PF

Type for power flow routines.

Common Parameters: pd

Common Vars: pg

Available routines: DCPF, PFlow, CPF, PFlow0, DCPF0

DCPF

DC power flow.

Objective

Unit	Expression
$	\(min. 0\)

Expressions

Name	Description	Expression	Unit	Source
plf	Line flow	\(B_{f} \theta_{bus} + P_{f}^{inj}\)	p.u.	Line

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	\(c_{sb} \theta_{bus} = 0\)
pvb	PV generator	\(C_{PV} (p_g - u_{g} p_{g, 0}) = 0\)

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

Services

Name	Symbol	Description	Type
csb	\(c_{sb}\)	select slack bus	VarSelect
cpv	\(C_{PV}\)	Select PV 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
genpv	\(g_{DG}\)	gen of PV		PV.idx

PFlow

Power flow analysis using ANDES PFlow routine.

More settings can be changed via PFlow2._adsys.config and PFlow2._adsys.PFlow.config.

All generator output powers, bus voltages, and angles are included in the variable definitions. However, not all of these are unknowns; the definitions are provided for easy access.

References

1. 13. 12. Crow, Computational methods for electric power systems. 2015.

2. ANDES Documentation - Simulation and Plot. https://docs.andes.app/en/latest/_examples/ex1.html

Objective

Unit	Expression
$	\(min. 0\)

Expressions

Name	Description	Expression	Unit	Source
plf	Line flow	\(B_{f} \theta_{bus} + P_{f}^{inj}\)	p.u.	Line

Vars

Name	Symbol	Description	Unit	Source	Properties
pg	\(p_g\)	Gen active power	p.u.	StaticGen.p
qg	\(q_g\)	Gen reactive power	p.u.	StaticGen.q
aBus	\(\theta_{bus}\)	Bus voltage angle	rad	Bus.a
vBus	\(V_{bus}\)	Bus voltage magnitude	p.u.	Bus.v

Parameters

Name	Symbol	Description	Unit	Source
Bf	\(B_{f}\)	Bf matrix		MatProcessor.Bf
Pfinj	\(P_{f}^{inj}\)	Line power injection vector		MatProcessor.Pfinj

Config Fields in [PFlow]

Option	Symbol	Value	Info	Accepted values
tol		0.000	convergence tolerance	float
max_iter		25	max. number of iterations	>=10
method		NR	calculation method	('NR', 'dishonest', 'NK')
check_conn		1	check connectivity before power flow	(0, 1)
n_factorize		4	first N iterations to factorize Jacobian in dishonest method	>0

CPF

Continuous power flow.

Still under development, not ready for use.

Objective

Unit	Expression
$	\(min. 0\)

Expressions

Name	Description	Expression	Unit	Source
plf	Line flow	\(B_{f} \theta_{bus} + P_{f}^{inj}\)	p.u.	Line

Vars

Name	Symbol	Description	Unit	Source	Properties
pg	\(p_g\)	Gen active power	p.u.	StaticGen.p
qg	\(q_g\)	Gen reactive power	p.u.	StaticGen.q
aBus	\(\theta_{bus}\)	Bus voltage angle	rad	Bus.a
vBus	\(V_{bus}\)	Bus voltage magnitude	p.u.	Bus.v

Parameters

Name	Symbol	Description	Unit	Source
Bf	\(B_{f}\)	Bf matrix		MatProcessor.Bf
Pfinj	\(P_{f}^{inj}\)	Line power injection vector		MatProcessor.Pfinj

Config Fields in [CPF]

Option	Symbol	Value	Info	Accepted values
tol		0.000	convergence tolerance	float
max_iter		25	max. number of iterations	>=10
method		NR	calculation method	('NR', 'dishonest', 'NK')
check_conn		1	check connectivity before power flow	(0, 1)
n_factorize		4	first N iterations to factorize Jacobian in dishonest method	>0

PFlow0

AC Power Flow using PYPOWER.

This class is deprecated as of version 0.9.12 and will be removed in 1.1.0.

Notes

1. AC pwoer flow is solved with PYPOWER runpf function.

2. AC power flow formulation in AMS style is NOT DONE YET, but this does not affect the results because the data are passed to PYPOWER for solving.

Vars

Name	Symbol	Description	Unit	Source	Properties
pg	\(p_{g}\)	Gen active power	p.u.	StaticGen.p
aBus	\(a_{Bus}\)	bus voltage angle	rad	Bus.a
plf	\(p_{lf}\)	Line flow	p.u.	Line
vBus	\(v_{Bus}\)	bus voltage magnitude	p.u.	Bus.v
qg	\(q_{g}\)	reactive power generation	p.u.	StaticGen.q

Parameters

Name	Symbol	Description	Unit	Source
ug	\(u_{g}\)	Gen connection status		StaticGen.u
x	\(x\)	line reactance	p.u.	Line.x
tap	\(t_{ap}\)	transformer branch tap ratio	float	Line.tap
phi	\(\phi\)	transformer branch phase shift in rad	radian	Line.phi
pd	\(p_{d}\)	active deman	p.u.	StaticLoad.p0
qd	\(q_{d}\)	reactive power load in system base	p.u.	StaticLoad.q0

Config Fields in [PFlow0]

Option	Symbol	Value	Info	Accepted values
qlim		0	Enforce generator q limits	(0, 1, 2)

DCPF0

DC power flow using PYPOWER.

This class is deprecated as of version 0.9.12 and will be removed in 1.1.0.

Notes

1. DCPF is solved with PYPOWER runpf function.

2. DCPF formulation is not complete yet, but this does not affect the results because the data are passed to PYPOWER for solving.

Vars

Name	Symbol	Description	Unit	Source	Properties
pg	\(p_{g}\)	Gen active power	p.u.	StaticGen.p
aBus	\(a_{Bus}\)	bus voltage angle	rad	Bus.a
plf	\(p_{lf}\)	Line flow	p.u.	Line

Parameters

Name	Symbol	Description	Unit	Source
ug	\(u_{g}\)	Gen connection status		StaticGen.u
x	\(x\)	line reactance	p.u.	Line.x
tap	\(t_{ap}\)	transformer branch tap ratio	float	Line.tap
phi	\(\phi\)	transformer branch phase shift in rad	radian	Line.phi
pd	\(p_{d}\)	active deman	p.u.	StaticLoad.p0