G. Bergna

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.

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.

Modular Multilevel Converter-energy difference controller in rotating reference frame

This paper presents a control strategy capable of eliminating the mean value of the energy differences between the upper and lower arms in a three-phase Modular Multilevel Converter (MMC) in Park Coordinates for HVDC applications. This is achieved by controlling the active and reactive differential currents using a rotating reference frame at fundamental frequency in order to eliminate the zero sequence energy difference components by means of an inner and outer control loops. All feed-forward equations are demonstrated, with specific attention being paid to the cross-coupled terms.

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.

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.