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Provision of secondary frequency regulation by coordinated dispatch of industrial loads and thermal power plants
Demand responsive industrial loads with high thermal inertia have potential to provide ancillary service for frequency regulation in the power market. To capture the benefit, this study proposes a new hierarchical framework to coordinate the demand responsive industrial loads with thermal power plants in an industrial park for secondary frequency control. In the proposed framework, demand responsive loads and generating resources are coordinated for optimal dispatch in two-time scales: (1) the regulation reserve of the industrial park is optimally scheduled in a day-ahead manner. The stochastic regulation signal is replaced by the specific extremely trajectories. Furthermore, the extremely trajectories are achieved by the day-ahead predicted regulation mileage. The resulting benefit is to transform the stochastic reserve scheduling problem into a deterministic optimization; (2) a model predictive control strategy is proposed to dispatch the industry park in real time with an objective to maximize the revenue. The proposed technology is tested using a real-world industrial electrolysis power system based upon Pennsylvania, Jersey, and Maryland (PJM) power market. Various scenarios are simulated to study the performance of the proposed approach to enable industry parks to provide ancillary service into the power market. The simulation results indicate that an industrial park with a capacity of 500 MW can provide up to 40 MW ancillary service for participation in the secondary frequency regulation. The proposed strategy is demonstrated to be capable of maintaining the economic and secure operation of the industrial park while satisfying performance requirements from the real world regulation market
Computational burden reduction in Min-Max MPC
Min–max model predictive control (MMMPC) is one of the strategies used to control plants subject to bounded uncertainties. The implementation of MMMPC suffers a large computational burden due to the complex numerical optimization problem that has to be solved at every sampling time. This paper shows how to overcome this by transforming the original problem into a reduced min–max problem whose solution is much simpler. In this way, the range of processes to which MMMPC can be applied is considerably broadened. Proofs based on the properties of the cost function and simulation examples are given in the paper
On generalized terminal state constraints for model predictive control
This manuscript contains technical results related to a particular approach
for the design of Model Predictive Control (MPC) laws. The approach, named
"generalized" terminal state constraint, induces the recursive feasibility of
the underlying optimization problem and recursive satisfaction of state and
input constraints, and it can be used for both tracking MPC (i.e. when the
objective is to track a given steady state) and economic MPC (i.e. when the
objective is to minimize a cost function which does not necessarily attains its
minimum at a steady state). It is shown that the proposed technique provides,
in general, a larger feasibility set with respect to existing approaches, given
the same computational complexity. Moreover, a new receding horizon strategy is
introduced, exploiting the generalized terminal state constraint. Under mild
assumptions, the new strategy is guaranteed to converge in finite time, with
arbitrarily good accuracy, to an MPC law with an optimally-chosen terminal
state constraint, while still enjoying a larger feasibility set. The features
of the new technique are illustrated by three examples.Comment: Part of the material in this manuscript is contained in a paper
accepted for publication on Automatica and it is subject to Elsevier
copyright. The copy of record is available on http://www.sciencedirect.com
Robust optimization based energy dispatch in smart grids considering demand uncertainty
In this study we discuss the application of robust optimization to the problem of economic energy dispatch in smart grids. Robust optimization based MPC strategies for tackling uncertain load demands are developed. Unexpected additive disturbances are modelled by defining an affine dependence between the control inputs and the uncertain load demands.
The developed strategies were applied to a hybrid power system connected to an electrical power grid. Furthermore, to demonstrate the superiority of the standard Economic MPC over the MPC tracking, a comparison (e.g average daily cost) between the standard MPC tracking, the standard Economic MPC, and the integration of both in one-layer and two-layer approaches was carried out. The goal of this research is to design a controller based on Economic MPC
strategies, that tackles uncertainties, in order to minimise economic costs and guarantee service reliability of the system.Postprint (author's final draft
Economic MPC of Nonlinear Systems with Non-Monotonic Lyapunov Functions and Its Application to HVAC Control
This paper proposes a Lyapunov-based economic MPC scheme for nonlinear sytems
with non-monotonic Lyapunov functions. Relaxed Lyapunov-based constraints are
used in the MPC formulation to improve the economic performance. These
constraints will enforce a Lyapunov decrease after every few steps. Recursive
feasibility and asymptotical convergence to the steady state can be achieved
using Lyapunov-like stability analysis. The proposed economic MPC can be
applied to minimize energy consumption in HVAC control of commercial buildings.
The Lyapunov-based constraints in the online MPC problem enable the tracking of
the desired set-point temperature. The performance is demonstrated by a virtual
building composed of two adjacent zones
On control of discrete-time state-dependent jump linear systems with probabilistic constraints: A receding horizon approach
In this article, we consider a receding horizon control of discrete-time
state-dependent jump linear systems, particular kind of stochastic switching
systems, subject to possibly unbounded random disturbances and probabilistic
state constraints. Due to a nature of the dynamical system and the constraints,
we consider a one-step receding horizon. Using inverse cumulative distribution
function, we convert the probabilistic state constraints to deterministic
constraints, and obtain a tractable deterministic receding horizon control
problem. We consider the receding control law to have a linear state-feedback
and an admissible offset term. We ensure mean square boundedness of the state
variable via solving linear matrix inequalities off-line, and solve the
receding horizon control problem on-line with control offset terms. We
illustrate the overall approach applied on a macroeconomic system
Risk-Averse Model Predictive Operation Control of Islanded Microgrids
In this paper we present a risk-averse model predictive control (MPC) scheme
for the operation of islanded microgrids with very high share of renewable
energy sources. The proposed scheme mitigates the effect of errors in the
determination of the probability distribution of renewable infeed and load.
This allows to use less complex and less accurate forecasting methods and to
formulate low-dimensional scenario-based optimisation problems which are
suitable for control applications. Additionally, the designer may trade
performance for safety by interpolating between the conventional stochastic and
worst-case MPC formulations. The presented risk-averse MPC problem is
formulated as a mixed-integer quadratically-constrained quadratic problem and
its favourable characteristics are demonstrated in a case study. This includes
a sensitivity analysis that illustrates the robustness to load and renewable
power prediction errors
A Moral Framework for Understanding of Fair ML through Economic Models of Equality of Opportunity
We map the recently proposed notions of algorithmic fairness to economic
models of Equality of opportunity (EOP)---an extensively studied ideal of
fairness in political philosophy. We formally show that through our conceptual
mapping, many existing definition of algorithmic fairness, such as predictive
value parity and equality of odds, can be interpreted as special cases of EOP.
In this respect, our work serves as a unifying moral framework for
understanding existing notions of algorithmic fairness. Most importantly, this
framework allows us to explicitly spell out the moral assumptions underlying
each notion of fairness, and interpret recent fairness impossibility results in
a new light. Last but not least and inspired by luck egalitarian models of EOP,
we propose a new family of measures for algorithmic fairness. We illustrate our
proposal empirically and show that employing a measure of algorithmic
(un)fairness when its underlying moral assumptions are not satisfied, can have
devastating consequences for the disadvantaged group's welfare
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