N O M EN C LA TU R E
(I)
List of Symbols
Bjj
: Imaginary part o f Zy
Co
: State o f charge o f RPB
C2 ,C3
: Domain characteristics of RFB
D
:
Ed
: Generator Voltage behind transient reactance (p.u.)
Ed"
Damping Co-efficient (p.u. Kw/p.u.Hz)
: Generator Voltage behind subtransient reactance Xd"(p.u.)
Ed
: SMES Coil voltage (volts)
Efd
: Synchronous generator field voltage
Edo
• Maximum output voltage o f 6 -pulse converter (volts)
n
It
Eq
: Generator voltage behind subtransient reactance Xq (p.u.)
f
: System frequency (Hz)
Gij
: Real part o f Zy
Ha
:
Total wind turbine and wind generator inertia constant (sec)
Hb
:
Width o f current band o f hysterises current controller
Hd
: Inertia constant o f synchronous machine coupled to diesel engine (sec)
[I]
:
Identity matrix
io
:
Self discharge current of RFB
Ism
:
SMES coil current (Amp)
losm
•
Direct axis component o f SMES current injected at the AC bus
Igsm
•Quadrature axis component o f SMES current injected at the AC bus
Id Iq
: Direct and quadrature axis components o f synchronous machine injected
current It (p.u.)
Id, Iq
: Direct and quadrature axis components o f induction machine injected
current It (p.u.)
I d rfbj Iq rfb
• Direct and Quadrature components o f redox flow battery current (p.u.)
xvi
Ido
♦Nominal value o f SMES coil current (Amp)
Idc
‘ DC current through SMES
Ies
‘ Energy storage injected current into network (p.u.)
ia, ip
: Current components in stationary reference frame
j
: imaginary axis operator
Ka
Kd
: Gain constant of AVR Amplifier
: Proportionality constant relating torque of diesel engine with diesel fuel
consumption rate
Ke
: Gain constant of AVR exciter
Kr
: Gain constant o f AVR input filter
L
: SMES coil inductance
Lf
: Coupling reactor inductance (mh)
Lt
: Inductance per unit length o f transmission line
me
: Diesel fuel consumption rate (kg/sec)
Pbat
: Active power supplied by Redox flow battery
?c
Pdem
: Diesel governor integral controller output
• Active power demanded from energy storage unit
?E
: Active power supplied by energy storage unit
?L
: Active power component o f load
Pr
: Real power supplied by SMES unit
Q bat
: Reactive power supplied by RFB
Q dem
: Reactive power demanded by energy storage unit
Qe
: Reactive power supplied by energy storage unit
Qr
: Reactive power supplied by SMES unit
R
: Speed regulation (%)
Ri
: Contact resistance o f RFB
R2 , R3
: Domain characteristics o f RFB
Rf
: Coupling reactor resistance (Q)
Rl
: Resistance per unit length o f transmission line
Tr
: Induction machine rotor resistance
Ts
: Induction machine stator resistance
xvii
S
: Induction machine slip
s
: Laplace operator
Sa, Sb, Sc
: Switching functions (1 or 0) of VSC
Ta
• Time constant o f AVR Amplifier
Tac
• Electromagnetic torque developed by induction generator (p.u.)
Taiti
: Mechanical torque developed by synchronous machine (p.u.)
Toe
: Electromagnetic torque developed by synchronous machine (p.u.)
Tom
• Torque developed by diesel engine (p.u.)
Tdo , Tdo"
: Synchronous generator open circuit transient and subtransient time
constants o f direct axis (sec)
Te
: Time constant o f AVR Exciter (sec)
Tf
: Time constant o f AVR stabilizer (sec)
To'
Tqo"
: Induction machine rotor time constant (sec)
: Synchronous generator open circuit subtransient time constant of
quadrature axis (sec)
Tr
: Time constant o f AVR input filter (sec)
Tw
: Wash-out time constant (sec)
Vd
: Real component o f machine terminal voltage (p.u.)
Vd
: Direct axis component of machine terminal voltage (p.u.)
Vf
: Output o f AVR stabilizer
Vq
: Imaginary component o f machine terminal voltage (p.u.)
Vq
: Quadrature axis component o f machine terminal voltage (p.u.)
Vr
: Output o f AVR input filter
Vref
: Reference voltage for AVR
Vt|
: Magnitude o f machine terminal voltage (p.u.)
Va,Vp
: Voltage components in stationary reference fi-ame
X
: Induction machine open circuit reactance (p.u.)
Xc
: Reactance o f capacitor banks (p.u.)
Xd, Xq
: Synchronous generator reactance o f direct and quadrature
Xd, Xq'
: Synchronous generator transient reactance o f direct and quadrature axis
(p.u.)
xvin
axis (p.u.)
Xd", Xq*’
: Synchronous generator subtransient reactance o f direct and quadrature
axis (p.u.)
X ls
‘ Commutation Reactance, 27rfLs
Xm
: Reactance o f magnetizing branch o f induction machine
Xr
: Induction machine rotor reactance (p.u.)
Xs
: Induction machine stator reactance (p.u.)
[ Y bus]
• Bus admittance matrix
[ Ytt]
• Matrix o f driving point and transfer admittances
[ Y tt]
: Admittances matrix, obtained after elimination o f all the buses, excepting
generator energy storage and load buses.
[Z tt]
’ Matrix o f driving point and transfer impedances
T
: Governor time constant (sec)
coa
: Wind generator angular velocity (p.u.)
coo
: Nominal frequency (2nf, elect rad/sec)
6
: Electrical angle o f synchronous generator (rad)
a
: Firing angle o f converters in equal a mode
tt], 0 2
: Firing angles o f converters in unequal a mode
A
: Incremental change o f the associated variable (prefix)
Acod
: Speed deviation o f diesel unit (p.u.)
: Membership function value
XIX
( I I ) Abbreviations
AC
Alternating current
AVR
Automatic voltage regulator
CBS
Compensating capacitor banks
CC VSI
Current Controlled Voltage Source Inverter
DC
Direct current
EDLC
Electric double layer capacitor
FAM
Fuzzy associative memory
GF
Governor Free
GTO
Gate Turn Off
IEEE
The Institute of Electric and Electronics Engineers Inc
ISTEC
International Superconductivity Technology Center
IGBT
Insulated gate bipolar transistor
LFC
Load Frequency control
LN
Large negative
LP
Large positive
MN
Medium negative
MP
Medium positive
P
Proportional
PCS
Power Conversion System
Pf
Power factor
p.u.
Per unit
PI
Proportional integral
PID
Proportional integral derivative
PWM
Pulse width modulation
RFB
Redox flow battery
SEI
Sumitomo Electric Industries
SMBS
Superconducting magnetic energy storage
SN
Small negative
SOC
State o f charge
SP
Small positive
XX
SUP_MIN
Supremum-Minimum
SVC
Static var compensator
TCR
Thyristor Controlled reactor
VAR
Volt ampere reactive
VSC
Voltage source converter
WECS
Wind energy conversion system
Z
Zero
XXI