# Dc Electrical Current Generated by Upstream Neutral Modes

Ankur Das<EMAIL_ADDRESS>Department of Condensed Matter Physics,
Weizmann Institute of Science, Rehovot, 76100 Israel  Sumathi Rao  Harish-
Chandra Research Institute, HBNI, Chhatnag Road, Jhunsi, Allahabad 211 019,
India  International Centre for Theoretical Sciences (ICTS-TIFR), Shivakote,
Hesaraghatta Hobli, Bangalore 560089, India  Yuval Gefen  Department of
Condensed Matter Physics, Weizmann Institute of Science, Rehovot, 76100 Israel
Ganpathy Murthy  Department of Physics and Astronomy, University of Kentucky,
Lexington, KY 40506, USA

###### Abstract

Quantum Hall phases are gapped in the bulk but support chiral edge modes, both
charged and neutral. Here we consider a circuit where the path from the source
of electric current to the drain necessarily passes through a segment
consisting solely of neutral modes. We find that upon biasing the source, a dc
electric current is detected at the drain, provided there is backscattering
between counter-propagating modes under the contacts placed in certain
locations. Thus, neutral modes carry information that can be used to
nonlocally reconstruct a dc charge current. Our protocol can be used to detect
any neutral mode that counterpropagates with respect to all charge modes. Our
protocol applies not only to the edge modes of a quantum Hall system, but also
to systems that have neutral modes of non-quantum Hall origin. We conclude
with a possible experimental realization of this phenomenon.

##  I Introduction

The quantum Hall effects (QHE) Klitzing et al. (1980) are the earliest known
example of topological insulators Hasan and Kane (2010). They have a charge
gap in the bulk, and all currents are carried by edge/surface modes, which can
be either charged (with fractional charge in the fractional QHE) or neutral
chiral modes. While the charge modes produce quantized electrical conductance,
neutral modes are a manifestation of topology, electron-electron interactions,
and possibly disorder, and contribute to heat transport. Neutral edge modes in
quantum Hall systems have been detected by shot noise experiments Bid et al.
(2010) and also by their quantized heat transport coefficients Venkatachalam
et al. (2012); Deviatov et al. (2011). Apart from quantum Hall systems,
neutral (e.g. Goldstone) modes arise in systems in which a continuous symmetry
is broken spontaneously.

In this work, we design a geometry where the unique current path from the
source to the drain is forced to pass through a segment consisting of neutral
modes only. We assume that the $U(1)$ symmetry of each channel is broken by
the contacts; thus backscattering between channels is present under them. The
breaking of these $U(1)$ symmetries results in a non-zero dc current at the
drain D. This protocol can be used either as a transformer, which converts
charge current to neutral current, and then back to charge current, or as an
efficient detector of neutral modes as long as the neutral counterpropagates
with respect to all charge modes.

Figure 1: A single right-moving chiral charged mode (solid black line)
represents the edge of a $\nu=1$ quantum Hall system extending above the
figure, which is the “probe” system. Charges are injected at the source S and
detected at the drain D. The “test” system extends below the figure, and has
two counterpropagating neutral modes (dashed black lines), and possibly other
charged chiral modes (dash-dotted orange lines), which all have to be right-
moving for our scheme to be relevant. The edges of the two systems overlap
only in regions II and IV, separated from the active region III by boundaries
B2, B3. Density-density interactions between the chiral modes of the top and
bottom systems exist only in regions II and IV, which also host the contacts
C1 and C2. Regions I and V are present to specify boundary conditions.
Tunneling/scattering between the chiral modes occurs solely under the
contacts. Reflection and transmission of a right-moving charge injected at S
is shown schematically at B3, while a similar process for a left-moving
neutral excitation is shown at B2.

The proposed geometry is shown in Fig. 1. The relevant physics can be
extracted by focusing on regions II, III, and IV. The solid black line at the
top is a right-moving chiral charge mode, arising from a $\nu=1$ quantum Hall
system extending above Fig. 1, constituting the “probe” system. The dashed
lines at the bottom in region III are a pair of counter-propagating gapless,
bosonic bos , neutral modes, presumed to arise from a “test” system extending
below Fig. 1. The test system may be quantum Hall, so long as all its charge
modes (dash-dotted orange lines) are right-moving, or it may be a system with
neutral modes only, such as an $XXZ$ chain. Electrons are injected from the
source S via tunnelling into the probe chiral edge mode and detected at the
drain D. The source and drain are separated by a grounded contact G. Clearly,
current cannot flow from S to D along the right-moving, chiral top edge. The
edge modes of the probe and test systems overlap, and thus interact, only in
regions II and IV. The interaction is of the density-density form, with
separate number conservation in the “bare” charged and neutral modes. These
interactions renormalize the bare charged and neutral modes such that,
generically, all three renormalized eigenmodes have nonuniversal charge.
Regions II and IV also host the contacts C1 and C2 respectively Spånslätt et
al. (2021), which we assume can be decoupled from the interacting modes at
will. Finally, regions I and V are semi-infinite “free” regions, where the
edges of the probe and test systems are fully decoupled and are present to fix
the asymptotic boundary conditions.

Before proceeding we discuss the notion of ideal contacts. The latter refers
to terminals connected to the edge modes, which absorb the entire impinging
current with no detectable signal away from the contact Kane and Fisher
(1995). Ideal contacts have been discussed in Refs. Slobodeniuk et al., 2013;
Protopopov et al., 2017; Nosiglia et al., 2018; Spånslätt et al., 2021 in the
absence of interactions, and, in the presence of interactions, in Spånslätt et
al., 2021, where it was shown that a microscopic realization of an ideal
contact for counterpropagating edge modes requires backscattering between
them.

Our results can be encapsulated in two ways: Firstly, neutral modes can carry
information about the charge current, information that can be used to
reconstruct the charge current at a different location. Secondly, one can use
the charge chiral mode (top mode of Fig. 1) as a “probe”, and apply it to a
“test” system (bottom of Fig. 1). In this functionality, our device can be
used to detect coherently propagating bosonic bos  neutral modes in the test
system. A dc charge current at the drain is direct evidence for neutral modes.

More concretely, let us assume there is at least one left-moving neutral mode
in the test system. When electrons are injected at the source S if both C1 and
C2 are coupled to the modes in region II and IV respectively, a dc current
will be detected at D, regardless of whether the test system has (right-
moving) charge chirals or not. The presence of right moving chiral charge
modes in the test system will not change this conclusion qualitatively.

Let us understand the physics in two extreme limits, when (i) both the
contacts are coupled, or (ii) both of the contacts are decoupled.

Case (i) Both contacts coupled: Assuming no charge chiral modes in the test
system, consider a charge (positive by fiat) injected into the probe chiral at
S, which travels to the boundary B3. There, a lump of positive neutral density
(a neutralon) is reflected into the left-moving neutral mode in region III and
lumps of nonuniversal charge are transmitted into the two right-moving modes
in region IV to be fully absorbed at C2. The left-moving neutralon in III
travels to B2, at which point a positive (electrically) charged lump is
reflected into the probe chiral, and an equal and opposite charge is
transmitted into the left-moving mode in the region II, to be fully absorbed
at C1. There will also be a neutralon reflected into the right-moving neutral
chiral in region III, which travels to B3. As usual, this will undergo
transmission and reflection, with the transmitted part being completely
absorbed at C2. The reflected neutralon part has the same sign as the original
neutralon, and repeats the process described earlier with a smaller amplitude.
With both contacts coupled, an infinite sequence of charge lumps of the same
sign is detected at D. Thus, a dc current at S implies a dc current of the
same sign (but with a nonuniversal magnitude) at D.

This is already an instance of the effect we are looking for. Now we add
(right-moving) charge chirals to the test system. All proceeds as before until
the left-moving neutralon impinges on B2. Now, in addition to the reflected
neutral lump, charge lumps will be transmitted into the nonuniversal charge
modes in region II (to be absorbed at C1), and reflected into the probe and
test charge chirals. The magnitude and sign of the charges are determined by
the interaction parameters in region II. Recall that the
reflection/transmission is deterministic because no tunneling between the
different modes is involved. Thus, there is a dc current at D.

To summarize, when both contacts are coupled, if a left-moving neutral is
present in the test system, there is always a dc current at D, as long as the
charge chirals (if any) of the test system are all right-moving.

Case (ii) Both contacts decoupled: Initially, let us assume that no charge
chiral modes are present in the test system. The first step (the injected lump
of electric charge traveling from S to B3, resulting in the reflection of a
neutralon and transmission of lumps of nonuniveral charge in the two right-
moving chirals in region IV) is the same as before. However, now the right-
moving lumps in region IV travel to B4 and undergo repeated partial reflection
and transmission. Similarly, the left-moving neutralon, upon arriving at B2,
results in a charge lump in the probe charge chiral in III, and a left-moving
charge lump in region II. This latter lump will undergo partial
transmission/reflection at B1. This leads to multiple scattering at all the
boundaries. However, we can assert, based on charge conservation, that no dc
current is observed at D. Since no left-moving charge modes enter region III,
the entire charge injected at $S$ has to proceed to region V (after multiple
scattering in region IV) Safi and Schulz (1995); *Maslov_Stone_1995;
*Ponomarenko_1995; *Oreg_Finkelstein_1996. Any charge detected at D is
initiated by a neutralon arriving at B2 via the left-moving neutral in III and
its descendants via multiple scattering. Since no total (time-integrated)
charge enters region III from either of regions II or IV, the time-integrated
charge entering the drain D must vanish. Evidently, charge noise will be
detected at D. Similar logic ensures that the dc charge current exiting region
IV into region V is the entire charge current injected at S.

These conclusions do not change when we allow (right-moving) charge modes in
the test system. Since the interactions in regions II and region IV are
density-density interactions, the total $U(1)$ “charge” (which is completely
independent of electric charge) of each mode has to be conserved in the dc
limit. Thus, we conclude, that in the presence of (right-moving) charge chiral
modes in the test system, we still need both the contacts to be coupled in
order to have a non-zero current at the drain D.

In what follows, we will present an outline of the calculations leading to our
results, relegating straightforward mathematical details to the supplemental
material (SM SM ). For simplicity, we will focus on the case where the test
system has neutral modes only.

We model the neutrals by an XXZ spin chain and the interaction between the
spin chain and the spin-polarized charged mode as a spin-spin interaction. The
model is described by the action in Eq. 1 where the probe charged mode is
represented by the bosonic field $\phi_{1}$, the right-moving test neutral by
$\phi_{2}$ and the left-moving test neutral by $\phi_{3}$. The interaction
between the neutrals $\phi_{2}$ and $\phi_{3}$ is denoted by
$\lambda_{23}\left(x\right)$. The interaction between the charged mode and the
spin chain, (the same for both the left- and right-moving neutrals), is
denoted by $\lambda_{12}\left(x\right)$ (= $\lambda_{13}\left(x\right)$)

$\displaystyle S=$ $\displaystyle\frac{1}{4\pi}\int
dxdt\Big{[}-\partial_{x}\phi_{1}\left(\partial_{t}\phi_{1}+v_{1}\partial_{x}\phi_{1}\right)$
$\displaystyle-\partial_{x}\phi_{2}\left(\partial_{t}\phi_{2}+v_{2}\partial_{x}\phi_{2}\right)+\partial_{x}\phi_{3}\left(\partial_{t}\phi_{3}-v_{2}\partial_{x}\phi_{3}\right)$
$\displaystyle-2\lambda_{12}(x)\partial_{x}\phi_{1}(\partial_{x}\phi_{2}+\partial_{x}\phi_{3})-2\lambda_{23}(x)\partial_{x}\phi_{2}\partial_{x}\phi_{3}\Big{]}.$
(1)

Assuming the interactions are turned on abruptly in regions II and IV, we
calculate the reflection ($r^{\text{B}_{\alpha}}_{ij}$) and transmission
coefficients ($t^{\text{B}_{\alpha}}_{ij}$) at B2 and B3, which allows us to
compute the current at D as a function of time via multiple reflections Safi
and Schulz (1995); *Maslov_Stone_1995; *Ponomarenko_1995;
*Oreg_Finkelstein_1996.

Figure 2: The dc current at D as a function of the $\lambda_{12}$ and
$\lambda_{23}$ for two different values of $v_{1},v_{2}$, when C1 C2 is
coupled.

##  II Computation of current and noise

When both C1 and C2 are coupled, the fraction of the current that reaches D as
a function of time is

$\displaystyle
r_{\text{D}}(t)=r^{\text{B}_{3}}_{13}r^{\text{B}_{2}}_{31}\sum_{n=0}^{\infty}\left(r^{\text{B}_{2}}_{32}r^{\text{B}_{3}}_{23}\right)^{n}\delta(t-t_{d_{n}})$
(2)

where $t_{d_{n}}=t_{0}+n\Delta t$. Here $t_{0}$ is the time for the first
signal and $\Delta t$ is the time for one full reflection between B3 and B2.
The dc current at D is the zero-frequency limit of the Fourier transform.

$I_{\text{D}}(\omega\rightarrow
0)=\frac{r_{13}^{B_{3}}r_{31}^{B_{2}}}{1-r_{32}^{B_{2}}r_{23}^{B_{3}}}\langle
I_{\text{tun}}\rangle$ (3)

Similarly, we calculate the noise at D Martin (2005); Chamon et al. (1995);
Berg et al. (2009) via the current-current correlation function on a
Schwinger-Keldysh contour to obtain

$N_{\text{D}}\left(\omega\rightarrow
0\right)=\frac{e(r_{13}^{B_{3}}r_{31}^{B_{2}})^{2}}{1-(r_{32}^{B_{3}}r_{23}^{B_{3}})^{2}}\langle
I_{\text{tun}}\rangle$ (4)

The noise when one or both of the contacts are decoupled can be computed very
similarly SM .

When C2 is decoupled the interactions in region IV are purely density-density,
implying that the $U(1)$ “charge” of each mode (as previously mentioned,
completely independent of electric charge) is conserved. Thus if we sum up all
the multiple reflections from boundary B3 and B4 (dc limit), the total $U(1)$
“charge” of the neutral reflected from region IV to region III must vanish.
Hence the total dc current at D will be zero. The dc current at the drain is
only non-zero if and only if both the contacts C1 and C2 are coupled.

##  III Experimental Realization

We now discuss an experimental realization of our setup. For monolayer
graphene, Hartree-Fock calculations suggest Kharitonov (2012) that at charge
neutrality ($\nu=0$), there is a quantum phase transition between a canted
antiferromagnetic (CAF) phase, stabilized for purely perpendicular magnetic
field, and a spin-polarized phase which can be stabilized by increasing the
Zeeman energy $E_{Z}$ with an in-plane $B$ field. The spin-polarized phase has
a fully gapped bulk and a pair of gapless helical edge modes Abanin et al.
(2006); Brey and Fertig (2006), whereas the CAF phase breaks U(1) spin-
rotation symmetry and has a neutral Goldstone mode in the bulk, but no gapless
charged edge modes Murthy et al. (2014, 2016). Experimentally, the phase
transition has been seen Young et al. (2014), but evidence that the phase at
purely perpendicular $B$ is the CAF phase is indirect, via the detection of
magnon transmission above the Zeeman energy Wei et al. (2018). Indeed, recent
scanning tunneling spectroscopy measurements indicate that the ground state
has bond-order Li et al. (2019); Liu et al. (2022); Coissard et al. (2021). To
confirm that the system has CAF order one would need to detect gapless
collective excitations, as has been done recently in bilayer graphene Fu et
al. (2021).

A potential experimental realization of the central idea of this paper is
shown in Fig. 3. A sheet of graphene in a perpendicular $B$ field is gated
such that the left half is at filling $\nu=1$, while the right half is at
$\nu=0$. In the central part of the $\nu=0$ region, we overlay graphene with a
ferromagnetic insulator, whose exchange field makes the graphene under it
fully polarized and gapped. However, the annular periphery of $\nu=0$ region
is in the putative CAF phase, with a gapless Goldstone mode. No topological
edge modes exist between the two phases at $\nu=0$. Confinement in the
“radial” direction in the $\nu=0$ region will reconstruct the continuum of
bulk Goldstone modes into bands of clockwise-moving and anticlockwise-moving
neutral modes. The lowest two bands will be gapless, and represent the
counterpropagating neutral modes in Fig. 1. These counter-propagating neutral
modes interact with the charge edge mode of the $\nu=1$ quantum Hall phase on
the left in the regions where they are proximate (Fig. 3). Adding the source
S, drain D, and grounded contact G at appropriate locations realizes the setup
of Fig. 1, and provides a way to unambiguously detect the gapless neutral
Goldstone mode of the CAF.

Figure 3: A sheet of graphene in a perpendicular $B$-field is gated to have
$\nu=1$ on the left and $\nu=0$ on the right. The central region of $\nu=0$ is
overlain by an insulating ferromagnet, inducing the fully polarized phase of
$\nu=0$ graphene in this region. The periphery of $\nu=0$ is presumed to be in
the CAF state, with gapless Goldstone modes. The lowest subband of the
radially confined Goldstone modes interacts with the $\nu=1$ edge mode and is
detected by the scheme described in the text.

##  IV Summary and outlook

In this work we have proposed a setup that has two functionalities: (i) Given
a system known to have a neutral mode (the bottom system in Fig. 1), we encode
information about the charge current into the neutral current, and
subsequently read it out as a dc charge current at a different spatial
location. (ii) Given a test system suspected of having coherently propagating,
bosonic bos , neutral modes, we place it along the bottom part of Fig. 1 and
use our device as a neutral mode detector. An important condition for our
protocol to work is that the neutral mode to be detected should
counterpropagate with respect to all charge modes, else the charge modes will
“short-circuit” the neutral mode. However, measurements of the upstream and
downstream charge conductance along the edge of the test system are sufficient
to determine whether all charge modes co-propagate in a given system.
Backscattering under the contacts breaks the $U(1)$ symmetry of each mode;
without backscattering no dc current at the drain is possible.

Let us elaborate a bit on the functionality of our setup as a neutral mode
detector. Our setup can detect coherently propagating, bosonic bos , neutral
edge modes when all the charge modes in the test system are gapped, and
gapless modes represent spin/valley fluctuations. Trivial insulators with
spontaneous symmetry breaking of a continuous symmetry, such as the putative
CAF phase of graphene at charge neutrality, are prime examples of such
systems. Moreover, our setup will detect coherently propagating, bosonic,
neutral edge modes in QH systems as well, as long as two conditions are met:
(i) all chiral charge modes of the test QH system are co-propagating, and (ii)
there is at least one neutral mode which counter-propagates with respect to
the charge modes. For example, the neutral mode of $\nu=2/3$ at the Kane-
Fisher-Polchinski fixed point Kane et al. (1994) could be detected by our
setup. Using monolayer graphene for the probe system allows one to reverse the
propagation direction of the probe charge chiral in situ by gating to obtain
$\nu=\pm 1$ in order to realize the geometry of Fig. 1. It must be noted that
pairs of neutral edge modes can be generated by edge reconstructions in
quantum Hall systems Khanna et al. (2017); Saha et al. (2021). We emphasize
that our setup can detect coherently propagating bosonic neutral modes
regardless of their physical origin.

Let us compare our setup with previous approaches to neutral mode detection.
In one approach, the passage of upstream neutral modes through a quantum point
contact was detected through the generation of charge noise Bid et al. (2010,
2009); Cohen et al. (2019); Biswas et al. . More recently, measurements of
heat transport “upstream” as compared to charge transport have been employed
Yacoby et al. (1994); Banerjee et al. (2017); Srivastav et al. (2021). Not
only are these hard measurements, (they require a precise determination of the
temperature at a given contact), but they cannot determine whether the heat
propagating upstream reflects coherent neutral modes rather than incoherent
transport (e.g., due to diffusive modes). The latter is the result of charge
and heat equilibration Protopopov et al. (2017); Nosiglia et al. (2018), and
also leads to upstream charge noise Spånslätt et al. (2019).

A second theoretical approach for detecting neutral modes in certain quantum
Hall systems Feldman and Li (2008); Cano and Nayak (2014) via dc currents
depends on tunneling between QH edges at quantum point contacts, and only
specific neutral modes in specific configurations lead to dc currents. In our
proposal, tunneling between different chiral modes occurs only under the
contacts.

There are a few unresolved issues of broad import: (i) How does one understand
the formulation of linear and non-linear response in the charge-neutral-charge
circuit? (ii) Certain exotic spin systems are believed to have neutral
Majorana modes Kitaev (2006); Kasahara et al. (2018), as is the $\nu=5/2$
state Banerjee et al. (2017). Our proposed device can detect bosonic bos
neutral modes, but can some extension thereof be used to detect Majorana modes
as well?

###### Acknowledgements.

We thank A. Mirlin, I. Gornyi, D. Polyakov, and K. Snizhko for their extremely
valuable comments and proposed modifications which significantly improved our
manuscript. AD was supported by the German-Israeli Foundation Grant No.
I-1505-303.10/2019 and the GIF. AD also thanks Israel planning and budgeting
committee (PBC) and Weizmann Institute of Science, Israel Dean of Faculty
fellowship, and Koshland Foundation for financial support. YG was supported by
CRC 183 of the DFG, the Minerva Foundation, DFG Grant No. MI 658/10-1 and the
GIF. SR and GM would like to thank the VAJRA scheme of SERB, India for its
support. GM would like to thank the US-Israel Binational Science Foundation
for its support via grant no. 2016130, and the Aspen Center for Physics (NSF
grant PHY-1607611) where this work was completed.

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# What May Future Electricity Markets Look Like?

Pierre Pinson Pierre Pinson has primary affiliation with Imperial College
London, Dyson School of Design Engineering (London, U.K.). He has a secondary
affiliation with the Technical University of Denmark, Department of
Technology, Management and Economics (Kongens Lyngby, Denmark), as well as
Halfspace (Copenhagen, Denmark). Email<EMAIL_ADDRESS>
###### Abstract

Should the organization, design and functioning of electricity markets be
taken for granted? Definitely not. While decades of evolution of electricity
markets in countries that committed early to restructure their electric power
sector made us believe that we may have found the right and future-proof
model, the substantially and rapidly evolving context of our power and energy
systems is challenging this idea in many ways. Actually, that situation brings
both challenges and opportunities. Challenges include accommodation of
renewable energy generation, decentralization and support to investment, while
opportunities are mainly that advances in technical and social sciences
provide us with many more options in terms of future market design. We here
take a holistic point of view, by trying to understand where we are coming
from with electricity markets and where we may be going. Future electricity
markets should be made fit for purpose by considering them as a way to
organize and operate a socio-techno-economic system.

###### Index Terms:

Digitalization, Electricity markets, Mechanism design, Optimization, Renewable
energy

##  I Introduction

Power and energy systems have evolved tremendously over the last few decades,
as pushed by various parallel (and inter-related) processes towards
decarbonisation, digitalisation and liberalisation. On that last point, there
has been a clear trend in many Western countries (e.g., in Europe, North
America and Australia/New Zealand) among others, to design and deploy markets
for the exchange of electric energy primarily, but also to support power
system operations through the procurement of ancillary services, as well as
investment in generation assets through capacity and auction mechanisms.
Today, in regions of the world like Scandinavia and the U.K., there have been
wholesale and retail electricity markets operating for nearly 30 years. Many
academics, practitioners in industry and policy-makers continuously underlined
over that period that this approach to the liberalisation of electric power
systems was an undeniable success. At the same time, over the last 10-15
years, existing electricity markets have been challenged by various evolutions
of power and energy systems (decentralisation, increase in renewable energy
penetration, etc.), and more recently by, e.g., tensions in the procurement of
gas as well as availability of the nuclear generator fleet in Europe. In a
way, we already got many hints of the fact that existing electricity markets
may not be suitable for our current situation with a strong push for an energy
transition, as well as for future power and energy systems that would be
dominated by carbon-neutral and renewable-based power generation. For
instance, in the context of power systems without fuels, Ref. [1] insisted on
the fact existing electricity markets will be fundamentally challenged.

A key question then arises: “what may (or what should) future electricity
markets look like?” This question has attracted substantial attention recently
– see, e.g., [2, 3, 4]. We could surely stick to the status quo and regularly
find a few patches to add to existing markets hoping to contain their
limitations. Though, alternatively, we could consider their necessary and
profound evolution towards mechanisms that are fit for purpose. Power and
energy networks are complex socio-techno-economic systems that are of utmost
important to industries, economies and societies, while being at the core of
the necessary ongoing energy transition. Obviously, the answer to this
question may be different if taking the perspective of an economist, of an
engineer, of a policy-maker or of a social scientist. The necessity to
accommodate different perspectives to such complex system was for instance
recently discussed _(i)_ in the context of the energy transition generally
[5], and _(ii)_ for the specific case of electricity distribution systems [6].
More holistically, taking a designer’s perspective, one should recognize that
markets are an object (or a mechanism, following the terminology within
economics and applied mathematics) with a purpose, for that complex socio-
techno-economic system. There are certainly laws of physics that cannot be
avoided (e.g., Kirchoff laws) and economic principles that cannot be
circumvented (e.g., marginal pricing of energy, as discussed by [7] in this
same issue). But then, there are actually a myriad of options that could be
considered in terms of market organization and operations, depending on the
purpose we seek for electricity markets.

Since we cannot start from a blank page, we argue that it is important to
appraise the reasons why electricity markets have been designed and operated
in such a way so far, to understand how they may be to evolve in different
directions in the future. Therefore, Section II gives a succinct overview of
the key aspects of the development of electricity markets from both academic
and actual implementation points of view. Subsequently in Section III, we will
consider alternative perspectives (economical, engineering and related to
environmental, societal and governance – ESG, aspects), allowing us to ask a
number of key questions about the purpose and relevant drivers for the design
of current and future electricity markets. Eventually in Section IV, we will
then describe some of the potential features we foresee for future electricity
markets, for them to be able to meet their purpose. Finally, the paper will
close with Section V, gathering a set of conclusions and perspectives.

##  II Understanding and Learning from the Past

Even though many countries are only recently engaging in developing and
deploying electricity markets, these are not fundamentally new mechanisms as
they have been around for decades in certain areas of the world. Their
existence originates from the convergence of ideas born in academia that are
at the basis for such markets, combined with a will from policy-makers and
industry to restructure electricity markets, with a view towards more
transparent and efficient operations of power systems. Today, still, we expect
that future evolutions of electricity markets should be grounded within
rigorous and well-motivated academic considerations, at the interface between
relevant disciplines, e.g., power system engineering and operations research,
economics and social sciences more generally. We therefore concentrate in the
following on both regulatory and academic sides of the early development of
electricity markets. Readers aiming to have an exhaustive overview of current
electricity markets and their specific challenges are referred to [8, 9].

###  II-A On the Regulatory and Real-world Deployment Side

The large-scale deployment of electric power infrastructure, in parallel to
the electrification of our industries and societies, made access to
electricity a primary need for many, if not a basic human right [10]. Today,
looking at the most important requirements for developing and fast-growing
countries, electrification stands high on the list, while generally, high
reliability in the delivery of electricity is seen as of utmost importance in
many advanced economies and their industry. In principle, when considering
such large, expensive, complex and strategic infrastructures, it makes sense
for those to be handled by governments or government-controlled organizations
since forming natural monopolies. This is has been the case for a long period
for electric power system infrastructures throughout the world, following the
so-called vertically integrated structure [13]. Such an approach has allowed
many countries to develop and maintain large infrastructures, support
ambitious generation development plans (as for the case of nuclear energy in
France), while providing electricity to citizens with high reliability levels.
Even though vertically integrated and highly linked to governments, these were
already seen as electricity markets, since also involving monetary
transactions all the way from final consumers to the generation side.

Following the wave of liberal thinking of the 1980s in, e.g., the U.K. and the
U.S.A., it was envisaged to restructure such electricity markets by
liberalizing some of its components, and more generally to consider
alternative ways to look at the organization of generation, transmission and
distribution, as well as retail of electric energy. A gentle overview of the
various approaches to electricity market organization are presented in [13],
while more advanced discussion of organizational aspects of electricity
markets can be found in [14, 15] – we do not aim here to go into detail with
such matters. The key point of this restructuring process, similarly to other
strategic infrastructure and industry, was to find a way to separate
activities that would form a natural monopoly like the management of
transmission and distribution, to activities where competition could be
introduced, as for the case of generation and retail. In principle, this then
means that there are two sides to thoroughly analyse within liberalized
electricity markets: _(i)_ the generation side and the related wholesale
electricity markets, and _(ii)_ the retail side and the advent of retail
markets. We will mostly focus on the former one, since being the side where
most of today’s challenges are most visible and pressing. We will see later on
that we may also see a stronger convergence of such markets in the future, as
supported by digitalisation and decentralisation of power and energy systems.

Eventually, three countries acted as front runners for the liberalization of
electricity markets, and for the deployment of wholesale electricity markets,
which are Chile, the U.K. and Norway. For an exhaustive overview of the
Chilean process and experience, the reader is referred to [11], while a broad
coverage of the U.K. and Norway, as well as subsequent developments over the
whole European area, is provided by [12]. At the time, liberalized electricity
markets appeared as the natural way to more efficiently operate power networks
and to eventually make electricity cheaper for final consumers. Even though
the development of electricity markets in different regions of the world has
placed varying focus levels on accommodating operational constraints and on
the way to meet desirable market properties, the main and core ideas are very
similar and supported by the strong academic contributions to the design and
functioning of modern electricity markets.

###  II-B On the Academic Side

Many consider that the fundamental methodological concepts underlying the
development of modern electricity markets can be traced back to 1988 and the
seminal book of Schweppe and co-authors about spot pricing of electrical
energy [16]. The concept of spot pricing is there proposed to accommodate the
temporally and spatially varying costs of electricity, accounting for both
operational and capital costs, while also accommodating operational
constraints related to power system operation (e.g., network constraints).
Arguably, this also builds on earlier results related to networked resource
allocation and economics based on the foundational works of Samuelson [17].
Since then, academia has continuously supported the developments of
electricity markets through direct interaction with regulators and market
operators, as well as by proposing novel ideas that would allow to improve the
design and functioning of electricity markets.

At stages, the academic contributions to the functioning of electricity
markets first consisted in observing and documenting outcomes of electricity
markets that may be seen as counter-intuitive or unintended. This is often
complemented by simulations and scenario-based analysis to foresee how
electricity markets may behave in the future. A clear example is that of
negative electricity prices, which have been increasingly observed in
electricity markets like Nord Pool for instance (see, e.g., [18]). In that
market, it was decided in 2009 that supply offers with negative prices were
accepted by the market, hence opening to the possibility of market-clearing
prices to be negative. While this appears to be a natural consequence of the
balance with supply and demand when supply is plentiful, this may also have
major consequences, e.g., for the pricing of derivatives, and by not sending
the right signal for investment in future capacities.

In parallel, the role of academics is also to help with specific challenges
that emerge in electricity markets, owing to their evolution. As an example,
the increasing penetration of renewable energy generation from wind and solar
power sources brought inherent change in terms of variability and limited
predictability, which have to be accommodated within the current realm of
electricity markets. This has led to the rethinking of the sizing of reserves
to be procured through markets [19], the definition of new market products,
e.g., ramp products (recently reviewed in [20]), etc.

Most importantly, academics have continuously taken a more exploratory and
visionary role in their consideration of electricity markets. To start with,
fundamentally, electricity markets were originally seen as a way to coordinate
and remunerate supply to meet demand. Though, early works, e.g., in [21],
hinted at the fact that demand had a role to play in electricity markets
through their flexibility and elasticity. This has now opened up to the strong
emphasis placed on demand-side flexibility. Pushing it further, one may see
this leading to a change of paradigm where, instead of supply following
demand, it may be that demand should follow supply (if mostly coming from non-
dispatchable renewable energy generation). Similarly, electricity markets were
designed based on the idea that supply was dispatchable (up to a reliability-
related uncertainty), hence making that supply offers in the market should be
seen as deterministic. The limited predictability of renewable energy
generation has challenged this idea, while leading to various proposals
towards using stochastic optimization approaches to the clearing of
electricity markets [22] and more generally novel approaches to pricing energy
in wholesale electricity markets [23].

On a more exploratory note, different works are pointing at the fact it is not
new products, clearing and pricing approaches that are necessary, but more
fundamentally new views of electricity markets. For instance in a future of
power systems without fuels, pricing may negligibly rely on the marginal cost
of producing renewable energy generation, but relying on strategic behaviour
of producers and consumers to recover capital investment costs instead [24].
Alternatively, as we see that energy systems are increasingly interconnected
(i.e., among gas, heat and electricity) and that such inter-dependencies may
further support the integration of renewables, alternative approaches are put
forward for markets that would accommodate energy systems altogether [3].

##  III The Purpose of Future Electricity Markets

Most often, researchers and practitioners concentrate on the actual
functioning of electricity markets, while aiming to accommodate their evolving
context, e.g., with increasing penetration of renewable energy sources, the
need for additional flexibility, etc. However, more fundamentally, it may not
just be the functioning of electricity markets that ought to be rethought, but
their very purpose instead. This was for instance recently illustrated by a
report produced by Energinet, the Transmission System Operator (TSO) in
Denmark [26], which challenged some common thoughts about what markets are
for.

Let us explore in the following what the purpose of future electricity markets
may be, by considering three different perspectives: the economic one, the
engineering one, and the Environmental, Societal and Governance (ESG) one. For
all of those, we additionally describe important challenges ahead.

###  III-A The Economic Perspective

Conventionally, the term “market” is given an economic meaning, as it relates
to the organization of buyers and sellers, for the exchange and pricing of a
given or multiple commodities. For electricity, the market principally deals
with electric energy as a commodity, even though we usually consider the
extension to the procurement of ancillary services (i.e., all services that
system operators may require for the safe and efficient operation of the power
system) as part of electricity markets. This is since ancillary services are
commonly provided by the same agents who buy and sell electric energy. The
purpose of electricity markets, from the economic perspective, is _(i)_ to
optimally allocate resource, _(ii)_ to reveal prices as a basis for payment
and revenues, and _(iii)_ to provide the right signals to support investment
in relevant assets.

Within the market, the way buyers and sellers interact can be through direct
contracts (for a given quantity, time period and price). This situation is for
futures contracts and over-the-counter (OTC) trading. However, at the day-
ahead stage, it is more common today to see wholesale markets as an exchange
or a pool. There, the interaction between buyers and sellers is standardized,
for instance by having set the lead times, periods, product types, etc., while
using a common software platform. Principles from mechanism design are
employed to define these products (e.g., quantity-price bids, offer curves,
etc.) and the market-clearing algorithm eventually yields the dispatch
(quantities to be supplied on the supply side, quantities to be consumed on
the demand side), while allowing for price discovery.

The principle of price discovery follows a social welfare maximization
process, which, given stated constraints (to be discussed in the following
section), aims at maximizing both supplier and consumer surpluses. A stylized
representation of these principles is given in Figure 1 for a given market
time unit (say, an hour of the day). Market participants on the supply side
place offers expressed in terms of quantity and price. These are to be
interpreted as the maximum amount of energy they can produce at that time and
the minimum price they are willing to accept to be paid for. These offers are
ordered with increasing price and yield the supply curve depicted. On the
demand side, market participants place similar offers. Inversely though, these
are to be interpreted as the maximum amount of energy they can consume and the
maximum price they are ready to pay. The demand offers are ordered with
decreasing price and form the demand curve that can be seen in the figure.

pricequantitysupply curvedemand curveequilibrium pricesocial welfare Figure 1:
Stylized representation of the approach to clearing of wholesale electricity
markets based on a social welfare maximization principle. Market clearing
yields both dispatch (i.e., production and consumption quantities for all
participants) and equilibrium price.

Doing so graphically, for such a stylized setup, is equivalent to employing
the optimization-based approach used to clear wholesale electricity markets,
where the aim is to maximize social welfare. Social welfare is formally
defined as the signed area below the demand curve and above the supply curve
(in light gray in Figure 1). It is signed in the sense it is positive if the
demand curve is above the supply one, and negative if demand is below supply.
The crossing point between the two curves reveal the equilibrium price, which
is used as a basis for pricing electricity. All offers (both demand and
supply) on the left of that point are accepted, while those on the right are
not. If using the equilibrium price for both buyers and sellers, consumers
whose offers are accepted pay less than they were willing to, while sellers
receive a price higher than what they required.

The design and clearing of electricity markets rely on relevant principles
from optimization and game theory (mechanism design, more precisely), allowing
them to enjoy certain properties that are crucial for its functioning. As we
aim at keeping the exposition of this paper concise, we will not go through
all these properties individually. For instance, one would expect that market
participants do not enter markets in a loss-making position (individual
rationality), are incentivized to participate in an honest manner (incentive
compatibility), and that the sum of revenues is equal to the sum of payments
(budget balance). While it is fairly straightforward to get these properties
in a very simplified environment, real world constraints (e.g., congestion on
power networks, start-up/shut-down of individual assets) challenge these
properties and potentially require adaptations (e.g., uplift payments). More
importantly, there are expectations such that markets cleared based on the
social welfare maximization principle also allow for the suppliers to recover
investments (as discussed by, e.g., [7, 25]).

###  III-B The Engineering Perspective

While many will give a purely economic meaning to the concept of market, the
reality of electricity markets is that they must also have a strong technical
component111We refer to this technical component as the “engineering”
perspective, since it is mainly engineers who focus on such technical
aspects., since they deal with the operation of the largest and most complex
engineering system ever built by humans, i.e., the electric power
infrastructure. This comes with a number of constraints related to of how
power systems are to be operated, as well as constraints related to the power
production and consumption assets themselves. These constraints ought to be
accommodated in one way or another by the market. Eventually though, there are
limits to what can be handled through markets [26]. Maybe the biggest
challenge from an engineering perspective is to find the fine line between
what can (and should) be handled through markets, and what can (and should)
not. And, for the operational constraints and aspects that are to be handled
through market, one should find a way to embed those in the market design
(possibly through the definition of market products) and in the market
clearing algorithms (which needs to be kept tractable).

There are variations in the way constraints stemming from power system
operation are accommodated. For instance, in terms of network constraints and
flows, the historical model in Europe has been to use markets zones and an
import-export representation of cross-zonal exchanges, while a detailed power
flow-based network-constrained representation of the network has been employed
in the USA. Even if employing the more advanced approach of embedding power
flows and their constraints in market clearing, these are simplified and
linearised (following a DC linearisation – see [27] for clarifications). Such
simplification and linearisation still yield a gap between the outcome of
market clearing and actual power system operation since, basically, DC power
flow outcomes are not AC feasible [28].

Besides network-related aspects, substantial emphasis is to be placed on
constraints to ensure the secure operations of the power system. This is done
by ensuring the availability of relevant resources in case of contingencies,
e.g., through the provision of ancillary services. However, this has to be
done in a way that incentivize market participants to provide services, while
also coordinating markets for various products to get consistent and non-
conflicting outcomes (typically, if a given share of capacity of a production
asset is booked to provide reserves, it should not be used to produce energy).
This has then led to the proposal and implementation of security-constrained
market-clearing approaches [29], and to varied proposals for the joint
clearing and pricing of energy and ancillary services – see [30, 31] among
others.

While some of the aspects from power system operation are accommodated within
market design and clearing procedures, others are internalized by the market
participants when offering in electricity markets. Indeed, some of the
characteristics of the assets of market participants may not be well
accommodated in market clearing procedures and pricing approaches that rely on
linear programming. This is the case of non-convexities of these assets, for
instance related to commitment decisions. Alternative pricing principles,
e.g., convex hull pricing [32, 33], were proposed to deal with such asset-
based operational constraints. Recently, some even advocated for a necessary
shift from a linear to a conic programming paradigm [34], which would allow to
better accommodate more complex operational constraints and uncertainty in
market clearing procedures and related pricing approaches.

The same goes with asset flexibility: as we want to have more flexible assets,
and more specifically energy storage assets, in the energy system landscape,
emphasis must be placed on how to optimally accommodate those in electricity
markets. As of now, storage is mainly seen as a merchant asset, i.e.,
participating in electricity markets as for other production and consumption
assets (and focused on short-term incentives). However, there is a path
towards having non-merchant storage assets in electricity markets, allowing to
perform temporal arbitrage, the same way that transmission is often seen as
non-merchant asset allowing for spatial arbitrage. Accommodating storage in
electricity markets comes with challenges, e.g., related to locational pricing
[35] and more generally impact in social welfare [36], though they are also
novel instruments generalizing financial transmission rights [37, 38] that
comprise promising approaches.

###  III-C The ESG Perspective

Over the last decade, we witnessed a substantially increased focus on
Sustainable Development Goals (SDGs), leading to an Environment, Societal and
Governance (ESG) perspective to investment and operations of our industries.
In many ways, the power and energy system is at the core of this transition,
with a clear shift towards renewable energy sources, but not only. Indeed,
while the restructuring and liberalization of electricity markets has meant a
shift towards wholesale and retail markets as we know them today in many
Western countries, this focus on ESG could be one of the drivers of how we
rethink the organization and purpose of electricity markets. An obvious
example is the push towards various forms of community-based and peer-to-peer
electricity markets, along with the associated novel business models [39].

So, what would be the purpose of electricity markets from an ESG perspective?
For one, markets should support the decarbonization of power and energy
systems, in line with national and international objectives. So far, the
actual functioning of markets, as well as additional measures and subsidies,
have amply supported the deployment of renewable energy generation. As of
today, however, it is not only investment in actual renewable energy
generation capacities that is required, but a general transformation of the
infrastructures and practices. Integration of renewable energy generation in
existing power and energy systems requires additional temporal and spatial
arbitrage flexibility, e.g., provided by power networks, storage, as well as
various forms of demand response and energy conversion.

More than the decarbonization of power and energy systems, the design of
electricity markets reflects the way we envisage how we should produce,
exchange and consume electric energy. Indeed, with a transition towards more
distributed energy sources and for which the marginal cost of producing
electricity is close to 0, many potential paradigm changes are in sight.
Instead of having supply following demand, it may just be that part of the
demand (i.e., except for crucial uses and infrastructures) will have to follow
supply. Another change of paradigm relate to the fact the ownership of power
production units will also be more distributed (think of solar panels on
houses, car parks, small businesses, etc.) and they may want to have a say
about how the surplus energy they produce is consumed. This social component
of future electricity markets is for instance illustrated by the approach of
[40] and the concept of federated power plants, in which some of the
participants may have an altruistic behaviour by expressing their wish to
share their energy with others potentially in need. This idea was recently
pushed further based on the concept of smart energy neighborhood [41], where
the agents involved in a local energy system and market are seen as community
with shared interested and objectives. Electricity consumers are increasingly
interested in expressing preferences in the way they source (in terms of
location, energy type, etc.) and use electricity. Certain forms of peer-to-
peer electricity markets allow for such heterogenous preferences [42]. This
may substantially change the way all think of electricity as a commodity: even
if being ubiquitous when sourced from any socket being available, the fact
that consumers express their views on the sourcing of their electric energy is
a form of empowerment that could have substantial consequences, e.g., on
investment in generation, storage and energy conversion assets222A relevant
recent example is that of Ripple Energy in the UK (www.rippleenergy.com),
offering collaborative investment in wind generation capacities, with direct
impact on subsequent energy procurement costs..

Besides the traditional economic and engineering perspectives to electricity
markets, we expect that this ESG perspective will allow to embrace important
concepts from social science to rethink the purpose of energy infrastructures
and electricity markets in the coming century. Historically, emphasis has been
placed on giving access to plentiful amounts of energy to support industry
growth and the comfort of the population. Many other considerations are
emerging and now gaining importance, e.g. focusing on energy poverty, fairness
in terms of access and costs of electric energy, etc. Several academics have
been pushing to revisit some of the basic economic principles in our society,
see e.g. [43, 44] towards a better use of resources and a cooperative
approach. Such concepts are directly relevant for design of future electricity
markets, for instance to be thought of within the energy justice framework
discussed in [45].

##  IV Expected Features

In view of the purpose of future electricity markets and the various
perspectives (economical, engineering and ESG-related ones) discussed in the
above, we introduce here some of the resulting expected features of future
electricity markets.

###  IV-A Variability, Uncertainty and Flexibility

Future power and energy systems will heavily rely on renewable energy
generation sources, with their variability and limited predictability. Energy
uses are also changing, with increasing electrification and the deployment of
new types of electricity consumption assets, e.g., heat pumps and electric
vehicles. All in all, this means more variability and uncertainty in
electricity markets. This also calls for more flexibility, as for instance
underlined in the new strategy of Energinet, a TSO that deals with one of the
power systems with the highest penetration of renewable energy generation
[46]333Actually, it is also the case that Denmark has the advantage to have a
highly interconnected power system (see presentation and discussion in [47]
for instance). Hence, penetration of renewable energy sources should also be
seen as relative to interconnection capacity, making countries like Ireland
and Spain/Portugal facing possibly bigger challenges at lower penetration
levels already..

When modern electricity markets were first designed and implemented, such
variability and uncertainty was not so prominent and the main source of
uncertainty was on the electric load side (see, for instance, the pioneering
works in load forecasting in [48]). Hence, electricity markets were thought
off in a deterministic setup, with the possibility to handle the consequences
of uncertain demand at the balancing stage (and based on adequate reserves
procured a priori). However, increasing uncertainty may justify rethinking
electricity markets in a stochastic framework instead, e.g., based on
stochastic programming [22] or chance-constrained optimization [49]. We may
generally refer to these markets as stochastic electricity markets. And, since
most suppliers and consumers should be seen as uncertain, a potential approach
is for markets to allow for offers expressed in a probabilistic manner [50],
for instance in the form of distributions or prediction intervals.

Since stochastic electricity markets may be difficult to implement in
practice, an alternative is to find ways to define new products that would
allow to better cope with uncertainty and variability on the one hand, and
bring some desired additional flexibility on the other hand. For the latter
case, relevant examples are that of _(i)_ policy-based reserves [51], since
reserves should not be thought only in terms of capacity, but in terms of how
they can react to how uncertainty unfolds, and _(ii)_ price-region bids [52],
which allow to naturally accommodate flexibility characteristics for assets at
the interface between multiple energy systems (e.g., combined heat and power
plants at the interface between electricity and heat energy systems).

A consequence of the profound changes to electricity markets driven by
variability, uncertainty and flexibility is that it will eventually have an
impact on our approach to pricing. Today, pricing is mainly related to the
energy commodity itself and to capacity if providing ancillary services. In
the future, pricing may also be driven by reliability and security of supply
concepts, in terms of firmness of supply on the production side, and
flexibility in consumption on the demand side. In that direction, an
interesting example is that of risky power markets introduced by [53].

###  IV-B Distributed and Coordinated

Electricity markets have always been thought of as a way to coordinate the
operation of power systems in a somewhat decentralized manner since allowing
for all agents involved to be in control of their decision-making process [4].
Even though the decision-making is decentralized, one still relies on a
central marketplace that serves as an interface to all agents involved. In
contrast, novel approaches involving transactive energy, community-based and
peer-to-peer electricity markets, also aim at decentralizing the marketplace
itself. Eventually this may lead to a convergence between wholesale and retail
markets by having a direct connection between producers and consumers [54].

Future electricity markets are expected to adapt their level of
decentralization and coordination to the fact that assets are increasingly
distributed, while additionally allowing for small consumer and prosumers to
actively participate in such markets. There are obviously both benefits and
caveats if going for more or less decentralization [55]. As an example, in a
centralized pool setup, the minimum bid size (in the order of a MWh) in
electricity markets has traditionally been a barrier to entry for small
agents. However, as increasing flexibility is sought after, flexibility which
can be provided by smaller assets in power and energy systems (e.g., at the
consumer level), there is a trend towards lowering the minimum bid size, while
also supporting the emergence of so-called aggregators that would coordinate
groups of smaller assets [56]. Again, this participates to an increase in
decentralization and coordination. Ideally in peer-to-peer and community-based
electricity markets, there should be a virtually no minimum bid size,
reflecting setups with very low transaction costs.

Coordination is also motivated by the necessary interplay between various
energy systems (electricity, gas and heat) in the future, to optimally support
the integration of renewable energy sources. A substantial challenge though is
that these energy systems have different operational constraints driven by
their underlying physics (e.g., gas and water flows are not the same as power
flows), as well as established operational and market practices. Aligning such
practices for these interconnected and complementary energy systems will
already be a big step towards their improved coordination. Eventually, the
design of optimal interfaces between these energy markets, e.g., through co-
optimization under a leader-follower setup [57] or information exchange [58],
and alternatively joint energy markets [3], will yield an agile coordination
approach to these energy systems.

###  IV-C Data-driven and Fair

Digitalization has already had a fundamental impact on electricity markets,
with an increasing role of forecasting and data-driven decision-making. Most
importantly, data and data-driven techniques have been enablers for many of
the current and foreseen evolution paths of electricity markets. For instance,
peer-to-peer electricity markets [54] and the business models of aggregators
[59] necessarily rely on _(i)_ the availability of data at the level of
consumers (and possibly at the detailed level of their assets), possibly with
high temporal resolution, and _(ii)_ on advanced analytical approaches to get
value from such data.

At some point though, with increased decentralization and digitalization,
comes the scalability challenge. While it is possible to clear a pool-based
markets with 1000s of participants, and generally not prohibitevely
computationally expensive, clearing a peer-to-peer market with the same number
of participants requires a lot of communication among peers, it is
computationally expensive and it may not even be feasible. Therefore, new
computational approaches are necessary if aiming to further decentralize
electricity markets. Going beyond decomposition and distributed optimization,
this is where AI-based approaches (more precisely, based on machine learning)
to market clearing may become very relevant, since such approaches could learn
from the past and clear market based on contextual information (e.g., about
the weather, the state of the power system, etc.). AI and machine learning are
becoming more prominent in power system operations anyway, hence possibly
supporting their potential role in electricity markets too. Another advantage
from AI-based approaches is that they may allow to rethink electricity markets
by bringing some relevant ideas from theoretical computer sciences and
economics. Here, we mainly think of the concept of fairness. Indeed, one of
the regular complaints against electricity markets (at both wholesale and
retail levels) is about their lack of fairness. Maximizing social welfare is a
key principle, it could be complemented by fairness objectives and or
constraints.

When the operation of power and energy systems, as well as electricity
markets, is to crucially rely on data, we are reaching a point where the value
of data is non-negligible. One could even argue that in a future where
renewable energy comes with a marginal cost that is close to 0, the value of
data will be more than the value of energy itself. In practice though, data is
collected and owned by many distributed agents, e.g. small consumers,
retailers, power producers, system operators. These agents have a very low
willingness to share their data in principle, since they believe that this may
yield a loss in privacy, the loss of a competitive advantage, or potential
exposure of critical asset information. To unleash the value of distributed
data, it is difficult to envisage future electricity markets without data
sharing and data monetization platforms, also with privacy-preserving
components.

##  V Conclusions and Perspectives

Current times have witnessed an increased focus on electricity markets in most
countries that have had a long experience with seemingly well-functioning
electricity markets. While the debate was mainly contained to a limited
community gathering academics, system operators and policy makers until
recently, the recent increase in prices in wholesale electricity markets have
broad intense scrutiny to the functioning and very nature of electricity
markets. While some technical and economical basics of electricity markets are
not negotiable, we have aimed to show here that many aspects of modern
electricity markets may (and even ought to) to be rethought. Today’s context
is not what is was when electricity markets were first designed and
implemented. Electricity markets are to be fit for purpose – and, their
purpose will necessarily change with time.

If revisiting the previous paragraphs, we have explained that electricity
markets should go from deterministic to stochastic, that reserves should not
be seen as just capacity but procured based on control policies, that markets
will be more decentralized, that data may be more valuable than energy and
that AI could be used to clear electricity markets. To this, we could actually
add that since renewable-dominated power and energy systems mark a transition
from low-capital investment and high operational costs to high-capital
investment and low operational costs, there is a shift from wholesale
electricity markets to auctions and other capacity remuneration mechanisms to
insure that market participants recover their investment. Overall, that means
that a part of the very role of wholesale electricity markets is fundamentally
changing. Similarly, it will impact the retail side of electricity markets.
This opens the door to a wealth of new business models, some of which we
already see emerging. Some of these new business models take a more
cooperative view for instance by allowing to co-invest in renewable energy
generation capacities, to share surplus solar power production with others, to
pay a subscription for having a storage unit at one’s house, etc.

Today, we see strong needs for supporting the energy transition, insuring the
reliability and resilience of power and energy systems, and for making
electricity markets fair for all. The context has also changed in the sense
that the status quo within the underlying science, as well as the availability
of data and computational power, allows to rethink electricity markets in ways
that could not be envisaged a few decades ago. These are exciting and
challenging times for electricity markets, requiring a multi-disciplinary
approach and broad expertise (in, e.g., mathematics, economics, computer
science, power system engineering, social sciences) to re-design electricity
markets that fully acknowledge the socio-techno-economic nature of power and
energy systems.

## Acknowledgements

Acknowledgements are due to many colleagues in academia and industry for many
regular discussions about current and future electricity markets, but also to
numerous funding bodies and agencies for supporting my research on that topic
over the years. The author is also grateful for the detailed feedback provided
by Antonio Conejo and Antonio Gómez-Expósito, which allowed to improve the
manuscript originally submitted.

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Pierre Pinson received the M.Sc. degree in applied mathematics from the
National Institute of Applied Sciences (INSA), Toulouse, France, in 2002 and
the Ph.D. degree in energetics from Ecole des Mines de Paris, France, in 2006.
He is the chair of data-centric design engineering at Imperial College London,
United Kingdom, Dyson School of Design Engineering. He is also an affiliated
professor of operations research and analytics with the Technical University
of Denmark and Chief Scientist at Halfspace (Denmark). He is the editor-in-
chief of the _International Journal of Forecasting_. His research interests
include analytics, forecasting, optimization and game theory, with application
to energy systems mostly, but also logistics, weather-driven industries and
business analytics. He is a Fellow of the IEEE, an INFORMS member and a
director of the International Institute of Forecasters (IIF).