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and current phasors for capacitive load.Figure 5.22 Reactive capacitive power phasor
in complex plane.Figure 5.23 Resistive–inductive load (
R +
jωL) with
and
.Figure 5.24 Voltage and current phasors for resistive–inductive load.Figure 5.25 Reactive resistive–inductive power phasor
in complex plane.Figure 5.26 Capacitive load (
R + 1/
jωC) = (
R−
j/
ωC) with
and
.Figure 5.27 Voltage and current phasors for resistive–capacitive load.Figure 5.28 Reactive resistive–capacitive power phasor
in complex plane.Figure E5.3.1 Transmission/distribution line feeder.Figure E5.3.2 Load voltage and load current.Figure E5.3.3 Load real and reactive powers
P load and
Q load, respectively,...Figure E5.3.4 Phasor rms voltages of the load and the source as well as the ...Figure 5.29 Circuit for power factor correction.Figure 5.30 Power relationships before the capacitor
C is connected. Note
P Figure 5.31 Power phasors for old (uncompensated) and new (compensated) cond...Figure E5.4.1 Power factor increase of a (
R +
jωL) load with parallel c...Figure E5.4.2 Real power (
P load old) and inductive reactive power (
Q Figure 5.32 Residential power circuit consisting of a center‐tapped
S pole =...Figure 5.33 Residential Δ‐Y‐connected substation transformer, allowing for l...Figure E5.6.1 Typical three‐branch circuit of a residence.Figure 5.34 Two three‐phase systems suspended on transmission tower.Figure 5.35 Reduction of magnetic fields on the ground by employing a revers...Figure 5.36 Time‐domain representation of balanced voltages
v an(
t),
v bn(
t)...Figure 5.37 Three‐phase Y‐connected voltage sources, for example, in an elec...Figure 5.38 Three‐phase Y‐connected phasor voltages
,
,
in the complex p...Figure 5.39 Y‐Y configuration.Figure 5.40 Y‐Δ configuration.Figure 5.41 Δ‐Y configuration.Figure 5.42 Δ‐Δ configuration.Figure 5.43 (a) Balanced Y‐Y connections at source and at load, respectively...Figure 5.44 Balanced Y‐Δ connections at source and at load, respectively.Figure 5.45 (a) Line‐to‐line (L‐L) voltage definition for Δ‐connected balanc...Figure 5.46 (a) Balanced Y‐connection (either source or load) definition of ...Figure 5.47 (a) Balanced Δ connection (either source or load). (b) Phasor di...Figure P5.1.1 Calculation of instantaneous current
i s(
t) and instantaneous ...Figure P5.2.1 Calculation of average power
P and reactive power
Q absorbed b...Figure P5.3.1 Computation of average power
P and reactive power
Q absorbed b...Figure P5.4.1 Conservation of real (
P) power.Figure P5.5.1 (a) Root‐mean‐square value of (asymmetric) sawtooth voltage. (...Figure P5.6.1 Transmission line with load and source.Figure P5.7.1 Voltage and power factor to be computed at the sending end (so...Figure P5.8.1 Calculation of the complex powers at the source and at the loa...Figure P5.9.1 Single‐phase transmission line with impedance
.Figure P5.10.1 Fundamental power factor correction as applied to a bank of s...Figure P5.12.1 Y‐Y configuration with given transmission line and load data....Figure P5.13.1 Y‐Δ configuration with given line current and load data.Figure P5.14.1 Δ‐Y configuration with given source voltages, load, and line ...Figure P5.15.1 Δ‐Δ configuration with given source voltages, load, and line ...Figure P5.16.1 (a) Lightning instantaneous current
i lightning(
t). (b) Light...
7 Chapter 6Figure 6.1 Single permanent magnet and associated magnetic flux Φ, magnetic ...Figure 6.2 Pair of permanent magnets and associated magnetic fields resultin...Figure 6.3 Pair of permanent magnets and associated magnetic fields resultin...Figure 6.4 (a) Application of Ampere's law to a uniform long wire located in...Figure 6.5 Right‐hand rule [3], where current I generates HΦ, which is ...Figure E6.1.1 Infinitely long single wire conducting a DC current of I = 50 ...Figure E6.1.2 Magnetic field densities inside and outside of a single conduc...Figure 6.6 C‐type iron core with one winding/coil having N turns and an air ...Figure 6.7 Equivalent circuit for Figure 6.6 with mmf = ℱ = N i(t), flux Φ, ...Figure E6.2.1 C‐type iron‐core magnetic circuit with gap g = 0.02 m and rela...Figure 6.8 Magnetically coupled circuit with two windings. The dot (•) conve...Figure 6.9 Magnetic arrangement of two coupled windings residing on iron cor...Figure 6.10 Electric equivalent circuit of a coupled two‐winding system resi...Figure 6.11 Detailed electric equivalent circuit with zero leakage fluxes; LFigure 6.12 Single‐phase transformer with voltage source
, load impedance
Figure 6.13 Magnetic circuit of ideal transformer.Figure 6.14 Circuit symbol for ideal (single‐phase) transformer. The two par...Figure E6.4.1 Electric circuit with two coupled inductors supplied by curren...Figure E6.5.1 Electric circuit with ideal single‐phase transformer and given...Figure E6.6.1 Ideal transformer fed by current source
supplying resistive–...Figure E6.7.1 Electric circuit with ideal single‐phase transformer and given...Figure 6.15 Single‐phase transformer with input power
Pin, output power
PoutFigure 6.16 Shell‐form, single‐phase transformer with interleaved primary an...Figure 6.17 (a) Butt‐to‐butt, (b) wound, and (c) mitered iron cores: for eit...Figure 6.18 Winding arrangement of one‐eighth of an
S = 25 kVA oil‐cooled si...Figure 6.19 Linear
T‐equivalent circuit of two‐winding, single‐phase transfo...Figure 6.20 Phasor diagram of two‐winding single‐phase transformer derived f...Figure E6.8.1 Linear single‐phase transformer at resistive load
Rload = 1.15...Figure E6.8.2 Not‐to‐scale phasor diagram for the linear transformer equival...Figure E6.9.1 Linear single‐phase transformer at resistive–inductive load
...Figure E6.9.2 Not‐to‐scale phasor diagram for the linear transformer equival...Figure E6.10.1 Linear single‐phase transformer at resistive–inductive load w...Figure E6.10.2 Not‐to‐scale phasor diagram for the linear transformer equiva...Figure 6.21 (a) Grid structure for numerical field calculation [9] (see Chap...Figure 6.22 Magnetostatic flux distribution in (
x–
y) plane [9]. The flux tub...Figure 6.23 Magnetostatic flux distribution in
y–
z plane [9]. Flux tubes do ...Figure 6.24 Measured and calculated nonlinear (
λ–
i) characteristics [9]...Figure 6.25 (a) Balanced instantaneous three‐phase voltages
leading the ...Figure E6.11.1 Y‐Y three‐phase transformer at Y‐connected resistive load, re...Figure E6.11.2 Not‐to‐scale phasor diagram of primary and secondary phase vo...Figure E6.11.3 Single‐phase equivalent circuit of Figure E6.11.1. In the fol...Figure E6.12.1 Y‐Y three‐phase transformer at Δ‐connected resistive–inductiv...Figure E6.12.2 Not‐to‐scale phasor diagram of primary and secondary phase vo...Figure E6.12.3 Single‐phase equivalent circuit of Figure E6.12.1. In the fol...Figure E6.13.1 Δ‐Y three‐phase transformer at Y‐connected resistive–inductiv...Figure E6.13.2 Not‐to‐scale phasor diagram of primary line‐to‐line and secon...Figure E6.13.3 Single‐phase equivalent circuit of Figure E6.13.1.Figure E6.14.1 Δ‐Y three‐phase transformer at Y‐connected resistive–inductiv...Figure E6.14.2 Not‐to‐scale phasor diagram of primary line‐to‐line
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