E. Berne

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.

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.

Modular Multilevel Converter leg-energy controller in rotating reference frame for voltage oscillations reduction

This work consists of the presentation of a regulation strategy capable of controlling the energy stored in the DC capacitors of the upper and lower arms of a Modular Multilevel Converter (MMC) for each phase. This is achieved by regulating the positive, negative and zero sequences in dqo coordinates of the differential current using a rotating reference frame at twice the fundamental value. Active and reactive components of the differential current are used to eliminate the oscillations of the three-phased leg-energy which reduces significantly the capacitor voltage oscillations, while the zero sequence component is used to regulate the whole system energy at a given value. All feed-forwards equations are demonstrated, and cross-coupled leg-energy terms are introduced.

Generalized ABC frame differential current control ensuring constant DC power for modular multilevel converters under unbalanced operation

This work presents a generalized and versatile approach for controlling Modular Multilevel Converters (MMC), with three or more phases, by means of Lagrange Multipliers in the ABC frame. The resulting control method is suitable for operation of HVDC converters under both balanced and unbalanced AC grid voltages, since it is designed for eliminating oscillations in the DC power flow independently of the AC grid voltage conditions. This is achieved by the analytical resolution of a mathematical optimization problem using Lagrange multipliers in order to calculate the differential current references for the converter directly in the ABC frame. The resulting equation for current reference calculation is generalized by a weighting factor introduced in the objective function for the optimization problem, and this allows to select between the following two operating conditions or any intermediate point between them: I) minimum differential current oscillations (Δidiffk), or II) minimum capacitive phase energy oscillations (ΔwΣk). Furthermore, the constraints defined in the optimization regulate the average energy distribution inside the MMC; i.e., the capacitive phase average energy sum (wΣk) and difference (wΔk) whilst ensuring non-oscillatory power output (PDC) on the DC terminals of the MMC.

A generalized power control approach in ABC frame for modular multilevel converters based on Lagrange multipliers

This work presents a generalized and versatile control approach for Modular Multilevel Converters using Lagrange Multipliers in the ABC frame. 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, whilst obtaining the result with minimum I) differential current oscillations (Δi_diffk), or II) capacitive phase energy oscillations (Δw_Σk). Furthermore, the energy distribution inside the MMC; i.e., the capacitive phase average energy sum (w_Σk) and difference (w_Δk), is being regulated by means of the constraint definitions.

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.

Earth currents in HVDC grids: An example based on 5 terminal bipolar configurations

With the rapid development of Voltage Source Converters and the recent progresses for DC fault management through DC breakers or inherent fault limiting converters, HVDC has become more and more attractive to grid operators and the possibility of a DC grid layer superimposed to the AC grid is gaining ground. Still, a lot of questions remain concerning the appropriate operation of such a grid. One question that has only attracted limited interest is the possibility of ground currents circulating between stations of the grid. The current levels and the criticity of this question are highly dependent on the topology of these hypothetical DC grids and theirs modes of operation. Still, the environmental and legal issues associated with ground currents as well justify the need to study this aspect as well as the mission profile information required for the proper HVDC station electrode design. The aim of this document is to provide illustration of ground current circulation in the case of bipolar HVDC grids with 5-terminal meshed and radial examples. The influence of the mode of operation of the grid is studied, in the transient case with a DC-fault and in the permanent case of operation with a faulted pole. The influence of the impedance connection to ground is illustrated with both high and low resistance cases. Finally, the possibility of using a pole voltage balancing control unit is investigated and its limits are demonstrated, showing the need for a supervision unit or an enhanced local ground current control.

Analysis of Modular Multilevel Converters under unbalanced grid conditions with different load current control strategies and Lagrange-based differential current control

This work studies the performance of the Modular Multilevel Converter (MMC) under unbalanced conditions when the internal circulating currents are controlled to follow a reference value given by Lagrange-based optimization applied in the abc frame. The Lagrange-based current reference calculation is constrained to ensure that the MMC is providing constant, non-oscillatory, power flow at the DC-side even the case the AC grid voltage is unbalanced. Such operation can be achieved by the investigated Lagrange-based control while either controlling the differential currents of the MMC to have only a DC-component or while minimizing the sum energy oscillations in each phase of the MMC. The objective of preventing DC power oscillations can also be achieved independently of the power control strategy applied to control the three-phase currents on the AC side of the converter. The operation of the MMC is studied with three different objectives for the control of the AC currents: 1) Constant instantaneous three-phase power with sinusoidal currents, 2) Balanced sinusoidal three-phase currents, and 3) Constant instantaneous reactive power with sinusoidal currents. The impact of these different AC power control strategies on the oscillations of capacitor voltages and stored energy in the MMC is then analyzed and discussed, verifying how the Lagrange-based control is always able to keep the DC power flow free of second harmonic oscillations.

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.