Abstract – Voltage source inverters in micro-grid applications
need the effective control of the filter output voltages. Harmonic
compensation is a mandatory request to eliminate voltage
distortion due to non-linear and unbalanced loads. The use of
resonant controllers allows achieving high quality voltage
regulation. The proposed paper investigates a closed form tuning
strategy for controllers’ parameters selection based on the
symmetrical frequency behavior of the whole resonant controller
structure. Symmetrically tuned controllers allow achieving the
largest bandwidth around the resonance frequency in a multi-
resonance controller structure.
Index Terms – Resonant controllers, integral resonant control,
harmonic compensator, four-leg inverter, closed form control
tuning, power generation systems.
I. INTRODUCTION
Over the years, power inverters have found several
applications in numerous either grid-tied or stand-alone
systems. More stringent regulations on harmonic distortion
and power quality require even more complex control
architectures, that conventional PI and PID controllers are not
able to effectively provide. Compensation of distorted loads is
mandatory in both grid connected and off-grid systems.
In micro-grid applications the regulation of the inverter output
voltage is required to provide constant voltage constant
frequency to the loads. As in grid-tied applications, also in
stand-alone systems the ability of the inverter control structure
to regulate to zero the injected DC-component is a mandatory
requirement. However, the feedback signals to control the DC-
component are different in grid-tied configurations with
respect to off-grid applications. In grid-connected systems, the
feedback is usually closed on the inverter current, either grid
side or inverter side, and its DC-current component is forced
to be zero. In stand-alone application, main control loop is
closed on the filtered output voltages and the DC-voltage
component must be forced to be zero.
The ability of resonant controllers to track sinusoidal
references and saving computational load have made this
controller topology widely used when sinusoidal current or
voltage must be regulated at inverter output. However, they
are totally blind from DC-component point of view (definitely
unsuitable for regulating to zero the injected DC-component),
as it is shown in Section III.A of the present paper.
Several studies have been proposed so far concerning the use
of Resonant Controller (RC) structures in both grid-tied and
off-grid applications. The benefits in adopting this kind of
controllers are well known and deeply explained as in [1-5].
Moreover, RCs have been combined in both single loop and
double loop control schemes to accomplish voltage and
current regulation when needed [6-9]. Usually in a single
control loop, the control action is performed only on the
inverter output voltage or current. When a double control loop
is implemented, the outer loop is the VSI output voltage
whereas the inner loop regulates the supplied current.
Different combinations of transfer functions as proportional-
resonant and integral-resonant have been analyzed in [8]. In
[8] a single loop control structure with integral compensation
and current limiting feature is finally proposed for a 50 Hz
stand-alone generation system.
Also in [9] the single loop architecture is preferred and applied
to a 400 Hz ground power unit.
Resonant controllers’ application has been extended also to
electric drives. Both induction motor and permanent-magnet
base drives have been considered to be controlled by RCs as
shown in [13- 15].
Some basic criteria for RCs tuning have been preliminary
depicted in [17] where the resonant control structure is
compared with the H-infinity algorithm. Controllers gain and
width are mainly selected by the designer using a trial and
error procedure which is usually verified through root-locus
and Bode diagrams. After that, the controller is digitally
implemented and the performances are verified by simulations
and experimental tests.
In [18] a different approach based on the Nyquist diagram is
proposed for Proportional+Resonant (PR) and Vector
Proportional+Integral (VPI) controllers.
However, the mathematical-analytical tuning approach for
RCs is usually missing; for this reason, the aim of the paper is
to provide a closed form tuning procedure to be used to select
the parameters of each controller being part of a Multi
Resonant Control System. According to the proposed
approach, the control designer is able to select the desired
controller gain with respect to the harmonic to be regulated,
and the controller width will be automatically selected by the
tuning algorithm. When two or more resonant controllers are
combined together, the achieved tuned controller structure
results in a symmetrical form in terms of magnitude and phase
distribution around each controller resonance frequency. The
symmetrical tuning assures the maximum distance in term of
frequency between two adjacent resonant controllers reducing
their reciprocal interaction. The extension of the tuning
procedure from the pure Resonant (R) structure to the more
suitable Integral+Resonant (I+R) scheme, which is able to
compensate the DC-component, is also shown and
experimentally verified.
Symmetrical Tuning for Resonant Controllers in
Inverter based Micro-Grid Applications
A. Lidozzi, G. Lo Calzo, L. Solero, F. Crescimbini
University of ROMA TRE, Department of Engineering
Via della Vasca Navale 79, 00146 Roma (Italy). lidozzi@uniroma3.it
755 978-1-4799-0336-8/13/$31.00 ©2013 IEEE