The recently introduced proportional-resonant (PR) controllers and filters, and their suitability for current/voltage control of grid-connected converters, are described. Using the PR controllers, the converter reference tracking performance can be enhanced and previously known shortcomings associated with conventional PI controllers can be alleviated. These shortcomings include steady-state errors in single-phase systems and the need for synchronous d-q transformation in three-phase systems. Based on similar control theory, PR filters can also be used for generating the harmonic command reference precisely in an active power filter, especially for single-phase systems, where d-q transformation theory is not directly applicable. Another advantage associated with the PR controllers and filters is the possibility of implementing selective harmonic compensation without requiring excessive computational resources. Given these advantages and the belief that PR control will find wide-ranging applications in grid-interfaced converters, PR control theory is revised in detail with a number of practical cases that have been implemented previously, described clearly to give a comprehensive reference on PR control and filtering.

Proportional-resonant controllers and filters for grid-connected voltage-source converters

This paper discusses the evaluation of different current controllers employed for grid-connected distributed power generation systems having variable input power, such as wind turbines and photovoltaic systems. The focus is mainly set on linear controllers such as proportional-integral, proportional-resonant, and deadbeat (DB) controllers. Additionally, an improved DB controller robust against grid impedance variation is also presented. Since the paper discusses the implementation of these controllers for grid-connected applications, their evaluation is made in three operating conditions. First, in steady-state conditions, the contribution of controllers to the total harmonic distortion of the grid current is pursued. Further on, the behavior of controllers in the case of transient conditions like input power variations and grid voltage faults is also examined. Experimental results in each case are presented in order to evaluate the performance of the controllers.

Evaluation of Current Controllers for Distributed Power Generation Systems

Many grid connected power electronic systems, such as STATCOMs, UPFCs, and distributed generation system interfaces, use a voltage source inverter (VSI) connected to the supply network through a filter. This filter, typically a series inductance, acts to reduce the switching harmonics entering the distribution network. An alternative filter is a LCL network, which can achieve reduced levels of harmonic distortion at lower switching frequencies and with less inductance, and therefore has potential benefits for higher power applications. However, systems incorporating LCL filters require more complex control strategies and are not commonly presented in literature. This paper proposes a robust strategy for regulating the grid current entering a distribution network from a three-phase VSI system connected via a LCL filter. The strategy integrates an outer loop grid current regulator with inner capacitor current regulation to stabilize the system. A synchronous frame PI current regulation strategy is used for the outer grid current control loop. Linear analysis, simulation, and experimental results are used to verify the stability of the control algorithm across a range of operating conditions. Finally, expressions for ""harmonic impedance" of the system are derived to study the effects of supply voltage distortion on the harmonic performance of the system.

Grid current regulation of a three-phase voltage source inverter with an LCL input filter

The paper proposes several concepts of integrators for sinusoidal signals. Parallel and series associations of the basic PI units using the stationary frame generalized integrators are used for current control of active power filters. Zero steady state error for the concerned current harmonics are realized, with reduced computation, under unbalanced utility or load conditions. Designing of the PI constants, digital realization of the generalized integrators, as well as compensation of the computation delay etc. are studied. Extensive test results from a 10 kW active power filter prototype are demonstrated.

Stationary-frame generalized integrators for current control of active power filters with zero steady-state error for current harmonics of concern under unbalanced and distorted operating conditions

This paper analyzes the small-signal impedance of three-phase grid-tied inverters with feedback control and phase-locked loop (PLL) in the synchronous reference ( d-q ) frame. The result unveils an interesting and important feature of three-phase grid-tied inverters – namely, that its q–q channel impedance behaves as a negative incremental resistor. Moreover, this paper shows that this behavior is a consequence of grid synchronization, where the bandwidth of the PLL determines the frequency range of the resistor behavior, and the power rating of the inverter determines the magnitude of the resistor. Advanced PLL, current, and power control strategies do not change this feature. An example shows that under weak grid conditions, a change of the PLL bandwidth could lead the inverter system to unstable conditions as a result of this behavior. Harmonic resonance and instability issues can be analyzed using the proposed impedance model. Simulation and experimental measurements verify the analysis.

Analysis of D-Q Small-Signal Impedance of Grid-Tied Inverters

Stationary frame linear PI current regulators are conventionally regarded as unsatisfactory for AC systems because they cannot eliminate steady state errors. Consequently, synchronous frame regulators are perceived to be superior, since they achieve zero steady state error by acting on DC signals in a rotating frame of reference. However, a synchronous frame regulator is more complex, and requires in particular a way of transforming a measured stationary frame AC current (or error) to rotating frame DC quantities, and transforming the resultant control action back to the stationary frame for implementation. This paper presents a technique for interpreting the stationary/rotating frame transformations as modulation processes in the Laplace domain which move the control function from one part of the frequency spectrum to another. The technique is used to compare stationary and synchronous frame PI regulators on a common basis to better understand the advantages of a synchronous frame regulator, and then to develop a new form of stationary frame resonant regulator which achieves zero steady state error without requiring the complex transformations of a synchronous frame regulator. The performance of this new regulator is evaluated and found to be equivalent to that of the synchronous frame PI regulator.

Gerwich Bode

Papers

Frequency domain analysis of three phase linear current regulators

Frequency Domain Analysis of Three Phase Linear Current Regulators