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Vadim Borokhov

Publications and source records attributed to Vadim Borokhov.

11 recordsLinked to original sources
arXiv2022

The uplift payment elimination through the Lagrangian relaxation of the redundant constraints

In the presence of non-convexities, the power market may not have an equilibrium price for power that provides economic stability of the centralized dispatch outcome. In this case, to achieve an economically stable outcome, the uplift payments to the market players are introduced as part of the pricing principle. Given the general pricing principle that involves the lost profit compensation in the form of the uplift payments, we study a question if it is possible to introduce new products/services at the market and the associated prices such that the set of the optimal solutions to the centralized dispatch optimization problem is unaffected, the profit received by each market player at the centralized dispatch schedule is unchanged, and no market player has lost profit. These new products/services and the corresponding prices can be viewed as originating from the Lagrangian relaxation of redundant constraints, which dot not change the centralized dispatch schedule. For any given market price (or a pricing algorithm that sets the producer revenue as a function of its output volume) in a uninode multi-period power market with fixed load, we explicitly construct a family of the redundant constraints that do not change the maximum profit of any producer and result in zero total uplift payment. The analysis can be straightforwardly extended to a multi-node multi-period market with price-sensitive demand.

math.OC↗
arXiv2021

Antimonopoly regulation method in energy markets based on the Vickrey-Clarke-Groves mechanism

We evaluate the applicability of the generic Vickrey-Clarke-Groves (VCG) mechanism as an antimonopoly measure against a profit-maximizing producer with market power operating a portfolio of generating units at the centralized two-settlement energy market. The producer may indicate in its bid not only the altered cost function but also the distorted values of the technical parameters of its generating units, which enter the system-wide constraints of the centralized dispatch optimization problem. To ensure the applicability of the VCG method in this setting, we identify an additional assumption on the changes of the feasible set of the centralized dispatch optimization problem induced by variations of the producer's technical parameters. In the framework of the generic VCG mechanism, we propose an antimonopoly regulation method based on a regulator estimate of the producer's truthful bid. If this estimate is exact, the producer's maximum profit coincides with that in the case of the truthful bidding when no antimonopoly measure is applied. If the estimate is not exact, the error affects neither the producer's (weakly) dominant bid nor its optimal nodal output but manifests itself in the total uplift payment. This ensures an efficient allocation in the form of the optimal output/consumption schedule and shields the (pre-uplift) market prices from the producer's market power. We compare the suggested method with the alternative antimonopoly regulation approach based on the replacement of the producer's bid by a bid composed by the regulator.

math.OC↗
arXiv2020

Modified convex hull pricing for fixed load power markets

We consider fixed load power market with non-convexities originating from start-up and no-load costs of generators. The convex hull (minimal uplift) pricing method results in power prices minimizing the total uplift payments to generators, which compensate their potential profits lost by accepting centralized dispatch solution, treating as foregone all opportunities to supply any other output volume allowed by generator internal constraints. For each generator we define a set of output volumes, which are economically and technologically feasible in the absence of centralized dispatch, and propose to exclude output volumes outside the set from lost profit calculations. New pricing method results in generally different set of market prices and lower (or equal) total uplift payment compared to convex hull pricing algorithm.

math.OC↗
arXiv2019

Utilizing the redundant constraints for the uplift payment elimination

A power market with non-convexities may not have an equilibrium price for power that provides economic stability of the centralized dispatch outcome. In this case, the market players are entitled to receive the uplift payments that compensate the economic profit lost when following the centralized dispatch. We consider a special class of the (possibly non-linear) redundant constraints that are redundant not only on the feasible set of the centralized dispatch optimization problem (and, therefore, do not change the centralized dispatch outcome) but also on the larger set obtained when the power balance constraint is relaxed. We show that the Lagrangian relaxation of these redundant constraints may reduce the uplift payments without changing the duality gap. For any given market price (or a pricing algorithm that sets the producer revenue as a function of its output volume) in a uninode multi-period power market with fixed load, we explicitly construct a family of the redundant constraints that do not change the maximum profit of the producer and result in zero uplift payment. We show that the introduction and subsequent Lagrangian relaxation of just one redundant constraint in the centralized dispatch problem suffice to eliminate the uplift payments for all the producers. In the case of the convex hull pricing method, the introduction of these redundant constraints affects neither the duality gap nor the market price for power. The results can be straightforwardly generalized to a power market with the price-sensitive load.

math.OC↗
arXiv2018

Modified convex hull pricing for power markets with price-sensitive load

We consider a general power market with price-sensitive consumer bids and non-convexities originating from supply (start-up and no-load costs, nonzero minimum output limits of generating units, etc.) and demand. The convex hull (minimum-uplift) pricing method produces the set of power prices that minimizes the total uplift payments to the market players needed to compensate their potential profits lost by accepting the centralized dispatch solution. All opportunities to supply (consume) any other output (consumption) volumes allowed by market player individual operational constraints are considered as foregone in the convex hull pricing method. We modify the convex hull pricing algorithm by defining for each market player a modified individual feasible set that is utilized in the lost profit calculation. These sets are based on the output (consumption) volumes that are economically and technologically feasible in the centralized dispatch. The new pricing method results in the generally different set of market prices and lower (or equal) total uplift payment compared to the convex hull pricing algorithm.

math.OC↗
arXiv2004

Monopole operators in three-dimensional N=4 SYM and mirror symmetry

We study non-abelian monopole operators in the infrared limit of three-dimensional SU(N_c) and N=4 SU(2) gauge theories. Using large N_f expansion and operator-state isomorphism of the resulting superconformal field theories, we construct monopole operators which are (anti-)chiral primaries and compute their charges under the global symmetries. Predictions of three-dimensional mirror symmetry for the quantum numbers of these monopole operators are verified.

hep-th↗
arXiv2003

Non-supersymmetric deformations of the dual of a confining gauge theory

We introduce a computational technique for studying non-supersymmetric deformations of domain wall solutions of interest in AdS/CFT. We focus on the Klebanov-Strassler solution, which is dual to a confining gauge theory. From an analysis of asymptotics we find that there are three deformations that leave the ten-dimensional supergravity solution regular and preserve the global bosonic symmetries of the supersymmetric solution. Also, we show that there are no regular near-extremal deformations preserving the global symmetries, as one might expect from the existence of a gap in the gauge theory.

hep-th↗
arXiv2002

Topological Disorder Operators in Three-Dimensional Conformal Field Theory

Many abelian gauge theories in three dimensions flow to interacting conformal field theories in the infrared. We define a new class of local operators in these conformal field theories which are not polynomial in the fundamental fields and create topological disorder. They can be regarded as higher-dimensional analogues of twist and winding-state operators in free 2d CFTs. We call them monopole operators for reasons explained in the text. The importance of monopole operators is that in the Higgs phase, they create Abrikosov-Nielsen-Olesen vortices. We study properties of these operators in three-dimensional QED using large N_f expansion. In particular, we show that monopole operators belong to representations of the conformal group whose primaries have dimension of order N_f. We also show that monopole operators transform non-trivially under the flavor symmetry group, with the precise representation depending on the value of the Chern-Simons coupling.

hep-th↗
arXiv2002

Monopole Operators and Mirror Symmetry in Three Dimensions

We study vortex-creating, or monopole, operators in 3d CFTs which are the infrared limit of N=2 and N=4 supersymmetric QEDs in three dimensions. Using large-Nf expansion, we construct monopole operators which are primaries of short representations of the superconformal algebra. Mirror symmetry in three dimensions makes a number of predictions about such operators, and our results confirm these predictions. Furthermore, we argue that some of our large-Nf results are exact. This implies, in particular, that certain monopole operators in N=4 d=3 SQED with Nf=1 are free fields. This amounts to a proof of 3d mirror symmetry in a special case.

hep-th↗
arXiv2002

Belinfante Tensors Induced by Matter-Gravity Couplings

We show that any generally covariant coupling of matter fields to gravity gives rise to a conserved, on-shell symmetric energy-momentum tensor equivalent to the canonical energy-momentum tensor of the flat-space theory. For matter fields minimally coupled to gravity our algorithm gives the conventional Belinfante tensor. We establish that different matter-gravity couplings give metric energy-momentum tensors differing by identically conserved tensors. We prove that the metric energy-momentum tensor obtained from an arbitrary gravity theory is on-shell equivalent to the canonical energy-momentum tensor of the flat-space theory.

hep-th↗