Control design and parameter tuning for islanded microgrids by combining different optimization algorithms

Load and supply parameters may be uncertain in microgrids (MGs) due for instance to the intermittent nature of renewable energy sources among others. Guaranteeing reliable and stable MGs despite parameter uncertainties is crucial for their correct operation. Their stability and dynamical features are directly related to the controllers’ parameters and power-sharing coefficients. Hence, to maintain power good quality within the desirable range of system parameters and to have a satisfactory response to sudden load changes, careful selection of the controllers and power-sharing coefficients are necessary. In this paper, a simple design approach for the optimal design of controllers’ parameters is presented in an islanded MG. To that aim, an optimization problem is formulated based on a small-signal state-space model and solved by three different optimization techniques including particle swarm optimization (PSO), genetic algorithm (GA), and a proposed approach based on the combination of both PSO and GA. The optimized coefficients are selected to guarantee desirable static and dynamic responses in a wide range of operations regardless of the number of inverters, system configuration, output impedance differences, and load types. Through the proposed design and tuning method, the performance of the MG is improved as compared to those obtained using state-of-art techniques. This fact is demonstrated by using numerical simulations performed on a detailed model implemented in PSIM© software

Bifurcation Boundary Conditions for Switching DC-DC Converters Under Constant On-Time Control

Sampled-data analysis and harmonic balance analysis are applied to analyze switching DC-DC converters under constant on-time control. Design-oriented boundary conditions for the period-doubling bifurcation and the saddle-node bifurcation are derived. The required ramp slope to avoid the bifurcations and the assigned pole locations associated with the ramp are also derived. The derived boundary conditions are more general and accurate than those recently obtained. Those recently obtained boundary conditions become special cases under the general modeling approach presented in this paper. Different analyses give different perspectives on the system dynamics and complement each other. Under the sampled-data analysis, the boundary conditions are expressed in terms of signal slopes and the ramp slope. Under the harmonic balance analysis, the boundary conditions are expressed in terms of signal harmonics. The derived boundary conditions are useful for a designer to design a converter to avoid the occurrence of the period-doubling bifurcation and the saddle-node bifurcation.Comment: Submitted to International Journal of Circuit Theory and Applications on August 10, 2011; Manuscript ID: CTA-11-016

A Time-Domain Asymptotic Approach to Predict Saddle-Node and Period Doubling Bifurcations in Pulse Width Modulated Piecewise Linear Systems

In this paper closed-form conditions for predicting the boundary of period-doubling (PD) bifurcation or saddle-node (SN) bifurcation in a class of PWM piecewise linear systems are obtained from a time-domain asymptotic approach. Examples of switched system considered in this study are switching dc-dc power electronics converters, temperature control systems and hydraulic valve control systems among others. These conditions are obtained from the steady-state discrete-time model using an asymptotic approach without resorting to frequency-domain Fourier analysis and without using the monodromy or the Jacobian matrix of the discrete-time model as it was recently reported in the existing literature on this topic. The availability of such design-oriented boundary expressions allows to understand the effect of the different parameters of the system upon its stability and its dynamical behavior

Modeling, Dynamics, Bifurcation Behavior and Stability Analysis of a DC-DC Boost Converter in Photovoltaic Systems

Modeling, Dynamics, Bifurcation Behavior and Stability Analysis of a DC-DC Boost Converter in Photovoltaic SystemsA study of a DC–DC boost converter fed by a photovoltaic (PV) generator and supplying a constant voltage load is presented. The input port of the converter is controlled using fixed frequency pulse width modulation (PWM) based on the loss-free resistor (LFR) concept whose parameter is selected with the aim to force the PV generator to work at its maximum power point. Under this control strategy, it is shown that the system can exhibit complex nonlinear behaviors for certain ranges of parameter values. First, using the nonlinear models of the converter and the PV source, the dynamics of the system are explored in terms of some of its parameters such as the proportional gain of the controller and the output DC bus voltage. To present a comprehensive approach to the overall system behavior under parameter changes, a series of bifurcation diagrams are computed from the circuit-level switched model and from a simplified model both implemented in PSIM© software showing a remarkable agreement. These diagrams show that the first instability that takes place in the system period-1 orbit when a primary parameter is varied is a smooth period-doubling bifurcation and that the nonlinearity of the PV generator is irrelevant for predicting this phenomenon. Different bifurcation scenarios can take place for the resulting period-2 subharmonic regime depending on a secondary bifurcation parameter. The boundary between the desired period-1 orbit and subharmonic oscillation resulting from period-doubling in the parameter space is obtained by calculating the eigenvalues of the monodromy matrix of the simplified model. The results from this model have been validated with time-domain numerical simulation using the circuit-level switched model and also experimentally from a laboratory prototy

Prediction of subharmonic oscillation in switching converters under different control strategies

10.1109/TCSII.2011.2180097Subharmonic oscillation is an undesired phenomenon in switching converters. In past studies, its prediction has been mainly tackled by explicitly deriving a discrete-time model and then linearizing it in the vicinity of the operating point. However, the results obtained from such an approach cannot be applied for design purpose except for simple cases such as peak or valley current-mode control (CMC). Alternatively, in this brief, this phenomenon is analyzed by using a unified formal symbolic approach that can be applied for different control strategies. This approach is based on expressing the condition for subharmonic oscillation occurrence using Fourier series and then converting the result into a matrix-form expression that explicitly depends on the system parameters, making the results directly applicable for design purpose. Under certain practical conditions concerning these parameters, the matrix-form expression can be approximated by standard polynomial functions depending on the operating duty cycle. The results presented in this work clearly generalize the well-known stability condition of peak/valley CMC

Dynamics of PFC power converters subject to time-delayed feedback control

10.1002/cta.703Power factor correction converters are power electronics circuits used as AC-DC power supplies. These systems are well known to exhibit nonlinear phenomena such as subharmonic oscillations and chaotic regimes. These undesirable behaviors increase the THD and therefore can jeopardize enormously the system performances. In this paper, time delay feedback control is applied to stabilize a two-stage power factor correction AC-DC converter when it exhibits these instabilities under traditional controllers. This control technique introduces many advantages to the most and widely used average current mode control through widening the stability domain of the system. By appropriately selecting the time delay feedback gain and the time delay period, the undesirable subharmonic components are eliminated, whereas the desired ones remain unchanged. A harmonic balance approach is used for studying the dynamics of the system under the new control scheme and to obtain the stabilization domain

Analog-mixed-signal simulation of DC-DC Boost-Based MPPT system taking into account weather conditions variations

DC-DC converters are widely used as interfaces between photovoltaic (PV) sources and loads in different applications. These devices use inductors as energy storage elements for controlling the power flow from the PV source to the load. These systems are usually designed using conventional linear small-signal approaches in the vicinity of an operating point. However, the operating point of a PV system is highly dependent on the environmental conditions such as the irradiance and the temperature. Irradiance and temperature changes make the system work at different power and current levels. The inductance of a nonlinear real inductor strongly depends on the operating current. In this paper, a study of a boost converter used for maximum power point tracking is presented by taking into account the inductor nonlinearity till saturation and the variation of its inductance with the weather conditions. To this end analog-mixed-signal circuit simulations are used to show the effects of the weather conditions on the dynamical behavior of the overall PV system

Unfolding nonsmooth bifurcation patterns in A 1-D PWL MAP as a model of a single-inductor two-output DC-DC switching converter

10.1142/S021812741330008