Frequency domain analysis of three phase linear current regulators
03 Oct 1999-Vol. 37, Iss: 2, pp 601-610
TL;DR: In this article, a technique for interpreting the stationary/rotating frame transformations as modulation processes in the Laplace domain is presented, which moves the control function from one part of the frequency spectrum to another.
Abstract: 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.
Citations
More filters
09 Oct 2006
TL;DR: The proportional-resonant (PR) controllers and filters, and their suitability for current/voltage control of grid-connected converters, are described in this article.
Abstract: 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.
1,483 citations
TL;DR: In this article, the performance of linear controllers such as proportional-integral, proportional-resonant, and deadbeat (DB) controllers for grid-connected distributed power generation systems has been evaluated.
Abstract: 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.
886 citations
TL;DR: In this paper, a robust control strategy for regulating the grid current entering a distribution network from a three-phase VSI system connected via a LCL filter is proposed, which integrates an outer loop grid current regulator with inner capacitor current regulation to stabilize the system.
Abstract: 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.
869 citations
08 Oct 2000
TL;DR: In this paper, the authors proposed several concepts of integrators for sinusoidal signals, including parallel and series associations of the basic PI units using the stationary frame generalized integrators, for current control of active power filters.
Abstract: 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.
838 citations
TL;DR: In this article, 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 is analyzed.
Abstract: 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.
825 citations
References
More filters
TL;DR: Current control techniques for three-phase voltage-source pulsewidth modulated converters, including bang-bang (hysteresis, delta modulation) controllers and predictive controllers with on-line optimization are reviewed.
Abstract: The aim of this paper is to present a review of current control techniques for three-phase voltage-source pulsewidth modulated converters. Various techniques, different in concept, have been described in two main groups: linear and nonlinear. The first includes proportional integral (stationary and synchronous) and state feedback controllers, and predictive techniques with constant switching frequency. The second comprises bang-bang (hysteresis, delta modulation) controllers and predictive controllers with on-line optimization. New trends in current control-neural networks and fuzzy-logic-based controllers-are discussed, as well. Selected oscillograms accompany the presentation in order to illustrate properties of the described controller groups.
2,086 citations
"Frequency domain analysis of three ..." refers background in this paper
...Over the last few decades, three major classes of voltage-source-inverter (VSI)-based current regulators have evolved, being hysteresis regulators, linear proportional plus integral (PI) regulators, and predictive deadbeat regulators [ 1 ]....
[...]
Book•
26 Sep 1996
TL;DR: In this article, the authors present a d-q model for solid state power converters and present a complex vector analysis of induction machines and synchronous machines with respect to vector control and field orientation.
Abstract: 1. Introduction to AC drives 2. d-q modelling of induction and synchronous machines 3. d-q models for solid state power converters 4. Complex vector analysis of induction machines 5. Principles of vector control and field orientation 6. Dynamics of vector control and field orientation 7. Current regulation in power converters 8. Parameter sensitivity and saturation effects in indirect field orientation 9. Field weakening operation Index
1,239 citations
"Frequency domain analysis of three ..." refers background or methods in this paper
...Much of the definitive analysis in the area of linear current regulation has been done using time-domain formulations of the regulators and loads, with a three-phase motor system described by a complex space-vector model [2]‐[ 5 ]....
[...]
...From [2] and [ 5 ], the time-domain form of a synchronous frame ‐ current regulator referred to the stationary frame can be expressed as...
[...]
...Fig. 4 shows the frame representation of the synchronous frame PI regulator, which is functionally equivalent to the frequency-domain form of the synchronous frame regulator given in Table II. Note that, similar to [2] and [ 5 ], this implementation in the stationary frame feeds back the output variables and is a more efficient implementation than the transfer function form shown in Table II. Even so, the complexity and cross-coupling ......
[...]
...The stationary frame regulator becomes the well-known synchronous frame regulator [2], [ 5 ], [6] if the stationary ‐ frame variables are transformed in the time domain to the synchronous frame before the PI control action occurs, using...
[...]
08 Oct 1995
TL;DR: In this article, the internal model control (IMC) method is introduced and applied to AC machine current control, and it is shown that IMC is able to outperform PI control with and without decoupling with respect to dq variable interaction in the presence of parameter deviations.
Abstract: In the present paper, the internal model control (IMC) method is introduced and applied to AC machine current control. A permanent magnet synchronous machine is used as an example. It is shown that the IMC design is straightforward and the resulting controller is simple to implement. The controller parameters are expressed in the machine parameters and the desired closed-loop rise time. The extra cost of implementation compared to PI control is negligible. It is further shown that IMC is able to outperform PI control with as well as without decoupling with respect to dq variable interaction in the presence of parameter deviations.
623 citations
"Frequency domain analysis of three ..." refers methods in this paper
...Reference [ 7 ] provides a detailed discussion of these issues....
[...]
...These classes can be further divided into stationary and synchronous ‐ reference frame implementations by applying ac machine rotating field theory [2]‐[ 7 ]....
[...]
TL;DR: In this article, a detailed model for the stationary and synchronous sine-triangle current regulators is presented, and the results demonstrate the limitations of the two most often used current regulators and the robustness of the synchronous current regulator.
Abstract: Detailed models are presented for the stationary and synchronous sine-triangle current regulators. Analytical and test results are compared for purposes of model verification and regulator evaluation. The results demonstrate the limitations of the two most often used current regulators and the robustness of the synchronous current regulator. The stationary sine-triangle and hysteretic current regulators are shown to have steady-state characteristics that depend on slip, operating frequency, and motor impedance. In contrast the synchronous regulator, because it lacks these dependencies, exhibits ideal steady-state current regulator characteristics without sacrificing bandwidth. Moreover, the complexities traditionally associated with the synchronous regulator are overcome with a simple equivalent implementation.
472 citations
"Frequency domain analysis of three ..." refers background or methods in this paper
...From [ 2 ] and [5], the time-domain form of a synchronous frame ‐ current regulator referred to the stationary frame can be expressed as...
[...]
...Time-domain results from [ 2 ] are, therefore, used to validate the transformations, so they can then be used confidently to transform current regulators between reference frames for comparison and analysis....
[...]
...These classes can be further divided into stationary and synchronous ‐ reference frame implementations by applying ac machine rotating field theory [ 2 ]‐[7]....
[...]
...Fig. 4 shows the frame representation of the synchronous frame PI regulator, which is functionally equivalent to the frequency-domain form of the synchronous frame regulator given in Table II. Note that, similar to [ 2 ] and [5], this implementation in the stationary frame feeds back the output variables and is a more efficient implementation than the transfer function form shown in Table II. Even so, the complexity and cross-coupling ......
[...]
...Much of the definitive analysis in the area of linear current regulation has been done using time-domain formulations of the regulators and loads, with a three-phase motor system described by a complex space-vector model [ 2 ]‐[5]....
[...]
01 Jan 1998
317 citations