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Use the SOGI PLL.

Introduction

The Second Order Generalized Integrator based PLL SOGI-PLL is a filter used to retrieve phase information from a mono phase or three phased system. It is included in the filters.cpp module.

Digital implementation of the SOGI PLL is done using the impulse invariant using \(R_{1h}\) discretization method.

block diagram of SOGI PLL
  • SOGI QSG stands for Quadrature Signal Generator. It takes an input signal and output the signal in \(\(\alpha\beta\)\) frame. This QSG is particularily useful for single phase systems where a simple Clark transform can not be used.
  • SRF PLL stands for Synchronous Reference Frame Phase Lock Loop. It takes an input signal in the \(\(\alpha\beta\)\) frame and retrieve the angle \(\(\theta\)\) and the pulsation \(\(\omega\)\)

Parameters:

The SOGI PLL is discretized form is the following:

\(R_{1hd} = Kr \times Ts \left(. \cos(\phi') . \dfrac{1- z^{-1}.cos(\omega .T_s)}{1 - 2.z^{-1}cos(\omega T_s)+z^{-2}} -sin(\phi').\dfrac{z^{-1}.sin(\omega .T_s)}{1 - 2.z^{-1}cos(\omega T_s)+z^{-2}}\right)\)

Kr parameter augment SOGI PLL dynamic but decrease its selectivity.

Retrieve Quadrature signal

Following equations are expanded :

\[cos(\theta_k) = cos(\theta_{k-1} +\omega.Ts)\]
\[sin(\theta_k) = sin(\theta_{k-1} +\omega.Ts)\]

Hence we derive the quadrature sinus term

\[sin(\theta_k) = -\dfrac{cos(\omega . Ts)}{sin(\omega .Ts)}.cos(\theta_k) + \dfrac{1}{sin(\omega . Ts)}.cos(\theta_{k-1})\]

Use of the SOGI filter.

The use of the `Sogi is based on 3 steps.

  1. Object instanciation (declaration).
  2. Initialisation.
  3. Execution.

Example

We define constants used to initialize the parameter structure. 

#include "filters.h"

static float32_t kr = 500;                // Sogi filter gain defining dynamics
static float32_t Ts = 100.0e-6F;          // sampling time of the control period [s]

We define the variable sogi_filter which is an instance of Sogi object. 

static Sogi sogi_filter;

In the setup_routine() of the OwnTech Power API, you must initialize the sogi_filter with its parameters.

sogi_filter.init(Ts, kr);

In the loop_critical_task() you can call the method calculateWithReturn()

sogi_data = sogi_filter.calculateWithReturn(signal_to_track);

sogi_data is a structure which kept the results of the sogi_filter calculation for one step.

the SogiData structure has 3 fields: 

struct SogiData {
    float32_t theta;      // estimated angle [rad]
    float32_t alpha;      // cosinus term
    float32_t beta;       // sinus term
};

Note

Remind that the loop_critical_task() is called at the sampling time you define and must be equal to \(T_s\).

Example

You can find a Sogi use with the grid following example which requires a synchronisation to inject current in parallel with a voltage source.