Gilbert Bergna

An Energy-Based Controller for HVDC Modular Multilevel Converter in Decoupled Double Synchronous Reference Frame for Voltage Oscillation Reduction

This paper consists of the presentation of a regulation strategy capable of controlling the energy stored in the modular multilevel converter (MMC) in an HVDC configuration. This is achieved by regulating the positive, negative, and zero sequences in dqo coordinates of the differential current using two rotating reference frames: at once and at twice the fundamental grid frequency value. The active and reactive negative sequence components of the differential current at twice the fundamental frequency are used to eliminate the oscillations of the three-phased leg energy, reducing significantly the capacitor voltage oscillations, while the zero-sequence component is used to regulate the total energy stored at a given reference. Meanwhile, active and reactive positive sequence components of the circulating current are used for eliminating the average energy difference between the upper and lower arms in a three-phase MMC. In order to decouple efficiently the differential current components, the decoupled-double-synchronous-reference-frame current control strategy is used. Finally, simulation results validate the performance of the MMC in an HVDC configuration with the proposed control. Control equations are demonstrated, and cross-coupled leg-energy terms are introduced.

A Generalized Power Control Approach in ABC Frame for Modular Multilevel Converter HVDC Links Based on Mathematical Optimization

This paper presents a generalized and versatile control approach using Lagrange multipliers in the ABC frame for a modular multilevel converter-based HVDC system. The methodology is capable of analytically obtaining desired operative conditions by calculating the differential current references previously established by the constraints in the optimization formulation, while obtaining the result with minimum: 1) differential current oscillations (Δi_diffk) or 2) capacitive phase-energy oscillations (Δω_Σk). Furthermore, the energy distribution inside the MMC (i.e., the capacitive phase average energy sum (ω̅_Σk) and difference (ω̅_Δk)) is being regulated by means of the constraint definitions. The optimization yields a differential current reference in “abc” coordinates with a similar structure to instantaneous power theories: as the addition of the product between varying conductances and the MMC internal dynamics input voltages (i.e., the dc bus voltage (v_dc) and the MMC load electromotice force (emf) (e_vk) on the one hand; and a contribution proportional to the ac load power (e_vki_vk) on the other. Both the objective function minimization and the energy constraints are achieved with one single current reference resulting from the optimization process, without the application of linear superposition techniques.

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.

Mitigating DC-side power oscillations and negative sequence load currents in Modular Multilevel Converters under unbalanced faults- first approach using resonant PI

This work presents a simple approach to eliminate DC power ripple in a three-phase Modular Multilevel Converter (MMC) while operating with balanced (load) currents during unbalanced grid faults. In this study, the MMC is connected to an AC grid on one of its terminals, and to a constant ideal DC source on the other, while a single phase fault takes place. The presented “first” approach is based on the combined application of a Notch filter and a Resonant PI controller. The main idea is to eliminate the zero-sequence oscillations that occur in the MMC differential currents when the unbalanced fault takes place. This strategy may be applied jointly with a constant circulating current controller on the one hand or with a constant energy per phase (implying an injection of a second harmonic to the differential current), on the other. Moreover, the load currents are kept balanced even during the fault in order to demonstrate the potential application of the MMC as a power oscillation firewall of some sort; i.e., to simultaneously keep constant DC power and balanced load currents at all time.

State-space modelling of modular multilevel converters for constant variables in steady-state

This paper presents an approach for obtaining a dynamic model of a Modular Multilevel Converter (MMC) where all state variables settle at a constant point of equilibrium during steady-state operation. The resulting model can be expressed as a steady-state time-invariant (SSTI) state-space model, which can be linearized for assessment of small-signal stability by eigenvalue analysis or can be utilized for applying advanced control methods. The proposed modelling approach relies on an aggregated voltage-based representation of the internal capacitor dynamics of the MMC, and the derivation is based on the application of three Park transformations at different frequencies (+ω, -2ω and +3ω). The presented voltage-based modelling is suitable when the MMC insertion indexes for the modulation of the individual arms are calculated directly from the controller output references, without compensating for the dynamic variations and continuous oscillations in the internal capacitor voltages of the individual arms. Time-domain simulations with comparison to established MMC models are presented to verify that the proposed state-space model is accurately representing the dynamics of an MMC.

Global tracking passivity-based PI control for power converters: An application to the boost and modular multilevel converters

This paper deals with the problem of trajectory tracking of a class of power converters. To analyze the stability of these systems we consider the bilinear structure they admit. First, we propose the theoretical framework for which it is possible to ensure global tracking of trajectories. To do so, a construction of an output signal respect to which the incremental model becomes passive is carried out. This leads to a simple linear PI controller for the plant. Then, we apply this result in a realistic simulation for two well-known converters systems: the boost and the modular multilevel converter (MMC).

Impact on small-signal dynamics of using circulating currents instead of AC-currents to control the DC voltage in MMC HVDC terminals

The traditional approach for controlling the dc-voltage in Voltage Source Converter (VSC) HVDC terminals is to act on the reference for the active current or active power on the ac-side. For a Modular Multilevel Converter (MMC) with explicit control of the internally stored energy, this implies that the total energy sum must be controlled by acting on the dc-components of the circulating currents. However, the internal energy storage of an MMC acts as a buffer between the transient dynamics on the ac- and dc-sides. Thus, the dynamic response of the dc-voltage will depend on the closed loop dynamics of the internal energy control. Different system characteristics can be obtained if the reference signals from the dc-voltage control and the sum energy control are interchanged. As a result, the dc-voltage controller can provide the reference value for the dc-components of the circulating current, while the sum energy controller will provide the ac-side active current reference. In this paper, it will be demonstrated by time domain simulations and eigenvalue analysis that dc-voltage control by acting on the circulating current reference introduces a decoupling between the dynamics of the ac- and dc-side interfaces. This decoupling will also make the system dynamics less sensitive with respect to the operating conditions, which enables improved dynamic performances and less strict tuning requirements for the dc-voltage and sum energy controllers.

Improving Small-Signal Stability of an MMC With CCSC by Control of the Internally Stored Energy

The dc-side dynamics of modular multilevel converters (MMCs) can be prone to poorly damped oscillations or stability problems when the second-harmonic components of the arm currents are mitigated by a circulating current suppression controller (CCSC). This paper demonstrates that the source of these oscillations is the uncontrolled interaction of the dc-side current and the internally stored energy of the MMC, as resulting from the CCSC. Stable operation and improved performance of the MMC control system can be ensured by introducing the closed-loop control of the energy and the dc-side current. The presented analysis relies on a detailed state-space model of the MMC, which is formulated to obtain constant variables in steady state. The resulting state-space equations can be linearized to achieve a linear time invariant model, allowing for eigenvalue analysis of the small-signal dynamics of the MMC. Participation factor analysis is utilized to identify the source of the poorly damped dc-side oscillations, and indicates the suitability of introducing control of the internal capacitor voltage or the corresponding stored energy. An MMC connected to a dc power source with an equivalent capacitance, and operated with dc voltage droop in the active power flow control, is used as an example for the presented analysis. The developed small-signal models and the improvement in small-signal dynamics achieved by introducing control of the internally stored energy are verified by time-domain simulations in comparison to an electro-magnetic transient (EMT) simulation model of an MMC with 400 submodules per arm.

An optimization-based control strategy for modular multilevel converters: Design and implementation

In this paper we present an optimization-based procedure for designing a reference circulating current which stabilizes the internal dynamics of a modular multilevel converter. This procedure relies on unconstrained convex optimization and it takes into account conflicting performance requirements such as reducing the oscillating components of circulating current and arm voltages. Tracking of such a reference signal is ensured by a robust tracking controller with gains chosen in order to attenuate the measurement noise. Since we were interested in implementation of the control algorithm by using a digital simulator, the design procedure is carried out in the discrete-time domain. Effectiveness of the proposed strategy is confirmed on a prototype of three-phase modular multilevel converter with five sub-modules per arm and RL load.

Improving the dynamics of lagrange-based MMC controllers by means of adaptive filters for single-phase voltage, power and energy estimation

A generalized and versatile approach for control of the circulating currents of Modular Multilevel Converters (MMC) has been recently proposed by using Lagrange Multipliers in the ABC frame. This approach is capable of analytically obtaining the differential current references associated with the desired operating conditions imposed to the optimization procedure. Previous implementations of this control approach have been sensitive to harmonic distortion of the control signals when applied to systems with a low number of levels, and have depended on average value calculations of sinusoidal variables, slowing down the dynamics of the control and making the tuning of the control system difficult under certain conditions. This work demonstrates that the performance of the versatile Lagrange-based control can be improved by introducing adaptive filtering based on Second Order Generalized Integrators (SOGIs) for processing the system variables needed for calculating the circulating current references. In addition to improved control dynamics and easier tuning of system controllers, the use of the adaptive filters provides inherent capability for operation under frequency variations, and is therefore suitable for control of MMCs operating in weak grids as well as for high- or medium-voltage motor drives.