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## The revolution: VSC technology

The Insulated Gate Bipolar Transistor (IGBT) was introduced as the main building block of the HVDC converter valves in the late 1990s. In contrast with thyristors, the IGBT is capable of “turning-off” whenever it is required to do so, independently of the AC voltage of the system. This seemingly small difference has completely revolutionized the world of HVDC, announcing the start of a new era in HVDC technology [12]. Furthermore, the IGBT required a complete change in the way that HVDC stations were designed and controlled, as the implementation of a Voltage Source Converter (VSC) HVDC station was now possible. As the devices are “selfcommutating” they do not need a strong AC grid offering the possibility of black-start capability. Moreover, VSCs may switch at higher frequencies (1-2 kHz). This implies lower space requirements compared to LCCs, as smaller filters are now required to mitigate significantly smaller high-frequency harmonics [14]. In addition, the VSC has the inherent capability to control active and reactive power [12] adding an important degree of flexibility in power systems. VSCs have gone through a distinct series of transformations. The first generations of VSCs, illustrated in Fig. 2.1, were based on two-levels (+vdc=2, vdc=2) using Pulse Width Modulation (PWM) techniques with high switching frequencies as depicted in Fig. 2.2, resulting in large converter losses (3%) [13]. The two level PWM-based VSC topology, was first commercialized by ABB under the name “HVDC-Light 1rst Generation” in 1997. ABB’s second generation of VSC was based on both the Three-level Neutral Point Clamped (NPC) converters, reducing total losses from 3% to 1.8% [14]. Their 3rd generation of VSCs that appeared in 2006 decreased the losses even further (1.4%) by returning to the two-level version using an optimized PWM. The most recent VSC topology breakthrough is however the Modular Multilevel Converter (MMC) based on the proposal of Prof. Marquardt [2]. It was first commercially introduced by Siemens in 2010 under the name “HVDC Plus” in the “Trans Bay Cable” Project in the United States, operating at 400 MW and 200 kV. It is estimated that the MMC is able to produce evenlower losses than its predecessor (between 0.9% and 1%) and has almost no filtering requirements.

Alstom’s “HVDC MaxSine” as well as ABB’s “HVDC Light 4th Generation” have introduced similar concepts based on the MMC in 2014 and 2015, respectively [13]. The MMC approach offers theoretically no limit on the number of modules [12] thanks to its modular property. Each of the individual SMs is controlled to generate a small voltage step, acting as a discrete voltage source, as illustrated in Fig. 2.3 and Fig. 2.4. By incrementally controlling each step, a nearly sinusoidal voltage is generated at the AC output of the “multivalves,”, which substantially reduces the need for any filtering.

### Basic structure and functionality of the MMC

A general phase of the MMC topology is depicted in Fig. 2.5. The converter topology is synthesized by connecting several SMs in series to constitute one “multi-valve”. Two of these multivalves are present in each phase, one on the upper part or arm of the converter and one in the lower one, denoted by the sub-indexes u and l respectively. The number of the SMs in series usually depends on the application, however it is possible to generalize the analysis by assuming N SMs in each arm, equivalent to 2N per phase. An individual SM is formed by a capacitor, IGBTs and their corresponding free-wheel diodes. The two most common SM configurations found in literature are the Half-Bridge (HB) SM and the the Full-Bridge (FB) SM, as illustrated in Fig. 2.6- a) and 2.6-b). The FB-SM version of the MMC has twice as much semiconductor devices than the HB version, which results in higher losses, but confers certain advantages as well [15, 16]. For the present analysis, and throughout the Thesis in general, the MMC under study is considered to be based on HB-SMs (Fig. 2.6-a)).

#### Equations representing the operation of the MMC

The MMC topology is known to have several advantages with respect to modularity, scalability and availability as briefly introduced in [18, 6]. However, the converter structure also implies additional dynamics and complexity of the control compared to conventional two-level or multilevel VSCs. This is mainly because the MMC has additional degrees of freedom in the sensethat the internal currents circulating between the upper and lower arms of one leg, and by that the voltage (or energy) of the capacitors in each arm can be controlled independently from the output AC currents. It is of course necessary to get familiarized with the mathematical model of the MMC so that an appropriate control strategy can be design to exploit the full potential of the converter. This section is devoted to the mathematical modeling of the converter. A step-by-step derivation of the converter equations is carried out in section 2.4.1, whereas the state equations of the MMC in matrix form are presented in section 2.4.2.

**Two mathematical models in matrix representation for the MMC**

Based on the step-by-step derivation described above, it is possible to obtain two different mathematical models of the MMC, expressed matrix representation. These are reffered to as:

1. State equations model.

2. Energy equations model.

Throughout this Thesis, both models have been used for different purposes; for instance in section 2.5 of this chapter, it is described how the circuit model of the MMC has been simplified by means of the mathematical model in state equations. The control scheme contribution of this Thesis, detailed in chapters 3, 4 and 5 are based on the MMC energy equations. Chapter B relies once again on the state equations model of the MMC in order to analyze stability while in chapter A, both the energy equations as well as the state equations model of the MMC are used, for different purposes, in order to successfully synthesize the non-linear control proposal. Due to the important role that both mathematical models played in this work, they are therefore described in the following lines for a generalized MMC phase k.

**Table of contents :**

Acknowledgments

Abstract

Nomenclature and Abbreviations

R´esum´e de la th`ese en Langue Fran¸caise

**1 Introduction **

1.1 Objectives

1.1.1 General objective

1.1.2 Specific objectives

1.2 Main contributions

1.3 Scope

1.4 List of publications

1.5 Layout of the Thesis

**2 The Modular Multilevel Converter **

2.1 Introduction

2.2 HVDC technology

2.2.1 Beginings

2.2.2 The revolution: VSC technology

2.3 Basic structure and functionality of the MMC

2.3.1 Sub-module analysis

2.3.2 Balancing algorithm

2.3.3 Grid connected MMCs

2.4 Equations representing the operation of the MMC

2.4.1 Step by step derivation of the MMC main equations

2.4.2 Two mathematical models in matrix representation for the MMC

2.4.3 Considerations for controlling the capacitive energy

2.5 Circuit modeling approaches for the modular multilevel converter

2.5.1 Detailed or high-fidelity model of the MMC

2.5.2 Reduced circuit modelling based on ON/OFF resistors

2.5.3 Controlled voltage sources-based models

2.5.4 Analytical models

2.5.5 Averaged MMC models

2.6 MMC models comparison and validation

2.6.1 Comparison under balanced and unbalanced AC grid conditions

2.6.2 Models validation under DC short-circuits

2.6.3 Concluding remarks on the MMC modelling techniques

2.7 On the need of a circulating current control

2.8 Insertion index “continuous” modulation methods classification

2.9 State of the art of circulating current control schemes

2.9.1 Direct Modulation

2.9.2 Open loop control based on estimation of stored energy

2.9.3 Circulating current suppression controller

2.9.4 Arm energy closed-loop control scheme in the “abc” frame

2.9.5 Double decoupled synchronous reference frame (DDSRF) control for 3- phase MMC

2.10 Motivation for a new circulating current control scheme for the MMC

**3 Optimization of the Circulating Current Signal for Phase Independent Energy Shaping and Regulation **

3.1 Introduction

3.2 Introduction to the instantaneous abc theory

3.2.1 Active and nonactive current calculation by means of a minimization method

3.2.2 Generalized compensation theory for active filters based on mathematical optimization

3.3 MMC circulating current calculation for phase independent control

3.3.1 MMC constant circulating current

3.3.2 MMC constant energy sum

3.3.3 Generalized equation

3.4 Implementation by means of stationary multi-resonant controllers

3.5 Simulation results

3.5.1 Steady state performance

3.5.2 Operating under unequal arm energy references

3.5.3 Comparison with the existing controllers

3.5.4 MMC-HVDC simulation

3.6 Conclusion

**4 Circulating Current Signal Estimation based on Adaptive Filters: Faster Dynamics and Reduced THD **

4.1 Introduction

4.2 On harmonic sensitivity and slow dynamics of the circulating current reference signal generation based on Lagrange multipliers

4.2.1 Harmonic sensitiviy

4.2.2 Risk of slow dynamics

4.3 The second order generalized integrator configured as a quadrature signal generator

4.4 Circulating current reference calculation based on single-phase voltage, power and energy estimation for MMCs

4.4.1 Estimation of single-phase fundamental frequency voltage and power

4.4.2 Estimation of the single-phase RMS voltage

4.4.3 Estimation of the single-phase average power

4.4.4 Estimation of the single-phase average values for the MMC energy sum and difference

4.5 Simulation results

4.6 Proof of concept via lab experimental prototype

4.6.1 Experimental setup

4.6.2 Experimental Results

4.7 Conclusion

**5 Circulating Current Signal for Constant Power under Unbalanced Grid Conditions: The MMC Energy Buffer **

5.1 Introduction

5.2 Investigating MMC conceptual possibilities under unbalanced operation using a simplified energetic macroscopic representation

5.3 Circulating current reference adapted for unbalanced operation

5.4 Grid current control strategies

5.5 Power references assignment

5.6 Results

5.6.1 Former control equation for independent control per phase

5.6.2 Performance of the novel circulating current reference formulation adapted

for unbalanced operation under different grid current control strategies

5.6.3 Influence of the power reference assignment in transient state under unbalances

5.7 Conclusion

**6 Stability of the MMC: Passivity-based Stabilization **

6.1 Introduction

6.2 Global tracking passivity-based PI controller for modular multilevel converters

6.2.1 Tracking problem for the MMC

6.2.2 Passivity of the bi-linear incremental model

6.2.3 A PI tracking controller

6.2.4 MMC controller summary

6.3 Generating the reference signals using a closed loop virtual energy estimator .

6.3.1 Phase independent energy regulation

6.3.2 Generation of references for constant DC power under unbalanced grid conditions

6.4 Results

6.4.1 Phase independent control

6.4.2 Constant DC power control

6.5 Conclusions

**7 Conclusions and Future Research **

7.1 Conclusions

7.1.1 On the proposed control philosophy and linear control scheme

7.1.2 On stability issues and non-linear control proposal

7.2 Future research

7.2.1 Minimizing the energy difference during unbalances

7.2.2 Perspectives on weak grid operation of MMCs

7.2.3 Improving the MMC state estimation

7.2.4 Adaptive PI stabilization of the MMC

7.2.5 Control by interconnection applied to the MMC

**Appendices **

A Global Tracking Passivity-based PI Controller

A.1 Introduction

A.2 Global tracking problem

A.3 Passivity of the bilinear incremental model

A.4 A PI global tracking controller

A.5 Conclusions

**B Lyapunov’s Global Asymptotic Stability Proof **

B.1 Introduction

B.2 Revisiting the MMC equations

B.2.1 State equations

B.2.2 Control equations

B.3 Single-phase MMC stability proof

B.3.1 Deviation variables equation system

B.3.2 Global asymptotic stability

B.4 Three-phase voltage source MMC stability proof

B.4.1 Deviation equations

B.4.2 Global asymptotic stability

B.5 Conclusion