32 research outputs found
Chance-Constrained Equilibrium in Electricity Markets With Asymmetric Forecasts
We develop a stochastic equilibrium model for an electricity market with
asymmetric renewable energy forecasts. In our setting, market participants
optimize their profits using public information about a conditional expectation
of energy production but use private information about the forecast error
distribution. This information is given in the form of samples and incorporated
into profit-maximizing optimizations of market participants through chance
constraints. We model information asymmetry by varying the sample size of
participants' private information. We show that with more information
available, the equilibrium gradually converges to the ideal solution provided
by the perfect information scenario. Under information scarcity, however, we
show that the market converges to the ideal equilibrium if participants are to
infer the forecast error distribution from the statistical properties of the
data at hand or share their private forecasts
Electricity Market Equilibrium under Information Asymmetry
We study a competitive electricity market equilibrium with two trading
stages, day-ahead and real-time. The welfare of each market agent is exposed to
uncertainty (here from renewable energy production), while agent information on
the probability distribution of this uncertainty is not identical at the
day-ahead stage. We show a high sensitivity of the equilibrium solution to the
level of information asymmetry and demonstrate economic, operational, and
computational value for the system stemming from potential information sharing
A Consensus-ADMM Approach for Strategic Generation Investment in Electricity Markets
This paper addresses a multi-stage generation investment problem for a
strategic (price-maker) power producer in electricity markets. This problem is
exposed to different sources of uncertainty, including short-term operational
(e.g., rivals' offering strategies) and long-term macro (e.g., demand growth)
uncertainties. This problem is formulated as a stochastic bilevel optimization
problem, which eventually recasts as a large-scale stochastic mixed-integer
linear programming (MILP) problem with limited computational tractability. To
cope with computational issues, we propose a consensus version of alternating
direction method of multipliers (ADMM), which decomposes the original problem
by both short- and long-term scenarios. Although the convergence of ADMM to the
global solution cannot be generally guaranteed for MILP problems, we introduce
two bounds on the optimal solution, allowing for the evaluation of the solution
quality over iterations. Our numerical findings show that there is a trade-off
between computational time and solution quality
Price-Aware Deep Learning for Electricity Markets
While deep learning gradually penetrates operational planning, its inherent
prediction errors may significantly affect electricity prices. This letter
examines how prediction errors propagate into electricity prices, revealing
notable pricing errors and their spatial disparity in congested power systems.
To improve fairness, we propose to embed electricity market-clearing
optimization as a deep learning layer. Differentiating through this layer
allows for balancing between prediction and pricing errors, as oppose to
minimizing prediction errors alone. This layer implicitly optimizes fairness
and controls the spatial distribution of price errors across the system. We
showcase the price-aware deep learning in the nexus of wind power forecasting
and short-term electricity market clearing
Multi-Stage Decision Rules for Power Generation & Storage Investments with Performance Guarantees
We develop multi-stage linear decision rules (LDRs) for dynamic power system
generation and energy storage investment planning under uncertainty and propose
their chance-constrained optimization with performance guarantees. First, the
optimized LDRs guarantee operational and carbon policy feasibility of the
resulting dynamic investment plan even when the planning uncertainty
distribution is ambiguous. Second, the optimized LDRs internalize the tolerance
of the system planner towards the stochasticity (variance) of uncertain
investment outcomes. They can eventually produce a quasi-deterministic
investment plan, which is insensitive to uncertainty (as in deterministic
planning) but robust to its realizations (as in stochastic planning). Last, we
certify the performance of the optimized LDRs with the bound on their
sub-optimality due to their linear functional form. Using this bound, we
guarantee that the preference of LDRs over less restrictive -- yet poorly
scalable -- scenario-based optimization does not lead to financial losses
exceeding this bound. We use a testbed of the U.S. Southeast power system to
reveal the trade-offs between the cost, stochasticity, and feasibility of
LDR-based investments. We also conclude that the LDR sub-optimality depends on
the amount of uncertainty and the tightness of chance constraints on
operational, investment and policy variables
Emission-Aware Optimization of Gas Networks: Input-Convex Neural Network Approach
Gas network planning optimization under emission constraints prioritizes gas
supply with the least CO intensity. As this problem includes complex
physical laws of gas flow, standard optimization solvers cannot guarantee
convergence to a feasible solution. To address this issue, we develop an
input-convex neural network (ICNN) aided optimization routine which
incorporates a set of trained ICNNs approximating the gas flow equations with
high precision. Numerical tests on the Belgium gas network demonstrate that the
ICNN-aided optimization dominates non-convex and relaxation-based solvers, with
larger optimality gains pertaining to stricter emission targets. Moreover,
whenever the non-convex solver fails, the ICNN-aided optimization provides a
feasible solution to network planning
Stochastic Control and Pricing for Natural Gas Networks
We propose stochastic control policies to cope with uncertain and variable
gas extractions in natural gas networks. Given historical gas extraction data,
these policies are optimized to produce the real-time control inputs for nodal
gas injections and for pressure regulation rates by compressors and valves. We
describe the random network state as a function of control inputs, which
enables a chance-constrained optimization of these policies for arbitrary
network topologies. This optimization ensures the real-time gas flow
feasibility and a minimal variation in the network state up to specified
feasibility and variance criteria. Furthermore, the chance-constrained
optimization provides the foundation of a stochastic pricing scheme for natural
gas networks, which improves on a deterministic market settlement by offering
the compensations to network assets for their contribution to uncertainty and
variance control. We analyze the economic properties, including efficiency,
revenue adequacy and cost recovery, of the proposed pricing scheme and make
them conditioned on the network design.Comment: for associated GitHub repository, see
https://github.com/anubhavratha/ng_stochastic_control_and_pricin
Multi-Stage Linear Decision Rules for Stochastic Control of Natural Gas Networks with Linepack
The disturbances from variable and uncertain renewable generation propagate
from power systems to natural gas networks, causing gas network operators to
adjust gas supply nominations to ensure operational security. To alleviate
expensive supply adjustments, we develop control policies to leverage instead
the flexibility of linepack -- the gas stored in pipelines -- to balance
stochastic gas extractions. These policies are based on multi-stage linear
decision rules optimized on a finite discrete horizon to guide controllable
network components, such as compressors and valves, towards feasible
operations. Our approach offers several control applications. First, it treats
the linepack as a main source of flexibility to balance disturbances from power
systems without substantial impacts on nominal gas supply. Second, these
policies can be optimized to minimize the variability (due to intermittency of
renewables) and variance (due to their uncertainty) of network state variables,
such as pressures. Finally, it enables topology optimization to decouple
network parts and prevent uncertainty propagation through the network. This is
demonstrated using illustrative numerical experiments
Differentially Private Optimal Power Flow for Distribution Grids
Although distribution grid customers are obliged to share their consumption
data with distribution system operators (DSOs), a possible leakage of this data
is often disregarded in operational routines of DSOs. This paper introduces a
privacy-preserving optimal power flow (OPF) mechanism for distribution grids
that secures customer privacy from unauthorised access to OPF solutions, e.g.,
current and voltage measurements. The mechanism is based on the framework of
differential privacy that allows to control the participation risks of
individuals in a dataset by applying a carefully calibrated noise to the output
of a computation. Unlike existing private mechanisms, this mechanism does not
apply the noise to the optimization parameters or its result. Instead, it
optimizes OPF variables as affine functions of the random noise, which weakens
the correlation between the grid loads and OPF variables. To ensure feasibility
of the randomized OPF solution, the mechanism makes use of chance constraints
enforced on the grid limits. The mechanism is further extended to control the
optimality loss induced by the random noise, as well as the variance of OPF
variables. The paper shows that the differentially private OPF solution does
not leak customer loads up to specified parameters