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# PLL, 1-ph

The PLL, 1-ph component models a Phase Lock Loop (PLL) closed-loop control system, which tracks the frequency and phase of a sinusoidal signal by using an internal frequency oscillator.

The input signal **u** is mixed with an internal oscillator signal. The DC component of the mixed signal is extracted with a variable frequency mean value (Phase detector section). A Proportional-Integral-Derivative (PID) controller keeps the phase difference to 0 by acting on a controlled oscillator.

The controlled oscillator output corresponds to the output angular velocity signal defined by **wt**. The PID output is filtered using a low-pass filter (rate limited) and converted to frequency, which is used by the mean value. The filtered signal corresponds to the output frequency signal defined by **f**.

# Symbol

## Mask Parameters

### Main Tab

Name | Description | Unit | Variable = {Possible Values} | |
---|---|---|---|---|

Description | Use this field to add all kinds of information about the component | Description = {'string'} | ||

Initial frequency | Initial frequency for the first simulation cycle. This value cannot be modified during the simulation | Hz | Finit = { [0, 1e12] } | |

Minimum frequency | Minimum expected frequency of the input signal. This value cannot be modified during the simulation | Hz | Fmin = { [0, 1e12] } | |

Initial phase | Initial value of the phase of the output signal for the first simulation cycle. This value cannot be modified during the simulation | deg. | InitialPhase = { [0, 360] } |

### PID Controller tab

Name | Description | Unit | Variable = {Possible Values} | |
---|---|---|---|---|

Kp | Internal PID controller proportional gain | Kp = { [0, 1e12] } | ||

Ki | Internal PID controller integral gain | Ki = { [0, 1e12] } | ||

Kd | Internal PID controller derivative gain | Kd = { [0, 1e12] } | ||

Lower limit | Lower limit of the PI integral action. This value cannot be modified during the simulation | LowerLimit = { [-1e64, 1e64] } | ||

Upper limit | Upper limit of the PI integral action. This value should be greater than the value of the Lower limit parameter. This value cannot be modified during the simulation | UpperLimit = { [-1e64, 1e64] } | ||

Initial condition | Integrator initial condition. This value cannot be modified during the simulation | Integrator_InitialCondition = { [0, 1e12] } | ||

Time constant for derivative action | Time constant for the first-order filter of the derivative action from the internal PID controller | s | Tc_Derivative = { [0, 1e12] } | |

Duration of initial value | Duration of the initial value of the internal PID controller output signal. This value cannot be modified during the simulation | s | Tinit = { [0, 1e12] } |

### Second-Order Filter tab

Name | Description | Unit | Variable = {Possible Values} | |
---|---|---|---|---|

Maximum rate of change of frequency | Maximum positive and negative slope of the frequency of the second-order low pass filter input signal | Hz/s | Freq_RateLimiter = { [0, 1e12] } | |

Filter natural frequency | Internal second-order natural low-passe filter frequency | Hz | FreqFilter_fn = { [0, 1e12] } | |

Filter damping ratio | Second-order low-pass filter damping rate. The damping ratio is typically a value between 0 and 1 | FreqFilter_zeta = { [0, 1] } |

## Input/Output Signals

Name | Description | Unit | Type |
---|---|---|---|

In | Input signal | pu | Input |

f | Measured frequency signal. | Hz | Output |

wt | Angle signal varying between 0 and 2 * pi, synchronized to the zero-crossing (ascending) of the fundamental of the input signal. | rad | Output |

## Sensor Descriptions

Name | Description | Unit |
---|---|---|

In | Input signal | pu |

f | Measured frequency signal. | Hz |

wt | Angle signal varying between 0 and 2 * pi, synchronized to the zero-crossing (ascending) of the fundamental of the input signal. | rad |

# Internal Circuit of Component

### Limitations

In the PLL, 1-ph component, since the internal Proportional-Integral-Derivative (PID) controller has no automatic gain control, the input signal should be in pu and have a value not too distant from one.

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