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Notation

Capital English Letters

A	component availability (Chapter 11)
A	levelized annual cost, $ (Chapter 7)
A	weighted average Btu/kWh net generation (Chapter 2)
A, B, C	phase designation
A, B, C, D	general line (circuit) constants (Chapter 5)
AFDR	feeder availability (Chapter 11)
Ai	availability of component i (Chapter 11)
An	area served by one of n substation feeders, mi2
ASD	service-drop conductor size, cmil (Chapter 6)
ASL	secondary-line conductor size, cmil (Chapter 6)
Asys	system availability (Chapter 11)
AEC	annual equivalent of energy cost, $
AEICc	annual equivalent of total installed capacitor bank cost, $ (Chapter 8)
AIC	annual equivalent of feeder investment cost, $
B	average fuel cost, $/MBtu (Chapter 2)
BEC	original (base) annual kWh energy consumption
BVR	bus voltage regulator
BW	bandwidth of voltage-regulating relay
C	capacitance, F
C	common winding (Chapter 3)
CF	installed feeder cost, $/kVA (Chapter 8)
CG	generation system cost, $/kVA
CS	distribution substation cost, $/kVA
CT	transmission system cost, $/kVA
CT	transmission cost, $/kVA (Equation 8.26)
CT	total reactive compensation (= cn) (Equation 8.85)
CR	corrective ratio (Chapter 9)
CTP	primary-side rating of current transformer (Chapter 9)
CTR	current transformer ratio
D	distance or separation, ft
D	load density, kVA/mi2
D	ratio of kWh losses to net system input (Chapter 2)
Dg	coincident maximum group demand, W
Di	demand of load i, W
DFi	demand factor of load group i
DTA(ij, k)	downtime array coefficients (Chapter 11)
E	source emf; voltage
Ei	event that component i operates successfully (Chapter 11)
EC	energy cost, $/kWh
ECoff	incremental cost of off-peak electric energy, $/kWh
ECon	incremental cost of on-peak electric energy, $/kWh (Chapter 6)
ECL1	eddy-current loss at rated fundamental current
E(T)	expected time during which a component will survive
F	fault point
F’LD	reactive load factor (= Q/S)
Fc	coincident factor
FD	diversity factor
FLD	load factor
FLL	load-location factor (Chapter 7)
FLS	loss factor
FLSA	loss-allowance factor (Chapter 7)
FPR	peak-responsibility factor
FR	reserve factor
Fu	utilization factor
FCAF	fuel cost adjustment factor, $/kWh
FDR	feeder (Chapter 11)
F(t)	unreliability function (Chapter 11)
H	transformer higher-voltage-side winding
HFI	current harmonic factor
HFV	voltage harmonic factor
I	failed zone-branch array coefficient (Chapter 11)
I	rms phasor current, A
I	current matrix
IAB	current in higher-voltage-side winding between phases A and B, A
Iab	current in lower-voltage-side winding between phases a and b, A
Ia,3ϕ	current in phase a due to single-phase load, A
IB	base current, A
IC	current in common winding (Chapter 3)
Ic	core-loss component of excitation current (Chapter 3)
Ie	excitation current (Chapter 3)
Iexc	per unit excitation current (Chapter 6)
If,a, If,b If,c	fault currents in phases a, b, and c
If,3ϕ	three-phase fault current, A
If,3ϕ	three-phase fault current referred to subtransmission voltage, A (Chapter 10)
(IF,3ϕ)max	maximum three-phase fault current, A (Chapter 10)
IF, HV	fault current in transformer high-voltage side, A
If,L–G	line-to-ground fault current, A
If, LV	fault current in transformer low-voltage side, A
If,L–L	line-to-line fault current, A
Iϕ1	current due to single-phase load, A
Ih	harmonic current
IL	line current; load current, A
Im	magnetizing current component of excitation current (Chapter 3)
Im	current in feeder main at substation, A
IN	current in primary neutral, A
In	current in secondary neutral, A
Iop	operating current, A
IP, pu	no-load primary current at substation transformer, pu
Ira	rated current, A
IS	current in series winding (Chapter 3)
ICc	installed cost of capacitor bank, $/kvar (Chapter 8)
ICcap	total installed cost of shunt capacitors, $
ICF	installed feeder cost, $ (Chapter 7)
ICPH	annual installed cost of pole and its hardware, $ (Chapter 6)
ICSD	annual installed cost of service drop, $ (Chapter 6)
ICSL	annual installed cost of secondary line, $ (Chapter 6)
ICsys	average investment cost of power system upstream, $/kVA
ICT	annual installed cost of distribution transformer, $
K	percent voltage drop per kilovolt-ampere-mile
$\tilde{K}$ $\tilde{K}$	per unit voltage drop per 10,000 A · ft
$\hat{K}$ $\hat{K}$	constant (Equation 5.63)
Kh	watt-hour meter constant (Chapter 2)
KR	conversion factor for resistance (Chapter 7)
Kr	number of watt-hour meter disk revolutions (Chapter 2)
KX	conversion factor for reactance (Chapter 7)
K1	a constant to convert energy-loss savings to dollars, $/kWh (Equation 8.87)
K2	a constant to convert power-loss savings to dollars, $/kWh (Equation 8.87)
K3	a constant to convert total fixed capacitor size to dollars, $/kWh (Equation 8.95)
Lsc	system inductance, H (Equation 8.108)
LCDH	losses in capacitors due to harmonics
LD	load diversity, W
LD	load (Chapters 2 and 5)
LDC	line-drop compensator
LS	loss
LTC	load tap changer
LV	low voltage
MTTR	mean time to repair ( $= \bar{r}$ $= \bar{r}$ ) (Chapter 11)
MTBF	mean time between failures ( $= \bar{T}$ $= \bar{T}$ ) (Chapter 11)
MTTF	mean time to failure ( $= \bar{m}$ $= \bar{m}$ ) (Chapter 11)
N	expected duration of normal weather (Chapter 11)
N	neutral primary terminal
0	row vector of zeros (Chapter 11)
OCexc	annual operating cost of transformer excitation current, $ (Chapter 6)
OCSD, Cu	annual operating cost of service-drop cable due to copper losses, $ (Chapter 6)
OCSL, Cu	annual operating cost of secondary line due to copper losses, $ (Chapter 6)
OCT, Cu	annual operating cost of transformer due to copper losses, $ (Chapter 6)
OCT, Fe	annual operating cost of transformer due to core losses, $
P	average power, W
P	transition (or stochastic) matrix (Chapter 11)
P’LS	power loss after capacitor bank addition, W (Equation 8.46)
Pav	average power, W
PLS, av	average power loss, W
Pi	peak load i, W
PLD	average power of load, W
PLS	average power loss, W
PLS, i	peak loss at peak load i, W
PLS, max	maximum power loss, W
PLS,1ϕ	single-phase power loss, W (Chapter 7)
PLS,3ϕ	three-phase power loss, W (Chapter 7)
Pn	load at year n, W (Chapter 2)
P0	initial load, W
Pr	receiving-end average power, VA
PT, Cu	transformer copper loss, W (Chapter 6)
PT, Fe	transformer core loss, W (Chapter 6)
PSL, Cu	power loss of secondary line due to copper losses, W
PF	power factor
PTR	potential transformer ratio
PTN	turns ratio of potential transformer (Chapter 9)
Q	average reactive power, var
Qc	reactive power due to corrective capacitors, var (Chapter 8)
Qc,3ϕ	three-phase reactive power due to corrective capacitors, var (Equation 8.30)
Qi	unreliability of component i (Chapter 11)
Qr	receiving-end average reactive power, VA
Qsys	system unreliability (Chapter 11)
R	resistance, Ω
Reff	effective resistance, Ω (Chapter 9)
RL	resistance of load impedance, Ω
Rset	R dial setting of line-drop compensator (Chapter 9)
Rsys	system reliability (Chapter 11)
RIA(ij, k)	recognition and isolation array coefficients (Chapter 11)
RP	regulating point
S	apparent power, VA
$\bar{S}$ $\bar{S}$	= P + jQ, complex apparent power, VA
S	expected duration of adverse weather (Chapter 11)
S	series winding (Chapter 3)
SB	base apparent power, VA
Ssc	short-circuit apparent power, VA
Sckt	circuit capacity, VA (Chapter 9)
SG	generation capacity, VA (Chapter 8)
SL	load apparent power, VA
SLi	apparent power of load i, VA
$S_{∠ - ∠}$ $S_{∠ - ∠}$	apparent power rating of an open-delta bank
Slump	apparent power of lumped load, VA
SL,3ϕ	three-phase apparent power of load, VA (Chapter 8)
Sm	total kVA load served by one feeder main
Sn	kVA load served by one of n substation feeders
SPK	feeder apparent power at peak load, VA
Sreg	regulator capacity, VA (Chapter 9)
SS	substation capacity, VA (Equation 8.27)
ST	transformer apparent power, VA
ST	transmission capacity, VA (Equation 8.24)
ST, ab	apparent power rating of single-phase transformer connected between phases a and b, VA
STi	apparent power rating of transformer i, VA
ST,3ϕ	three-phase transformer apparent power, VA
S1ϕ	single-phase VA rating
S3ϕ	three-phase VA rating
SΔ–Δ	apparent power rating of a delta-delta bank
SD	service drop (Chapter 6)
SW	switchable capacitors (Chapter 8)
T	a random variable representing failure time (Chapter 11)
T	time
T	transformer
TAn	total area served by all n feeders, mi2
TAC	total annual cost, $
TAELcu	total annual energy loss due to copper losses, W
TCDi	total connected group demand i, W
TD	time delay
TECL	total eddy-current loss (Chapter 8)
TSn	total kVA load served by a substation with n feeders
U	component unavailability (Chapter 11)
UFDR	feeder unavailability (Chapter 11)
UG	underground
URD	underground residential distribution
V	volt, unit symbol abbreviation for voltage
V	voltage matrix
Vab, pu	voltage between phases a and b, pu
VB,ϕ	single-phase base voltage, V
VB,3ϕ	three-phase base voltage, V
VC	voltage across common winding (Chapter 3)
VH	higher-voltage-side voltage, V (Chapter 3)
Vh	rms voltage of hth harmonic
VL-L	line-to-line distribution voltage, V (Chapter 10)
VL-L	line-to-line voltage, V
VL-N	line-to-neutral voltage, V
Yl, pu	per unit voltage at feeder end (Chapter 9)
VP	primary distribution voltage, V (Chapter 9)
VP, max	maximum primary distribution voltage, V
Vr	receiving-end voltage
Vreg	output voltage of regulator, V
VRP	voltage at regulating point, V
VS	voltage across series winding (Chapter 3)
VS	sending-end voltage
VST	subtransmission voltage, V (Chapter 9)
VST, L–L	line-to-line subtransmission voltage, V (Chapter 10)
VX	lower-voltage-side voltage, V (Chapter 3)
VD	voltage drop, V
VDpu	per unit voltage drop
VDpu,1ϕ	single-phase voltage drop, pu
VDpu,3ϕ	three-phase voltage drop, pu
VDSD	voltage drop in service-drop cable, V
VDSL	voltage drop in secondary line, V
VDT	voltage drop in transformer, V
% VDab	percent voltage drop between a and b
% VDm	percent voltage drop in feeder main
VDIP	voltage dip, V
VDIPSD	voltage dip in service-drop cable, V
VDIPSL	voltage dip in secondary line, V
VDIPT	voltage dip in transformer, V
VRl, pu	per unit voltage rise at distance 1 (Chapter 9)
VRpu	per unit voltage regulation
% VR	percent voltage regulation
% VR	percent voltage rise (Chapter 8)
% VRNSW	percent voltage rise due to nonswitchable capacitors (Chapter 8)
% VRSW	percent voltage rise due to switchable capacitors (Chapter 8)
VRR	voltage-regulating relay
VRRpu	per unit setting of voltage-regulating relay
W	wire (in transformer connections) (Chapter 3)
X	reactance, Ω; transformer lower-voltage-side winding
Xc	capacitive reactance
XL	reactance of load impedance, Ω
Xsc	system reactance, Ω (Equation 8.107)
Xset	X dial setting of line-drop compensator (Chapter 9)
X(tn)	sequence of discrete-valued random variables (Chapter 11)
Y	admittance, Ω; wye connection
Y	admittance matrix
Z	impedance, Ω
Z	secondary-winding impedance, Ω (Equation 10.71)
Z	impedance matrix
Zeq	equivalent (total) impedance to fault, Ω (Chapter 10)
Zf	fault impedance, Ω
ZG	impedance to ground, Ω
ZG, ckt	impedance to ground of circuit, Ω
ZLD	load impedance, Ω
ZM	impedance of secondary main, Ω
ZT	transformer impedance, Ω
ZT	equivalent impedance of distribution transformer, Ω
ZT, pu	per unit transformer impedance
ZΔ	equivalent delta impedance, Ω (Equation 10.54)
Z0	zero-sequence impedance, Ω
Z0, ckt	zero-sequence impedance of circuit, Ω
Z1	positive-sequence impedance, Ω
Z1, ckt	positive-sequence impedance of circuit, Ω
Z1, SL	positive-sequence impedance of secondary line, Ω (Chapter 10)
Z1, ST	positive-sequence impedance of subtransmission line, Ω
Z1, sys	positive-sequence impedance of system, Ω
Z1, T	positive-sequence impedance of transformer, Ω
Z2	negative-sequence impedance, Ω

Lowercase English Letters

a, b, c	phase designation
c	capacitor compensation ratio (Chapter 8)
ci	contribution factor of load i
dn	mutual geometric mean distance of phase and neutral wires, ft
dp	mutual geometric mean distance between phase wires, ft
$\bar{f}$ $\bar{f}$	mean failure frequency (Chapter 11)
fP	parallel resonant frequency, Hz
f1	fundamental frequency, Hz
fsys	average failure frequency of a system (Chapter 11)
f(t)	probability density function
h	harmonic order
h(t)	hazard rate (Chapter 11)
i	investment fixed charge rate (Chapter 6)
ic	annual fixed charge rate for capacitors
iF	annual fixed rate for feeder
iG	annual fixed charge rate for generation system
is	annual fixed charge rate for distribution substation
iT	annual fixed charge rate for transmission system
k	constant used in computing loss factor (Chapter 2)
l	inductance per unit length; leakage inductance
l	feeder length, mi
ln	linear dimension of primary-feeder service area, mi
mi	observed time to failure for cycle i (Chapter 11)
${\bar{m}}_{s}$ ${\bar{m}}_{s}$	mean time to failure of series system (Chapter 11)
n	total number of cycles (Chapter 11)
n	transfer ratio (inverse of turns ratio) (Chapter 10)
n	= n1/n2, turns ratio; neutral secondary terminal; number of feeders emanating from a substation
n1	number of turns in primary winding
n2	number of turns in secondary winding
P(n)	vector of state probabilities at time tn (Chapter 11)
pij	transition probabilities (Chapter 11)
pij	probability of proper operation of isolating equipment in zone branch ij (Chapter 11)
q	probability of component failure (Chapter 11)
qij	probability of failure of isolating equipment in zone branch ij (Chapter 11) receiving end
r	radius; internal (source) resistance; resistance per unit length
ra	resistance of phase wires, Ω/ 1000 ft
re	earth resistance, Ω/ 1000 ft
req	transformer equivalent resistance, Ω
ri	observed time to repair for cycle i (Chapter 11)
rl	lateral resistance per unit length
rm	resistance of feeder main, Ω/ mi
${\bar{r}}_{s}$ ${\bar{r}}_{s}$	mean time to repair of series system (Chapter 11)
s	sending end; effective feeder (main) length, mi (Chapter 4)
s	series system (Chapter 11)
t	time
x	line reactance per unit length; internal (source) reactance
xa	self-inductive reactance of a phase conductor, Ω/ mi
xap	reactance of phase wire with 1 ft spacing, Ω/ 1000 ft
xan	reactance of neutral wire with 1 ft spacing, Ω/ 1000 ft
xd	inductive reactance spacing factor, Ω /mi
xdn	mutual reactance between phase and neutral wires, Ω/ 1000 ft
xdp	mutual reactance of phase wires, Ω/ 1000 ft
xe	earth reactance, Ω/ 1000 ft
xeq	transformer equivalent reactance, Ω
xi, opt	optimum location of capacitor bank i in per unit length
xL	inductive line reactance (Chapters 5 and 8)
x1	lateral reactance per unit length
xm	reactance of feeder main, Ω/ mi
xRP	regulating point distance from substation, mi (Chapter 9)
xT	transformer reactance, % Ω (Chapter 8)
Z	impedance per unit length
Zl	lateral impedance per unit length
zm	impedance of feeder main, Ω/ mi
Z0, a	zero-sequence self-impedance of phase circuit, Ω/ 1000 ft
Z0, ag	zero-sequence mutual impedance between phase and ground wires, Ω/ 1000 ft
Z0, g	zero-sequence self-impedance of ground wire, Ω/ 1000 ft

Capital Greek Letters

Δ	delta connection; determinant
Δ	difference; increment; savings; benefits
ΔACE	annual conserved energy, Wh (Chapter 8)
ΔBEC	additional energy consumption increase
ΔEL	energy-loss reduction
ΔPLS	additional decrease in power loss, W (Chapter 8)
ΔPLS, opt	optimum loss reduction, W (Chapter 8)
ΔQc	required additional capacitor size, var (Chapter 8)
ΔSF	released feeder capacity, VA (Chapter 8)
ΔSG	released generation capacity, VA (Chapter 8)
ΔSS	released substation capacity, VA (Equation 8.29)
ΔST	released transmission capacity, VA (Equation 8.24)
ΔSsys	released system capacity, W (Chapter 8)
Δ$ACE	annual benefits due to conserved energy, $ (Chapter 8)
Δ$F	annual benefits due to released feeder capacity, $ (Equation 8.36)
Δ$G	annual benefits due to released generation capacity, $ (Chapter 8)
Δ$S	annual benefits due to released substation capacity, $ (Equation 8.29)
Δ$T	annual benefits due to released transmission capacity, $ (Equation 8.26)
Δ	transition rate matrix (Chapter 11)
Π	unconditional steady-state probability matrix (Chapter 11)
Σ	total savings due to capacitor installation, $ (Equation 8.86)

Lowercase Greek Letters

α	a constant [=(1 + λ + λ2)]−1 (Chapter 11) 6
δ	power angle
θ	power-factor angle
θmax	power-factor angle at maximum voltage drop
λ	ratio of reactive current at line end to reactive current at line beginning
λ	failure rate (Chapter 11)
$\bar{λ}$ $\bar{λ}$	complex flux linkages, (Wb · T)/m
λCT	annual fault rate of cable terminations (Chapter 11)
λFDR	annual feeder fault rate (Chapter 11)
λij	total failure rate of zone branch ij (Chapter 11)
λijB	breaker failure rate in zone i branch j (Chapter 11)
λijM	zone branch ij failure rate due to preventive maintenance (Chapter 11)
λijW	zone branch ij failure rate due to adverse weather (Chapter 11)
λOH	annual fault rate of overhead feeder section (Chapter 11)
λs	failure rate of supply (substation) (Chapter 11)
λUG	annual fault rate of underground feeder section (Chapter 11)
μ	mean repair rate (Chapter 11)
μij	zone branch ij repair rate (Chapter 11)
μsijc	reclosing rate of reclosing equipment in zone branch ij (Chapter 11)
μsijo	isolation rate of isolating equipment in zone branch ij (Chapter 11)
ϕ	= tan−1(X/R), impedance angle
ϕ	magnetic flux; phase angle
ω	radian frequency

Subscripts

A	phase a
a	phase a
B	phase b
b	phase b
B	base quantity
C	phase C; common winding (Chapter 3)
c	phase c
c	capacity; capacitive; coincident (Chapter 3)
cap	shunt capacitor
ckt	circuit
CT	cable termination (Chapter 11)
Cu	copper
eff	effective
eq	equivalent circuit quantity
exc	excitation
D	diversity
F	feeder; fault point; referring to fault
f	referring to fault
FDR	feeder
Fe	iron
H	high-voltage side (HV)
L	inductive (reactance); load (Chapter 3)
L	line; load
l	lateral; inductive (reactance); length
LD	load
L-G	line-to-ground
L-L	line-to-line
LL	load location (Chapter 7)
L-N	line-to-neutral
LS	loss (Chapters 2 and 5)
LSA	loss allowance
M	secondary main
m	feeder main
max	maximum
min	minimum
N	turns ratio
N	primary neutral
n	number of feeders emanating from a substation
n	neutral
NSW	nonswitchable (fixed) capacitors (Chapter 9)
off	off-peak
OH	overhead (Chapter 11)
op	operating
opt	optimum
on	on-peak
•	primary
PK	peak
PR	peak responsibility (Chapter 7)
pu	per unit
r	receiving end
ra	rated
reg	regulator
S	substation; series winding (Chapter 3)
s	sending end
sc	short circuit
SD	service drop
set	dial setting (line-drop compensator)
SL	secondary line (Chapter 6)
ST	subtransmission
SW	switchable (capacitors)
sys	power system
T	transformer
Ti	transformer i
X	low-voltage side (LV)
Y	wye connection
1ϕ, 3ϕ	single-phase, three-phase
0, 1, 2	zero-, positive-, negative-sequence quantity
Δ	delta connection
∠	open-delta connection

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Notation

Capital English Letters

Lowercase English Letters

Capital Greek Letters

Lowercase Greek Letters

Subscripts

Table of Contents for
Notation