41,890 research outputs found
Computing large market equilibria using abstractions
Computing market equilibria is an important practical problem for market
design (e.g. fair division, item allocation). However, computing equilibria
requires large amounts of information (e.g. all valuations for all buyers for
all items) and compute power. We consider ameliorating these issues by applying
a method used for solving complex games: constructing a coarsened abstraction
of a given market, solving for the equilibrium in the abstraction, and lifting
the prices and allocations back to the original market. We show how to bound
important quantities such as regret, envy, Nash social welfare, Pareto
optimality, and maximin share when the abstracted prices and allocations are
used in place of the real equilibrium. We then study two abstraction methods of
interest for practitioners: 1) filling in unknown valuations using techniques
from matrix completion, 2) reducing the problem size by aggregating groups of
buyers/items into smaller numbers of representative buyers/items and solving
for equilibrium in this coarsened market. We find that in real data
allocations/prices that are relatively close to equilibria can be computed from
even very coarse abstractions
Consensus-based approach to peer-to-peer electricity markets with product differentiation
With the sustained deployment of distributed generation capacities and the
more proactive role of consumers, power systems and their operation are
drifting away from a conventional top-down hierarchical structure. Electricity
market structures, however, have not yet embraced that evolution. Respecting
the high-dimensional, distributed and dynamic nature of modern power systems
would translate to designing peer-to-peer markets or, at least, to using such
an underlying decentralized structure to enable a bottom-up approach to future
electricity markets. A peer-to-peer market structure based on a Multi-Bilateral
Economic Dispatch (MBED) formulation is introduced, allowing for
multi-bilateral trading with product differentiation, for instance based on
consumer preferences. A Relaxed Consensus+Innovation (RCI) approach is
described to solve the MBED in fully decentralized manner. A set of realistic
case studies and their analysis allow us showing that such peer-to-peer market
structures can effectively yield market outcomes that are different from
centralized market structures and optimal in terms of respecting consumers
preferences while maximizing social welfare. Additionally, the RCI solving
approach allows for a fully decentralized market clearing which converges with
a negligible optimality gap, with a limited amount of information being shared.Comment: Accepted for publication in IEEE Transactions on Power System
A New Approach to Electricity Market Clearing With Uniform Purchase Price and Curtailable Block Orders
The European market clearing problem is characterized by a set of
heterogeneous orders and rules that force the implementation of heuristic and
iterative solving methods. In particular, curtailable block orders and the
uniform purchase price (UPP) pose serious difficulties. A block is an order
that spans over multiple hours, and can be either fully accepted or fully
rejected. The UPP prescribes that all consumers pay a common price, i.e., the
UPP, in all the zones, while producers receive zonal prices, which can differ
from one zone to another.
The market clearing problem in the presence of both the UPP and block orders
is a major open issue in the European context. The UPP scheme leads to a
non-linear optimization problem involving both primal and dual variables,
whereas block orders introduce multi-temporal constraints and binary variables
into the problem. As a consequence, the market clearing problem in the presence
of both blocks and the UPP can be regarded as a non-linear integer programming
problem involving both primal and dual variables with complementary and
multi-temporal constraints.
The aim of this paper is to present a non-iterative and heuristic-free
approach for solving the market clearing problem in the presence of both
curtailable block orders and the UPP. The solution is exact, with no
approximation up to the level of resolution of current market data. By
resorting to an equivalent UPP formulation, the proposed approach results in a
mixed-integer linear program, which is built starting from a non-linear integer
bilevel programming problem. Numerical results using real market data are
reported to show the effectiveness of the proposed approach. The model has been
implemented in Python, and the code is freely available on a public repository.Comment: 15 pages, 7 figure
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