Search

This paper considers a risk-averse Markov decision process (MDP) with non-risk constraints as a dynamic optimization framework to ensure robustness against unfavorable outcomes in high-stakes sequential decision-making situations such as disaster response. In this regard, strong duality is proved while making no assumptions on the problem's convexity. This is necessary for some real-world issues, e.g., in the case of deprivation costs in the context of disaster relief, where convexity cannot be ensured. Our theoretical results imply that the problem can be exactly solved in a dual domain where it becomes convex. Based on our duality results, an augmented Lagrangian-based constraint handling mechanism is also developed for risk-averse reinforcement learning algorithms. The mechanism is proved to be theoretically convergent. Finally, we have also empirically established the convergence of the mechanism using a multi-stage disaster response relief allocation problem while using a fixed negative reward scheme as a benchmark. [ABSTRACT FROM AUTHOR]

We propose a new decomposition method to solve multistage non-convex mixed-integer (stochastic) nonlinear programming problems (MINLPs). We call this algorithm non-convex nested Benders decomposition (NC-NBD). NC-NBD is based on solving dynamically improved mixed-integer linear outer approximations of the MINLP, obtained by piecewise linear relaxations of nonlinear functions. Those MILPs are solved to global optimality using an enhancement of nested Benders decomposition, in which regularization, dynamically refined binary approximations of the state variables and Lagrangian cut techniques are combined to generate Lipschitz continuous non-convex approximations of the value functions. Those approximations are then used to decide whether the approximating MILP has to be dynamically refined and in order to compute feasible solutions for the original MINLP. We prove that NC-NBD converges to an ε -optimal solution in a finite number of steps. We provide promising computational results for some unit commitment problems of moderate size. [ABSTRACT FROM AUTHOR]

Bi-level optimization constitutes the most popular mathematical methodology for modeling the deregulated electricity market. However, state-of-the-art models neglect the physical non-convex operating characteristics of market participants, due to their inherent inability to capture binary decision variables in their representation of the market clearing process, rendering them problematic in modeling markets with complex bidding and unit commitment (UC) clearing mechanisms. This paper addresses this fundamental limitation by proposing a novel modeling approach enabling incorporation of these non-convexities into bi-level optimization market models, which is based on the relaxation and primal-dual reformulation of the original, non-convex lower level problem and the penalization of the associated duality gap. Case studies demonstrate the ability of the proposed approach to closely approximate the market clearing solution of the actual UC clearing algorithm and devise more profitable bidding decisions for strategic producers than the state-of-the-art bi-level optimization approach, and reveal the potential of strategic behavior in terms of misreporting non-convex operating characteristics. [ABSTRACT FROM AUTHOR]

This article establishes a dynamic programming argument for a maximin optimization problem where the agent completes a minimization over a set of discount rates. Even though the consideration of a maximin criterion results in a program that is not convex and not stationary over time, it is proved that a careful reference to extended dynamic programming principles and a maxmin functional equation however allows for circumventing these difficulties and recovering an optimal sequence that is time consistent. [ABSTRACT FROM AUTHOR]

As part of the German transition towards a low-carbon economy, renewable energies are set to account for more than half of the gross electricity consumption by 2035, resulting in a rising flexibility demand. Flexibility is required to balance fluctuations in the residual load. In addition, uncertainties in the wind and solar power generation cause an increased demand for control reserve. A unit commitment model of the German power system is used to analyze the value of power plant flexibility in systems with high shares of variable renewables. To investigate the value of power plant flexibility, the additional revenue that can be generated by flexibility improvements is calculated. The results indicate, that power plant flexibility has a small positive impact on the power plant's contribution margin in 2014. A future power system configuration according to the German Grid Development Plan would provide sufficient flexibility to integrate high shares of renewables without power plant flexibility being very valuable. However, integrating variable renewables into a system relying on coal-fired and nuclear power stations results in power plants being able to significantly increase their revenue with improved flexibility. Under these circumstances, power plant flexibility has a considerable value. [ABSTRACT FROM AUTHOR]

This paper proposes a pricing scheme for the day-ahead market in power systems with a large percentage of renewable stochastic production. To clear the day-ahead market, instead of a simplistic deterministic model, we use a two-stage stochastic programming model that embodies a prognosis of future operating conditions. Non-convexities due to start-up costs and the on/off status of generators and their minimum power outputs are properly taken into account. Our goal is to obtain uniform day-ahead clearing prices that deviate in the least possible manner from marginal prices and that allow producers to recover their costs without uplifts. The proposed methodology is illustrated using a simple example and a realistic case study. [ABSTRACT FROM AUTHOR]

Auctions with non-convexities, as considered in this paper, use a multi-period optimal power flow (OPF) model based on generators' offers to calculate efficient schedules. The standard locational marginal prices (LMPs) may not support these schedules and uplifts are needed to help the generators break even. This paper presents a direct minimum-uplift (DMU) pricing model, which is formulated as a mixed integer linear programming problem with uplift minimization objective. New DMU prices are major variables constrained with decomposition formula based on shift factors, similar to the actual practice of developing LMPs. The remaining constraints reflect the generators' profits and uplifts modeled as functions of the DMU prices. The main feature of the DMU model is individual rationality attained in pool-based auction, under prices properly reflecting network constraints, complemented with minimum uplifts. The model is validated on several cases, including the IEEE 24-node system. [ABSTRACT FROM PUBLISHER]

This letter considers a stochastic electricity market in which the uncertainty is handled using a proportional control law and chance security constraints. We prove that in this framework, market clearing prices yielding a robust competitive market equilibrium can be computed and used for stochastic market settlements by risk-aware system operators. An illustrative case study corroborates the usefulness of the proposed approach. [ABSTRACT FROM AUTHOR]

We consider a market in which suppliers with asymmetric capacities and asymmetric marginal and fixed costs compete to satisfy a deterministic and inelastic demand of a commodity in a single period. The suppliers bid their costs to an auctioneer who determines the optimal allocation and the resulting payments, a typical situation in deregulated electricity markets. Under classical marginal-cost pricing, the nonconvexity of the total cost may result in losses for some suppliers because they may fail to recover their fixed cost through commodity payments only. To address this problem, various pricing schemes that lift the price above marginal cost and/or provide side-payments (uplifts) have been proposed in the literature. We review several of these schemes, also proposing a new variant, in a two-supplier setting. We derive closed-form expressions for the price, uplifts, and profits that each scheme generates that enable us to analytically compare these schemes along these three dimensions. Our analysis complements known numerical comparisons available in the literature. We extend some of our analytical comparisons to the case of more than two suppliers and discuss extant numerical comparisons for this case. Further, we present known results concerning the potential for supplier strategic bidding behavior in the context of the considered pricing schemes, emphasizing when possibilities for market manipulation exist. [ABSTRACT FROM AUTHOR]

We consider the canonical non-cooperative multilateral bargaining game with a set of feasible payoffs that is closed and comprehensive from below, contains the disagreement point in its interior, and is such that the individually rational payoffs are bounded. We show that a pure stationary subgame perfect equilibrium having the no-delay property exists, even when the space of feasible payoffs is not convex. We also have the converse result that randomization will not be used in this environment in the sense that all stationary subgame perfect equilibria do not involve randomization on the equilibrium path. Nevertheless, mixed strategy profiles can lead to Pareto superior payoffs in the non-convex case. [ABSTRACT FROM AUTHOR]

In centralized day-ahead electricity markets with marginal pricing, unit commitment costs and capacity constraints give rise to non-convexities which may result in losses to some of the participating generating units. To compensate them for these losses, a recovery mechanism is required. In Part I of this two-part paper, we present certain recovery mechanisms that result in recovery payments after the market is cleared. We also propose a methodology for evaluating the bidding strategy behavior of the participating units for each mechanism. In this paper (Part II), we apply this methodology to evaluate the performance and incentive compatibility properties of each recovery mechanism on a test case model representing the Greek joint energy/reserve day-ahead electricity market. Lastly, we perform sensitivity analysis with respect to key parameters and assumptions and we provide directions for further research. [ABSTRACT FROM PUBLISHER]

In centralized day-ahead electricity markets with marginal pricing, unit commitment costs and capacity constraints give rise to non-convexities which may result in losses to some of the participating generating units. Therefore, a recovery mechanism is required to compensate them. In this paper, we present and analyze several recovery mechanisms that result in recovery payments after the market is cleared. Each of these mechanisms results in a different type and/or amount of payments for each participating unit that exhibits losses. We also propose a methodology for evaluating the bidding strategy behavior of the participating units for each mechanism. This methodology is based on the execution of a numerical procedure aimed at finding joint optimal bidding strategies of the profit-maximizing units. In a companion follow-up paper (Part II), we apply this methodology to evaluate the performance and incentive compatibility of the suggested recovery mechanisms on a simplified test case model of the Greek electricity market. [ABSTRACT FROM PUBLISHER]

The paper analyses the management of an infectious disease in a sympatric metapopulation, under both Nash and cooperative behaviour, through the development of a differential game and an optimal control problem with connected local state variables. As pathogens are renewable resources with negative value, the problem may be non-convex. Since the disease can be transmitted across various connected populations, externalities may be involved. A numerical application is presented, with reference to a livestock disease that can be transmitted between herds on common pastures. The results suggest that optimal eradication in finite time should be pursued when possible. However, optimal eradication is not always feasible (sometimes eradication can be only achieved asymptotically), and the ecology of the disease is of paramount importance in this respect. Also, convergence to an internal steady-state does not minimise the present value of the disease damage and control cost (a result consistent with the existing literature). Ignoring these results may lead to inadequate policy design. [ABSTRACT FROM AUTHOR]

Soil erosion is one of the most important of today’s environmental externalities and a major threat to sustainability of agricultural system. It constitutes the most widespread forms of land degradation throughout the world. The aim of this paper is to estimate the amount of soil erosion generated by the current cropping systems in Tunisia and to assess the economic and ecological impacts of policy instruments designed to handle this problem. The analysed policy options are based on soil conservation practices and direct incentive farming anti-erosive measures. The selected measures are the reduction of tillage, the avoidance of bare fallow and the use of legume-based crop rotation. A bio-economic modelling framework coupling the biophysical model EPIC to a non-linear dynamic programming farm model was used for this impact analysis. It was performed in a set of representative farms belonging to a region in North-Eastern Tunisia (Zaghouan) strongly affected by this phenomenon. The main finding of this research is the non-convexity of the crop yield—soil erosion space. That is, the use of more intensive techniques to increase productivity (i.e. crop yield) may be accompanied by rough changes in soil erosion (damage) curves, manifested either by non-monotony or non-convexity. In term of policy options and because of giving up convexity assumptions, incentive anti-erosive measures appear more efficient than conventional environmental policies such as Pigouvian taxes or quota systems. The implementation of soil conservation practices would leads to a net decrease in soil erosion and an increase in farm income. However, with the current interest rate of 7% the possible rise in income is not enough to stimulate farmers to invest on these practices. A maximum rate of 4% would be necessary to make this policy option more effective. [ABSTRACT FROM AUTHOR]

This paper considers implementation of marginal cost pricing equilibrium allocations with transfers for production economies with increasing returns to scale. We present a mechanism whose Nash equilibrium allocations coincide with the set of marginal cost pricing equilibrium allocations with transfers that characterizes Pareto efficient allocations for economies with non-convex production technologies. We allow production sets and preferences to be unknown to the planner. The mechanism has some nice properties such as feasibility, continuity, and finite-dimension of message space. Furthermore, it works not only for three or more agents, but also for two-agent economies. [ABSTRACT FROM AUTHOR]

General equilibrium is a central concept of economic theory. Unlike partial equilibrium analysis which study the equilibrium of a particular market under the clause "ceteris paribus" that revenues and prices on the other markets stay approximately unaffected, the ambition of a general equilibrium model is to analyze the simultaneous equilibrium in all markets of a competitive economy. Definition of the abstract model, some of its basic results and insights are presented. The important issues of uniqueness and local uniqueness of equilibrium are sketched; they are the condition for a predictive power of the theory and its ability to allow for statics comparisons. Finally, we review the main extensions of the general equilibrium model. Besides the natural extensions to infinitely many commodities and to a continuum of agents, some examples show how economic theory can accommodate the main ideas in order to study some contexts which were not thought of by the initial model. [ABSTRACT FROM AUTHOR]

Economists have relied on convexity assumptions for a long time but many natural resources that stem from ecosystems have non-convexities in their dynamics. This article illustrates the consequences of relaxing convexity assumptions for management and the role of fast and slow variables. The paper presents a general framework to handle systems with fast and slow variables, and illustrates the method using a model of coral reefs subject to fishing pressure. The insights obtained are used to discuss alternative management strategies. [ABSTRACT FROM AUTHOR]

This paper analyzes the impact on exhaustible resource markets of setup costs, a sparsely analyzed category of nonconvex production technologies. This paper proves that, even under idealized circumstances for competition, a competitive equilibrium will fail to exist in the presence of setup costs, for any utility and cost functions such that a planner would exploit exhaustible resource pools sequentially. [ABSTRACT FROM AUTHOR]

• Market-clearing prices of energy and ancillary services in a non-convex SCUC problem. • Considering all kinds of reserves in the day-ahead stage. • Zero uplift payments and uniform ancillary services and nodal energy prices. • Calculating lost opportunity as an index of willingness to follow the SO's dispatch. • A model for fast-start generators in the pricing method. This paper introduces a day-ahead clearing model for the simultaneous energy and ancillary services market in high penetration of renewable energy sources (RESs) considering fast-start generators' behaviors as non-spinning reserve providers. For managing the uncertainties of RESs, the system operator takes the advantages of the stochastic model of security-constrained unit commitment (SCUC) problem considering plausible scenarios. The non-convexities due to the startup costs, minimum power outputs, and commitment variables make the stochastic SCUC problem and market-clearing non-convex. Meanwhile, with traditional market-clearing methods for energy and ancillary services based on marginal costs or dual variables, the net profit of some generators may become negative. In this situation, more financial losses will be imposed on fast-start generators since they are marginal/intermittent units for managing the uncertainties of RESs. Using a duality gap minimization and profit insurance, this paper presents a pricing model to solve these issues. The proposed market-clearing model leads to uniform prices for ancillary services and nodal prices for energy guaranteeing the non-negative net profit of all generators. The results of the 3-buses system and IEEE 118-buses system are analyzed to illustrate the applications of the proposed pricing approach. [ABSTRACT FROM AUTHOR]