Santiago Sanchez

Conditions for Existence of Equilibria of Systems With Constant Power Loads

In this paper we investigate the sine qua non condition of existence of equilibria for electrical systems with external (AC or DC) sources furnishing constant power to the loads, which is a scenario encountered in modern applications. Two general cases are considered, when the system is i) linear time-invariant or ii) nonlinear, with dynamic behavior described by a port-Hamiltonian model with constant dissipation and switching interconnection matrix. The latter class includes the practically important case of power converters. For both cases necessary and sufficient conditions for existence of equilibria are given, which give an upper bound on the power dissipated in steady-state that should exceed the extracted constant power. The existence of the equilibrium is ensured if and only if the inequality is satisfied.

Large Signal Stability Analysis at the Common Coupling Point of a DC Microgrid: A Grid Impedance Estimation Approach Based on a Recursive Method

The design of microgrids at the level of distribution systems requires a stable behavior for multiple operation states. The tools used to study the stability of such systems require the estimation of the grid impedance. By the use of the grid impedance estimation around an operation point, it is possible to define a space variable-parameter to obtain a qualitative or quantitative measure from the operation to the unstable boundary. This study presents a comparison of the Kalman filter and the recursive least squares method for the estimation of the grid impedance. The grid impedance is estimated by the technique based on two neighbor operation points. The results were validated by a hardware in the loop and an experimental setup. Finally, the estimated values of the grid impedance of a microgrid are used with a large signal stability study of a dc constant power load.

Degree of Influence of System States Transition on the Stability of a DC Microgrid

The classical distribution system can evolve in a new concept of grid, where the distributed generation has a big impact. These changes take into account the use of power electronic devices. With these devices it is necessary to study the stability of the system in a new form due to their multi-current domain and the influence of the controllers applied to each device. The paper presents a methodology that takes into account the structure of a DC microgrid system and evaluates its stability. The stability analysis uses the computational continuation to obtain the conclusions. The real time simulation results present the grid behavior and validate the limits of operation.

Conditions for existence of equilibrium points of systems with constant power loads

In this paper we investigate the sine qua non condition of existence of equilibria for electrical systems with external sources furnishing constant power to the loads, which is a scenario encountered in modern applications. Two general cases are considered, when the system is (i) linear time-invariant or (ii) nonlinear, with dynamic behavior described by a port-Hamiltonian model with constant dissipation and switching interconnection matrix. The latter class includes the practically important case of power converters. For both cases necessary and sufficient conditions for existence of equilibria are given, which impose that the power dissipated in steady-state should exceed the extracted constant power. The equilibrium is ensured if and only if the inequality is satisfied.

Assessment of a stability analysis tool for constant power loads in DC-grids

This paper presents an analysis with nonlinear tools for stability in systems dominated by the interconnection of power electronics and supplied by distributed generation. Systems like renewable and not renewable energy sources can supply power to the micro-grid, and their loads can behave as CPL. Hence, the search of Hopf bifurcation points is used to prevent oscillations and instabilities in the system.

Speed regulation of a wind turbine with current source or matrix converter: Tuning procedure

In DC series-connection of wind turbines the common variable for the turbines is the DC current and thus the simplest control approach is to use current source type converter to perform the speed control of the generators for maximum power extraction. When using current source type converters like the Current Source or the matrix converter, LC filters are needed at the input of the generator to remove switching harmonics. Thus resonance can be an issue and special care needs to be taken when designing controllers. In this article a wind farm topology with series connected turbines is presented along with the wind energy conversion system inside in which a matrix converter performs speed control of the generator. To counteract resonance, three nested loops controlling respectively the turbine rotational speed, the stator current and the filter capacitor voltage are implemented. The tuning should be performed carefully so that the control is fast, stable and tracking the maximum power point. The system model is analyzed in the dq reference frame to find appropriate controllers for each loop and a method is presented to tune each controller in a systematic manner for a satisfactory system response. Simulation results are presented.

Port-Hamiltonian modelling of Modular Multilevel Converters with fixed equilibrium point

The paper presents the derivation of a port-Hamiltonian model of an averaged Modular Multilevel Converter (MMC) that reaches a fixed equilibrium point solution. This MMC model can not be expressed in a straightforward way in a port-Hamiltonian framework due to the lack of skew-symmetry of its interconnection matrices. This work proposes a change of variable and a new per unit notation to overcome this limitation, obtaining a port-Hamiltonian model of the MMC with static equilibrium, useful for control design purposes.

Residential photovoltaic and battery energy system with grid support functionalities

This paper presents the design of a control system for a grid connected residential photovoltaic (PV) system with battery energy storage (BES). The control methods for the power electronic converters are presented and the potential of utilizing BES for participating in primary frequency regulation of the grid is investigated. The charging/ discharging rate of the battery is controlled based on the frequency droop characteristic. The performance of the control system is validated in a simulation study, in which fast response and perfect tracking of the set points are observed in (i) normal operating condition and (ii) a case where the grid frequency varies. The amount of the batterys capacity that can be utilized for this purpose depends on the quantity of power generated by the PV system, as well as the load level. The study shows that sometimes the rated capacity of the battery could be fully utilized for serving the primary frequency regulation purposes.

Evaluation of the system parameters degree of influence on the stability of a DC microgrid

The classical distribution system can evolve in a new concept of grid, where the distributed generation is a great factor. These changes take into account the use of power electronic devices. With these devices it is necessary to study the stability of the system in a new form due to their multi-current domain and the influence of the controllers applied to the each device. The paper presents a methodology that takes into account the structure of a DC system and evaluates its stability. The stability analysis applies the computational continuation to obtain the conclusions over the limits of safe operation. Finally, the simulation results present the grid behavior.

HVDC meshed multi-terminal networks for offshore wind farms: Dynamic model, load flow and equilibrium

This paper presents sufficient conditions for the existence of an equilibrium point of multi-terminal HVDC (MT-HVDC) network for offshore applications. Newtons method is used both as a computational tool and as the basis for proving the existence and uniqueness of the equilibrium. A simple but generalized dynamic model of the MT-HVDC grid for offshore wind farm applications is presented which is non-linear due to the constant power loads with droop regulation. The classic Kantorovitch theorem is used to define the requirements for the existence of the equilibrium and the super-convergence of Newtons method starting from voltages close to 1pu. Finding this equilibrium is equivalent to the power flow in power systems applications. Computational results corroborate the requirements for equilibrium as well as the convergence of the algorithm in a realistic MT-HVDC grid.