StaticLoad#
Static load group.
Common Parameters: u, name
Available models: PQ
PQ#
PQ load model.
Implements an automatic pq2z conversion during power flow when the voltage is outside [vmin, vmax]. The conversion can be turned off by setting pq2z to 0 in the Config file.
Before timedomain simulation, PQ load will be converted to impedance, current source, and power source based on the weights in the Config file.
Weights (p2p, p2i, p2z) corresponds to the weights for constant power, constant current and constant impedance. p2p, p2i and p2z must be in decimal numbers and sum up exactly to 1. The same rule applies to (q2q, q2i, q2z).
To alter the PQ load in terms of power during simulation, one needs to set the conversion weights to preserve the constant power portion. For example, the PQ can remain as constant power load by setting
ss.PQ.config.p2p = 1.0
ss.PQ.config.p2i = 0
ss.PQ.config.p2z = 0
ss.PQ.config.q2q = 1.0
ss.PQ.config.q2i = 0
ss.PQ.config.q2z = 0
Then, the constant power portion can be altered by
changing the Ppf
and Qpf
constants for active power
and reactive power.
The equivalent constant current components are in
constants Ipeq
and Iqeq
for active and reactive current,
and the equivalent impedances are in Req
and Xeq
.
Parameters#
Name 
Symbol 
Description 
Default 
Unit 
Properties 

idx 
unique device idx 

u 
\(u\) 
connection status 
1 
bool 

name 
device name 

bus 
linked bus idx 
mandatory 

Vn 
\(V_n\) 
AC voltage rating 
110 
kV 
non_zero 
p0 
\(p_0\) 
active power load in system base 
0 
p.u. 

q0 
\(q_0\) 
reactive power load in system base 
0 
p.u. 

vmax 
\(v_{max}\) 
max voltage before switching to impedance 
1.200 

vmin 
\(v_{min}\) 
min voltage before switching to impedance 
0.800 

owner 
owner idx 
Variables#
Name 
Symbol 
Type 
Description 
Unit 
Properties 

a 
\(\theta\) 
ExtAlgeb 

v 
\(V\) 
ExtAlgeb 
Initialization Equations#
Name 
Symbol 
Type 
Initial Value 

a 
\(\theta\) 
ExtAlgeb 

v 
\(V\) 
ExtAlgeb 
Algebraic Equations#
Name 
Symbol 
Type 
RHS of Equation "0 = g(x, y)" 

a 
\(\theta\) 
ExtAlgeb 
\(u \left(I_{peq} V \gamma_{p2i} + P_{pf} \gamma_{p2p} + R_{eq} V^{2} \gamma_{p2z}\right) \operatorname{Indicator}{\left(t_{dae} > 0 \right)} + u \left(R_{lb} V^{2} z_{l}^{vcmp} + R_{ub} V^{2} z_{u}^{vcmp} + p_{0} z_{i}^{vcmp}\right) \operatorname{Indicator}{\left(t_{dae} \leq 0 \right)}\) 
v 
\(V\) 
ExtAlgeb 
\(u \left(I_{qeq} V \gamma_{q2i} + Q_{pf} \gamma_{q2q} + V^{2} X_{eq} \gamma_{q2z}\right) \operatorname{Indicator}{\left(t_{dae} > 0 \right)} + u \left(V^{2} X_{lb} z_{l}^{vcmp} + V^{2} X_{ub} z_{u}^{vcmp} + q_{0} z_{i}^{vcmp}\right) \operatorname{Indicator}{\left(t_{dae} \leq 0 \right)}\) 
Services#
Name 
Symbol 
Equation 
Type 

Rub 
\(R_{ub}\) 
\(\frac{p_{0}}{v_{max}^{2}}\) 
ConstService 
Xub 
\(X_{ub}\) 
\(\frac{q_{0}}{v_{max}^{2}}\) 
ConstService 
Rlb 
\(R_{lb}\) 
\(\frac{p_{0}}{v_{min}^{2}}\) 
ConstService 
Xlb 
\(X_{lb}\) 
\(\frac{q_{0}}{v_{min}^{2}}\) 
ConstService 
Ppf 
\(P_{pf}\) 
\(R_{lb} V_{0}^{2} z_{l}^{vcmp} + R_{ub} V_{0}^{2} z_{u}^{vcmp} + p_{0} z_{i}^{vcmp}\) 
ConstService 
Qpf 
\(Q_{pf}\) 
\(V_{0}^{2} X_{lb} z_{l}^{vcmp} + V_{0}^{2} X_{ub} z_{u}^{vcmp} + q_{0} z_{i}^{vcmp}\) 
ConstService 
Req 
\(R_{eq}\) 
\(\frac{P_{pf}}{V_{0}^{2}}\) 
ConstService 
Xeq 
\(X_{eq}\) 
\(\frac{Q_{pf}}{V_{0}^{2}}\) 
ConstService 
Ipeq 
\(I_{peq}\) 
\(\frac{P_{pf}}{V_{0}}\) 
ConstService 
Iqeq 
\(I_{qeq}\) 
\(\frac{Q_{pf}}{V_{0}}\) 
ConstService 
Discretes#
Name 
Symbol 
Type 
Info 

vcmp 
\(vcmp\) 
Limiter 
Config Fields in [PQ]
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) 

pq2z 
\(z_{pq2z}\) 
1 
pq2z conversion if out of voltage limits 
(0, 1) 
p2p 
\(\gamma_{p2p}\) 
0 
P constant power percentage for TDS. Must have (p2p+p2i+p2z)=1 
float 
p2i 
\(\gamma_{p2i}\) 
0 
P constant current percentage 
float 
p2z 
\(\gamma_{p2z}\) 
1 
P constant impedance percentage 
float 
q2q 
\(\gamma_{q2q}\) 
0 
Q constant power percentage for TDS. Must have (q2q+q2i+q2z)=1 
float 
q2i 
\(\gamma_{q2i}\) 
0 
Q constant current percentage 
float 
q2z 
\(\gamma_{q2z}\) 
1 
Q constant impedance percentage 
float 