# Issues on Dynamic Modeling and Design of Grid-Connected Three-Phase VSIs in Photovoltaic Applications

##### Puukko, Joonas (2012)

Puukko, Joonas

Tampere University of Technology

2012

Tieto- ja sähkötekniikan tiedekunta - Faculty of Computing and Electrical Engineering

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**Julkaisun pysyvä osoite on**

http://urn.fi/URN:ISBN:978-952-15-2956-6

##### Tiivistelmä

Power electronics (PE) plays an important role in grid integration of photovoltaic (PV) power systems. According to present knowledge, the PV modules are said to be the most reliable component and PE is said to possess most of the reliability problems in the power processing chain. Solving the reliability issues is of high priority since these phenomena will naturally increase because the annual growth rate of distributed generation is constantly growing. Practical time-domain testing and simulations are of great value in designing PE converters but they do not necessarily give comprehensive information according to which the observed problems can be solved. Therefore, the key for solving these problems lies in frequency-domain modeling of PV power systems.

This thesis analyzes the dynamic properties of grid-connected voltage source inverters (VSI) and shows that the inverter dynamics are determined not only by the power stage but also by the application where it is to be used. In power production, under grid-parallel mode, a VSI controls its input voltage and has to be analyzed as a current-fed topology having corresponding dynamic properties. Important information e.g. about the control dynamics is lost if the same power-stage is analyzed as a voltage-fed topology.

In addition, a general method to model the dynamic effect of source/load non-idealities in grid-connected current-fed and voltage-fed inverters regardless of the topology is presented. The source/load non-idealities can include either the internal impedance of the source/load subsystem and/or the dynamic effect of a passive input/output filter.

It is also demonstrated that a grid-connected input-voltage-controlled VSI incorporates an operating-point-dependent pole in the input-voltage-control loop caused by the cascaded input-voltage-output-current control scheme. The location of the pole on the complex plane can be given explicitly according to the input capacitance, operating point voltage and current, and the dynamic resistance of the PV generator. The pole shifts between the left and right halves of the complex plane according to the PVG operating point. Naturally, the pole causes control-system-design constraints when it is located on the right half of the complex plane (RHP). Furthermore, the RHP pole frequency is inversely proportional to the input capacitance, which implies that minimizing the input capacitance can lead to an unstable input voltage loop because the control loop has to be designed so that the loop crossover frequency is higher than the RHP pole frequency.

Therefore, a design rule between the input-capacitor sizing and input-voltage-control design is proposed. Typically, the input capacitor design is based on energy-based design criteria, e.g. input-voltage ripple or transient behavior. The energy-based criteria are important, although subjective, and do not necessarily guarantee the inverter stability. Therefore, in addition to the energy-based criteria, the control-based rule proposed in this thesis has to always be considered because it can be used to determine the inverter stability, which results in more reliable and robust PV inverter design.

This thesis analyzes the dynamic properties of grid-connected voltage source inverters (VSI) and shows that the inverter dynamics are determined not only by the power stage but also by the application where it is to be used. In power production, under grid-parallel mode, a VSI controls its input voltage and has to be analyzed as a current-fed topology having corresponding dynamic properties. Important information e.g. about the control dynamics is lost if the same power-stage is analyzed as a voltage-fed topology.

In addition, a general method to model the dynamic effect of source/load non-idealities in grid-connected current-fed and voltage-fed inverters regardless of the topology is presented. The source/load non-idealities can include either the internal impedance of the source/load subsystem and/or the dynamic effect of a passive input/output filter.

It is also demonstrated that a grid-connected input-voltage-controlled VSI incorporates an operating-point-dependent pole in the input-voltage-control loop caused by the cascaded input-voltage-output-current control scheme. The location of the pole on the complex plane can be given explicitly according to the input capacitance, operating point voltage and current, and the dynamic resistance of the PV generator. The pole shifts between the left and right halves of the complex plane according to the PVG operating point. Naturally, the pole causes control-system-design constraints when it is located on the right half of the complex plane (RHP). Furthermore, the RHP pole frequency is inversely proportional to the input capacitance, which implies that minimizing the input capacitance can lead to an unstable input voltage loop because the control loop has to be designed so that the loop crossover frequency is higher than the RHP pole frequency.

Therefore, a design rule between the input-capacitor sizing and input-voltage-control design is proposed. Typically, the input capacitor design is based on energy-based design criteria, e.g. input-voltage ripple or transient behavior. The energy-based criteria are important, although subjective, and do not necessarily guarantee the inverter stability. Therefore, in addition to the energy-based criteria, the control-based rule proposed in this thesis has to always be considered because it can be used to determine the inverter stability, which results in more reliable and robust PV inverter design.

##### Kokoelmat

- Väitöskirjat [4136]