Guzmán Díaz

Scheduling of Droop Coefficients for Frequency and Voltage Regulation in Isolated Microgrids

This paper details a procedure based on bifurcation theory to evaluate the impact that droops and primary reserve scheduling have on the microgrid stability. The methodology is based on finding the worst primary reserve share-that is, the share closest to instability-that can be found after rescheduling the droops of selected generating units that support frequency (and voltage) regulation. The solution-which consists of a measure of the distance to instability in a given direction-is found in a multi-parameter space endowed with coordinates corresponding to the droop coefficients. Two stages are proposed to achieve the solution. First, an investigation of the distance to bifurcation is computed in a one-dimensional parameter space in a defined search direction. Then the direction of this search is updated by calculating the normal vector at the found bifurcation point. The procedure is iteratively repeated until the closest bifurcation is found. The proposed approach is analyzed in a 69-bus and 11-generation unit isolated microgrid. It is shown through the analysis of some scenarios how the distances and normal vectors provide valuable insight on the correct scheduling from the stability point of view, giving advice on how the primary reserve should be more reliably scheduled.

Complex-Valued State Matrices for Simple Representation of Large Autonomous Microgrids Supplied by

This paper focuses on representing the state space model of a microgrid in which power regulated (PQ ) and voltage/frequency regulated (Vf) generation units share a distribution system. The generation units considered in this paper are inverter interfaced. This introduces some interesting modeling problems which are treated in the paper, such as the decoupled cascaded control schemes or the non-negligible grid dynamics. A modeling approach is proposed based on four defined complex vectors. These vectors allow for complex-valued system matrices to be formed in a quite automated way. Moreover, a convenient partition of the system matrices is proposed, which in turn allows fast and easy modifications. Additionally, a multivariable methodology is proposed to simultaneously find the control system gains in an optimal sense. A 69-bus radial system, supplied by 20 generation units, is used to demonstrate how the proposal is of easy implementation to conduct small-signal stability analyses.

PQ

This paper adds some new contributions to the unified alternating current/direct current (ac/dc) power-flow method that is applied to railway power supply systems. These contributions are mainly focused on the way that the unified power-flow problem is implemented. The authors propose a new technique based on graph theory to model the motion of the trains without varying the system topology and dimensions, as well as the solution vector. Furthermore, a new matrix formulation is developed to provide an easy way of setting out the problem. The combination of these techniques makes the unified ac/dc power flow easier to implement, and the comparison among different instants can directly be done, representing the major contribution of this paper. Finally, as a minor contribution, a new technique based on previous matrix formulation is developed to easily obtain all active and reactive power magnitudes in compact form.

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This paper details a modeling procedure that incorporates composite loads in stand-alone microgrids in which, because of the low system inertia provided by inverter-interfaced generation units, the grid dynamics is not neglected. The paper introduces a methodology based on 1) separately treating the plants (RL grid elements) from reference frames and control systems; and 2) establishing a vector valued function to methodologically describe all plants in a similar way. Induction motors equations are rearranged to be integrated within the model, giving as a result a highly structured, compact system model. Next, bifurcation theory is adapted to the problem to show that composite loads are a need in the microgrid modeling if more realistic results about oscillations and mainly about load margin are pursued. Thanks to the modeling procedure, this is proven by means of a series of analyses conducted in a microgrid of considerable larger dimensions than those presented to date in the literature.

Vf

This paper gives theoretical foundation to a procedure for modeling in a simply way the behavior of a droop-regulated islanded microgrid when, due to reserve scheduling considerations, the power reserves might be exhausted. The main problem observed for computing the operating point of those microgrids is that the droop formulation that is to be entered in the computation depends on the knowledge of the final result, which indeed means that the solution by means of Newton-Raphson-like methods is hindered. The proposed procedure reduces the complexity by formulating the problem as a complementarity problem. A discussion is offered then on the specific problem of droop formulation: two states are possible (with and without power limit reached), with the particularity that the power must be considered constant only when the power limit is reached, whereas the frequency can freely vary in both states, searching for an equilibrium in the load share among all the generation units endowed with droop regulation. Further, the problem is simplified by resorting to the use of Fischer-Burmeister NCP-functions (NCP for nonlinear complementarity problem), which substitutes the piecewise-defined droop function by an only scalar function (Fischer-Burmeister function) that makes the problem tractable to be solved by Newton-Raphson-like methods. The paper concludes with an exposition of numerical simulations in which the consequences of considering the power exhaustion on stability and operating points are demonstrated.

Generation

We propose an approach to allocate and delimit a region in which the rotational losses are of most importance in the stator core of induction motors. The delimitation is based on the analysis of points at which the minimum flux density is not null. The analysis of flux paths and values of flux density over a number of motors allows a model of flux density to be proposed for the chosen rotational region. We conducted the process by post-processing finite-element results. A comparison with bench test results shows that the approach can confine the effects of rotational losses within a region allocated in the tooth roots without significant loss of accuracy. We give analytical expressions based on geometrical data. The approach provides a quick method to evaluate the rotational losses by analytical means, bypassing the use of numerical methods at those design stages at which is preferable to reduce the accuracy in favor of computational speed.

Unified AC/DC Power Flow for Traction Systems: A New Concept

This paper presents the methodological basis for the computation of the capacity factor (CF) of the power delivered by an off-grid droop-regulated microgrid when the power is injected by distributed stochastic generation. More particularly, the paper is focused on wind generation and its modeling particularities. It shows how the availability of power can be efficiently sampled by a low variation Latin Hypercube Sampling (LHS) method, supplemented with a restricted pairing technique to account for correlation among generating units. The paper also presents a minimization problem that, combined with a Fischer-Burmeister-based formulation, permits obtaining the maximum deliverable power at each sample. This paper additionally shows a first numerical analysis of a 14-node microgrid supplied by five Enercon E40. The analysis includes an investigation into the best model that represents the CF of the microgrid, and highlights the effects of correlation and maximum loadability.

Composite Loads in Stand-Alone Inverter-Based Microgrids—Modeling Procedure and Effects on Load Margin

The aim of the present work is to propose a complete Photovoltaic (PV) Direct Current (DC) source model, considering non linear effects with ambient temperature and solar irradiance. The main advantage of this model is that all non ideal characteristics of the PV source are taking into account, and complex weather conditions patterns can be considered. This model includes: The PV array and boost-buck DC-DC converter that operates to assure maximum power extraction. The Maximum Power Point Tracking (MPPT) algorithm, which is based on the incremental conductance method, is also described. The model can be used for example, as a DC source to supply grid connected or islanded inverters, to study the interaction of PV generators with the power system.

Fischer-Burmeister-Based Method for Calculating Equilibrium Points of Droop-Regulated Microgrids

In this article, multiresolution analysis (MRA) and wavelets are applied to the study of the existence of an internal short circuit in a transformer. An analytical support is given to the proposal of a relaying technique based on the derivation of the existence of specific singularities in the modulus of the space vector as obtained from the three differential signals. The proposal stems from the quite different travel angles of the space vector: maximum 120 degrees for healthy inrush and 360 degrees for fault. The sharp notches in the modulus of the space-vector are then detected using de first detail in MRA.

Analytical Interpretation and Quantification of Rotational Losses in Stator Cores of Induction Motors

A new method for simulating faulted transformers is presented in this paper. Unlike other methods proposed in the literature, this method uses the data obtained from any sound transformer simulation to obtain the damaged condition by simply adding a set of calculated currents. These currents are obtained from the definition of the fault. The model is fully based on determining the incremental values exhibited by the currents in phases and lines from the prefault to the postfault condition. As a consequence, data obtained from simulation of the sound transformer may be readily used to define the damaged condition. The model is described for light and severe faults, introducing this latter feature as a further add-on feature to the low-level faults simulation. The technique avoids the use of complex routines and procedures devoted to specially simulate the internal fault. Of prompt application to relay testing, the proposed analytical model also gives an insight into the fault nature by means of the investigation of symmetrical components. In contrast with its low complexity, the method has shown to present large accuracy for simulating the fault performance.