DCED

Type for DC-based economic dispatch.

Common Parameters: c2, c1, c0, pmax, pmin, pd, ptdf, rate_a

Common Vars: pg

Common Constraints: pb, lub, llb

Available routines: DCOPF, DCOPF2, ED, EDDG, EDES, RTED, RTEDDG, RTEDES, RTEDVIS

DCOPF

DC optimal power flow (DCOPF).

Notes

1. The nodal price is calculated as pi in pic.

2. Devices online status of StaticGen, StaticLoad, and Shunt are considered in the connectivity matrices Cft, Cg, Cl, and Csh.

References

1. R. D. Zimmerman, C. E. Murillo-Sanchez, and R. J. Thomas, “MATPOWER: Steady-State Operations, Planning, and Analysis Tools for Power Systems Research and Education,” IEEE Trans. Power Syst., vol. 26, no. 1, pp. 12-19, Feb. 2011

Objective

Unit	Expression
$	\(min. \sum(c_{2} p_g^{2})+ \sum(c_{1} p_g)+ \sum(u_{g} c_{0})\)

Expressions

Name	Description	Expression	Unit	Source
plf	Line flow	\(B_{f} \theta_{bus} + P_{f}^{inj}\)	p.u.	Line
pmaxe	Effective pmax	\(c_{trl,n,e} p_{g, 0} + c_{trl, e} p_{g, max}\)	p.u.	StaticGen
pmine	Effective pmin	\(c_{trl,n,e} p_{g, 0} + c_{trl, e} p_{g, min}\)	p.u.	StaticGen

Constraints

Name	Description	Expression
pb	power balance	\(B_{bus} \theta_{bus} + P_{bus}^{inj} + C_{l} p_{d} + C_{sh} g_{sh} - C_{g} p_g = 0\)
sbus	align slack bus angle	\(c_{sb} \theta_{bus} = 0\)
pglb	pg min	\(-p_g + p_{g, min, e} \leq 0\)
pgub	pg max	\(p_g - p_{g, max, e} \leq 0\)
plflb	line flow lower bound	\(-p_{lf} - u_{l} R_{ATEA} \leq 0\)
plfub	line flow upper bound	\(p_{lf} - u_{l} R_{ATEA} \leq 0\)
alflb	line angle difference lower bound	\(-C_{ft}^T \theta_{bus} + \theta_{bus, min} \leq 0\)
alfub	line angle difference upper bound	\(C_{ft}^T \theta_{bus} - \theta_{bus, max} \leq 0\)

Vars

Name	Symbol	Description	Unit	Source	Properties
pg	\(p_g\)	Gen active power	p.u.	StaticGen.p
vBus	\(v_{Bus}\)	Bus voltage magnitude, placeholder	p.u.	Bus.v
aBus	\(\theta_{bus}\)	Bus voltage angle	rad	Bus.a

ExpressionCalcs

Name	Description	Expression	Unit	Source
pi	LMP, dual of <pb>	\(\phi[pb]\)	$/p.u.	Bus

Services

Name	Symbol	Description	Type
csb	\(c_{sb}\)	select slack bus	VarSelect
ctrle	\(c_{trl, e}\)	Effective Gen controllability	NumOpDual
nctrl	\(c_{trl,n}\)	Effective Gen uncontrollability	NumOp
nctrle	\(c_{trl,n,e}\)	Effective Gen uncontrollability	NumOpDual

Parameters

Name	Symbol	Description	Unit	Source
ug	\(u_{g}\)	Gen connection status		StaticGen.u
pg0	\(p_{g, 0}\)	Gen initial active power	p.u.	StaticGen.p0
gsh	\(g_{sh}\)	shunt conductance		Shunt.g
buss	\(B_{us,s}\)	Bus slack		Slack.bus
pd	\(p_{d}\)	active demand	p.u.	StaticLoad.p0
Cg	\(C_{g}\)	Gen connection matrix		MatProcessor.Cg
Cl	\(C_{l}\)	Load connection matrix		MatProcessor.Cl
CftT	\(C_{ft}^T\)	Transpose of line connection matrix		MatProcessor.CftT
Csh	\(C_{sh}\)	Shunt connection matrix		MatProcessor.Csh
Bbus	\(B_{bus}\)	Bus admittance matrix		MatProcessor.Bbus
Bf	\(B_{f}\)	Bf matrix		MatProcessor.Bf
Pbusinj	\(P_{bus}^{inj}\)	Bus power injection vector		MatProcessor.Pbusinj
Pfinj	\(P_{f}^{inj}\)	Line power injection vector		MatProcessor.Pfinj
c2	\(c_{2}\)	Gen cost coefficient 2	$/(p.u.^2)	GCost.c2
c1	\(c_{1}\)	Gen cost coefficient 1	$/(p.u.)	GCost.c1
c0	\(c_{0}\)	Gen cost coefficient 0	$	GCost.c0
ctrl	\(c_{trl}\)	Gen controllability		StaticGen.ctrl
pmax	\(p_{g, max}\)	Gen maximum active power	p.u.	StaticGen.pmax
pmin	\(p_{g, min}\)	Gen minimum active power	p.u.	StaticGen.pmin
ul	\(u_{l}\)	Line connection status		Line.u
rate_a	\(R_{ATEA}\)	long-term flow limit	p.u.	Line.rate_a
amax	\(\theta_{bus, max}\)	max line angle difference		Line.amax
amin	\(\theta_{bus, min}\)	min line angle difference		Line.amin

DCOPF2

DC optimal power flow (DCOPF) using PTDF. For large cases, it is recommended to build the PTDF first, especially when incremental build is necessary.

Notes

1. This routine requires PTDF matrix.

2. Nodal price pi is calculated with three parts.

3. Bus angle aBus is calculated after solving the problem.

Objective

Unit	Expression
$	\(min. \sum(c_{2} p_g^{2})+ \sum(c_{1} p_g)+ \sum(u_{g} c_{0})\)

Expressions

Name	Description	Expression	Unit	Source
plf	Line flow	\(P_{TDF} (C_{g} p_g - C_{l} p_{d} - C_{sh} g_{sh} - P_{bus}^{inj})\)	p.u.	Line
pmaxe	Effective pmax	\(c_{trl,n,e} p_{g, 0} + c_{trl, e} p_{g, max}\)	p.u.	StaticGen
pmine	Effective pmin	\(c_{trl,n,e} p_{g, 0} + c_{trl, e} p_{g, min}\)	p.u.	StaticGen

Constraints

Name	Description	Expression
pb	power balance	\(B_{bus} \theta_{bus} + P_{bus}^{inj} + C_{l} p_{d} + C_{sh} g_{sh} - C_{g} p_g = 0\)
sbus	align slack bus angle	\(c_{sb} \theta_{bus} = 0\)
pglb	pg min	\(-p_g + p_{g, min, e} \leq 0\)
pgub	pg max	\(p_g - p_{g, max, e} \leq 0\)
plflb	line flow lower bound	\(-p_{lf} - u_{l} R_{ATEA} \leq 0\)
plfub	line flow upper bound	\(p_{lf} - u_{l} R_{ATEA} \leq 0\)
alflb	line angle difference lower bound	\(-C_{ft}^T \theta_{bus} + \theta_{bus, min} \leq 0\)
alfub	line angle difference upper bound	\(C_{ft}^T \theta_{bus} - \theta_{bus, max} \leq 0\)

Vars

Name	Symbol	Description	Unit	Source	Properties
pg	\(p_g\)	Gen active power	p.u.	StaticGen.p
vBus	\(v_{Bus}\)	Bus voltage magnitude, placeholder	p.u.	Bus.v
aBus	\(\theta_{bus}\)	Bus voltage angle	rad	Bus.a

ExpressionCalcs

Name	Description	Expression	Unit	Source
pi	LMP, dual of <pb>	\(\phi[pb] + C_{ft} (\phi[plfub] - \phi[plflb])\)	$/p.u.	Bus
pilb	Congestion price, dual of <plflb>	\(\phi[plflb]\)		Line
piub	Congestion price, dual of <plfub>	\(\phi[plfub]\)		Line
pib	Energy price, dual of <pb>	\(\phi[pb]\)		Bus

Services

Name	Symbol	Description	Type
csb	\(c_{sb}\)	select slack bus	VarSelect
ctrle	\(c_{trl, e}\)	Effective Gen controllability	NumOpDual
nctrl	\(c_{trl,n}\)	Effective Gen uncontrollability	NumOp
nctrle	\(c_{trl,n,e}\)	Effective Gen uncontrollability	NumOpDual
ued	\(u_{e,d}\)	Effective load connection status	NumOp
uesh	\(u_{e,sh}\)	Effective shunt connection status	NumOp

Parameters

Name	Symbol	Description	Unit	Source
ug	\(u_{g}\)	Gen connection status		StaticGen.u
pg0	\(p_{g, 0}\)	Gen initial active power	p.u.	StaticGen.p0
gsh	\(g_{sh}\)	shunt conductance		Shunt.g
buss	\(B_{us,s}\)	Bus slack		Slack.bus
pd	\(p_{d}\)	active demand	p.u.	StaticLoad.p0
Cg	\(C_{g}\)	Gen connection matrix		MatProcessor.Cg
Cl	\(C_{l}\)	Load connection matrix		MatProcessor.Cl
CftT	\(C_{ft}^T\)	Transpose of line connection matrix		MatProcessor.CftT
Csh	\(C_{sh}\)	Shunt connection matrix		MatProcessor.Csh
Bbus	\(B_{bus}\)	Bus admittance matrix		MatProcessor.Bbus
Bf	\(B_{f}\)	Bf matrix		MatProcessor.Bf
Pbusinj	\(P_{bus}^{inj}\)	Bus power injection vector		MatProcessor.Pbusinj
Pfinj	\(P_{f}^{inj}\)	Line power injection vector		MatProcessor.Pfinj
c2	\(c_{2}\)	Gen cost coefficient 2	$/(p.u.^2)	GCost.c2
c1	\(c_{1}\)	Gen cost coefficient 1	$/(p.u.)	GCost.c1
c0	\(c_{0}\)	Gen cost coefficient 0	$	GCost.c0
ctrl	\(c_{trl}\)	Gen controllability		StaticGen.ctrl
pmax	\(p_{g, max}\)	Gen maximum active power	p.u.	StaticGen.pmax
pmin	\(p_{g, min}\)	Gen minimum active power	p.u.	StaticGen.pmin
ul	\(u_{l}\)	Line connection status		Line.u
rate_a	\(R_{ATEA}\)	long-term flow limit	p.u.	Line.rate_a
amax	\(\theta_{bus, max}\)	max line angle difference		Line.amax
amin	\(\theta_{bus, min}\)	min line angle difference		Line.amin
PTDF	\(P_{TDF}\)	PTDF		MatProcessor.PTDF
Cft	\(C_{ft}\)	Line connection matrix		MatProcessor.Cft

ED

DC-based multi-period economic dispatch (ED). Dispatch interval config.t ($T_{cfg}$) is introduced, 1 [Hour] by default. ED extends DCOPF as follows:

• Vars pg, pru, prd are extended to 2D

• 2D Vars rgu and rgd are introduced

• Param ug is sourced from EDTSlot.ug as generator commitment

Notes

1. Formulations has been adjusted with interval config.t

2. The tie-line flow is not implemented in this model.

3. EDTSlot.ug is used instead of StaticGen.u for generator commitment.

4. Following reserves are balanced for each "Area": RegUp reserve rbu, RegDn reserve rbd, and Spinning reserve rsr.

Objective

Unit	Expression
$	\(min. \sum(T_{cfg}^{2} c_{2} p_g^{2})+ T_{cfg} \sum(c_{1} p_g + c_{sr} p_{r,s})+ \sum(u_{g} c_{0} 1_{tl})\)

Expressions

Name	Description	Expression	Unit	Source
plf	2D Line flow	\(B_{f} \theta_{bus} + P_{f}^{inj} 1_{tl}\)	p.u.	Line
pmaxe	Effective pmax	\(c_{trl,n,e} p_{g, 0} 1_{tl} + c_{trl, e} 1_{tl} p_{g, max}\)	p.u.	StaticGen
pmine	Effective pmin	\(c_{trl,n,e} p_{g, 0} 1_{tl} + c_{trl, e} 1_{tl} p_{g, min}\)	p.u.	StaticGen

Constraints

Name	Description	Expression
pb	power balance	\(B_{bus} \theta_{bus} + P_{bus}^{inj} 1_{tl} + C_{l} p_{d,s} + C_{sh} g_{sh} 1_{tl} - C_{g} p_g = 0\)
sbus	align slack bus angle	\(c_{sb} \theta_{bus} = 0\)
pglb	pg min	\(-p_g + p_{g, min, e} \leq 0\)
pgub	pg max	\(p_g - p_{g, max, e} \leq 0\)
plflb	line flow lower bound	\(-B_{f} \theta_{bus} - P_{f}^{inj} 1_{tl} - u_{l} R_{ATEA} 1_{tl} \leq 0\)
plfub	line flow upper bound	\(B_{f} \theta_{bus} + P_{f}^{inj} 1_{tl} - u_{l} R_{ATEA} 1_{tl} \leq 0\)
alflb	line angle difference lower bound	\(-C_{ft}^T \theta_{bus} + \theta_{bus, min} 1_{tl} \leq 0\)
alfub	line angle difference upper bound	\(C_{ft}^T \theta_{bus} - \theta_{bus, max} 1_{tl} \leq 0\)
rbu	RegUp reserve balance	\(S_{g} u_{g} p_{r,u} - d_{u, d} 1_{tl} = 0\)
rbd	RegDn reserve balance	\(S_{g} u_{g} p_{r,d} - d_{d, d} 1_{tl} = 0\)
rru	RegUp reserve source	\(p_g + p_{r,u} - u_{g} p_{g, max} 1_{tl} \leq 0\)
rrd	RegDn reserve source	\(-p_g + p_{r,d} + u_{g} p_{g, min} 1_{tl} \leq 0\)
rgu	Gen ramping up	\(p_g M_{r} - T_{cfg} R_{30,R} \leq 0\)
rgd	Gen ramping down	\(-p_g M_{r} - T_{cfg} R_{30,R} \leq 0\)
prsb	spinning reserve balance	\(u_{g} p_{g, max} 1_{tl} - p_g - p_{r,s} = 0\)
rsr	spinning reserve requirement	\(-S_{g} p_{r,s} + d_{s,r,z} \leq 0\)
rgu0	Initial gen ramping up	\(u_{g}[: 0], p_g[:, 0] - p_{g, 0}[:, 0] - R_{30} \leq 0\)
rgd0	Initial gen ramping down	\(u_{g}[: 0], -p_g[:, 0] + p_{g, 0}[:, 0] - R_{30} \leq 0\)

Vars

Name	Symbol	Description	Unit	Source	Properties
pg	\(p_g\)	2D Gen power	p.u.	StaticGen.p
vBus	\(v_{Bus}\)	2D Bus voltage	p.u.	Bus.v
aBus	\(\theta_{bus}\)	2D Bus angle	rad	Bus.a
pru	\(p_{r,u}\)	2D RegUp power	p.u.	StaticGen	nonneg
prd	\(p_{r,d}\)	2D RegDn power	p.u.	StaticGen	nonneg
prs	\(p_{r,s}\)	spinning reserve	p.u.	StaticGen	nonneg

ExpressionCalcs

Name	Description	Expression	Unit	Source
pi	LMP, dual of <pb>	\(\phi[pb]\)	$/p.u.	Bus

Services

Name	Symbol	Description	Type
csb	\(c_{sb}\)	select slack bus	VarSelect
ctrle	\(c_{trl, e}\)	Effective Gen controllability	NumOpDual
nctrl	\(c_{trl,n}\)	Effective Gen uncontrollability	NumOp
nctrle	\(c_{trl,n,e}\)	Effective Gen uncontrollability	NumOpDual
gs	\(S_{g}\)	Sum Gen vars vector in shape of area	ZonalSum
ds	\(S_{d}\)	Sum pd vector in shape of area	ZonalSum
pdz	\(p_{d,z}\)	zonal total load	NumOpDual
dud	\(d_{u, d}\)	zonal RegUp reserve requirement	NumOpDual
ddd	\(d_{d, d}\)	zonal RegDn reserve requirement	NumOpDual
tlv	\(1_{tl}\)	time length vector	NumOp
pds	\(p_{d,s}\)	Scaled load	LoadScale
Mr	\(M_{r}\)	Subtraction matrix for ramping	RampSub
RR30	\(R_{30,R}\)	Repeated ramp rate	NumHstack
dsrpz	\(d_{s,r, p, z}\)	zonal spinning reserve requirement in percentage	NumOpDual
dsr	\(d_{s,r,z}\)	zonal spinning reserve requirement	NumOpDual
ugt	\(u_{g}\)	input ug transpose	NumOp

Parameters

Name	Symbol	Description	Unit	Source
ug	\(u_{g}\)	unit commitment decisions		EDTSlot.ug
pg0	\(p_{g, 0}\)	Gen initial active power	p.u.	StaticGen.p0
gsh	\(g_{sh}\)	shunt conductance		Shunt.g
buss	\(B_{us,s}\)	Bus slack		Slack.bus
pd	\(p_{d}\)	active demand	p.u.	StaticLoad.p0
Cg	\(C_{g}\)	Gen connection matrix		MatProcessor.Cg
Cl	\(C_{l}\)	Load connection matrix		MatProcessor.Cl
CftT	\(C_{ft}^T\)	Transpose of line connection matrix		MatProcessor.CftT
Csh	\(C_{sh}\)	Shunt connection matrix		MatProcessor.Csh
Bbus	\(B_{bus}\)	Bus admittance matrix		MatProcessor.Bbus
Bf	\(B_{f}\)	Bf matrix		MatProcessor.Bf
Pbusinj	\(P_{bus}^{inj}\)	Bus power injection vector		MatProcessor.Pbusinj
Pfinj	\(P_{f}^{inj}\)	Line power injection vector		MatProcessor.Pfinj
c2	\(c_{2}\)	Gen cost coefficient 2	$/(p.u.^2)	GCost.c2
c1	\(c_{1}\)	Gen cost coefficient 1	$/(p.u.)	GCost.c1
c0	\(c_{0}\)	Gen cost coefficient 0	$	GCost.c0
ctrl	\(c_{trl}\)	Gen controllability		StaticGen.ctrl
pmax	\(p_{g, max}\)	Gen maximum active power	p.u.	StaticGen.pmax
pmin	\(p_{g, min}\)	Gen minimum active power	p.u.	StaticGen.pmin
ul	\(u_{l}\)	Line connection status		Line.u
rate_a	\(R_{ATEA}\)	long-term flow limit	p.u.	Line.rate_a
amax	\(\theta_{bus, max}\)	max line angle difference		Line.amax
amin	\(\theta_{bus, min}\)	min line angle difference		Line.amin
zg	\(z_{one,g}\)	Gen area		StaticGen.area
zd	\(z_{one,d}\)	Load area		StaticLoad.area
R10	\(R_{10}\)	10-min ramp rate	p.u./h	StaticGen.R10
cru	\(c_{r,u}\)	RegUp reserve coefficient	$/(p.u.)	SFRCost.cru
crd	\(c_{r,d}\)	RegDown reserve coefficient	$/(p.u.)	SFRCost.crd
du	\(d_{u}\)	RegUp reserve requirement in percentage	%	SFR.du
dd	\(d_{d}\)	RegDown reserve requirement in percentage	%	SFR.dd
sd	\(s_{d}\)	zonal load factor for ED		EDTSlot.sd
timeslot	\(t_{s,idx}\)	Time slot for multi-period ED		EDTSlot.idx
R30	\(R_{30}\)	30-min ramp rate	p.u./h	StaticGen.R30
dsr	\(d_{sr}\)	spinning reserve requirement in percentage	%	SR.demand
csr	\(c_{sr}\)	cost for spinning reserve	$/(p.u.*h)	SRCost.csr

Config Fields in [ED]

Option	Symbol	Value	Info	Accepted values
t	\(T_{cfg}\)	1	time interval in hours

EDDG

ED with distributed generation DG.

Note that EDDG only inlcudes DG output power. If ESD1 is included, EDES should be used instead, otherwise there is no SOC.

Objective

Unit	Expression
$	\(min. \sum(T_{cfg}^{2} c_{2} p_g^{2})+ T_{cfg} \sum(c_{1} p_g + c_{sr} p_{r,s})+ \sum(u_{g} c_{0} 1_{tl})\)

Expressions

Name	Description	Expression	Unit	Source
plf	2D Line flow	\(B_{f} \theta_{bus} + P_{f}^{inj} 1_{tl}\)	p.u.	Line
pmaxe	Effective pmax	\(c_{trl,n,e} p_{g, 0} 1_{tl} + c_{trl, e} 1_{tl} p_{g, max}\)	p.u.	StaticGen
pmine	Effective pmin	\(c_{trl,n,e} p_{g, 0} 1_{tl} + c_{trl, e} 1_{tl} p_{g, min}\)	p.u.	StaticGen

Constraints

Name	Description	Expression
pb	power balance	\(B_{bus} \theta_{bus} + P_{bus}^{inj} 1_{tl} + C_{l} p_{d,s} + C_{sh} g_{sh} 1_{tl} - C_{g} p_g = 0\)
sbus	align slack bus angle	\(c_{sb} \theta_{bus} = 0\)
pglb	pg min	\(-p_g + p_{g, min, e} \leq 0\)
pgub	pg max	\(p_g - p_{g, max, e} \leq 0\)
plflb	line flow lower bound	\(-B_{f} \theta_{bus} - P_{f}^{inj} 1_{tl} - u_{l} R_{ATEA} 1_{tl} \leq 0\)
plfub	line flow upper bound	\(B_{f} \theta_{bus} + P_{f}^{inj} 1_{tl} - u_{l} R_{ATEA} 1_{tl} \leq 0\)
alflb	line angle difference lower bound	\(-C_{ft}^T \theta_{bus} + \theta_{bus, min} 1_{tl} \leq 0\)
alfub	line angle difference upper bound	\(C_{ft}^T \theta_{bus} - \theta_{bus, max} 1_{tl} \leq 0\)
rbu	RegUp reserve balance	\(S_{g} u_{g} p_{r,u} - d_{u, d} 1_{tl} = 0\)
rbd	RegDn reserve balance	\(S_{g} u_{g} p_{r,d} - d_{d, d} 1_{tl} = 0\)
rru	RegUp reserve source	\(p_g + p_{r,u} - u_{g} p_{g, max} 1_{tl} \leq 0\)
rrd	RegDn reserve source	\(-p_g + p_{r,d} + u_{g} p_{g, min} 1_{tl} \leq 0\)
rgu	Gen ramping up	\(p_g M_{r} - T_{cfg} R_{30,R} \leq 0\)
rgd	Gen ramping down	\(-p_g M_{r} - T_{cfg} R_{30,R} \leq 0\)
prsb	spinning reserve balance	\(u_{g} p_{g, max} 1_{tl} - p_g - p_{r,s} = 0\)
rsr	spinning reserve requirement	\(-S_{g} p_{r,s} + d_{s,r,z} \leq 0\)
rgu0	Initial gen ramping up	\(u_{g}[: 0], p_g[:, 0] - p_{g, 0}[:, 0] - R_{30} \leq 0\)
rgd0	Initial gen ramping down	\(u_{g}[: 0], -p_g[:, 0] + p_{g, 0}[:, 0] - R_{30} \leq 0\)
cdgb	Select DG power from pg	\(C_{DG} p_g - p_{g,DG} = 0\)

Vars

Name	Symbol	Description	Unit	Source	Properties
pg	\(p_g\)	2D Gen power	p.u.	StaticGen.p
vBus	\(v_{Bus}\)	2D Bus voltage	p.u.	Bus.v
aBus	\(\theta_{bus}\)	2D Bus angle	rad	Bus.a
pru	\(p_{r,u}\)	2D RegUp power	p.u.	StaticGen	nonneg
prd	\(p_{r,d}\)	2D RegDn power	p.u.	StaticGen	nonneg
prs	\(p_{r,s}\)	spinning reserve	p.u.	StaticGen	nonneg
pgdg	\(p_{g,DG}\)	DG output power	p.u.	DG

ExpressionCalcs

Name	Description	Expression	Unit	Source
pi	LMP, dual of <pb>	\(\phi[pb]\)	$/p.u.	Bus

Services

Name	Symbol	Description	Type
csb	\(c_{sb}\)	select slack bus	VarSelect
ctrle	\(c_{trl, e}\)	Effective Gen controllability	NumOpDual
nctrl	\(c_{trl,n}\)	Effective Gen uncontrollability	NumOp
nctrle	\(c_{trl,n,e}\)	Effective Gen uncontrollability	NumOpDual
gs	\(S_{g}\)	Sum Gen vars vector in shape of area	ZonalSum
ds	\(S_{d}\)	Sum pd vector in shape of area	ZonalSum
pdz	\(p_{d,z}\)	zonal total load	NumOpDual
dud	\(d_{u, d}\)	zonal RegUp reserve requirement	NumOpDual
ddd	\(d_{d, d}\)	zonal RegDn reserve requirement	NumOpDual
tlv	\(1_{tl}\)	time length vector	NumOp
pds	\(p_{d,s}\)	Scaled load	LoadScale
Mr	\(M_{r}\)	Subtraction matrix for ramping	RampSub
RR30	\(R_{30,R}\)	Repeated ramp rate	NumHstack
dsrpz	\(d_{s,r, p, z}\)	zonal spinning reserve requirement in percentage	NumOpDual
dsr	\(d_{s,r,z}\)	zonal spinning reserve requirement	NumOpDual
ugt	\(u_{g}\)	input ug transpose	NumOp
cd	\(C_{DG}\)	Select DG power from pg	VarSelect

Parameters

Name	Symbol	Description	Unit	Source
ug	\(u_{g}\)	unit commitment decisions		EDTSlot.ug
pg0	\(p_{g, 0}\)	Gen initial active power	p.u.	StaticGen.p0
gsh	\(g_{sh}\)	shunt conductance		Shunt.g
buss	\(B_{us,s}\)	Bus slack		Slack.bus
pd	\(p_{d}\)	active demand	p.u.	StaticLoad.p0
Cg	\(C_{g}\)	Gen connection matrix		MatProcessor.Cg
Cl	\(C_{l}\)	Load connection matrix		MatProcessor.Cl
CftT	\(C_{ft}^T\)	Transpose of line connection matrix		MatProcessor.CftT
Csh	\(C_{sh}\)	Shunt connection matrix		MatProcessor.Csh
Bbus	\(B_{bus}\)	Bus admittance matrix		MatProcessor.Bbus
Bf	\(B_{f}\)	Bf matrix		MatProcessor.Bf
Pbusinj	\(P_{bus}^{inj}\)	Bus power injection vector		MatProcessor.Pbusinj
Pfinj	\(P_{f}^{inj}\)	Line power injection vector		MatProcessor.Pfinj
c2	\(c_{2}\)	Gen cost coefficient 2	$/(p.u.^2)	GCost.c2
c1	\(c_{1}\)	Gen cost coefficient 1	$/(p.u.)	GCost.c1
c0	\(c_{0}\)	Gen cost coefficient 0	$	GCost.c0
ctrl	\(c_{trl}\)	Gen controllability		StaticGen.ctrl
pmax	\(p_{g, max}\)	Gen maximum active power	p.u.	StaticGen.pmax
pmin	\(p_{g, min}\)	Gen minimum active power	p.u.	StaticGen.pmin
ul	\(u_{l}\)	Line connection status		Line.u
rate_a	\(R_{ATEA}\)	long-term flow limit	p.u.	Line.rate_a
amax	\(\theta_{bus, max}\)	max line angle difference		Line.amax
amin	\(\theta_{bus, min}\)	min line angle difference		Line.amin
zg	\(z_{one,g}\)	Gen area		StaticGen.area
zd	\(z_{one,d}\)	Load area		StaticLoad.area
R10	\(R_{10}\)	10-min ramp rate	p.u./h	StaticGen.R10
cru	\(c_{r,u}\)	RegUp reserve coefficient	$/(p.u.)	SFRCost.cru
crd	\(c_{r,d}\)	RegDown reserve coefficient	$/(p.u.)	SFRCost.crd
du	\(d_{u}\)	RegUp reserve requirement in percentage	%	SFR.du
dd	\(d_{d}\)	RegDown reserve requirement in percentage	%	SFR.dd
sd	\(s_{d}\)	zonal load factor for ED		EDTSlot.sd
timeslot	\(t_{s,idx}\)	Time slot for multi-period ED		EDTSlot.idx
R30	\(R_{30}\)	30-min ramp rate	p.u./h	StaticGen.R30
dsr	\(d_{sr}\)	spinning reserve requirement in percentage	%	SR.demand
csr	\(c_{sr}\)	cost for spinning reserve	$/(p.u.*h)	SRCost.csr
gendg	\(g_{DG}\)	gen of DG		DG.gen
gammapd	\(\gamma_{p,DG}\)	Ratio of DG.pge w.r.t to that of static generator		DG.gammap

Config Fields in [EDDG]

Option	Symbol	Value	Info	Accepted values
t	\(T_{cfg}\)	1	time interval in hours

EDES

ED with energy storage ESD1. The bilinear term in the formulation is linearized with big-M method.

Objective

Unit	Expression
$	\(min. \sum(T_{cfg}^{2} c_{2} p_g^{2})+ T_{cfg} \sum(c_{1} p_g + c_{sr} p_{r,s})+ \sum(u_{g} c_{0} 1_{tl})\)

Expressions

Name	Description	Expression	Unit	Source
plf	2D Line flow	\(B_{f} \theta_{bus} + P_{f}^{inj} 1_{tl}\)	p.u.	Line
pmaxe	Effective pmax	\(c_{trl,n,e} p_{g, 0} 1_{tl} + c_{trl, e} 1_{tl} p_{g, max}\)	p.u.	StaticGen
pmine	Effective pmin	\(c_{trl,n,e} p_{g, 0} 1_{tl} + c_{trl, e} 1_{tl} p_{g, min}\)	p.u.	StaticGen

Constraints

Name	Description	Expression
pb	power balance	\(B_{bus} \theta_{bus} + P_{bus}^{inj} 1_{tl} + C_{l} p_{d,s} + C_{sh} g_{sh} 1_{tl} - C_{g} p_g = 0\)
sbus	align slack bus angle	\(c_{sb} \theta_{bus} = 0\)
pglb	pg min	\(-p_g + p_{g, min, e} \leq 0\)
pgub	pg max	\(p_g - p_{g, max, e} \leq 0\)
plflb	line flow lower bound	\(-B_{f} \theta_{bus} - P_{f}^{inj} 1_{tl} - u_{l} R_{ATEA} 1_{tl} \leq 0\)
plfub	line flow upper bound	\(B_{f} \theta_{bus} + P_{f}^{inj} 1_{tl} - u_{l} R_{ATEA} 1_{tl} \leq 0\)
alflb	line angle difference lower bound	\(-C_{ft}^T \theta_{bus} + \theta_{bus, min} 1_{tl} \leq 0\)
alfub	line angle difference upper bound	\(C_{ft}^T \theta_{bus} - \theta_{bus, max} 1_{tl} \leq 0\)
rbu	RegUp reserve balance	\(S_{g} u_{g} p_{r,u} - d_{u, d} 1_{tl} = 0\)
rbd	RegDn reserve balance	\(S_{g} u_{g} p_{r,d} - d_{d, d} 1_{tl} = 0\)
rru	RegUp reserve source	\(p_g + p_{r,u} - u_{g} p_{g, max} 1_{tl} \leq 0\)
rrd	RegDn reserve source	\(-p_g + p_{r,d} + u_{g} p_{g, min} 1_{tl} \leq 0\)
rgu	Gen ramping up	\(p_g M_{r} - T_{cfg} R_{30,R} \leq 0\)
rgd	Gen ramping down	\(-p_g M_{r} - T_{cfg} R_{30,R} \leq 0\)
prsb	spinning reserve balance	\(u_{g} p_{g, max} 1_{tl} - p_g - p_{r,s} = 0\)
rsr	spinning reserve requirement	\(-S_{g} p_{r,s} + d_{s,r,z} \leq 0\)
rgu0	Initial gen ramping up	\(u_{g}[: 0], p_g[:, 0] - p_{g, 0}[:, 0] - R_{30} \leq 0\)
rgd0	Initial gen ramping down	\(u_{g}[: 0], -p_g[:, 0] + p_{g, 0}[:, 0] - R_{30} \leq 0\)
cdgb	Select DG power from pg	\(C_{DG} p_g - p_{g,DG} = 0\)
SOClb	SOC lower bound	\(-SOC + SOC_{min} \leq 0\)
SOCub	SOC upper bound	\(SOC - SOC_{max} \leq 0\)
cescb	Select pce from DG	\(C_{ESD} p_{g,DG} - p_{c,ESD} = 0\)
cesdb	Select pde from DG	\(C_{ESD} p_{g,DG} - p_{d,ESD} = 0\)
cdb	Charging decision bound	\(u_{c,ESD} + u_{d,ESD} - 1 = 0\)
zce1	zce bound 1	\(-z_{c,ESD} + p_{c,ESD} \leq 0\)
zce2	zce bound 2	\(z_{c,ESD} - p_{c,ESD} - M_{big} (1-u_{c,ESD}) \leq 0\)
zce3	zce bound 3	\(z_{c,ESD} - M_{big} u_{c,ESD} \leq 0\)
zde1	zde bound 1	\(-z_{d,ESD} + p_{d,ESD} \leq 0\)
zde2	zde bound 2	\(z_{d,ESD} - p_{d,ESD} - M_{big} (1-u_{d,ESD}) \leq 0\)
zde3	zde bound 3	\(z_{d,ESD} - M_{big} u_{d,ESD} \leq 0\)
SOCb	ESD1 SOC balance	\(E_{n,R} SOC M_{r,ES} - T_{cfg} \eta_{c,R} z_{c,ESD}[:, 1:] + T_{cfg} R_{\eta_d,R} z_{d,ESD}[:, 1:] = 0\)
SOCb0	ESD1 SOC initial balance	\(E_n SOC[:, 0] - SOC_{init} - T_{cfg} \eta_c z_{c,ESD}[:, 0] + T_{cfg} \frac{1}{\eta_d} z_{d,ESD}[:, 0] = 0\)
SOCr	SOC requirement	\(SOC[:, -1] - SOC_{init} = 0\)

Vars

Name	Symbol	Description	Unit	Source	Properties
pg	\(p_g\)	2D Gen power	p.u.	StaticGen.p
vBus	\(v_{Bus}\)	2D Bus voltage	p.u.	Bus.v
aBus	\(\theta_{bus}\)	2D Bus angle	rad	Bus.a
pru	\(p_{r,u}\)	2D RegUp power	p.u.	StaticGen	nonneg
prd	\(p_{r,d}\)	2D RegDn power	p.u.	StaticGen	nonneg
prs	\(p_{r,s}\)	spinning reserve	p.u.	StaticGen	nonneg
pgdg	\(p_{g,DG}\)	DG output power	p.u.	DG
SOC	\(SOC\)	ESD1 State of Charge	%	ESD1	pos
pce	\(p_{c,ESD}\)	ESD1 charging power	p.u.	ESD1	nonneg
pde	\(p_{d,ESD}\)	ESD1 discharging power	p.u.	ESD1	nonneg
uce	\(u_{c,ESD}\)	ESD1 charging decision		ESD1	boolean
ude	\(u_{d,ESD}\)	ESD1 discharging decision		ESD1	boolean
zce	\(z_{c,ESD}\)	Aux var for charging, \(z_{c,ESD}=u_{c,ESD}*p_{c,ESD}\)		ESD1	nonneg
zde	\(z_{d,ESD}\)	Aux var for discharging, \(z_{d,ESD}=u_{d,ESD}*p_{d,ESD}\)		ESD1	nonneg

ExpressionCalcs

Name	Description	Expression	Unit	Source
pi	LMP, dual of <pb>	\(\phi[pb]\)	$/p.u.	Bus

Services

Name	Symbol	Description	Type
csb	\(c_{sb}\)	select slack bus	VarSelect
ctrle	\(c_{trl, e}\)	Effective Gen controllability	NumOpDual
nctrl	\(c_{trl,n}\)	Effective Gen uncontrollability	NumOp
nctrle	\(c_{trl,n,e}\)	Effective Gen uncontrollability	NumOpDual
gs	\(S_{g}\)	Sum Gen vars vector in shape of area	ZonalSum
ds	\(S_{d}\)	Sum pd vector in shape of area	ZonalSum
pdz	\(p_{d,z}\)	zonal total load	NumOpDual
dud	\(d_{u, d}\)	zonal RegUp reserve requirement	NumOpDual
ddd	\(d_{d, d}\)	zonal RegDn reserve requirement	NumOpDual
tlv	\(1_{tl}\)	time length vector	NumOp
pds	\(p_{d,s}\)	Scaled load	LoadScale
Mr	\(M_{r}\)	Subtraction matrix for ramping	RampSub
RR30	\(R_{30,R}\)	Repeated ramp rate	NumHstack
dsrpz	\(d_{s,r, p, z}\)	zonal spinning reserve requirement in percentage	NumOpDual
dsr	\(d_{s,r,z}\)	zonal spinning reserve requirement	NumOpDual
ugt	\(u_{g}\)	input ug transpose	NumOp
cd	\(C_{DG}\)	Select DG power from pg	VarSelect
REtaD	\(\frac{1}{\eta_d}\)		NumOp
Mb	\(M_{big}\)	10 times of max of pmax as big M	NumOp
ces	\(C_{ESD}\)	Select ESD power from DG	VarSelect
Mre	\(M_{r,ES}\)	Subtraction matrix for SOC	RampSub
EnR	\(E_{n,R}\)	Repeated En as 2D matrix, (ng, ng-1)	NumHstack
EtaCR	\(\eta_{c,R}\)	Repeated Etac as 2D matrix, (ng, ng-1)	NumHstack
REtaDR	\(R_{\eta_d,R}\)	Repeated REtaD as 2D matrix, (ng, ng-1)	NumHstack

Parameters

Name	Symbol	Description	Unit	Source
ug	\(u_{g}\)	unit commitment decisions		EDTSlot.ug
pg0	\(p_{g, 0}\)	Gen initial active power	p.u.	StaticGen.p0
gsh	\(g_{sh}\)	shunt conductance		Shunt.g
buss	\(B_{us,s}\)	Bus slack		Slack.bus
pd	\(p_{d}\)	active demand	p.u.	StaticLoad.p0
Cg	\(C_{g}\)	Gen connection matrix		MatProcessor.Cg
Cl	\(C_{l}\)	Load connection matrix		MatProcessor.Cl
CftT	\(C_{ft}^T\)	Transpose of line connection matrix		MatProcessor.CftT
Csh	\(C_{sh}\)	Shunt connection matrix		MatProcessor.Csh
Bbus	\(B_{bus}\)	Bus admittance matrix		MatProcessor.Bbus
Bf	\(B_{f}\)	Bf matrix		MatProcessor.Bf
Pbusinj	\(P_{bus}^{inj}\)	Bus power injection vector		MatProcessor.Pbusinj
Pfinj	\(P_{f}^{inj}\)	Line power injection vector		MatProcessor.Pfinj
c2	\(c_{2}\)	Gen cost coefficient 2	$/(p.u.^2)	GCost.c2
c1	\(c_{1}\)	Gen cost coefficient 1	$/(p.u.)	GCost.c1
c0	\(c_{0}\)	Gen cost coefficient 0	$	GCost.c0
ctrl	\(c_{trl}\)	Gen controllability		StaticGen.ctrl
pmax	\(p_{g, max}\)	Gen maximum active power	p.u.	StaticGen.pmax
pmin	\(p_{g, min}\)	Gen minimum active power	p.u.	StaticGen.pmin
ul	\(u_{l}\)	Line connection status		Line.u
rate_a	\(R_{ATEA}\)	long-term flow limit	p.u.	Line.rate_a
amax	\(\theta_{bus, max}\)	max line angle difference		Line.amax
amin	\(\theta_{bus, min}\)	min line angle difference		Line.amin
zg	\(z_{one,g}\)	Gen area		StaticGen.area
zd	\(z_{one,d}\)	Load area		StaticLoad.area
R10	\(R_{10}\)	10-min ramp rate	p.u./h	StaticGen.R10
cru	\(c_{r,u}\)	RegUp reserve coefficient	$/(p.u.)	SFRCost.cru
crd	\(c_{r,d}\)	RegDown reserve coefficient	$/(p.u.)	SFRCost.crd
du	\(d_{u}\)	RegUp reserve requirement in percentage	%	SFR.du
dd	\(d_{d}\)	RegDown reserve requirement in percentage	%	SFR.dd
sd	\(s_{d}\)	zonal load factor for ED		EDTSlot.sd
timeslot	\(t_{s,idx}\)	Time slot for multi-period ED		EDTSlot.idx
R30	\(R_{30}\)	30-min ramp rate	p.u./h	StaticGen.R30
dsr	\(d_{sr}\)	spinning reserve requirement in percentage	%	SR.demand
csr	\(c_{sr}\)	cost for spinning reserve	$/(p.u.*h)	SRCost.csr
gendg	\(g_{DG}\)	gen of DG		DG.gen
gammapd	\(\gamma_{p,DG}\)	Ratio of DG.pge w.r.t to that of static generator		DG.gammap
En	\(E_n\)	Rated energy capacity	MWh	ESD1.En
SOCmax	\(SOC_{max}\)	Maximum allowed value for SOC in limiter	%	ESD1.SOCmax
SOCmin	\(SOC_{min}\)	Minimum required value for SOC in limiter	%	ESD1.SOCmin
SOCinit	\(SOC_{init}\)	Initial SOC	%	ESD1.SOCinit
EtaC	\(\eta_c\)	Efficiency during charging	%	ESD1.EtaC
EtaD	\(\eta_d\)	Efficiency during discharging	%	ESD1.EtaD
genesd	\(g_{ESD}\)	gen of ESD1		ESD1.idx

Config Fields in [EDES]

Option	Symbol	Value	Info	Accepted values
t	\(T_{cfg}\)	1	time interval in hours

RTED

DC-based real-time economic dispatch (RTED).

RTED extends DCOPF with:

• Vars for SFR reserve: pru and prd

• Param for linear SFR cost: cru and crd

• Param for SFR requirement: du and dd

• Param for ramping: start point pg0 and ramping limit R10

• Param pg0, which can be retrieved from dynamic simulation results.

The function dc2ac sets the vBus value from solved ACOPF. Without this conversion, dynamic simulation might fail due to the gap between DC-based dispatch results and AC-based dynamic initialization.

Notes

1. Formulations has been adjusted with interval config.t, 5/60 [Hour] by default.

2. The tie-line flow related constraints are ommited in this formulation.

3. The power balance is solved for the entire system.

4. The SFR is solved for each area.

Objective

Unit	Expression
$	\(min. T_{cfg}^{2} \sum(c_{2} p_g^{2}) + \sum(u_{g} c_{0})+ T_{cfg} \sum(c_{1} p_g + c_{r,u} p_{r,u} + c_{r,d} p_{r,d})\)

Expressions

Name	Description	Expression	Unit	Source
plf	Line flow	\(B_{f} \theta_{bus} + P_{f}^{inj}\)	p.u.	Line
pmaxe	Effective pmax	\(c_{trl,n,e} p_{g, 0} + c_{trl, e} p_{g, max}\)	p.u.	StaticGen
pmine	Effective pmin	\(c_{trl,n,e} p_{g, 0} + c_{trl, e} p_{g, min}\)	p.u.	StaticGen

Constraints

Name	Description	Expression
pb	power balance	\(B_{bus} \theta_{bus} + P_{bus}^{inj} + C_{l} p_{d} + C_{sh} g_{sh} - C_{g} p_g = 0\)
sbus	align slack bus angle	\(c_{sb} \theta_{bus} = 0\)
pglb	pg min	\(-p_g + p_{g, min, e} \leq 0\)
pgub	pg max	\(p_g - p_{g, max, e} \leq 0\)
plflb	line flow lower bound	\(-p_{lf} - u_{l} R_{ATEA} \leq 0\)
plfub	line flow upper bound	\(p_{lf} - u_{l} R_{ATEA} \leq 0\)
alflb	line angle difference lower bound	\(-C_{ft}^T \theta_{bus} + \theta_{bus, min} \leq 0\)
alfub	line angle difference upper bound	\(C_{ft}^T \theta_{bus} - \theta_{bus, max} \leq 0\)
rbu	RegUp reserve balance	\(S_{g} u_{g} p_{r,u} - d_{u, d} = 0\)
rbd	RegDn reserve balance	\(S_{g} u_{g} p_{r,d} - d_{d, d} = 0\)
rru	RegUp reserve source	\(u_{g} (p_g + p_{r,u}) - u_{g} p_{g, max, e} \leq 0\)
rrd	RegDn reserve source	\(u_{g} (-p_g + p_{r,d}) + u_{g} p_{g, min, e} \leq 0\)
rgu	Gen ramping up	\(u_{g} (p_g-p_{g, 0}-R_{10}) \leq 0\)
rgd	Gen ramping down	\(u_{g} (-p_g+p_{g, 0}-R_{10}) \leq 0\)

Vars

Name	Symbol	Description	Unit	Source	Properties
pg	\(p_g\)	Gen active power	p.u.	StaticGen.p
vBus	\(v_{Bus}\)	Bus voltage magnitude, placeholder	p.u.	Bus.v
aBus	\(\theta_{bus}\)	Bus voltage angle	rad	Bus.a
pru	\(p_{r,u}\)	RegUp reserve	p.u.	StaticGen	nonneg
prd	\(p_{r,d}\)	RegDn reserve	p.u.	StaticGen	nonneg

ExpressionCalcs

Name	Description	Expression	Unit	Source
pi	LMP, dual of <pb>	\(\phi[pb]\)	$/p.u.	Bus

Services

Name	Symbol	Description	Type
csb	\(c_{sb}\)	select slack bus	VarSelect
ctrle	\(c_{trl, e}\)	Effective Gen controllability	NumOpDual
nctrl	\(c_{trl,n}\)	Effective Gen uncontrollability	NumOp
nctrle	\(c_{trl,n,e}\)	Effective Gen uncontrollability	NumOpDual
gs	\(S_{g}\)	Sum Gen vars vector in shape of area	ZonalSum
ds	\(S_{d}\)	Sum pd vector in shape of area	ZonalSum
pdz	\(p_{d,z}\)	zonal total load	NumOpDual
dud	\(d_{u, d}\)	zonal RegUp reserve requirement	NumOpDual
ddd	\(d_{d, d}\)	zonal RegDn reserve requirement	NumOpDual

Parameters

Name	Symbol	Description	Unit	Source
ug	\(u_{g}\)	Gen connection status		StaticGen.u
pg0	\(p_{g, 0}\)	Gen initial active power	p.u.	StaticGen.p0
gsh	\(g_{sh}\)	shunt conductance		Shunt.g
buss	\(B_{us,s}\)	Bus slack		Slack.bus
pd	\(p_{d}\)	active demand	p.u.	StaticLoad.p0
Cg	\(C_{g}\)	Gen connection matrix		MatProcessor.Cg
Cl	\(C_{l}\)	Load connection matrix		MatProcessor.Cl
CftT	\(C_{ft}^T\)	Transpose of line connection matrix		MatProcessor.CftT
Csh	\(C_{sh}\)	Shunt connection matrix		MatProcessor.Csh
Bbus	\(B_{bus}\)	Bus admittance matrix		MatProcessor.Bbus
Bf	\(B_{f}\)	Bf matrix		MatProcessor.Bf
Pbusinj	\(P_{bus}^{inj}\)	Bus power injection vector		MatProcessor.Pbusinj
Pfinj	\(P_{f}^{inj}\)	Line power injection vector		MatProcessor.Pfinj
c2	\(c_{2}\)	Gen cost coefficient 2	$/(p.u.^2)	GCost.c2
c1	\(c_{1}\)	Gen cost coefficient 1	$/(p.u.)	GCost.c1
c0	\(c_{0}\)	Gen cost coefficient 0	$	GCost.c0
ctrl	\(c_{trl}\)	Gen controllability		StaticGen.ctrl
pmax	\(p_{g, max}\)	Gen maximum active power	p.u.	StaticGen.pmax
pmin	\(p_{g, min}\)	Gen minimum active power	p.u.	StaticGen.pmin
ul	\(u_{l}\)	Line connection status		Line.u
rate_a	\(R_{ATEA}\)	long-term flow limit	p.u.	Line.rate_a
amax	\(\theta_{bus, max}\)	max line angle difference		Line.amax
amin	\(\theta_{bus, min}\)	min line angle difference		Line.amin
zg	\(z_{one,g}\)	Gen area		StaticGen.area
zd	\(z_{one,d}\)	Load area		StaticLoad.area
R10	\(R_{10}\)	10-min ramp rate	p.u./h	StaticGen.R10
cru	\(c_{r,u}\)	RegUp reserve coefficient	$/(p.u.)	SFRCost.cru
crd	\(c_{r,d}\)	RegDown reserve coefficient	$/(p.u.)	SFRCost.crd
du	\(d_{u}\)	RegUp reserve requirement in percentage	%	SFR.du
dd	\(d_{d}\)	RegDown reserve requirement in percentage	%	SFR.dd

Config Fields in [RTED]

Option	Symbol	Value	Info	Accepted values
t	\(T_{cfg}\)	0.083	time interval in hours

RTEDDG

RTED with distributed generator DG.

Note that RTEDDG only inlcudes DG output power. If ESD1 is included, RTEDES should be used instead, otherwise there is no SOC.

Objective

Unit	Expression
$	\(min. T_{cfg}^{2} \sum(c_{2} p_g^{2}) + \sum(u_{g} c_{0})+ T_{cfg} \sum(c_{1} p_g + c_{r,u} p_{r,u} + c_{r,d} p_{r,d})\)

Expressions

Name	Description	Expression	Unit	Source
plf	Line flow	\(B_{f} \theta_{bus} + P_{f}^{inj}\)	p.u.	Line
pmaxe	Effective pmax	\(c_{trl,n,e} p_{g, 0} + c_{trl, e} p_{g, max}\)	p.u.	StaticGen
pmine	Effective pmin	\(c_{trl,n,e} p_{g, 0} + c_{trl, e} p_{g, min}\)	p.u.	StaticGen

Constraints

Name	Description	Expression
pb	power balance	\(B_{bus} \theta_{bus} + P_{bus}^{inj} + C_{l} p_{d} + C_{sh} g_{sh} - C_{g} p_g = 0\)
sbus	align slack bus angle	\(c_{sb} \theta_{bus} = 0\)
pglb	pg min	\(-p_g + p_{g, min, e} \leq 0\)
pgub	pg max	\(p_g - p_{g, max, e} \leq 0\)
plflb	line flow lower bound	\(-p_{lf} - u_{l} R_{ATEA} \leq 0\)
plfub	line flow upper bound	\(p_{lf} - u_{l} R_{ATEA} \leq 0\)
alflb	line angle difference lower bound	\(-C_{ft}^T \theta_{bus} + \theta_{bus, min} \leq 0\)
alfub	line angle difference upper bound	\(C_{ft}^T \theta_{bus} - \theta_{bus, max} \leq 0\)
rbu	RegUp reserve balance	\(S_{g} u_{g} p_{r,u} - d_{u, d} = 0\)
rbd	RegDn reserve balance	\(S_{g} u_{g} p_{r,d} - d_{d, d} = 0\)
rru	RegUp reserve source	\(u_{g} (p_g + p_{r,u}) - u_{g} p_{g, max, e} \leq 0\)
rrd	RegDn reserve source	\(u_{g} (-p_g + p_{r,d}) + u_{g} p_{g, min, e} \leq 0\)
rgu	Gen ramping up	\(u_{g} (p_g-p_{g, 0}-R_{10}) \leq 0\)
rgd	Gen ramping down	\(u_{g} (-p_g+p_{g, 0}-R_{10}) \leq 0\)
cdgb	Select DG power from pg	\(C_{DG} p_g - p_{g,DG} = 0\)

Vars

Name	Symbol	Description	Unit	Source	Properties
pg	\(p_g\)	Gen active power	p.u.	StaticGen.p
vBus	\(v_{Bus}\)	Bus voltage magnitude, placeholder	p.u.	Bus.v
aBus	\(\theta_{bus}\)	Bus voltage angle	rad	Bus.a
pru	\(p_{r,u}\)	RegUp reserve	p.u.	StaticGen	nonneg
prd	\(p_{r,d}\)	RegDn reserve	p.u.	StaticGen	nonneg
pgdg	\(p_{g,DG}\)	DG output power	p.u.	DG

ExpressionCalcs

Name	Description	Expression	Unit	Source
pi	LMP, dual of <pb>	\(\phi[pb]\)	$/p.u.	Bus

Services

Name	Symbol	Description	Type
csb	\(c_{sb}\)	select slack bus	VarSelect
ctrle	\(c_{trl, e}\)	Effective Gen controllability	NumOpDual
nctrl	\(c_{trl,n}\)	Effective Gen uncontrollability	NumOp
nctrle	\(c_{trl,n,e}\)	Effective Gen uncontrollability	NumOpDual
gs	\(S_{g}\)	Sum Gen vars vector in shape of area	ZonalSum
ds	\(S_{d}\)	Sum pd vector in shape of area	ZonalSum
pdz	\(p_{d,z}\)	zonal total load	NumOpDual
dud	\(d_{u, d}\)	zonal RegUp reserve requirement	NumOpDual
ddd	\(d_{d, d}\)	zonal RegDn reserve requirement	NumOpDual
cd	\(C_{DG}\)	Select DG power from pg	VarSelect

Parameters

Name	Symbol	Description	Unit	Source
ug	\(u_{g}\)	Gen connection status		StaticGen.u
pg0	\(p_{g, 0}\)	Gen initial active power	p.u.	StaticGen.p0
gsh	\(g_{sh}\)	shunt conductance		Shunt.g
buss	\(B_{us,s}\)	Bus slack		Slack.bus
pd	\(p_{d}\)	active demand	p.u.	StaticLoad.p0
Cg	\(C_{g}\)	Gen connection matrix		MatProcessor.Cg
Cl	\(C_{l}\)	Load connection matrix		MatProcessor.Cl
CftT	\(C_{ft}^T\)	Transpose of line connection matrix		MatProcessor.CftT
Csh	\(C_{sh}\)	Shunt connection matrix		MatProcessor.Csh
Bbus	\(B_{bus}\)	Bus admittance matrix		MatProcessor.Bbus
Bf	\(B_{f}\)	Bf matrix		MatProcessor.Bf
Pbusinj	\(P_{bus}^{inj}\)	Bus power injection vector		MatProcessor.Pbusinj
Pfinj	\(P_{f}^{inj}\)	Line power injection vector		MatProcessor.Pfinj
c2	\(c_{2}\)	Gen cost coefficient 2	$/(p.u.^2)	GCost.c2
c1	\(c_{1}\)	Gen cost coefficient 1	$/(p.u.)	GCost.c1
c0	\(c_{0}\)	Gen cost coefficient 0	$	GCost.c0
ctrl	\(c_{trl}\)	Gen controllability		StaticGen.ctrl
pmax	\(p_{g, max}\)	Gen maximum active power	p.u.	StaticGen.pmax
pmin	\(p_{g, min}\)	Gen minimum active power	p.u.	StaticGen.pmin
ul	\(u_{l}\)	Line connection status		Line.u
rate_a	\(R_{ATEA}\)	long-term flow limit	p.u.	Line.rate_a
amax	\(\theta_{bus, max}\)	max line angle difference		Line.amax
amin	\(\theta_{bus, min}\)	min line angle difference		Line.amin
zg	\(z_{one,g}\)	Gen area		StaticGen.area
zd	\(z_{one,d}\)	Load area		StaticLoad.area
R10	\(R_{10}\)	10-min ramp rate	p.u./h	StaticGen.R10
cru	\(c_{r,u}\)	RegUp reserve coefficient	$/(p.u.)	SFRCost.cru
crd	\(c_{r,d}\)	RegDown reserve coefficient	$/(p.u.)	SFRCost.crd
du	\(d_{u}\)	RegUp reserve requirement in percentage	%	SFR.du
dd	\(d_{d}\)	RegDown reserve requirement in percentage	%	SFR.dd
gendg	\(g_{DG}\)	gen of DG		DG.gen
gammapd	\(\gamma_{p,DG}\)	Ratio of DG.pge w.r.t to that of static generator		DG.gammap

Config Fields in [RTEDDG]

Option	Symbol	Value	Info	Accepted values
t	\(T_{cfg}\)	0.083	time interval in hours

RTEDES

RTED with energy storage ESD1. The bilinear term in the formulation is linearized with big-M method.

Objective

Unit	Expression
$	\(min. T_{cfg}^{2} \sum(c_{2} p_g^{2}) + \sum(u_{g} c_{0})+ T_{cfg} \sum(c_{1} p_g + c_{r,u} p_{r,u} + c_{r,d} p_{r,d})\)

Expressions

Name	Description	Expression	Unit	Source
plf	Line flow	\(B_{f} \theta_{bus} + P_{f}^{inj}\)	p.u.	Line
pmaxe	Effective pmax	\(c_{trl,n,e} p_{g, 0} + c_{trl, e} p_{g, max}\)	p.u.	StaticGen
pmine	Effective pmin	\(c_{trl,n,e} p_{g, 0} + c_{trl, e} p_{g, min}\)	p.u.	StaticGen

Constraints

Name	Description	Expression
pb	power balance	\(B_{bus} \theta_{bus} + P_{bus}^{inj} + C_{l} p_{d} + C_{sh} g_{sh} - C_{g} p_g = 0\)
sbus	align slack bus angle	\(c_{sb} \theta_{bus} = 0\)
pglb	pg min	\(-p_g + p_{g, min, e} \leq 0\)
pgub	pg max	\(p_g - p_{g, max, e} \leq 0\)
plflb	line flow lower bound	\(-p_{lf} - u_{l} R_{ATEA} \leq 0\)
plfub	line flow upper bound	\(p_{lf} - u_{l} R_{ATEA} \leq 0\)
alflb	line angle difference lower bound	\(-C_{ft}^T \theta_{bus} + \theta_{bus, min} \leq 0\)
alfub	line angle difference upper bound	\(C_{ft}^T \theta_{bus} - \theta_{bus, max} \leq 0\)
rbu	RegUp reserve balance	\(S_{g} u_{g} p_{r,u} - d_{u, d} = 0\)
rbd	RegDn reserve balance	\(S_{g} u_{g} p_{r,d} - d_{d, d} = 0\)
rru	RegUp reserve source	\(u_{g} (p_g + p_{r,u}) - u_{g} p_{g, max, e} \leq 0\)
rrd	RegDn reserve source	\(u_{g} (-p_g + p_{r,d}) + u_{g} p_{g, min, e} \leq 0\)
rgu	Gen ramping up	\(u_{g} (p_g-p_{g, 0}-R_{10}) \leq 0\)
rgd	Gen ramping down	\(u_{g} (-p_g+p_{g, 0}-R_{10}) \leq 0\)
cdgb	Select DG power from pg	\(C_{DG} p_g - p_{g,DG} = 0\)
SOClb	SOC lower bound	\(-SOC + SOC_{min} \leq 0\)
SOCub	SOC upper bound	\(SOC - SOC_{max} \leq 0\)
cescb	Select pce from DG	\(C_{ESD} p_{g,DG} - p_{c,ESD} = 0\)
cesdb	Select pde from DG	\(C_{ESD} p_{g,DG} - p_{d,ESD} = 0\)
cdb	Charging decision bound	\(u_{c,ESD} + u_{d,ESD} - 1 = 0\)
zce1	zce bound 1	\(-z_{c,ESD} + p_{c,ESD} \leq 0\)
zce2	zce bound 2	\(z_{c,ESD} - p_{c,ESD} - M_{big} (1-u_{c,ESD}) \leq 0\)
zce3	zce bound 3	\(z_{c,ESD} - M_{big} u_{c,ESD} \leq 0\)
zde1	zde bound 1	\(-z_{d,ESD} + p_{d,ESD} \leq 0\)
zde2	zde bound 2	\(z_{d,ESD} - p_{d,ESD} - M_{big} (1-u_{d,ESD}) \leq 0\)
zde3	zde bound 3	\(z_{d,ESD} - M_{big} u_{d,ESD} \leq 0\)
SOCb	ESD1 SOC balance	\(E_n (SOC - SOC_{init}) - T_{cfg} \eta_c z_{c,ESD}+ T_{cfg} \frac{1}{\eta_d} z_{d,ESD} = 0\)

Vars

Name	Symbol	Description	Unit	Source	Properties
pg	\(p_g\)	Gen active power	p.u.	StaticGen.p
vBus	\(v_{Bus}\)	Bus voltage magnitude, placeholder	p.u.	Bus.v
aBus	\(\theta_{bus}\)	Bus voltage angle	rad	Bus.a
pru	\(p_{r,u}\)	RegUp reserve	p.u.	StaticGen	nonneg
prd	\(p_{r,d}\)	RegDn reserve	p.u.	StaticGen	nonneg
pgdg	\(p_{g,DG}\)	DG output power	p.u.	DG
SOC	\(SOC\)	ESD1 State of Charge	%	ESD1	pos
pce	\(p_{c,ESD}\)	ESD1 charging power	p.u.	ESD1	nonneg
pde	\(p_{d,ESD}\)	ESD1 discharging power	p.u.	ESD1	nonneg
uce	\(u_{c,ESD}\)	ESD1 charging decision		ESD1	boolean
ude	\(u_{d,ESD}\)	ESD1 discharging decision		ESD1	boolean
zce	\(z_{c,ESD}\)	Aux var for charging, \(z_{c,ESD}=u_{c,ESD}*p_{c,ESD}\)		ESD1	nonneg
zde	\(z_{d,ESD}\)	Aux var for discharging, \(z_{d,ESD}=u_{d,ESD}*p_{d,ESD}\)		ESD1	nonneg

ExpressionCalcs

Name	Description	Expression	Unit	Source
pi	LMP, dual of <pb>	\(\phi[pb]\)	$/p.u.	Bus

Services

Name	Symbol	Description	Type
csb	\(c_{sb}\)	select slack bus	VarSelect
ctrle	\(c_{trl, e}\)	Effective Gen controllability	NumOpDual
nctrl	\(c_{trl,n}\)	Effective Gen uncontrollability	NumOp
nctrle	\(c_{trl,n,e}\)	Effective Gen uncontrollability	NumOpDual
gs	\(S_{g}\)	Sum Gen vars vector in shape of area	ZonalSum
ds	\(S_{d}\)	Sum pd vector in shape of area	ZonalSum
pdz	\(p_{d,z}\)	zonal total load	NumOpDual
dud	\(d_{u, d}\)	zonal RegUp reserve requirement	NumOpDual
ddd	\(d_{d, d}\)	zonal RegDn reserve requirement	NumOpDual
cd	\(C_{DG}\)	Select DG power from pg	VarSelect
REtaD	\(\frac{1}{\eta_d}\)		NumOp
Mb	\(M_{big}\)	10 times of max of pmax as big M	NumOp
ces	\(C_{ESD}\)	Select ESD power from DG	VarSelect

Parameters

Name	Symbol	Description	Unit	Source
ug	\(u_{g}\)	Gen connection status		StaticGen.u
pg0	\(p_{g, 0}\)	Gen initial active power	p.u.	StaticGen.p0
gsh	\(g_{sh}\)	shunt conductance		Shunt.g
buss	\(B_{us,s}\)	Bus slack		Slack.bus
pd	\(p_{d}\)	active demand	p.u.	StaticLoad.p0
Cg	\(C_{g}\)	Gen connection matrix		MatProcessor.Cg
Cl	\(C_{l}\)	Load connection matrix		MatProcessor.Cl
CftT	\(C_{ft}^T\)	Transpose of line connection matrix		MatProcessor.CftT
Csh	\(C_{sh}\)	Shunt connection matrix		MatProcessor.Csh
Bbus	\(B_{bus}\)	Bus admittance matrix		MatProcessor.Bbus
Bf	\(B_{f}\)	Bf matrix		MatProcessor.Bf
Pbusinj	\(P_{bus}^{inj}\)	Bus power injection vector		MatProcessor.Pbusinj
Pfinj	\(P_{f}^{inj}\)	Line power injection vector		MatProcessor.Pfinj
c2	\(c_{2}\)	Gen cost coefficient 2	$/(p.u.^2)	GCost.c2
c1	\(c_{1}\)	Gen cost coefficient 1	$/(p.u.)	GCost.c1
c0	\(c_{0}\)	Gen cost coefficient 0	$	GCost.c0
ctrl	\(c_{trl}\)	Gen controllability		StaticGen.ctrl
pmax	\(p_{g, max}\)	Gen maximum active power	p.u.	StaticGen.pmax
pmin	\(p_{g, min}\)	Gen minimum active power	p.u.	StaticGen.pmin
ul	\(u_{l}\)	Line connection status		Line.u
rate_a	\(R_{ATEA}\)	long-term flow limit	p.u.	Line.rate_a
amax	\(\theta_{bus, max}\)	max line angle difference		Line.amax
amin	\(\theta_{bus, min}\)	min line angle difference		Line.amin
zg	\(z_{one,g}\)	Gen area		StaticGen.area
zd	\(z_{one,d}\)	Load area		StaticLoad.area
R10	\(R_{10}\)	10-min ramp rate	p.u./h	StaticGen.R10
cru	\(c_{r,u}\)	RegUp reserve coefficient	$/(p.u.)	SFRCost.cru
crd	\(c_{r,d}\)	RegDown reserve coefficient	$/(p.u.)	SFRCost.crd
du	\(d_{u}\)	RegUp reserve requirement in percentage	%	SFR.du
dd	\(d_{d}\)	RegDown reserve requirement in percentage	%	SFR.dd
gendg	\(g_{DG}\)	gen of DG		DG.gen
gammapd	\(\gamma_{p,DG}\)	Ratio of DG.pge w.r.t to that of static generator		DG.gammap
En	\(E_n\)	Rated energy capacity	MWh	ESD1.En
SOCmax	\(SOC_{max}\)	Maximum allowed value for SOC in limiter	%	ESD1.SOCmax
SOCmin	\(SOC_{min}\)	Minimum required value for SOC in limiter	%	ESD1.SOCmin
SOCinit	\(SOC_{init}\)	Initial SOC	%	ESD1.SOCinit
EtaC	\(\eta_c\)	Efficiency during charging	%	ESD1.EtaC
EtaD	\(\eta_d\)	Efficiency during discharging	%	ESD1.EtaD
genesd	\(g_{ESD}\)	gen of ESD1		ESD1.idx

Config Fields in [RTEDES]

Option	Symbol	Value	Info	Accepted values
t	\(T_{cfg}\)	0.083	time interval in hours

RTEDVIS

RTED with virtual inertia scheduling.

This class implements real-time economic dispatch with virtual inertia scheduling. Please ensure that the parameters dvm and dvd are set according to the system base.

References

1. B. She, F. Li, H. Cui, J. Wang, Q. Zhang and R. Bo, "Virtual Inertia Scheduling (VIS) for Real-Time Economic Dispatch of IBR-Penetrated Power Systems," in IEEE Transactions on Sustainable Energy, vol. 15, no. 2, pp. 938-951, April 2024, doi: 10.1109/TSTE.2023.3319307.

Objective

Unit	Expression
$	\(min. T_{cfg}^{2} \sum(c_{2} p_g^{2}) + \sum(u_{g} c_{0})+ T_{cfg} \sum(c_{1} p_g + c_{r,u} p_{r,u} + c_{r,d} p_{r,d})+ T_{cfg} \sum(c_{m} M + c_{d} D)\)

Expressions

Name	Description	Expression	Unit	Source
plf	Line flow	\(B_{f} \theta_{bus} + P_{f}^{inj}\)	p.u.	Line
pmaxe	Effective pmax	\(c_{trl,n,e} p_{g, 0} + c_{trl, e} p_{g, max}\)	p.u.	StaticGen
pmine	Effective pmin	\(c_{trl,n,e} p_{g, 0} + c_{trl, e} p_{g, min}\)	p.u.	StaticGen

Constraints

Name	Description	Expression
pb	power balance	\(B_{bus} \theta_{bus} + P_{bus}^{inj} + C_{l} p_{d} + C_{sh} g_{sh} - C_{g} p_g = 0\)
sbus	align slack bus angle	\(c_{sb} \theta_{bus} = 0\)
pglb	pg min	\(-p_g + p_{g, min, e} \leq 0\)
pgub	pg max	\(p_g - p_{g, max, e} \leq 0\)
plflb	line flow lower bound	\(-p_{lf} - u_{l} R_{ATEA} \leq 0\)
plfub	line flow upper bound	\(p_{lf} - u_{l} R_{ATEA} \leq 0\)
alflb	line angle difference lower bound	\(-C_{ft}^T \theta_{bus} + \theta_{bus, min} \leq 0\)
alfub	line angle difference upper bound	\(C_{ft}^T \theta_{bus} - \theta_{bus, max} \leq 0\)
rbu	RegUp reserve balance	\(S_{g} u_{g} p_{r,u} - d_{u, d} = 0\)
rbd	RegDn reserve balance	\(S_{g} u_{g} p_{r,d} - d_{d, d} = 0\)
rru	RegUp reserve source	\(u_{g} (p_g + p_{r,u}) - u_{g} p_{g, max, e} \leq 0\)
rrd	RegDn reserve source	\(u_{g} (-p_g + p_{r,d}) + u_{g} p_{g, min, e} \leq 0\)
rgu	Gen ramping up	\(u_{g} (p_g-p_{g, 0}-R_{10}) \leq 0\)
rgd	Gen ramping down	\(u_{g} (-p_g+p_{g, 0}-R_{10}) \leq 0\)
Mub	M upper bound	\(M - M_{max} \leq 0\)
Dub	D upper bound	\(D - D_{max} \leq 0\)
Mreq	Emulated inertia requirement	\(-S_{g} M + d_{v,m} = 0\)
Dreq	Emulated damping requirement	\(-S_{g} D + d_{v,d} = 0\)

Vars

Name	Symbol	Description	Unit	Source	Properties
pg	\(p_g\)	Gen active power	p.u.	StaticGen.p
vBus	\(v_{Bus}\)	Bus voltage magnitude, placeholder	p.u.	Bus.v
aBus	\(\theta_{bus}\)	Bus voltage angle	rad	Bus.a
pru	\(p_{r,u}\)	RegUp reserve	p.u.	StaticGen	nonneg
prd	\(p_{r,d}\)	RegDn reserve	p.u.	StaticGen	nonneg
M	\(M\)	Emulated startup time constant (M=2H)	s	VSG.M	nonneg
D	\(D\)	Emulated damping coefficient	p.u.	VSG.D	nonneg

ExpressionCalcs

Name	Description	Expression	Unit	Source
pi	LMP, dual of <pb>	\(\phi[pb]\)	$/p.u.	Bus

Services

Name	Symbol	Description	Type
csb	\(c_{sb}\)	select slack bus	VarSelect
ctrle	\(c_{trl, e}\)	Effective Gen controllability	NumOpDual
nctrl	\(c_{trl,n}\)	Effective Gen uncontrollability	NumOp
nctrle	\(c_{trl,n,e}\)	Effective Gen uncontrollability	NumOpDual
gs	\(S_{g}\)	Sum Gen vars vector in shape of area	ZonalSum
ds	\(S_{d}\)	Sum pd vector in shape of area	ZonalSum
pdz	\(p_{d,z}\)	zonal total load	NumOpDual
dud	\(d_{u, d}\)	zonal RegUp reserve requirement	NumOpDual
ddd	\(d_{d, d}\)	zonal RegDn reserve requirement	NumOpDual
gvsg	\(S_{g}\)	Sum VSG vars vector in shape of area	ZonalSum

Parameters

Name	Symbol	Description	Unit	Source
ug	\(u_{g}\)	Gen connection status		StaticGen.u
pg0	\(p_{g, 0}\)	Gen initial active power	p.u.	StaticGen.p0
gsh	\(g_{sh}\)	shunt conductance		Shunt.g
buss	\(B_{us,s}\)	Bus slack		Slack.bus
pd	\(p_{d}\)	active demand	p.u.	StaticLoad.p0
Cg	\(C_{g}\)	Gen connection matrix		MatProcessor.Cg
Cl	\(C_{l}\)	Load connection matrix		MatProcessor.Cl
CftT	\(C_{ft}^T\)	Transpose of line connection matrix		MatProcessor.CftT
Csh	\(C_{sh}\)	Shunt connection matrix		MatProcessor.Csh
Bbus	\(B_{bus}\)	Bus admittance matrix		MatProcessor.Bbus
Bf	\(B_{f}\)	Bf matrix		MatProcessor.Bf
Pbusinj	\(P_{bus}^{inj}\)	Bus power injection vector		MatProcessor.Pbusinj
Pfinj	\(P_{f}^{inj}\)	Line power injection vector		MatProcessor.Pfinj
c2	\(c_{2}\)	Gen cost coefficient 2	$/(p.u.^2)	GCost.c2
c1	\(c_{1}\)	Gen cost coefficient 1	$/(p.u.)	GCost.c1
c0	\(c_{0}\)	Gen cost coefficient 0	$	GCost.c0
ctrl	\(c_{trl}\)	Gen controllability		StaticGen.ctrl
pmax	\(p_{g, max}\)	Gen maximum active power	p.u.	StaticGen.pmax
pmin	\(p_{g, min}\)	Gen minimum active power	p.u.	StaticGen.pmin
ul	\(u_{l}\)	Line connection status		Line.u
rate_a	\(R_{ATEA}\)	long-term flow limit	p.u.	Line.rate_a
amax	\(\theta_{bus, max}\)	max line angle difference		Line.amax
amin	\(\theta_{bus, min}\)	min line angle difference		Line.amin
zg	\(z_{one,g}\)	Gen area		StaticGen.area
zd	\(z_{one,d}\)	Load area		StaticLoad.area
R10	\(R_{10}\)	10-min ramp rate	p.u./h	StaticGen.R10
cru	\(c_{r,u}\)	RegUp reserve coefficient	$/(p.u.)	SFRCost.cru
crd	\(c_{r,d}\)	RegDown reserve coefficient	$/(p.u.)	SFRCost.crd
du	\(d_{u}\)	RegUp reserve requirement in percentage	%	SFR.du
dd	\(d_{d}\)	RegDown reserve requirement in percentage	%	SFR.dd
cm	\(c_{m}\)	Virtual inertia cost	$/s	VSGCost.cm
cd	\(c_{d}\)	Virtual damping cost	$/(p.u.)	VSGCost.cd
zvsg	\(z_{one,vsg}\)	VSG zone		VSG.zone
Mmax	\(M_{max}\)	Maximum inertia emulation	s	VSG.Mmax
Dmax	\(D_{max}\)	Maximum damping emulation	p.u.	VSG.Dmax
dvm	\(d_{v,m}\)	Emulated inertia requirement	s	VSGR.dvm
dvd	\(d_{v,d}\)	Emulated damping requirement	p.u.	VSGR.dvd

Config Fields in [RTEDVIS]

Option	Symbol	Value	Info	Accepted values
t	\(T_{cfg}\)	0.083	time interval in hours