ω = 2πf (radians/sec) Representation: Sine and Cosine functions over time EE1 – Power Part 1 Notes Fall 2011, Page 9
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Phasors EE1 – Power Part 1 Notes Fall 2011, Page 10
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Express leading or lagging as: Current wrt voltage
Phasing Convension: Express leading or lagging as: Current wrt voltage Angle less than 180 degrees EE1 – Power Part 1 Notes Fall 2011, Page 11
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ELI the ICE man EE1 – Power Part 1 Notes Fall 2011, Page 12
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Single Phase Power Ohms Law (V, I & Z) Note: V & I are phasors
Z is a vector EE1 – Power Part 1 Notes Fall 2011, Page 13
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VA = V * I* where I* = complex conjugate
Single Phase Power VA = W + jVAR (S = P + jQ ) VA = V * I* where I* = complex conjugate EE1 – Power Part 1 Notes Fall 2011, Page 14
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VA = V * I* where I* = complex conjugate
Single Phase Power VA = W + jVAR (S = P + jQ ) VA = V * I* where I* = complex conjugate EE1 – Power Part 1 Notes Fall 2011, Page 15
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Cos Θ = power factor (PF = W/VA)
Θ = power factor angle Cos Θ = power factor (PF = W/VA) EE1 – Power Part 1 Notes Fall 2011, Page 16
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Balanced Systems (V, I and Z)
3-Phase Power Balanced Systems (V, I and Z) EE1 – Power Part 1 Notes Fall 2011, Page 17
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Balanced Systems (V, I and Z)
3-Phase Power Balanced Systems (V, I and Z) EE1 – Power Part 1 Notes Fall 2011, Page 18
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Open vector representation
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Closed Vector Representation
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Phase-phase versus Phase Quantities
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Use phase quantities for ohms law Vpn, Ip, Zpn
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Ipp is usually Iwdg or Iload
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3-Phase equations EE1 – Power Part 1 Notes Fall 2011, Page 24
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3-Phase equations EE1 – Power Part 1 Notes Fall 2011, Page 25
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Power Transformer 375 MVA, 115 – 230 kV, 3-phase
Find FLI on 115 kV side EE1 – Power Part 1 Notes Fall 2011, Page 26
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Power Transformer 375 MVA, 115 – 230 kV, 3-phase
Find FLI on 230 kV side EE1 – Power Part 1 Notes Fall 2011, Page 27
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VABase (3-phase value for 3-phase systems)
Per-Unit System Normalize V, I Z & VA Base Values VABase (3-phase value for 3-phase systems) VBase (P-P value for 3-phase systems) IBase (“line” current for 3-phase systems) ZBase (P-N value) EE1 – Power Part 1 Notes Fall 2011, Page 28
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Choose VABase for convenience (Same across the entire circuit)
Per-Unit System Approach Choose VABase for convenience (Same across the entire circuit) Assign VBase = nominal system voltage (different at different points of the circuit) Calculate IBase and ZBase EE1 – Power Part 1 Notes Fall 2011, Page 29
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Calculate per-unit values of actual V, I & Z
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Converting Zpu from one base to another
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An Example: EE1 – Power Part 1 Notes Fall 2011, Page 32
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Choose Bases: EE1 – Power Part 1 Notes Fall 2011, Page 33
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Get everything on same base
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Draw the per-unit one-line
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Reduce the network EE1 – Power Part 1 Notes Fall 2011, Page 39
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Use voltage division to calculate Vload
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Use Vload to calculate PU load currents
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Use Ibase to calculate load currents
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