Optimal operation and design of modular multilevel converter for HVDC applications

Modular Multilevel Converters (MMCs) are a type of Voltage Source Converter (VSC) which have become the preferred topology choice for High Voltage Direct Current (HVDC) applications. Compare to its HVDC converter predecessors, such as the Line Commutated Converter (LCC), the MMC can control active and reactive power independently, requires smaller filter reactors and have blackstart capabilities. Regarding classical two- and three-level VSCs, the MMC has improved efficiency, easier scalability to higher voltage levels and better AC output voltage harmonic content. However, they need more complex regulation strategy due to its increased number of degrees of freedom (DOFs). Nevertheless, when these DOFs are fully exploited, the MMC can provide better responses than classical converters, especially during unbalanced network conditions. First, an in-depth steady-state mathematical analysis of the converter is performed to identify all its DOFs. Based on the DOFs and the currents imposed by them, the equations for the power transfer between the DC/AC networks and internally, between the upper and lower arms and among the phase-legs, are obtained. The resultant expressions indicate potential interactions between distinct DOFs. By taking advantage of those interactions, it is possible to improve existing circulating current reference calculation methods. Thus, enhancing the MMC response under balanced and unbalanced AC network conditions. The performance of the MMC can be further improved when optimization algorithms are used to calculate its references, in which this thesis proposed two different methods. In the initial proposal, an optimization-based current reference calculation in the natural $abc$ reference frame is presented. It considers the Transmission System Operator (TSO) requirements during AC network voltage sags in the form of active/reactive current set-points to provide Fault Ride Through (FRT) capability and the converter limitations. However, due its highly nonlinear characteristics it presents a high computation burden not allowing it to be solved in real-time applications. To cope with this issue, a second method is introduced whereby modifications are performed in the previous optimization formulation and linearization techniques are employed. The resultant linearized optimization-based reference calculation is then integrated with an energy-based control for MMCs and different case studies are analyzed to validate its performance compared to classical approaches. Finally, an optimization-based methodology to design the submodule (SM) capacitors is proposed. The algorithm considers all the DOFs of the MMC in order to size the SM capacitor while meeting the TSO's requirements and the converter's design limitations. The suggested method is compared with classical approaches for different operating points, and it is further exploited by considering AC network voltage sag conditions.Els convertidors multinivells modulars (MMC) són un tipus de convertidor de font de tensió (VSC) que s'han convertit en l'opció de topologia preferida per a les aplicacions de corrent continu d'alta tensió (HVDC). En comparació amb els seus predecessors convertidors HVDC, com ara el convertidor de commutació de línia (LCC), l'MMC pot controlar la potència activa i reactiva de manera independent, requereix reactors de filtre més petits i té capacitats d'arrencada en negre. Pel que fa als VSC clássics de dos i tres nivells, l'MMC té una eficiència millorada, una escalabilitat més fàcil a nivells de tensió més alts i un millor contingut harmònic de voltatge CA. Tanmateix, necessiten una estratègia de regulació mès complexa a causa del seu major nombre de graus de llibertat (DOF). No obstant això, quan aquests DOFs exploten completament, l'MMC pot proporcionar millors respostes que els convertidors clàssics, especialment en condicions de xarxa desequilibrades. En primer lloc, es realitza una anàlisi matemàtica en estat estacionari en profunditat del convertidor per identificar tots els seus DOF. A partir dels DOF i dels corrents imposats per aquests, s'obtenen les equacions de la transferència de potència entre les xarxes DC/AC i la transferència de potència interna, entre els braços superior i inferior i entre les potes de fase. Les expressions resultants indiquen interaccions potencials entre diferents DOF. Aprofitant aquestes interaccions, és possible millorar el mètode de càlcul de referència de corrent circulant existent. En fer-ho, es pot millorar el rendiment de l'MMC en condicions desequilibrades i amb errors. El rendiment de l'MMC es pot millorar encara més quan s'utilitzen algorismes d'optimització per calcular les seves referències. A la proposta inicial, es presenta un càlcul de referència actual basat en l'optimització en el marc de referència natural abc. Considera els requisits de l'operador del sistema de transmissió (TSO) durant les caigudes de tensió de la xarxa de CA en forma de punts de consigna de corrent actiu/reactiu per proporcionar la capacitat de transmissió de fallades (FRT) i les limitacions del convertidor. Tanmateix, a causa de les seves característiques altament no lineals, presenta una gran càrrega de càlcul que no permet resoldre'l en aplicacions en temps real. Per fer front a aquest problema, es realitzen modificacions en la seva formulació i s'utilitzen técniques de linealització. A continuació, el càlcul de referència basat en l'optimització linealitzada resultant s'integra amb un control basat en energia per a MMC i s'analitzen diferents casos pràctics per validar el seu rendiment en comparació amb els enfocaments clàssics. Finalment, es proposa una metodologia basada en l'optimització per dissenyar els condensadors de submòduls (SM). L'algorisme considera tots els DOF de l'MMC per tal de dimensionar el condensador SM alhora que compleix els requisits del TSO i les limitacions de disseny del convertidor. El mètode suggerit es compara amb els enfocaments clàssics per a diferents punts de funcionament, i s'aprofita encara més tenint en compte les condicions de caiguda de la tensió de la xarxa de CA.Postprint (published version

Analysis of equilibrium points and optimal grid support of grid-forming modular multilevel converter for balanced and unbalanced faults

This short-communication presents a steady-state analysis of a grid-forming Modular Multilevel Converter (MMC) providing optimal voltage support to the AC network under normal and constrained conditions. The analysis is performed based on a multi-objective function (OF) optimization problem which prioritizes to maximize the positive-sequence and to minimize the negative- and zero-sequence voltage components at the point of common coupling (PCC) while it also considers the minimization of the arm impedance losses, respectively. If the voltage condition at the PCC is satisfied, the optimization attempts to reduce the arm impedance losses; otherwise, the algorithm prioritizes the PCC’s voltage components in order to minimize the error. Different network voltage and internal fault scenarios are evaluated, where it is shown that the suggested problem formulation can be used to obtain the optimal MMC’s quantities, providing voltage support during the faults.This work was supported by the Ministerio de Ciencia e Innovación (Proyecto Equired) under Grant PID2021-124292OB-I00. This work was also supported by the Agencia Estatal De Investigación, Spain under Grant PID2021-127788OA-I00. Eduardo Prieto-Araujo is an associate professor of the Serra Húnter programme. The work of Oriol Gomis-Bellmunt was also supported by the Institució Catalana de Recerca i Estudis Avançats (ICREA), Spain Academia Program.Peer ReviewedPostprint (published version

Optimization-based reference calculation for Modular Multilevel Converters in balanced and unbalanced network conditions

© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksThe paper addresses an optimization-based algorithm to calculate the references of the Modular Multilevel Converter (MMC) during normal and constrained scenarios (when the prioritization of quantities is required). The optimization problem prioritizes to satisfy the positive- and negative-sequence active and reactive current set-points demanded by the Transmission System Operator (TSO) through the corresponding grid code. If the TSO’s requirements are achieved, the algorithm minimizes the arm impedances losses. Otherwise, it attempts to reduce the error between the current components and the TSO’s current set-points. The optimization-based current reference calculation is derived based on the steady-state equations of the MMC, considering the maximum currents that can flow through the MMC’s arms, the maximum and minimum arm applied voltages and the maximum sub-module capacitor’s voltage. Simulation in the time-domain have been conducted and the results indicate that this method can be potentially employed to calculate the converter’s references during both normal and faulted conditions.Peer ReviewedPostprint (author's final draft

Improved current reference calculation for MMCs internal energy balancing control

© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksThe paper addresses an improved inner current reference calculation to be employed in the control of modular multilevel converters operating during either balanced or unbalanced conditions. The suggested reference calculation is derived based on the AC and DC additive and differential voltage components applied to the upper and lower arms of the converter. In addition, the impacts caused not only by the AC networks impedances but also by the MMCs arm impedances are also considered during the derivation of the AC additive current reference expressions. Another issue discussed in this article regards that singular voltage conditions, where the positive-sequence component is equal to the negative one, may occur not only in the AC network but also internally (within the converters applied voltages). Several different inner current reference calculation methods are compared and their applicability during the former fault conditions is analyzed. The paper presents a detailed formulation of the inner current reference calculation and applies it to different unbalanced AC grid faults where it is shown that the presented approach can be potentially used to maintain the internal energy of the converter balanced during normal and fault conditions.Peer ReviewedPostprint (author's final draft

Optimization-based methodology to design the MMC's sub-module capacitors

© 2023 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksThis paper proposes an optimization-based size reduction methodology for Modular Multilevel Converters (MMC), focusing on minimizing the converter's sub-module capacitor CSM. The analysis is performed considering both the converter's current and voltage limitations and the Transmission System Operator (TSO) Fault Ride Through (FRT) requirements. By means of a steady-state analysis, the time-domain expressions of the converter's arms energies are obtained and their behavior throughout the MMC's operating range is shown. Based on these expressions, the optimization-based problem to reduce the CSM size is developed and its constraints are imposed to ensure that the converter's voltage and current levels are within its design limitations. The suggested method is compared with different approaches for distinct active and reactive power set-points, where it is shown that the SM capacitor size can be reduced up to 24% in comparison with the method with worst performance and up to 7% regarding the best method used for comparison purposes. Furthermore, time-domain simulations of the MMC considering several AC voltage sags are performed in order to demonstrate that the dynamics of the SM capacitor and the arm applied voltages are within acceptable margins during the different operations.Postprint (author's final draft

An Improved hybrid DC circuit breaker with self-adaptive fault current limiting capability

© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksThe effective fault current limiting is very significant for the dc distribution system. However, the traditional dc fault current limiting method, i.e., directly installing dc reactor, may trigger negative impacts the system normal operation and fast isolation of the circuit breaker. Therefore, an improved hybrid dc circuit breaker with self-adaptive fault current limiting capability is proposed in this article. Not only can it realize fault current limitation in a quick and efficient manner, but also ensures the continuous operation of the converter and the fault ride-through of the healthy network after the dc fault. In this sense, the requirements on the protection and arrester capacity are reduced. Compared with other types of fault current limiting methods, the proposed topology has the merit of few negative effects on system stability and transient response. It can effectively perform fault current limiting and fault isolation, with low conduction loss and low implementation difficulty. The working principle and advantages of the proposed topology are verified by experimental tests and simulation cases.Peer ReviewedPostprint (author's final draft

Real-time optimization-based reference calculation integrated control for MMCs considering converter limitations

© 2021 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting /republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other worksThe paper addresses a real-time optimization-based reference calculation integrated with a control structure for Modular Multilevel Converters (MMC) operating under normal and constrained situations (where it has reached current and/or voltage limitations, e.g. during system faults). The algorithm prioritizes to satisfy the Transmission System Operators (TSO) AC grid current demanded set-points. The constrained optimization problem is formulated based on the steady-state model of the MMC, whereby the prioritization is achieved through distinct weights defined in the Objective Function’s (OF) terms. The resultant optimization problem, however, is highly nonlinear requiring high computation burden to be solved in real-time. To overcome this issue, this paper applies a Linear Time-Varying (LTV) approximation, where the nonlinear dynamics of the system are represented as constant parameters, while a Linear Time-Invariant (LTI) system is used to formulate the optimization constraints. The converter's current references are determined in real-time by solving a constrained linearized optimization problem at each control time step, considering the TSO's demands, the current MMC operating point and its physical limitations. Finally, the linearized-optimization problem is integrated with the MMC controllers and evaluated under different network conditions, where the results indicated that method can be potentially employed to obtain the MMCs current references.Peer ReviewedPostprint (author's final draft

Steady-state analysis of the modular multilevel converter.

In this paper, the steady-state behavior of the modular multilevel converter (MMC) is studied under balanced and unbalanced AC grid voltage conditions. The suggested mathematical model is derived combining the converter internal arm variables and both AC and DC grids variables. Moreover, the steady-state solution of the system can be achieved by setting the internal power balance within the converter. In order to verify the steady-state model, different types of AC fault conditions are imposed, and the output values are compared with the simulation results of an average model of the MMC circuit. The results show that the proposed analysis is in close agreement with the simulations for all conditions evaluated, validating the developed equations.Peer ReviewedPostprint (author's final draft

Optimal current reference calculation for MMCs considering converter limitations

The paper addresses an optimization-based reference calculation method for Modular Multilevel Converters (MMC) operating in normal and constrained situations (when the converter needs to prioritize its quantities as it has reached voltage or current limitations, e.g. during system faults). The optimization problem prioritizes to satisfy the external AC active and reactive current set-points demanded by the grid operator through the corresponding grid code. If the operator demands are fulfilled, it uses the available MMC degrees of freedom to minimize the arm inductance losses. Otherwise, if the operator demanded AC set-points cannot be accomplished, the optimization attempts to minimize the error prioritizing between either AC active or reactive currents. The optimization problem constraints are imposed through a steady-state model considering simultaneously the external and internal AC and DC magnitudes of the converter. The steady-state model also includes the voltage variation in the equivalent arm capacitors (considering the ripple). Then, the imposed limitations are the maximum allowed grid and arm currents, the maximum allowed arm voltages and the sub-module capacitor maximum voltages. The paper presents a detailed formulation of the optimization problem and applies it to several case studies where it is shown that the presented approach can be potentially used to obtain the MMC references both in normal and fault conditions.Peer ReviewedPostprint (updated version

Control Design and Fault Handling Performance of MMC for MMC-Based DC Distribution System

Modular multilevel converters (MMCs) have emerged as a viable choice in future DC grid architectures due to their scalability to meet voltage level requirements. However, MMC-based DC distribution systems are at risk of short-term outages during the faults in either the DC or AC networks feeding the MMC, so it remains a challenge to accomplish AC and DC fault ride-through (FRT) capability in such applications. To ensure stable operations of the DC terminals, FRT strategies are required for the faults on both the AC and DC sides of the converter. This paper proposes a FRT strategy for the AC and DC side of the converter to ensure stable and economically viable operation of the DC distribution network. The asymmetrical faults in the upstream AC grids are managed by using the integrated energy of the MMC. Whereas, the DC FRT capability of the MMC is accomplished by changing the redundant submodules of the MMC to full-bridge submodules (FBSMs), thus allowing a DC FRT to be achieved by using DC circuit breakers that are low cost and reduced in size. Applying the proposed DC FRT strategy, which makes possible the use of low-cost and reduced in size DC circuit breakers in DC distribution, results in a reduction in the overall initial investments