Interface#

Group for interface models.

Available models: Fortescue

Fortescue#

Fortescue's symmetric component interface.

This model interfaces a positive-sequence, single-phase-equivalent bus with three buses representing three phases. It is effectively a transformer with one terminal on the primary side and three on the secondary. Only the positive sequence component on the secondary winding is used for simulation.

The positive-sequence voltage magnitude and angle of the secondary winding are named vp and ap.

The negative and zero sequence variables given in the d- and q-axis due the angle being undefined when the voltage is zero. The negative sequence voltages are vnd and vnq for the d- anx q-axis, respectively. Likewise, the zero-sequence voltages are vzd and vzq.

Parameters#

Name

Symbol

Description

Default

Unit

Properties

idx

unique device idx

u

\(u\)

connection status

1

bool

name

device name

bus

bus idx for the single-phase equivalent

mandatory

busa

bus idx for phase a

mandatory

busb

bus idx for phase b

mandatory

busc

bus idx for phase c

mandatory

Sn

\(S_n\)

Power rating

100

MW

non_zero

r

\(r\)

resistance

0.001

p.u.

z

x

\(x\)

short-circuit reactance

0.025

p.u.

non_zero,z

g

iron loss

0

p.u.

y

b

magnetizing susceptance

0.005

p.u.

y

Variables#

Name

Symbol

Type

Description

Unit

Properties

vp

\(V_{p}\)

Algeb

positive sequence voltage magnitude

v_str

ap

\(\theta_{p}\)

Algeb

positive sequence voltage phase

v_str

vnd

\(V_{nd}\)

Algeb

negative sequence voltage on d-axis (cos)

v_str

vnq

\(V_{nq}\)

Algeb

negative sequence voltage on q-axis (sin)

v_str

vzd

\(V_{zd}\)

Algeb

zero sequence voltage on d-axis (cos)

v_str

vzq

\(V_{zq}\)

Algeb

zero sequence voltage on q-axis (sin)

v_str

a

\(\theta_{1}\)

ExtAlgeb

phase angle of single-phase eq. bus

aa

\(\theta_{a}\)

ExtAlgeb

phase angle of bus for phase a

ab

\(\theta_{b}\)

ExtAlgeb

phase angle of bus for phase b

ac

\(\theta_{c}\)

ExtAlgeb

phase angle of bus for phase c

v

\(V_{1}\)

ExtAlgeb

voltage of single-phase eq. bus

va

\(V_{a}\)

ExtAlgeb

voltage of bus for phase a

vb

\(V_{b}\)

ExtAlgeb

voltage of bus for phase b

vc

\(V_{c}\)

ExtAlgeb

voltage of bus for phase c

Initialization Equations#

Name

Symbol

Type

Initial Value

vp

\(V_{p}\)

Algeb

\(\frac{V_{a}}{3} + \frac{V_{b}}{3} + \frac{V_{c}}{3}\)

ap

\(\theta_{p}\)

Algeb

\(\theta_{a} + \theta_{b} + \theta_{c}\)

vnd

\(V_{nd}\)

Algeb

\(0.0\)

vnq

\(V_{nq}\)

Algeb

\(0.0\)

vzd

\(V_{zd}\)

Algeb

\(0.0\)

vzq

\(V_{zq}\)

Algeb

\(0.0\)

a

\(\theta_{1}\)

ExtAlgeb

aa

\(\theta_{a}\)

ExtAlgeb

ab

\(\theta_{b}\)

ExtAlgeb

ac

\(\theta_{c}\)

ExtAlgeb

v

\(V_{1}\)

ExtAlgeb

va

\(V_{a}\)

ExtAlgeb

vb

\(V_{b}\)

ExtAlgeb

vc

\(V_{c}\)

ExtAlgeb

Algebraic Equations#

Name

Symbol

Type

RHS of Equation "0 = g(x, y)"

vp

\(V_{p}\)

Algeb

\(- V_{p} + \frac{\sqrt{\left(V_{b} \sin{\left(120^{o} - \theta_{a} + \theta_{b} \right)} - V_{c} \sin{\left(120^{o} + \theta_{a} - \theta_{c} \right)}\right)^{2} + \left(V_{a} + V_{b} \cos{\left(120^{o} - \theta_{a} + \theta_{b} \right)} + V_{c} \cos{\left(120^{o} + \theta_{a} - \theta_{c} \right)}\right)^{2}}}{3}\)

ap

\(\theta_{p}\)

Algeb

\(\theta_{a} - \theta_{p} + \operatorname{atan}_{2}{\left(V_{b} \sin{\left(120^{o} - \theta_{a} + \theta_{b} \right)} - V_{c} \sin{\left(120^{o} + \theta_{a} - \theta_{c} \right)},V_{a} + V_{b} \cos{\left(120^{o} - \theta_{a} + \theta_{b} \right)} + V_{c} \cos{\left(120^{o} + \theta_{a} - \theta_{c} \right)} \right)}\)

vnd

\(V_{nd}\)

Algeb

\(V_{a} \cos{\left(\theta_{a} \right)} + V_{b} \cos{\left(120^{o} - \theta_{b} \right)} + V_{c} \cos{\left(120^{o} + \theta_{c} \right)} - V_{nd}\)

vnq

\(V_{nq}\)

Algeb

\(V_{a} \sin{\left(\theta_{a} \right)} - V_{b} \sin{\left(120^{o} - \theta_{b} \right)} + V_{c} \sin{\left(120^{o} + \theta_{c} \right)} - V_{nq}\)

vzd

\(V_{zd}\)

Algeb

\(V_{a} \cos{\left(\theta_{a} \right)} + V_{b} \cos{\left(\theta_{b} \right)} + V_{c} \cos{\left(\theta_{c} \right)} - V_{zd}\)

vzq

\(V_{zq}\)

Algeb

\(V_{a} \sin{\left(\theta_{a} \right)} + V_{b} \sin{\left(\theta_{b} \right)} + V_{c} \sin{\left(\theta_{c} \right)} - V_{zq}\)

a

\(\theta_{1}\)

ExtAlgeb

\(u \left(V_{1}^{2} \left(g + g_{hk}\right) - V_{1} V_{p} \left(b_{hk} \sin{\left(\theta_{1} - \theta_{p} \right)} + g_{hk} \cos{\left(\theta_{1} - \theta_{p} \right)}\right)\right)\)

aa

\(\theta_{a}\)

ExtAlgeb

\(\frac{u \left(- V_{1} V_{a} \left(- b_{hk} \sin{\left(\theta_{1} - \theta_{a} \right)} + g_{hk} \cos{\left(\theta_{1} - \theta_{a} \right)}\right) + V_{a}^{2} \left(g + g_{hk}\right)\right)}{3}\)

ab

\(\theta_{b}\)

ExtAlgeb

\(\frac{u \left(- V_{1} V_{b} \left(b_{hk} \sin{\left(120^{o} - \theta_{1} + \theta_{b} \right)} + g_{hk} \cos{\left(120^{o} - \theta_{1} + \theta_{b} \right)}\right) + V_{b}^{2} \left(g + g_{hk}\right)\right)}{3}\)

ac

\(\theta_{c}\)

ExtAlgeb

\(\frac{u \left(- V_{1} V_{c} \left(- b_{hk} \sin{\left(120^{o} + \theta_{1} - \theta_{c} \right)} + g_{hk} \cos{\left(120^{o} + \theta_{1} - \theta_{c} \right)}\right) + V_{c}^{2} \left(g + g_{hk}\right)\right)}{3}\)

v

\(V_{1}\)

ExtAlgeb

\(u \left(- V_{1}^{2} \left(b + b_{hk}\right) - V_{1} V_{p} \left(- b_{hk} \cos{\left(\theta_{1} - \theta_{p} \right)} + g_{hk} \sin{\left(\theta_{1} - \theta_{p} \right)}\right)\right)\)

va

\(V_{a}\)

ExtAlgeb

\(\frac{u \left(V_{1} V_{a} \left(b_{hk} \cos{\left(\theta_{1} - \theta_{a} \right)} + g_{hk} \sin{\left(\theta_{1} - \theta_{a} \right)}\right) - V_{a}^{2} \left(b + b_{hk}\right)\right)}{3}\)

vb

\(V_{b}\)

ExtAlgeb

\(\frac{u \left(V_{1} V_{b} \left(b_{hk} \cos{\left(120^{o} - \theta_{1} + \theta_{b} \right)} - g_{hk} \sin{\left(120^{o} - \theta_{1} + \theta_{b} \right)}\right) - V_{b}^{2} \left(b + b_{hk}\right)\right)}{3}\)

vc

\(V_{c}\)

ExtAlgeb

\(\frac{u \left(V_{1} V_{c} \left(b_{hk} \cos{\left(120^{o} + \theta_{1} - \theta_{c} \right)} + g_{hk} \sin{\left(120^{o} + \theta_{1} - \theta_{c} \right)}\right) - V_{c}^{2} \left(b + b_{hk}\right)\right)}{3}\)

Services#

Name

Symbol

Equation

Type

yhk

\(y_{hk}\)

\(\frac{u}{r + i x}\)

ConstService

ghk

\(g_{hk}\)

\(\operatorname{re}{\left(y_{hk}\right)}\)

ConstService

bhk

\(b_{hk}\)

\(\operatorname{im}{\left(y_{hk}\right)}\)

ConstService

d120

\(120^o\)

\(\frac{2 \pi}{3}\)

ConstService

Config Fields in [Fortescue]

Option

Symbol

Value

Info

Accepted values

allow_adjust

1

allow adjusting upper or lower limits

(0, 1)

adjust_lower

0

adjust lower limit

(0, 1)

adjust_upper

1

adjust upper limit

(0, 1)