PLL#
Phase-locked loop models.
Common Parameters: u, name
Common Variables: am
PLL1#
Simple Phasor Lock Loop (PLL) using one PI controller. The PI controller minimizes the error between the input and output angle.
Input bus angle signal -> Lag filter 1 with Tf -> Output angle af_y.
(af_y - am) -> PI Controller (Kp, Ki) -> PI_y
Estimated angle ae = (2 * pi * fn * PI_y) -> Lag filter 2 with Tp -> am.
The output signal is am, a state variable.
Parameters#
Name |
Symbol |
Description |
Default |
Unit |
Properties |
|---|---|---|---|---|---|
idx |
unique device idx |
||||
u |
\(u\) |
connection status |
1 |
bool |
|
name |
device name |
||||
bus |
bus idx |
mandatory |
|||
fn |
\(f_n\) |
nominal frequency |
60 |
Hz |
|
Kp |
\(K_p\) |
proportional gain |
0.100 |
||
Ki |
\(K_i\) |
integral gain |
0.100 |
||
Tf |
\(T_f\) |
input digital filter time const |
0.050 |
sec |
|
Tp |
\(T_p\) |
output filter time const. |
0.050 |
sec |
Variables#
Name |
Symbol |
Type |
Description |
Unit |
Properties |
|---|---|---|---|---|---|
af_y |
\(af_{y}\) |
State |
State in lag transfer function |
v_str |
|
PI_xi |
\(\pi_{\xi}\) |
State |
Integrator output |
v_str |
|
ae |
\(ae\) |
State |
PLL angle output before filter |
v_str |
|
am |
\(am\) |
State |
PLL output angle after filtering |
v_str |
|
PI_y |
\(\pi_{y}\) |
Algeb |
PI output |
v_str |
|
a |
\(a\) |
ExtAlgeb |
Bus voltage angle |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
|---|---|---|---|
af_y |
\(af_{y}\) |
State |
\(a\) |
PI_xi |
\(\pi_{\xi}\) |
State |
\(0.0\) |
ae |
\(ae\) |
State |
\(a\) |
am |
\(am\) |
State |
\(a\) |
PI_y |
\(\pi_{y}\) |
Algeb |
\(Kp u \left(af_{y} - am\right)\) |
a |
\(a\) |
ExtAlgeb |
Differential Equations#
Name |
Symbol |
Type |
RHS of Equation "T x' = f(x, y)" |
T (LHS) |
|---|---|---|---|---|
af_y |
\(af_{y}\) |
State |
\(a - af_{y}\) |
\(T_f\) |
PI_xi |
\(\pi_{\xi}\) |
State |
\(Ki u \left(af_{y} - am\right)\) |
|
ae |
\(ae\) |
State |
\(2 \pi \pi_{y} fn\) |
|
am |
\(am\) |
State |
\(ae - am\) |
\(T_p\) |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
|---|---|---|---|
PI_y |
\(\pi_{y}\) |
Algeb |
\(Kp u \left(af_{y} - am\right) + \pi_{\xi} - \pi_{y}\) |
a |
\(a\) |
ExtAlgeb |
\(0\) |
Blocks#
Name |
Symbol |
Type |
Info |
|---|---|---|---|
af |
\(af\) |
Lag |
input angle signal filter |
PI |
\(PI\) |
PIController |
PI controller |
Config Fields in [PLL1]
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) |
PLL2#
Synchronously-rotating Reference Frame (SRF) Phasor Lock Loop (PLL).
The PLL minimizes vq = v sin(a - am) using a PI controller.
The output signal is am, a state variable.
Parameters#
Name |
Symbol |
Description |
Default |
Unit |
Properties |
|---|---|---|---|---|---|
idx |
unique device idx |
||||
u |
\(u\) |
connection status |
1 |
bool |
|
name |
device name |
||||
bus |
bus idx |
mandatory |
|||
fn |
\(f_n\) |
nominal frequency |
60 |
Hz |
|
Kp |
\(K_p\) |
proportional gain |
0.100 |
||
Ki |
\(K_i\) |
integral gain |
0.100 |
Variables#
Name |
Symbol |
Type |
Description |
Unit |
Properties |
|---|---|---|---|---|---|
PI_xi |
\(\pi_{\xi}\) |
State |
Integrator output |
v_str |
|
am |
\(am\) |
State |
PLL angle output |
v_str |
|
PI_y |
\(\pi_{y}\) |
Algeb |
PI output |
v_str |
|
a |
\(a\) |
ExtAlgeb |
Bus voltage angle |
||
v |
\(v\) |
ExtAlgeb |
Bus voltage magnitude |
Initialization Equations#
Name |
Symbol |
Type |
Initial Value |
|---|---|---|---|
PI_xi |
\(\pi_{\xi}\) |
State |
\(0\) |
am |
\(am\) |
State |
\(a\) |
PI_y |
\(\pi_{y}\) |
Algeb |
\(Kp v \sin{\left(a - am \right)}\) |
a |
\(a\) |
ExtAlgeb |
|
v |
\(v\) |
ExtAlgeb |
Differential Equations#
Name |
Symbol |
Type |
RHS of Equation "T x' = f(x, y)" |
T (LHS) |
|---|---|---|---|---|
PI_xi |
\(\pi_{\xi}\) |
State |
\(Ki v \sin{\left(a - am \right)}\) |
|
am |
\(am\) |
State |
\(2 \pi \pi_{y} fn\) |
Algebraic Equations#
Name |
Symbol |
Type |
RHS of Equation "0 = g(x, y)" |
|---|---|---|---|
PI_y |
\(\pi_{y}\) |
Algeb |
\(Kp v \sin{\left(a - am \right)} + \pi_{\xi} - \pi_{y}\) |
a |
\(a\) |
ExtAlgeb |
\(0\) |
v |
\(v\) |
ExtAlgeb |
\(0\) |
Blocks#
Name |
Symbol |
Type |
Info |
|---|---|---|---|
PI |
\(PI\) |
PIController |
Config Fields in [PLL2]
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) |