# Chapter 5

# Perspectives and scientific project

This concluding chapter aims at proposing a *road map of what I believe being of interest for my research activity from a medium- and long-term perspective*.

Generally speaking, I envisage to pursue the main directory lines of my present research by going deeper in certain directions. Being application-oriented, my research aims at finding its motivations in the actual scientific challenges and societal needs, always taking into account real-world constraints, as well as pertinence and feasibility of the corresponding proposed solutions and implementations. Some identified perspectives are detailed next.

## 5.1 Towards a comprehensive co-design approach for modern microgrids

The term "*co-design*" is presently at the core of rich debates, especially around economical and ecological issues. This term globally denotes complex interactions between heterogeneous subsystems composing the environment of a given engineering solution or product, including its initial sizing, investment, operational and maintenance costs, as well as quantification of its environmental effect and possibly recycling and/or dismantling costs. Recent works in the literature having approached MGs from a broader, techno-economical viewpoint, suggest that *suitable formalization of a co-design problem corresponds to a multi-criteria optimization problem* [166], [167].

To fix ideas and place co-design within the microgrids (MGs) topic, the MG Power Management System (PMS) design will be regarded from a larger perspective, where different economical elements are also considered, namely related to MG configuration and initial sizing, including number of sources and storages, their technologies, power levels and costs. Intuitively speaking, a "good" PMS design would have to explicitly suppose a *certain economical and ecological awareness* – reliability requirements are an example, as explained before – further implying that, with the promise of such a PMS, a more rational and sustainable MG overall operation will emerge in a long term.

### 5.1.1 Generic robust PMS design for multi-source microgrids

The term "generic" added to the design of robust and LPV optimal control methods for coordination inside of multi-source MGs regards the generalization of the PMS design procedures already proposed for three-source systems – and summarized in Section 4.2 in Chapter 4 – to *any number of sources*, while also taking into account the parameter-varying nature of all sources.

The LPV approach is nowadays increasingly used – possibly coupled with some other powerful control design techniques – because, being derived from classical linear control techniques, it allows representing relatively-general
classes of nonlinear systems, while taking account of time-varying objectives and effectively coordinating the various actuators of a multi-variable system. This flexibility renders LPV approaches quite easily acceptable in the industry, despite their relative complexity.

As renewable-based MGs are becoming ubiquitous in the future electrical energy distribution landscape, **storage units** are becoming at their turn ubiquitous within these MGs, representing technical means used in the first place for taming variations and uncertainties. Thus, taking into account constraints of maintaining the state of charge of the different storage units within some imposed limits is of great interest. Integrated into the MGs control, this objective can lead to a complex optimization problem as the number of sources/storages increases, as **scalability of the $H_\infty$-LPV design for this case** appears in a first place to be affordable, but still needs to be studied. This complexity – possibly alleviated by order reduction methods – is further repercuted onto the real-time embedding of the resulted controllers by challenging the computing performance of the numerical devices.

The experience we had with embedding an $H_\infty$-solution on a *general-purpose microcontroller* (of C2000 family of Texas Instruments), in the framework of the technology pre-transfer and transfer projects between 2017 and 2020, revealed that an *eight-order $H_\infty$ controller* requires *less than 25% of computation resources* (memory and run time), while preserving some suitable sampling time. Obviously, application to a more complex system would require more computation resources being mobilized. As a medium-term goal, systematic analysis and order-reduction methods are required to confort the real-world application acceptability.

From a different viewpoint, pursuing funding opportunities allowing TRL advancing of our PMS, K-INF, by validation on MG pilote sites remains a priority. At the present, the aim is to reach a concertation in an European context. Thus, our efforts are focused on joining an European consortium in order to apply for 2022 fall call of **EIC** (European Innovation Council) **Pathfinder Challenges**, a funding instrument specifically tailored for **boosting laboratory proof of concepts towards market and commercialization**. Within this call, our targeted theme is "Mid- to long-term and systems integrated energy storage".

### 5.1.2 Effective estimation methods of storage state of health

Also related to management of storage units in various MG applications, I have very recently been given the opportunity to begin exploration of estimation methods of state of health (SoH) parameters of batteries, namely in the framework of a research project funded in the context of national IDEX (*Investissements d'avenir*) programme through local IRGA (*Initiatives de Recherche à Grenoble Alpes*) funding scheme. The goal of this eighteen-month 2022–2024 project is that, starting from the partial-derivative-equation (PDE)-based (Enhanced) Single Particle Model [168]–[170] – which provides exhaustive description of battery internal governing phenomena, such as diffusion, intercalation and electrochemical kinetics, like suggested in Fig. 5.1 [171] – to explore the **systematic design, feasibility and effectiveness of battery SoH PDE-based estimators**.

For sake of accurate capturing of physical substrate, an as generic as possible approach is aimed at, in the sense of exploiting as deep as possible PDE features before applying different approximation methods needed for numerically solving them [172]. Thus, a **semigroup approach with infinite-dimensional Kalman filters** is chosen to solve the estimation problem. Collaboration with collegues at LEPMI (Laboratoire d'Électrochimie et de Physicochimie des Matériaux et des Interfaces) in Grenoble will further enable **benchmarking against objective SoH mesures** issued from real batteries cycling tests.

Such a goal is obviously subsumed to a control and/or optimization one, being **coherent with the MG PMS reliability-aware consensus design** summarized in Chapter 4. At a longer term, predictions of such an SoH estimator may also be used for **benchmarking against artificial-intelligence-based estimation methods**, as a substitute

<figure><img src="image_105.png" /><figcaption>Figure 5.1: Illustration of Single Particle Model for batteries [171].</figcaption></figure>
of objective mesures, which may be long and difficult to obtain. Extensions towards a more general, data-driven
paradigm can further be envisageable.

5.1.3 Towards formalizing microgrids co-design

Quantification of storage hybridization benefits performed for our PMS solution, K-INF, has allowed to conclude
that the service time of the low-frequency (long-term) storage – a battery in the considered case – is prolonged if
accompanied by a high-frequency (short-term) storage, like a supercapacitor.

This conclusion can be used in an *N*-source MG co-design context, as it can be extended to any complementary
storage pair and further to a set of *N* sources – not necessarily only storages – whose own (characteristic) frequencies,
$f_i$ can be put in relation with the pair (technology, power)$_i$, according to power sources taxonomy and Ragone's
plot. Thus, if *the length of dynamic interval where the source i is exploited* is further denoted by $\Delta f_i$,
then the above result indicates that *$\Delta f_i$ is in inverse relation with the source i's life and service time*.

Hence, reliability of long-term storages can be preserved if narrowing their respective exploitation dynamic
ranges by hybridization with one (or more) relatively shorter-term storage(s).

On the other hand, a preliminary analysis of MG load variation spectrum allows to determine the maximal
frequency $f_{load}$. Therefore, union of all intervals $\Delta f_i$ must cover the entire load spectrum, $f_{load}$, whereas the
intersection between all pairs of adjacent intervals $\Delta f_i$ should be minimized because these intervals should be as
disjoint as possible, in order to reflect complementary usage of sources.

Finally, the co-design problem can be stated as finding the minimum number of sources out of the *N* available,
such as to minimize the total investment cost and the cost-per-service-time ratio for each source *i*. The optimally
configured multi-source MG will operate in closed loop with the PMS ensuring "tuning" of each source *i* on its
"specialization" dynamic interval, $\Delta f_i$, around its own frequency, $f_i$.

## 5.2 Control of particular topologies of power electronic converters

Remaining in the domain of electrical energy conversion, it is worthy to look closer to the involved *actuators*, the
*power electronic converters*, which are themselves dynamic systems quite challenging from a control viewpoint.
International and industrial collaborations I have recently started have offered me an excellent opportunity to
go deeper into the modelling and control of some particular power electronic topologies, each of which presents
technical and operational gains, but also requires customized control approaches.

**Katium** is a specific patented DC-DC power converter topology [173], particularly well suited for railway
applications, being an isolated, current-input, high-frequency soft-switching system.

Katium converter modelling and control has been approached in 2020 in the context of its use as a battery
charger for railway applications, according to terms of collaboration with Faiveley Transport - WABTEC in Tours,
France. An *LPV state-space model subject to step, as well as periodic disturbances*, has been proposed
in our conference paper [174] and further exploited within a *resonant-integrator-based state-feedback control*
in the conference paper [175]. Preliminary validation tests on Faiveley plant in Tours have started during 2020 fall.

The idea of including resonant integrators within a classical state-feedback control design – with the aim of
rejecting periodic (sinusoidal) disturbances – originated in the conference paper [176] I co-authored together with
Professor Remus TEODORESCU from Aalborg University, dealing with another particular conversion topology,
that of *modular multi-level converters* (MMCs).

MMCs represent a shift in the power electronic converters technology, that consists in multiplying the number
of layers containing switching devices, which thus operate at a *lower switching frequency*. Lower losses and higher
operating efficiency are thus obtained. Multilevel topology also ensures improved harmonic performance at a given
switching frequency. MMCs are a promising solution to high-voltage direct-current (HVDC) transmission systems
over long distances, to facilitate grid integration of renewable energy systems, thus being coherent with long-term
European sustainability strategies.
<figure><img src="image_106.png" /><figcaption>Figure 5.2: Topology of a typical *M*-phase MMC, showing all the important variables, including DC and AC bus [177].</figcaption></figure>

Pertinent solutions to control problems of MMCs are still required, so this research direction is envisaged at long term. Actual solutions make extensive use of several-level hierarchical, highly-imbricated, generally linear, controls, which suffer of lack of robustness. Instead of a large DC-side capacitor, MMCs have many lower-capacity capacitors, behaving as a spatially-distributed energy storing capacity. The *dynamic energy balancing between submodule capacitors* over time has been identified as one of crucial problems to solve by control actions; its solution defines in general the lower limit for the switching frequency. Fig. 5.2 is introduced here for terminology clarification purposes.

*Control of circulating current* of each leg is necessary to ensure the energy balance between submodules. In our conference paper [176] a change of control viewpoint is proposed against the classical, hierarchical one, presently widely used in industry [177]: *a state-feedback control of both grid and circulating current* – ensuring that the input-coupled dynamics of the two currents to be MIMO controlled – proved to outperform the two-loop conventional control under unbalanced grid conditions. A genetic-algorithm-based selection of gains of such a state feedback has been subsequently investigated in our conference paper [178].

*Formal modelling of MMCs* is not trivial, because their original bilinear dynamics are complexified by presence of binary variables, like the ones indicating if a submodule is inserted or bypassed at a given time. Hybrid dynamics can thus be emphasized.

Like for the other converter types, MMC *averaged* and *switched* (exact) models exist; several types of averaged models are available, depending on which physical level average is made at (leg level, arm level, submodule level – see Fig. 5.2). Averaged models are suitable for most applications; however, switched models may be needed when binary variables are explicitly taken into account. Thus, it is pertinent to explore relevance of considering *modulation process modelling* within the control design for submodule energy balancing, as they are intimately linked by the switch instants of individual submodules. Such an approach would lead to an *optimization problem*, whose solution may require some pertinent relaxations corresponding to acceptable levels of sub-optimality in the solution. Similar points of view have been proposed in [179] – where the optimal-switching-sequence-based control (OSBC) is applied to matrix converters – and in [180], where convex optimization is combined with LMIs for robustly designing switching surfaces for multilevel inverters modelled as bilinear systems with binary inputs.

Another challenging modelling issue consists in deriving an *explicit MMC model under faulty and/or unbalanced conditions*, suitable to further use for fault-tolerant control design.

Last, but not least, interest may be oriented to some light topology variations in the MMCs, namely the case when *batteries – instead of capacitors* – are used in the submodules. In this case, because the energy balancing between submodules relies upon disposing of accurate and reliable *battery state of charge estimations*, solution may be found out in the above-mentioned investigation of PDE-based estimation of *state of health*, e.g., by means of Kalman filters.

## 5.3 Control-purpose modelling of energy-communication interaction in smart grids

It is of significant importance to obtain a reliable model of the communication traffic present within a smart grid, because a bad-quality communication negatively influences the grid global performance, leading even to
blackouts as catastrophic expression of loss of stability. Moreover, at the present none of the most-commonly
used communication protocols is accepted as a unique standard, thus rendering even more complex the
modelling and control tasks. This topic is perceived as quite a challenge and has been identified as a priority of
the European research on smart grids [181].

In France a multitude of research and proof-of-concept projects – among which AMI-ADEME GREENLYS, SOGRID, NICEGRID – showed a clear interest of both scientific and industrial communities, as well as of public authorities, to demonstrate the practical necessity and effectiveness of transition to smart grids. However, such projects aim at rather short-term technological advances, which must be accompanied by a formalization effort towards representative, accurate and flexible models of the energy-communication interaction.

In this context, the already obtained results concerning the traffic modelling – based on ARIMA time-series
models, as summarized in Section 5.3 in Chapter 2 earlier in this memoir – have shown that *processing of the
information provided by a network analyzer* needs a systematic method, in order to extract that traffic information
which is relevant for the communication delay estimation.

These results have great potential
of being used in an *interoperability*
*context*, that is, when two or several
smart grids – based on possibly differ-
ent communication protocols – are re-
quired to *cooperate for a common
goal*. In this context, I am already in-
volved in 2020–2022 ADAGIO (Anal-
yse des retarDs dans les smArt Grids
InterOpérables – Analysis of Delays
in Interoperable Smart Grids), project
funded by Institut Carnot Énergies du
Futur and led by G2ELab (Grenoble
Electrical Engineering Laboratory) and
CEA (Commissariat à l'Énergie Atom-
ique et aux Énergies Alternatives). A
possible test setup is suggested in

Fig. 5.3, where estimation of a delay propagated over a transmission line needs in a first place synchronization between the two concerned remote grid sectors.

Necessity of confining maximum delays within admissible limits is here of crucial importance. The already
obtained models must first be adapted and extended to the case when the communication network architecture is
a priori not known (e.g., Internet instead of proprietary communication network).

Pertinence of models used in the literature to characterize and analyze the communication (e.g., Internet) traffic
must be evaluated. Stochasticity and complexity of involved phenomena suggest the opportunity of combining more
classical models – such as, e.g., time-series-based or long short-term memory (LSTM)-based – with **black-box**,
**data-driven, possibly machine-learning-based models**. Some preliminary, yet only simulation-based results
have recently been reported in our conference paper [182]. At this stage of research development, necessity of
defining and putting in place relevant scenarios, representative of smart grid operation, is a key factor in advancing
comprehension. Real-time tests on interoperable platforms are on progress for model validation and maximum
delay estimation. This latter delay is habitually variable in the time, depending on the observation time window –
adaptive sliding windows will thus be necessary to compensate for it.

On a longer term, modelling should help at identifying *relevant classes of smart grids*, depending on the type of their communication networks and/or types of their energy-communication interactions. Their *global structural properties as variable-time-delay systems* – among which the stability – can further be assessed on this basis.

<figure><img src="image_107.png" /><figcaption>Figure 5.3: Synchronization of two remote smart grids for estimation of delays in a transmission-line-protection scenario.</figcaption></figure>
<figure><img src="image_108.png" /></figure>
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