EE1 PEEE Refresher Class Power Part 1 notes by T. Ernst EE1 – Power Part 1 Notes Fall 2011, Page 1

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

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

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

Static (don’t change over time) Impedance Vectors Static (don’t change over time) Impedance EE1 – Power Part 1 Notes Fall 2011, Page 5

Polar versus Rectangular Coordinate System EE1 – Power Part 1 Notes Fall 2011, Page 6

Polar versus Rectangular Coordinate System EE1 – Power Part 1 Notes Fall 2011, Page 7

Polar versus Rectangular Coordinate System EE1 – Power Part 1 Notes Fall 2011, Page 8

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

Phasors EE1 – Power Part 1 Notes Fall 2011, Page 10

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

ELI the ICE man EE1 – Power Part 1 Notes Fall 2011, Page 12

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

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

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

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

Balanced Systems (V, I and Z) 3-Phase Power Balanced Systems (V, I and Z) EE1 – Power Part 1 Notes Fall 2011, Page 17

Balanced Systems (V, I and Z) 3-Phase Power Balanced Systems (V, I and Z) EE1 – Power Part 1 Notes Fall 2011, Page 18

Open vector representation EE1 – Power Part 1 Notes Fall 2011, Page 19

Closed Vector Representation EE1 – Power Part 1 Notes Fall 2011, Page 20

Phase-phase versus Phase Quantities EE1 – Power Part 1 Notes Fall 2011, Page 21

Use phase quantities for ohms law Vpn, Ip, Zpn EE1 – Power Part 1 Notes Fall 2011, Page 22

Ipp is usually Iwdg or Iload EE1 – Power Part 1 Notes Fall 2011, Page 23

3-Phase equations EE1 – Power Part 1 Notes Fall 2011, Page 24

3-Phase equations EE1 – Power Part 1 Notes Fall 2011, Page 25

Power Transformer 375 MVA, 115 – 230 kV, 3-phase Find FLI on 115 kV side EE1 – Power Part 1 Notes Fall 2011, Page 26

Power Transformer 375 MVA, 115 – 230 kV, 3-phase Find FLI on 230 kV side EE1 – Power Part 1 Notes Fall 2011, Page 27

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

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

Calculate per-unit values of actual V, I & Z EE1 – Power Part 1 Notes Fall 2011, Page 30

Converting Zpu from one base to another EE1 – Power Part 1 Notes Fall 2011, Page 31

An Example: EE1 – Power Part 1 Notes Fall 2011, Page 32

Choose Bases: EE1 – Power Part 1 Notes Fall 2011, Page 33

Get everything on same base EE1 – Power Part 1 Notes Fall 2011, Page 34

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Draw the per-unit one-line EE1 – Power Part 1 Notes Fall 2011, Page 38

Reduce the network EE1 – Power Part 1 Notes Fall 2011, Page 39

Use voltage division to calculate Vload EE1 – Power Part 1 Notes Fall 2011, Page 40

Use Vload to calculate PU load currents EE1 – Power Part 1 Notes Fall 2011, Page 41

Use Ibase to calculate load currents EE1 – Power Part 1 Notes Fall 2011, Page 42

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