modelref

ACLine

Common Parameters: u, name

Available models: Line

Line

Group ACLine

Parameters

Name	Symbol	Description	Default	Unit	Type	Properties
u	u	connection status	1	bool	NumParam
name	name	device name			DataParam
bus1		idx of from bus			IdxParam
bus2		idx of to bus			IdxParam
Sn	Sn	Power rating	100		NumParam	non_zero
fn	f	rated frequency	60		NumParam
Vn1	Vn1	AC voltage rating	110		NumParam	non_zero
Vn2	Vn2	rated voltage of bus2	110		NumParam	non_zero
r	r	connection line resistance	0		NumParam
x	x	connection line reactance	0.000		NumParam
b		shared shunt susceptance	0		NumParam
g		shared shunt conductance	0		NumParam
b1	b1	from-side susceptance	0		NumParam
g1	g1	from-side conductance	0		NumParam
b2	b2	to-side susceptance	0		NumParam
g2	g2	to-side conductance	0		NumParam
trans		transformer branch flag	0		NumParam
tap	tap	transformer branch tap ratio	1		NumParam
phi	ϕ	transformer branch phase shift in rad	0		NumParam
owner		owner code			IdxParam
xcoord		x coordinates			DataParam
ycoord		y coordinates			DataParam

Variables

Name	Symbol	Initial Value	Description	Unit	Properties
a1	a1		phase angle of the from bus
a2	a2		phase angle of the to bus
v1	v1		voltage magnitude of the from bus
v2	v2		voltage magnitude of the to bus

Equations

Name	Symbol	Equation (x'=f or g=0)	Type
a1	a1	$u \left(- \frac{v_{1} v_{2} \left(- b_{hk} \sin{\left(\phi - a_{1} + a_{2} \right)} + g_{hk} \cos{\left(\phi - a_{1} + a_{2} \right)}\right)}{t_{ap}} + \frac{v_{1}^{2} \left(g_{h} + g_{hk}\right)}{t_{ap}^{2}}\right)$	ExtAlgeb
a2	a2	$u \left(v_{2}^{2} \left(g_{h} + g_{hk}\right) - \frac{v_{1} v_{2} \left(b_{hk} \sin{\left(\phi - a_{1} + a_{2} \right)} + g_{hk} \cos{\left(\phi - a_{1} + a_{2} \right)}\right)}{t_{ap}}\right)$	ExtAlgeb
v1	v1	$u \left(- \frac{v_{1} v_{2} \left(- b_{hk} \cos{\left(\phi - a_{1} + a_{2} \right)} - g_{hk} \sin{\left(\phi - a_{1} + a_{2} \right)}\right)}{t_{ap}} - \frac{v_{1}^{2} \left(b_{h} + b_{hk}\right)}{t_{ap}^{2}}\right)$	ExtAlgeb
v2	v2	$u \left(- v_{2}^{2} \left(b_{h} + b_{hk}\right) + \frac{v_{1} v_{2} \left(b_{hk} \cos{\left(\phi - a_{1} + a_{2} \right)} - g_{hk} \sin{\left(\phi - a_{1} + a_{2} \right)}\right)}{t_{ap}}\right)$	ExtAlgeb

Services

Name	Symbol	Equation	Type
gh	gh	0.5g + g1	ConstService
bh	bh	0.5b + b1	ConstService
gk	gk	0.5g + g2	ConstService
bk	bk	0.5b + b2	ConstService
yh	yh	u(ibh+gh)	ConstService
yk	yk	u(ibk+gk)	ConstService
yhk	yhk	$\frac{u}{r + i x}$	ConstService
ghk	ghk	re (yhk)	ConstService
bhk	bhk	im (yhk)	ConstService

ACTopology

Common Parameters: u, name

Common Variables: a, v

Available models: Bus

Bus

Group ACTopology

AC Bus model developed using the symbolic framework Parameters

Name	Symbol	Description	Default	Unit	Type	Properties
u	u	connection status	1	bool	NumParam
name	name	device name			DataParam
Vn	Vn	AC voltage rating	110	kV	NumParam	non_zero
vmax	Vmax	Voltage upper limit	1.100	p.u.	NumParam
vmin	Vmin	Voltage lower limit	0.900	p.u.	NumParam
v0	V0	initial voltage magnitude	1	p.u.	NumParam	non_zero
a0	θ0	initial voltage phase angle	0	rad	NumParam
xcoord		x coordinate (longitude)	0		DataParam
ycoord		y coordinate (latitude)	0		DataParam
area		Area code			IdxParam
zone		Zone code			IdxParam
owner		Owner code			IdxParam

Variables

Name	Symbol	Initial Value	Description	Unit	Properties
a	θ	θ0(1−flatstart) + 1.0 ⋅ 10 − 8flatstart	voltage angle	rad	v_str
v	V	V0(1−flatstart) + flatstart	voltage magnitude	p.u.	v_str

Equations

Name	Symbol	Equation (x'=f or g=0)	Type
a	θ	0	Algeb
v	V	0	Algeb

Exciter

Exciter group for synchronous generators.

Common Parameters: u, name

Common Variables: vout

Available models: EXDC2

EXDC2

Group Exciter

EXDC2 model. Parameters

Name	Symbol	Description	Default	Unit	Type	Properties
u	u	connection status	1	bool	NumParam
name	name	device name			DataParam
syn		Synchronous generator idx			IdxParam	mandatory
TR	TR	Sensing time constant	1	p.u.	NumParam
TA	TA	Lag time constant in anti-windup lag	0.040	p.u.	NumParam
TC	TC	Lead time constant in lead-lag	1	p.u.	NumParam
TB	TB	Lag time constant in lead-lag	1	p.u.	NumParam
TE	TE	Exciter integrator time constant	0.800	p.u.	NumParam
TF1	TF1	Feedback washout time constant	1	p.u.	NumParam	non_zero
KF1	KF1	Feedback washout gain	0.030	p.u.	NumParam
KA	KA	Gain in anti-windup lag TF	40	p.u.	NumParam
KE	KE	Gain added to saturation	1	p.u.	NumParam
VRMAX	VRMAX	Maximum excitation limit	7.300	p.u.	NumParam
VRMIN	VRMIN	Minimum excitation limit	-7.300	p.u.	NumParam
E1	E1	First saturation point	0	p.u.	NumParam
SE1	SE1	Value at first saturation point	0	p.u.	NumParam
E2	E2	Second saturation point	0	p.u.	NumParam
SE2	SE2	Value at second saturation point	0	p.u.	NumParam
Ae	Ae	Gain in saturation	0	p.u.	NumParam
Be	Be	Exponential coefficient in saturation	0	p.u.	NumParam
Sn	Sm	Rated power from generator		MVA	ExtParam
Vn	Vm	Rated voltage from generator		kV	ExtParam
bus	bus	Bus idx of the generators			ExtParam

Variables

Name	Symbol	Initial Value	Description	Unit	Properties
vp	Vp	vf0	Voltage after saturation feedback, before speed term	p.u.	v_str
LS_x	x′LS	1.0V	State in lag transfer function		v_str
LL_x	x′LL	Vi	State in lead-lag transfer function		v_str
LA_x	x′LA	KAyLL	State in lag transfer function		v_str
W_x	x′W	Vp	State in washout filter		v_str
omega	ω		Generator speed
vout	vout	vf0	Exciter final output voltage		v_str
Se	Se	Se0	Saturation output	p.u.	v_str
vref	Vref	Vref0	Reference voltage input	p.u.	v_str
vi	Vi	Vb0	Total input voltages	p.u.	v_str
LL_y	yLL	Vi	Output of lead-lag transfer function		v_str
W_y	yW	0	Output of washout filter		v_str
vf	vf		Excitation field voltage to generator
a	θ		Bus voltage phase angle
v	V		Bus voltage magnitude

Equations

Name	Symbol	Equation (x'=f or g=0)	Type
vp	Vp	$\frac{- K_{E} V_{p} - S_{e} V_{p} + x'_{LA}}{T_{E}}$	State
LS_x	x′LS	$\frac{1.0 V - x'_{LS}}{T_{R}}$	State
LL_x	x′LL	$\frac{V_{i} - x'_{LL}}{T_{B}}$	State
LA_x	x′LA	$\frac{LA_{lim zi} \left(K_{A} y_{LL} - x'_{LA}\right)}{T_{A}}$	State
W_x	x′W	$\frac{V_{p} - x'_{W}}{T_{F1}}$	State
omega	ω	0	ExtState
vout	vout	Vpω − vout	Algeb
Se	Se	AeeBevout − Se	Algeb
vref	Vref	Vref0 − Vref	Algeb
vi	Vi	− Vi + Vref − x′LS − yW	Algeb
LL_y	yLL	$x'_{LL} - y_{LL} + \frac{T_{C} \left(V_{i} - x'_{LL}\right)}{T_{B}}$	Algeb
W_y	yW	(KF1/TF1)W(Vp−x′W) − yW	Algeb
vf	vf	u(−vf0+vout)	ExtAlgeb
a	θ	0	ExtAlgeb
v	V	0	ExtAlgeb

Services

Name	Symbol	Equation	Type
Se0	Se0	AeeBevf0	ConstService
vr0	Vr0	vf0(KE+Se0)	ConstService
vb0	Vb0	$\frac{V_{r0}}{K_{A}}$	ConstService
vref0	Vref0	V + Vb0	ConstService
W_KT	(KF1/TF1)W	$\frac{K_{F1}}{T_{F1}}$	ConstService

Discrete

Name	Symbol	Type
LA_lim	limLA	AntiWindupLimiter

StaticGen

Static generator group for power flow calculation

Common Parameters: u, name, p0, q0

Common Variables: p, q, a, v

Available models: PV, Slack

PV

Group StaticGen

Parameters

Name	Symbol	Description	Default	Unit	Type	Properties
u	u	connection status	1	bool	NumParam
name	name	device name			DataParam
Sn	Sn	Power rating	100		NumParam	non_zero
Vn	Vn	AC voltage rating	110		NumParam	non_zero
bus		the idx of the installed bus			IdxParam
busr		the idx of remotely controlled bus			IdxParam
p0	p0	active power set point in system base	0	p.u.	NumParam
q0	q0	reactive power set point in system base	0	p.u.	NumParam
pmax	pmax	maximum active power in system base	999	p.u.	NumParam
pmin	pmin	minimum active power in system base	-1	p.u.	NumParam
qmax	qmax	maximim reactive power in system base	999	p.u.	NumParam
qmin	qmin	minimum reactive power in system base	-999	p.u.	NumParam
v0	v0	voltage set point	1		NumParam
vmax	vmax	maximum voltage voltage	1.400		NumParam
vmin	vmin	minimum allowed voltage	0.600		NumParam
ra	ra	armature resistance	0.010		NumParam
xs	xs	armature reactance	0.300		NumParam

Variables

Name	Symbol	Initial Value	Description	Unit	Properties
p	p	p0	actual active power generation	p.u.	v_str
q	q	q0	actual reactive power generation	p.u.	v_str
a	θ
v	V	v0			v_str,v_setter

Equations

Name	Symbol	Equation (x'=f or g=0)	Type
p	p	u(−p+p0)	Algeb
q	q	u(ziqlim(−V+v0)+zlqlim(−q+qmin)+zuqlim(−q+qmax))	Algeb
a	θ	− pu	ExtAlgeb
v	V	− qu	ExtAlgeb

Discrete

Name	Symbol	Type
qlim	qlim	SortedLimiter

Slack

Group StaticGen

Parameters

Name	Symbol	Description	Default	Unit	Type	Properties
u	u	connection status	1	bool	NumParam
name	name	device name			DataParam
Sn	Sn	Power rating	100		NumParam	non_zero
Vn	Vn	AC voltage rating	110		NumParam	non_zero
bus		the idx of the installed bus			IdxParam
busr		the idx of remotely controlled bus			IdxParam
p0	p0	active power set point in system base	0	p.u.	NumParam
q0	q0	reactive power set point in system base	0	p.u.	NumParam
pmax	pmax	maximum active power in system base	999	p.u.	NumParam
pmin	pmin	minimum active power in system base	-1	p.u.	NumParam
qmax	qmax	maximim reactive power in system base	999	p.u.	NumParam
qmin	qmin	minimum reactive power in system base	-999	p.u.	NumParam
v0	v0	voltage set point	1		NumParam
vmax	vmax	maximum voltage voltage	1.400		NumParam
vmin	vmin	minimum allowed voltage	0.600		NumParam
ra	ra	armature resistance	0.010		NumParam
xs	xs	armature reactance	0.300		NumParam
a0	θ0	reference angle set point	0		NumParam

Variables

Name	Symbol	Initial Value	Description	Unit	Properties
p	p	p0	actual active power generation	p.u.	v_str
q	q	q0	actual reactive power generation	p.u.	v_str
a	θ	θ0			v_str,v_setter
v	V	v0			v_str,v_setter

Equations

Name	Symbol	Equation (x'=f or g=0)	Type
p	p	u(ziplim(−θ+θ0)+zlplim(−p+pmin)+zuplim(−p+pmax))	Algeb
q	q	u(ziqlim(−V+v0)+zlqlim(−q+qmin)+zuqlim(−q+qmax))	Algeb
a	θ	− pu	ExtAlgeb
v	V	− qu	ExtAlgeb

Discrete

Name	Symbol	Type
qlim	qlim	SortedLimiter
plim	plim	SortedLimiter

StaticLoad

Static load group.

Common Parameters: u, name

Available models: PQ

PQ

Group StaticLoad

Parameters

Name	Symbol	Description	Default	Unit	Type	Properties
u	u	connection status	1	bool	NumParam
name	name	device name			DataParam
bus		linked bus idx			IdxParam	mandatory
Vn	Vn	AC voltage rating	110	kV	NumParam	non_zero
p0	p0	active power load in system base	0	p.u.	NumParam
q0	q0	reactive power load in system base	0	p.u.	NumParam
vmax	vmax	max voltage before switching to impedance	1.100		NumParam
vmin	vmin	min voltage before switching to impedance	0.900		NumParam
owner		owner idx			IdxParam

Variables

Name	Symbol	Initial Value	Description	Unit	Properties
a	θ
v	V

Equations

Name	Symbol	Equation (x'=f or g=0)	Type
a	θ	$u \left(Req V^{2} p2z + p2p p_{0}\right) \left(t_{dae} > 0\right) + u \left(\frac{V^{2} p_{0} z_{l}^{vcmp}}{v_{min}^{2}} + \frac{V^{2} p_{0} z_{u}^{vcmp}}{v_{max}^{2}} + p_{0} z_{i}^{vcmp}\right) \left(t_{dae} \leq 0\right)$	ExtAlgeb
v	V	$u \left(V^{2} Xeq q2z + q2q q_{0}\right) \left(t_{dae} > 0\right) + u \left(\frac{V^{2} q_{0} z_{l}^{vcmp}}{v_{min}^{2}} + \frac{V^{2} q_{0} z_{u}^{vcmp}}{v_{max}^{2}} + q_{0} z_{i}^{vcmp}\right) \left(t_{dae} \leq 0\right)$	ExtAlgeb

Services

Name	Symbol	Equation	Type
Req	Req	$\frac{p_{0}}{V_{0}^{2}}$	ConstService
Xeq	Xeq	$\frac{q_{0}}{V_{0}^{2}}$	ConstService

Discrete

Name	Symbol	Type
vcmp	vcmp	Limiter

StaticShunt

Static shunt compensator group.

Common Parameters: u, name

Available models: Shunt

Shunt

Group StaticShunt

Parameters

Name	Symbol	Description	Default	Unit	Type	Properties
u	u	connection status	1	bool	NumParam
name	name	device name			DataParam
bus		idx of connected bus			IdxParam
Sn	Sn	Power rating	100		NumParam	non_zero
Vn	Vn	AC voltage rating	110		NumParam	non_zero
g	g	shunt conductance (real part)	0		NumParam	y
b	b	shunt susceptance (positive as capatance)	0		NumParam	y
fn	f	rated frequency	60		NumParam

Variables

Name	Symbol	Initial Value	Description	Unit	Properties
a	θ
v	V

Equations

Name	Symbol	Equation (x'=f or g=0)	Type
a	θ	V2g	ExtAlgeb
v	V	− V2b	ExtAlgeb

SynGen

Synchronous generator group.

Common Parameters: u, name, Sn, Vn, fn, bus

Common Variables: omega, delta, tm, vf

Available models: GENCLS, GENROU

GENCLS

Group SynGen

Parameters

Name	Symbol	Description	Default	Unit	Type	Properties
u	u	connection status	1	bool	NumParam
name	name	device name			DataParam
bus		interface bus id			IdxParam	mandatory
gen		static generator index			IdxParam	mandatory
coi		center of inertia index			IdxParam
Sn	Sn	Power rating	100		NumParam
Vn	Vn	AC voltage rating	110		NumParam
fn	f	rated frequency	60		NumParam
D	D	Damping coefficient	0		NumParam	power
M	M	machine start up time (2H)	6		NumParam	non_zero,power
ra	ra	armature resistance	0		NumParam	z
xl	xl	leakage reactance	0		NumParam	z
xq	xq	q-axis synchronous reactance	1.700		NumParam	z
kp	kp	active power feedback gain	0		NumParam
kw	kw	speed feedback gain	0		NumParam
S10	S1.0	first saturation factor	0		NumParam
S12	S1.2	second saturation factor	1		NumParam	non_zero

Variables

Name	Symbol	Initial Value	Description	Unit	Properties
delta	δ	δ0			v_str
omega	ω	u			v_str
Id	Id	Id0			v_str
Iq	Iq	Iq0			v_str
vd	Vd	Vd0			v_str
vq	Vq	Vq0			v_str
tm	τm	τm0	mechanical torque		v_str,v_setter
te	τe	P0	electric torque		v_str,v_setter
vf	vf	vf0			v_str,v_setter
psid	ψd	ψd0			v_str
psiq	ψq	ψq0			v_str
a	θ		Bus voltage phase angle
v	V		Bus voltage magnitude

Equations

Name	Symbol	Equation (x'=f or g=0)	Type
delta	δ	2πfu(ω−1)	State
omega	ω	$\frac{u \left(- D \left(\omega - 1\right) - \tau_e + \tau_m\right)}{M}$	State
Id	Id	Idxq + ψd − vf	Algeb
Iq	Iq	Iqxq + ψq	Algeb
vd	Vd	Vsin (δ−θ) − Vd	Algeb
vq	Vq	Vcos (δ−θ) − Vq	Algeb
tm	τm	− τm + τm0	Algeb
te	τe	− Idψq + Iqψd − τe	Algeb
vf	vf	− vf + vf0	Algeb
psid	ψd	− ψd + u(Iqra+Vq)	Algeb
psiq	ψq	ψq + u(Idra+Vd)	Algeb
a	θ	− u(IdVd+IqVq)	ExtAlgeb
v	V	− u(IdVq−IqVd)	ExtAlgeb

Services

Name	Symbol	Equation	Type
_V	Vc	Veiθ	ConstService
_S	S	P0 − iQ0	ConstService
_I	Ic	$\frac{S}{\operatorname{conj}{\left(V_{c} \right)}}$	ConstService
_E	E	Ic(ra+ixq) + Vc	ConstService
_deltac	δc	$\log{\left(\frac{E}{\operatorname{abs}{\left(E \right)}} \right)}$	ConstService
delta0	δ0	uim (δc)	ConstService
vdq	Vdq	Vcue − δc + 0.5iπ	ConstService
Idq	Idq	Icue − δc + 0.5iπ	ConstService
Id0	Id0	re (Idq)	ConstService
Iq0	Iq0	im (Idq)	ConstService
vd0	Vd0	re (Vdq)	ConstService
vq0	Vq0	im (Vdq)	ConstService
tm0	τm0	u(Id0(Id0ra+Vd0)+Iq0(Iq0ra+Vq0))	ConstService
psid0	ψd0	Iq0rau + Vq0	ConstService
psiq0	ψq0	− Id0rau − Vd0	ConstService
vf0	vf0	Id0xq + Iq0ra + Vq0	ConstService

GENROU

Group SynGen

Parameters

Name	Symbol	Description	Default	Unit	Type	Properties
u	u	connection status	1	bool	NumParam
name	name	device name			DataParam
bus		interface bus id			IdxParam	mandatory
gen		static generator index			IdxParam	mandatory
coi		center of inertia index			IdxParam
Sn	Sn	Power rating	100		NumParam
Vn	Vn	AC voltage rating	110		NumParam
fn	f	rated frequency	60		NumParam
D	D	Damping coefficient	0		NumParam	power
M	M	machine start up time (2H)	6		NumParam	non_zero,power
ra	ra	armature resistance	0		NumParam	z
xl	xl	leakage reactance	0		NumParam	z
xq	xq	q-axis synchronous reactance	1.700		NumParam	z
kp	kp	active power feedback gain	0		NumParam
kw	kw	speed feedback gain	0		NumParam
S10	S1.0	first saturation factor	0		NumParam
S12	S1.2	second saturation factor	1		NumParam	non_zero
xd	xd	d-axis synchronous reactance	1.900		NumParam	z
xd1	x′d	d-axis transient reactance	0.302		NumParam	z
xd2	x′′d	d-axis sub-transient reactance	0.204		NumParam	z
xq1	x′q	q-axis transient reactance	0.500		NumParam	z
xq2	x′′q	q-axis sub-transient reactance	0.300		NumParam	z
Td10	T′d0	d-axis transient time constant	8		NumParam
Td20	T′′d0	d-axis sub-transient time constant	0.040		NumParam
Tq10	T′q0	q-axis transient time constant	0.800		NumParam
Tq20	T′′q0	q-axis sub-transient time constant	0.020		NumParam

Variables

Name	Symbol	Initial Value	Description	Unit	Properties
delta	δ	δ0			v_str
omega	ω	u			v_str
e1q	e′q	e′q0			v_str
e1d	e′d	e′d0			v_str
e2d	e″d	e″d0			v_str
e2q	e″q	e″q0			v_str
Id	Id	Id0			v_str
Iq	Iq	Iq0			v_str
vd	Vd	Vd0			v_str
vq	Vq	Vq0			v_str
tm	τm	τm0	mechanical torque		v_str,v_setter
te	τe	P0	electric torque		v_str,v_setter
vf	vf	vf0			v_str,v_setter
psid	ψd	ψd0			v_str
psiq	ψq	ψq0			v_str
psiaq	ψaq	ψaq0	q-axis air gap flux		v_str
psiad	ψad	ψad0	d-axis air gap flux		v_str
psia	ψa	abs (ψa0, dq)	air gap flux magnitude		v_str
Se	Se(|ψa|)	Se0	saturation output		v_str
a	θ		Bus voltage phase angle
v	V		Bus voltage magnitude

Equations

Name	Symbol	Equation (x'=f or g=0)	Type
delta	δ	2πfu(ω−1)	State
omega	ω	$\frac{u \left(- D \left(\omega - 1\right) - \tau_e + \tau_m\right)}{M}$	State
e1q	e′q	$\frac{- S_e(|\psi_{a}|) \psi_{ad} - e'_{q} + v_{f} - \left(- x \prime_d + x_{d}\right) \left(- I_{d} \left(1 - \gamma_{d1}\right) + I_{d} - \gamma_{d2} e''_{d} + \gamma_{d2} e'_{q}\right)}{T \prime_{d0}}$	State
e1d	e′d	$\frac{S_e(|\psi_{a}|) \gamma_{qd} \psi_{aq} - e'_{d} + \left(- x \prime_q + x_{q}\right) \left(- I_{q} \left(1 - \gamma_{q1}\right) + I_{q} - \gamma_{q2} e''_{q} - \gamma_{q2} e'_{d}\right)}{T \prime_{q0}}$	State
e2d	e″d	$\frac{- I_{d} \left(x \prime_d - x_{l}\right) - e''_{d} + e'_{q}}{T \prime \prime_{d0}}$	State
e2q	e″q	$\frac{- I_{q} \left(x \prime_q - x_{l}\right) - e''_{q} - e'_{d}}{T \prime \prime_{q0}}$	State
Id	Id	Idx′′d − γd1e′q + ψd − e″d(1−γd1)	Algeb
Iq	Iq	Iqx′′q + γq1e′d + ψq − e″q(1−γq1)	Algeb
vd	Vd	Vsin (δ−θ) − Vd	Algeb
vq	Vq	Vcos (δ−θ) − Vq	Algeb
tm	τm	− τm + τm0	Algeb
te	τe	− Idψq + Iqψd − τe	Algeb
vf	vf	− vf + vf0	Algeb
psid	ψd	− ψd + u(Iqra+Vq)	Algeb
psiq	ψq	ψq + u(Idra+Vd)	Algeb
psiaq	ψaq	Iqx′′q + ψq − ψaq	Algeb
psiad	ψad	γd1e′q + γd2e″d(x′d−xl) − ψad	Algeb
psia	ψa	$- \psi_{a} + \sqrt{\psi_{ad}^{2} + \psi_{aq}^{2}}$	Algeb
Se	Se(|ψa|)	$\frac{S_{B} z_{0}^{Slt} \left(- S_{A} + \psi_{a}\right)^{2}}{\psi_{a}} - S_e(|\psi_{a}|)$	Algeb
a	θ	− u(IdVd+IqVq)	ExtAlgeb
v	V	− u(IdVq−IqVd)	ExtAlgeb

Services

Name	Symbol	Equation	Type
gd1	γd1	$\frac{x \prime \prime_d - x_{l}}{x \prime_d - x_{l}}$	ConstService
gq1	γq1	$\frac{x \prime \prime_q - x_{l}}{x \prime_q - x_{l}}$	ConstService
gd2	γd2	$\frac{- x \prime \prime_d + x \prime_d}{\left(x \prime_d - x_{l}\right)^{2}}$	ConstService
gq2	γq2	$\frac{- x \prime \prime_q + x \prime_q}{\left(x \prime_q - x_{l}\right)^{2}}$	ConstService
gqd	γqd	$\frac{- x_{l} + x_{q}}{x_{d} - x_{l}}$	ConstService
Sa	Sa	$0.912870929175277 \sqrt{\frac{S_{1.0}}{S_{1.2}}}$	ConstService
SA	SA	$1.2 + \frac{0.2}{S_{a} - 1}$	ConstService
SB	SB	30.0S1.2(Sa−1)2((Sa>0)+(Sa<0))	ConstService
_V	Vc	Veiθ	ConstService
_S	S	P0 − iQ0	ConstService
_Zs	Zs	ra + ix′′d	ConstService
_It	It	$\frac{S}{\operatorname{conj}{\left(V_{c} \right)}}$	ConstService
_Is	Is	$I_{t} + \frac{V_{c}}{Z_{s}}$	ConstService
psia0	ψa0	IsZs	ConstService
psia0_arg	θψa0	arg (ψa0)	ConstService
psia0_abs	|ψa0|	abs (ψa0)	ConstService
_It_arg	θIt0	arg (It)	ConstService
_psia0_It_arg	θψaIt	− θIt0 + θψa0	ConstService
Se0	Se0	$\frac{S_{B} \left(- S_{A} + |\psi_{a0}|\right)^{2} \left(|\psi_{a0}| \geq S_{A}\right)}{|\psi_{a0}|}$	ConstService
_a	a	Se0γqd|ψa0| + |ψa0|	ConstService
_b	b	(x′′q−xq)abs (It)	ConstService
delta0	δ0	$\theta_{\psi a0} + \operatorname{atan}{\left(\frac{b \cos{\left(\theta_{\psi a It} \right)}}{- \theta + b \sin{\left(\theta_{\psi a It} \right)}} \right)}$	ConstService
_Tdq	Tdq	− isin (δ0) + cos (δ0)	ConstService
psia0_dq	ψa0, dq	Tdqψa0	ConstService
It_dq	It, dq	conj (ItTdq)	ConstService
psiad0	ψad0	re (ψa0, dq)	ConstService
psiaq0	ψaq0	im (ψa0, dq)	ConstService
Id0	Id0	im (It, dq)	ConstService
Iq0	Iq0	re (It, dq)	ConstService
vd0	Vd0	− Id0ra + Iq0x′′q − ψaq0	ConstService
vq0	Vq0	− Id0x′′d − Iq0ra + ψad0	ConstService
tm0	τm0	u(Id0(Id0ra+Vd0)+Iq0(Iq0ra+Vq0))	ConstService
vf0	vf0	Id0(−x′′d+x′d) + Id0(−x′d+xd) + Se0ψad0 + ψad0	ConstService
psid0	ψd0	Iq0rau + Vq0	ConstService
psiq0	ψq0	− Id0rau − Vd0	ConstService
e1q0	e′q0	Id0γd1(x′d−xd) − Id0γd2(−x′d+xd)(x′d−xl) − Se0ψad0 + vf0	ConstService
e1d0	e′d0	Iq0γq1(−x′q+xq) + Iq0γq2x′q(−x′q+xq) + Iq0γq2xl(x′q−xq) + Se0γqdψaq0	ConstService
e2d0	e″d0	Id0γd1(x′d−xd) − Id0(x′d−xl)(−γd2x′d+γd2xd+1) − Se0ψad0 + vf0	ConstService
e2q0	e″q0	Iq0γq1(x′q−xq) + Iq0γq2x′q(x′q−xq) + Iq0γq2xl(−x′q+xq) − Iq0x′q + Iq0xl − Se0γqdψaq0	ConstService

Discrete

Name	Symbol	Type
Slt	Slt	LessThan

TurbineGov

Turbine governor group for synchronous generator.

Common Parameters: u, name

Common Variables: pout

Available models: TG2, TGOV1

TG2

Group TurbineGov

Parameters

Name	Symbol	Description	Default	Unit	Type	Properties
u	u	connection status	1	bool	NumParam
name	name	device name			DataParam
syn		Synchronous generator idx			IdxParam	mandatory
R	R	Speed regulation gain under machine base	0.050	p.u.	NumParam	ipower
wref0	ωref0	Base speed reference	1	p.u.	NumParam
pmax	pmax	Maximum power output	999	p.u.	NumParam	power
pmin	pmin	Minimum power output	0	p.u.	NumParam	power
dbl	Ldb	Deadband lower limit	-0.000	p.u.	NumParam
dbu	Udb	Deadband upper limit	0.000	p.u.	NumParam
dbc	Cdb	Deadband neutral value	0	p.u.	NumParam
T1	T1	Transient gain time	0.200		NumParam
T2	T2	Governor time constant	10		NumParam
Sn	Sm	Rated power from generator		MVA	ExtParam
Vn	Vm	Rated voltage from generator		kV	ExtParam

Variables

Name	Symbol	Initial Value	Description	Unit	Properties
ll_x	x′ll	ωdmG	State in lead-lag transfer function		v_str
omega	ω		Generator speed	p.u.
pout	Pout	τm0	Turbine final output power		v_str
wref	ωref	ωref0	Speed reference variable		v_str
w_d	ωdev	0	Generator speed deviation before dead band (positive for under speed)		v_str
w_dm	ωdm	0	Measured speed deviation after dead band		v_str
w_dmg	ωdmG	0	Speed deviation after dead band after gain		v_str
ll_y	yll	ωdmG	Output of lead-lag transfer function		v_str
pnl	Pnl	τm0	Power output before hard limiter		v_str
tm	τm		Mechanical power to generator

Equations

Name	Symbol	Equation (x'=f or g=0)	Type
ll_x	x′ll	$\frac{\omega_{dmG} - x'_{ll}}{T_{2}}$	State
omega	ω	0	ExtState
pout	Pout	Pnlziplim − Pout + pmaxzuplim + pminzlplim	Algeb
wref	ωref	ωref0 − ωref	Algeb
w_d	ωdev	− ω − ωdev + ωref	Algeb
w_dm	ωdm	Ldbzlrwdb + Udbzurwdb + ωdev(1−ziwdb) − ωdm	Algeb
w_dmg	ωdmG	Gωdm − ωdmG	Algeb
ll_y	yll	$\frac{T_{1} \left(\omega_{dmG} - x'_{ll}\right)}{T_{2}} + x'_{ll} - y_{ll}$	Algeb
pnl	Pnl	− Pnl + τm0 + yll	Algeb
tm	τm	u(Pout−τm0)	ExtAlgeb

Services

Name	Symbol	Equation	Type
gain	G	$\frac{u}{R}$	ConstService

Discrete

Name	Symbol	Type
w_db	wdb	DeadBand
plim	plim	HardLimiter

TGOV1

Group TurbineGov

TGOV1 model. Parameters

Name	Symbol	Description	Default	Unit	Type	Properties
u	u	connection status	1	bool	NumParam
name	name	device name			DataParam
syn		Synchronous generator idx			IdxParam	mandatory
R	R	Speed regulation gain under machine base	0.050	p.u.	NumParam	ipower
wref0	ωref0	Base speed reference	1	p.u.	NumParam
VMAX	Vmax	Maximum valve position	1.200	p.u.	NumParam	power
VMIN	Vmin	Minimum valve position	0	p.u.	NumParam	power
T1	T1	Valve time constant	0.100		NumParam
T2	T2	Lead-lag lead time constant	0.200		NumParam
T3	T3	Lead-lag lag time constant	10		NumParam
Dt	Dt	Turbine damping coefficient	0		NumParam	power
Sn	Sm	Rated power from generator		MVA	ExtParam
Vn	Vm	Rated voltage from generator		kV	ExtParam

Variables

Name	Symbol	Initial Value	Description	Unit	Properties
LAG_x	x′LAG	Pd	State in lag transfer function		v_str
LL_x	x′LL	x′LAG	State in lead-lag transfer function		v_str
omega	ω		Generator speed	p.u.
pout	Pout	τm0	Turbine final output power		v_str
wref	ωref	ωref0	Speed reference variable		v_str
pref	Pref	Rτm0	Reference power input		v_str
wd	ωdev	0	Generator under speed	p.u.	v_str
pd	Pd	τm0	Pref plus under speed times gain	p.u.	v_str
LL_y	yLL	x′LAG	Lead-lag Output		v_str
tm	τm		Mechanical power to generator

Equations

Name	Symbol	Equation (x'=f or g=0)	Type
LAG_x	x′LAG	$\frac{LAG_{lim zi} \left(P_{d} - x'_{LAG}\right)}{T_{1}}$	State
LL_x	x′LL	$\frac{x'_{LAG} - x'_{LL}}{T_{3}}$	State
omega	ω	0	ExtState
pout	Pout	Dtωdev − Pout + yLL	Algeb
wref	ωref	ωref0 − ωref	Algeb
pref	Pref	− Pref + Rτm0	Algeb
wd	ωdev	− ω − ωdev + ωref	Algeb
pd	Pd	G(Pref+ωdev) − Pd	Algeb
LL_y	yLL	$\frac{T_{2} \left(x'_{LAG} - x'_{LL}\right)}{T_{3}} + x'_{LL} - y_{LL}$	Algeb
tm	τm	u(Pout−τm0)	ExtAlgeb

Services

Name	Symbol	Equation	Type
gain	G	$\frac{u}{R}$	ConstService

Discrete

Name	Symbol	Type
LAG_lim	limlag	AntiWindupLimiter

Undefined

Common Parameters: u, name

Available models: Area, Toggler, PI2

Area

Group Undefined

Parameters

Name	Symbol	Description	Default	Unit	Type	Properties
u	u	connection status	1	bool	NumParam
name	name	device name			DataParam
Bus					RefParam
ACTopology					RefParam
Vn					ExtParam

Variables

Name	Symbol	Initial Value	Description	Unit	Properties
a	a
v	v

Equations

Name	Symbol	Equation (x'=f or g=0)	Type
a	a	0	ExtAlgeb
v	v	0	ExtAlgeb

Toggler

Group Undefined

Parameters

Name	Symbol	Description	Default	Unit	Type	Properties
u	u	connection status	1	bool	NumParam
name	name	device name			DataParam
model		Model or Group of the device with this timer			DataParam	mandatory
dev		Idx of the device with this timer			IdxParam	mandatory
t		switch time for connection status	-1		TimerParam	mandatory

PI2

Group Undefined

Parameters

Name	Symbol	Description	Default	Unit	Type	Properties
u	u	connection status	1	bool	NumParam
name	name	device name			DataParam
Kp					NumParam
Ki					NumParam
Wmax					NumParam
Wmin					NumParam

Variables

Name	Symbol	Initial Value	Description	Unit	Properties
uin	uin	0			v_str
x	x	0.05			v_str
y	y	0.05			v_str
w	w	0.05			v_str

Equations

Name	Symbol	Equation (x'=f or g=0)	Type
uin	uin	$\begin{cases} 0 & \text{for}\: t_{dae} \leq 0 \\1 & \text{for}\: t_{dae} \leq 2 \\-1 & \text{for}\: t_{dae} < 6 \\1 & \text{otherwise} \end{cases}$	State
x	x	KiuinziHL	State
y	y	Kpuin + x − y	Algeb
w	w	WmaxzuHL + WminzlHL − w + yziHL	Algeb

Discrete

Name	Symbol	Type
HL	HL	HardLimiter