http://ieeexplore.ieee.org/iel5/5610941/5624686/05624745.pdf

Power electronics

Droop control is the basic control method for load current sharing in dc microgrid applications. The conventional dc droop control method is realized by linearly reducing the dc output voltage as the output current increases. This method has two limitations. First, with the consideration of line resistance in a droop-controlled dc microgrid, since the output voltage of each converter cannot be exactly the same, the output current sharing accuracy is degraded. Second, the dc-bus voltage deviation increases with the load due to the droop action. In this paper, in order to improve the performance of the dc microgrid operation, a low-bandwidth communication (LBC)-based improved droop control method is proposed. In contrast with the conventional approach, the control system does not require a centralized secondary controller. Instead, it uses local controllers and the LBC network to exchange information between converter units. The droop controller is employed to achieve independent operation, and the average voltage and current controllers are used in each converter to simultaneously enhance the current sharing accuracy and restore the dc bus voltage. All of the controllers are realized locally, and the LBC system is only used for changing the values of the dc voltage and current. Hence, a decentralized control scheme is accomplished. The simulation test based on MATLAB/Simulink and the experimental validation based on a 2 × 2.2 kW prototype were implemented to demonstrate the proposed approach.

/pdf/an-improved-droop-control-method-for-dc-microgrids-based-on-3a15g7qxoy.pdf

An Improved Droop Control Method for DC Microgrids Based on Low Bandwidth Communication With DC Bus Voltage Restoration and Enhanced Current Sharing Accuracy

A cooperative control paradigm is used to establish a distributed secondary/primary control framework for dc microgrids. The conventional secondary control, that adjusts the voltage set point for the local droop mechanism, is replaced by a voltage regulator and a current regulator. A noise-resilient voltage observer is introduced that uses neighbors’ data to estimate the average voltage across the microgrid. The voltage regulator processes this estimation and generates a voltage correction term to adjust the local voltage set point. This adjustment maintains the microgrid voltage level as desired by the tertiary control. The current regulator compares the local per-unit current of each converter with the neighbors’ and, accordingly, provides a second voltage correction term to synchronize per-unit currents and, thus, provide proportional load sharing. The proposed controller precisely handles the transmission line impedances. The controller on each converter communicates with only its neighbor converters on a communication graph. The graph is a sparse network of communication links spanned across the microgrid to facilitate data exchange. The global dynamic model of the microgrid is derived, and design guidelines are provided to tune the system's dynamic response. A low-voltage dc microgrid prototype is set up, where the controller performance, noise resiliency, link-failure resiliency, and the plug-and-play capability features are successfully verified.

Distributed Cooperative Control of DC Microgrids

This paper performs an extensive review on control schemes and architectures applied to dc microgrids (MGs). It covers multilayer hierarchical control schemes, coordinated control strategies, plug-and-play operations, stability and active damping aspects, as well as nonlinear control algorithms. Islanding detection, protection, and MG clusters control are also briefly summarized. All the mentioned issues are discussed with the goal of providing control design guidelines for dc MGs. The future research challenges, from the authors’ point of view, are also provided in the final concluding part.

/pdf/review-on-control-of-dc-microgrids-and-multiple-microgrid-2wzqd7rmgl.pdf

Review on Control of DC Microgrids and Multiple Microgrid Clusters

In this paper, a double-quadrant state-of-charge (SoC)-based droop control method for distributed energy storage system is proposed to reach the proper power distribution in autonomous dc microgrids. In order to prolong the lifetime of the energy storage units (ESUs) and avoid the overuse of a certain unit, the SoC of each unit should be balanced and the injected/output power should be gradually equalized. Droop control as a decentralized approach is used as the basis of the power sharing method for distributed energy storage units. In the charging process, the droop coefficient is set to be proportional to the nth order of SoC, while in the discharging process, the droop coefficient is set to be inversely proportional to the nth order of SoC. Since the injected/output power is inversely proportional to the droop coefficient, it is obtained that in the charging process the ESU with higher SoC absorbs less power, while the one with lower SoC absorbs more power. Meanwhile, in the discharging process, the ESU with higher SoC delivers more power and the one with lower SoC delivers less power. Hence, SoC balancing and injected/output power equalization can be gradually realized. The exponent n of SoC is employed in the control diagram to regulate the speed of SoC balancing. It is found that with larger exponent n, the balancing speed is higher. MATLAB/simulink model comprised of three ESUs is implemented and the simulation results are shown to verify the proposed approach.

/pdf/double-quadrant-state-of-charge-based-droop-control-method-mei987ztim.pdf

Double-Quadrant State-of-Charge-Based Droop Control Method for Distributed Energy Storage Systems in Autonomous DC Microgrids

Constant-power loads on dc microgrids create a destabilizing effect on the circuit that can lead to severe voltage and frequency oscillations. Amplitude death is a coupling induced stabilization of the fixed point of a dynamical system. This paper applies amplitude death methods to the stabilization problem in this constant-power setting. The amplitude death methods provide an open-loop control solution to stabilize the system. Two methods, one using delay, the other using circuit heterogeneity, are examined. Each method is demonstrated through numerical simulations.

Amplitude Death Solutions for Stabilization of DC Microgrids With Instantaneous Constant-Power Loads

This paper presents a master stability function (MSF) approach for analyzing the stability of amplitude death (AD) in networks of delay-coupled oscillators. Unlike the familiar MSFs for instantaneously coupled networks, which typically have a single input encoding for the effects of the eigenvalues of the network Laplacian matrix, for delay-coupled networks we show that such MSFs generally require two additional inputs: the time delay and the coupling strength. To utilize the MSF for determining the stability of AD of general networks for a chosen nonlinear system (node dynamics) and coupling function, we introduce the concept of master stability islands (MSIs), which are two-dimensional stability islands of the delay-coupling parameter space together with a third dimension (``altitude'') encoding for eigenvalues that result in stable AD. We numerically compute the MSFs and visualize the corresponding MSIs for several common chaotic systems including the R\"ossler, the Lorenz, and Chen's system and find that it is generally possible to achieve AD and that a nonzero time delay is necessary for the stabilization of the AD states.

/pdf/master-stability-islands-for-amplitude-death-in-networks-of-1lejlnylla.pdf

Master stability islands for amplitude death in networks of delay-coupled oscillators.

In this paper, we present a method to compute master stability islands (MSIs) for amplitude death in networks of delay-coupled oscillators using critical curves. We first demonstrate how critical curves can be used to compute boundaries and contours of MSIs in delay-coupling parameter space and then provide a general study on the effects of the oscillator dynamics and network topology on the number, size, and contour types of all MSIs. We find that the oscillator dynamics can be used to determine the number and size of MSIs and that there are six possible contour types that depend on the choice of oscillator dynamics and the network topology. We introduce contour sequences and use these sequences to study the contours of all MSIs. Finally, we provide example MSIs for several classical nonlinear systems including the van der Pol system, the Rucklidge system, and the Rossler system.

Using critical curves to compute master stability islands for amplitude death in networks of delay-coupled oscillators.

To show bioequivalence of generic and brand name drugs, the Food and Drug Administration (FDA) requires a statistical comparison of three pharmacokinetic values that measure aspects of the drugs’ c...

The Calculus Behind Generic Drug Equivalence

We consider the effect of constraints on the number of non-negative integer solutions of x+y+z = n, relating the number of solutions to linear combinations of triangular numbers. Our approach is geometric and may be viewed as an introduction to proofs without words. We use this geometrical perspective to prove identities by counting the number of solutions in two different ways, thereby combining combinatorial proofs and proofs without words.

/pdf/a-geometric-perspective-on-counting-non-negative-integer-2k1t8aidv4.pdf

Stanley R. Huddy

Papers

Amplitude Death Solutions for Stabilization of DC Microgrids With Instantaneous Constant-Power Loads

Master stability islands for amplitude death in networks of delay-coupled oscillators.

Using critical curves to compute master stability islands for amplitude death in networks of delay-coupled oscillators.

The Calculus Behind Generic Drug Equivalence

A geometric perspective on counting non-negative integer solutions and combinatorial identities