Optimal Reserve Research Articles

Simultaneous Energy and Reserve Market Clearing with Consideration of Interruptible Loads as One of Demand Response Resources and Different Reliability Requirements of Consumers

Abstract Determining the optimal reserve in power systems is closely related to uncertainties in power generation and risks of outage of supply to consumers. Distributed generation sources such as wind farms are usual reasons for uncertainties in MW production. This uncertainty can be alleviated by providing enough reserve in which demand response (DR) programs can play role of resources for reserve. In an electricity market structure, the mentioned points are usually handled by Independent System Operator (ISO) in energy and reserve markets. This paper deals with the problem of reliability-based reserve management. In the mentioned problem, the DR program in the form of interruptible loads is also considered. A new method is proposed in which ISO settle energy and reserve markets simultaneously while employing the DR in the first stage. In addition, consumers’ requirements of reliability are included by assuming that they have possibility to offer their desired levels of reliability to the ISO. The amount of reserve obtained from market settlement is adjusted based on the different reliability requirements of the consumers and different scenarios of the wind farm operation, in the second stage of the proposed method. Also the cost of the reserve adjustment is fairly allocated to producers and consumers. The proposed method applies stochastic programming formulation and its validity is assessed by the GAMS software. Simulation results show that how amount and cost of reserve could be adjusted to cover power balance, cost of power production and load interruption and required reliability of consumers.

Türkiye Rezerv Yeterliliği: Rezervlerin İthalat Ve Kısa Vadeli Dış Borçlarla Karşılaştırılması Üzerine Bir Analiz

Ülke ekonomisinin finansal gücünün bir göstergesi olan ve uluslararası yatırımcılar tarafından önemle dikkate alınan uluslararası rezervlerdeki değişimler, finansal istikrar açısından büyük öneme sahiptir ve akademik literatürde yaygın şekilde çalışılmaktadır. Ülkelerin rezerv yeterliliğinin hesaplanmasında, Uluslararası Para Fonu (IMF) tarafından, uluslararası rezervleri, yıllık ithalatın %25’i oranında belirtilen optimal rezerv seviyesi ve net uluslararası rezervleri, kısa vadeli dış borç toplamıyla karşılaştırmak şeklinde iki geleneksel yaklaşım kullanılmaktadır. Bu çalışmanın amacı, 2011:Ç3-2018:Ç4 döneminde Türkiye’de uluslararası rezervlerin yeterliliğini, Enders and Jones (2016) tarafından geliştirilen Fourier Granger nedensellik testini kullanarak araştırmaktır. Çalışma sonuçlarına göre, ilk yaklaşıma göre rezervler yeteliyken, ikinci yaklaşım dikkate alındığında rezervlerin yeterli olmadığı görülmektedir.

Anticipated rationing policy for inventory systems with two demand classes and backlogging costs

This paper studies a periodic-review, infinite-horizon, backlogging inventory model with two demand classes and a constant lead time, where inventory replenishment follows a base-stock policy. We consider an anticipated rationing policy which reserves inventory for future high-priority demands with higher backlogging costs by taking the coming delivery of the next period into consideration. Due to the lack of nice properties such as convexity, both the optimal base-stock level and the optimal critical level when minimising inventory costs have to be found by an exhaustive search. Instead, we study a single-period problem truncated from the original infinite-horizon problem and derive its optimal reservation level with a closed-form expression. Surprisingly, the solution form of the single-period problem coincides exactly with the anticipated rationing policy and hence this solution serves as a good approximation for the optimal critical level of the infinite-horizon problem. An empirical study further demonstrates that our closed-form approximation is quite attractive in both solution accuracy and computation efficiency based on spare parts inventory data from a petrochemical plant in China.

Mitigating supply disruption with a backup supplier under uncertain demand: competition vs. cooperation

In case of supply disruption following major disasters, many supply chains tend to break down due to stock-outs and take a long time to recover. However, by keeping emergency sources of supply, some supply chains continue to function smoothly even after a major disaster. In this work, using a game-theoretic-framework, we consider a two-suppliers-one-retailer supply chain with price-dependent stochastic demand in which suppliers are prone to disruption. To investigate the impact of supply disruption we consider two models: SC model, in which the retailer does not maintain any emergency sources of supply against any supply disruption, and SCB model, in which the retailer maintains a backup supplier to mitigate the impact of supply disruption. We mainly focus on the pricing strategies of the suppliers and the mitigating strategies of the retailer under supply and demand uncertainty. We address two coordinating mechanisms to enhance supply chain performance. Our results indicate that in the presence of supply disruption, even with lower probabilities, the retailer would always prefer to take the advantage of a backup supplier and the optimal reserve quantity increases with disruption probabilities. We further investigate the scenario in which the suppliers would always prefer to cooperate with each other.

Spatial conservation planning under uncertainty: adapting to climate change risks using modern portfolio theory.

Climate change and urban growth impact habitats, species, and ecosystem services. To buffer against global change, an established adaptation strategy is designing protected areas to increase representation and complementarity of biodiversity features. Uncertainty regarding the scale and magnitude of landscape change complicates reserve planning and exposes decision makers to the risk of failing to meet conservation goals. Conservation planning tends to treat risk as an absolute measure, ignoring the context of the management problem and risk preferences of stakeholders. Application of risk management theory to conservation emphasizes the diversification of a portfolio of assets, with the goal of reducing the impact of system volatility on investment return. We use principles of Modern Portfolio Theory (MPT), which quantifies risk as the variance and correlation among assets, to formalize diversification as an explicit strategy for managing risk in climate-driven reserve design. We extend MPT to specify a framework that evaluates multiple conservation objectives, allows decision makers to balance management benefits and risk when preferences are contested or unknown, and includes additional decision options such as parcel divestment when evaluating candidate reserve designs. We apply an efficient search algorithm that optimizes portfolio design for large conservation problems and a game theoretic approach to evaluate portfolio trade-offs that satisfy decision makers with divergent benefit and risk tolerances, or when a single decision maker cannot resolve their own preferences. Evaluating several risk profiles for a case study in South Carolina, our results suggest that a reserve design may be somewhat robust to differences in risk attitude but that budgets will likely be important determinants of conservation planning strategies, particularly when divestment is considered a viable alternative. We identify a possible fiscal threshold where adequate resources allow protecting a sufficiently diverse portfolio of habitats such that the risk of failing to achieve conservation objectives is considerably lower. For a range of sea-level rise projections, conversion of habitat to open water (14-180%) and wetland loss (1-7%) are unable to be compensated under the current protected network. In contrast, optimal reserve design outcomes are predicted to ameliorate expected losses relative to current and future habitat protected under the existing conservation estate.

Robustly Optimal Reserve Price

We study a robust version of the single-unit auction problem. The auctioneer has confidence in her estimate of the marginal distribution of a generic bidder's valuation, but does not have reliable information about the joint distribution. In this setting, we analyze the performance of second-price auctions with reserve prices in terms of revenue guarantee, that is, the greatest lower bound of revenue across all joint distributions that are consistent with the marginals. For any finite number of bidders, we solve for the robustly optimal reserve price that generates the highest revenue guarantee. Our analysis has interesting implications in large markets. For any marginal distribution, the robustly optimal reserve price converges to zero as the number of bidders gets large. Furthermore, the second-price auction with no reserve price is asymptotically optimal among all mechanisms.

Методика обоснования резерва запасных частей для работы специальной техники в ходе ликвидации чрезвычайной ситуации

The creation of material resources reserves for the elimination of consequences of natural disasters and technogenic accidents (emergency situations — ES) is one of the main tasks ofUnitedStatesystem of prevention and response to emergency situations. A sufficient amount of material resources, their rational placement, proper storage and quality service ensures the ability quickly to liquidate the immediate danger to human life and health, the organization of paramount life support for the population in the disaster area. Aims and purposes. There is an actual problem of preliminary assessment, accounting and justification of the spare parts reserve for work special technical means (STM) of the firefighting and rescue service in the course of emergency response, based on the principle of the necessary sufficiency and the maximum possible use of the available forces and means. Methods. For the planning the required amount of spare parts for STM, taking into account their cost, as well as for substantiating the decision on the optimal number of repair teams capable of ensuring timely replacement of failed units in an ES or its consequences, the methods of queuing theory and queuing systems are applicable. Results and discussion . The article proposes a method of calculating the optimal reserve of spare parts to ensure the normal operation of STM with economic justification, taking into account the material costs of their acquisition and maintenance of repair teams. There are presented the calculations that allow in practice to take into account the risks associated with insufficient reserve of spare parts and forced downtime of STM due to the inability to quickly troubleshoot during ES response and rescue operations. Practical recommendations for determination of economically expedient quantity of spare parts and number of the operators making repair of special equipment taking into account material costs and indicators of reliability are developed. Conclusions. The problems of the article correspond to the modern directions of scientific support of operational activities of Emercom of Russia and due to the presence of a wide range of tasks related to the creation, storage, use and replenishment of reserves of material resources during the liquidation of consequences of natural disasters and technogenic accidents.

Low Reserve Prices in Auctions*

AbstractA standard result in auction theory is that a seller’s profit-maximising reserve price is no less than his own value for the good. In practice, however, reserve prices often appear to be less than sellers’ values. This article revisits the theory of optimal reserves in the context of second-price auctions. The main result is that an optimal reserve is less than the seller’s value if the bidders are sufficiently risk averse and if their values are sufficiently interdependent. The resulting outcome may approximate that of an auction without reserve, i.e., an absolute auction.

Використання типологічного потенціалу основних лісотвірних порід в умовах Поділля

Наведено результати дослідження лісотипологічного потенціалу основних лісотвірних порід насіннєвого та вегетативного походження. Виявлено низку відмінностей між темпами росту та продуктивністю насіннєвих і порослевих насаджень основних лісотвірних порід Поділля. З'ясовано, що різниця між запасами дуба звичайного вегетативного походження модальних та оптимальних деревостанів чітко простежується вже у 2 класі віку. Найбільша різниця в запасі проявляється у віці 100 років і становить майже 50 %. Встановлено, що у дубових деревостанах насінного походження різниця між оптимальними та модальними деревостанами найбільше проявляється у 110-річному віці і продовжує зростати до 140 років. Також вивчено лісотипологічний потенціал насіннєвих ясеневих деревостанів. У ході проведених досліджень з'ясовано, що значне зниження запасу модальних ясеневих деревостанів спостерігається у 80–100-річному віці. Підраховано, що у 140-річному віці запас деревини в модальних деревостанах виявився на 170 м3∙га-1 нижчим, ніж в оптимальних. У букових деревостанах з віком відмінності за запасом між оптимальними і модальними показниками значно посилюються і у 80-річному віці різниця становить 100 м3∙га-1. За зведеними даними, середній оптимальний запас для основних деревостанів Поділля становить близько 340 м3∙га-1. Величина фактичного запасу становить 237 м3/га. Відхилення середніх запасів деревостанів становить 104 м3∙га-1 (32 %). Найбільші втрати від недовикористання лісорослинного потенціалу та запровадження неефективних лісогосподарських методів характерне для дубових (50,1 %) та букових (30,3 %) деревостанів. Згідно з отриманими даними встановлено, що основна частка втрат продуктивності деревостанів зумовлена недовикористанням лісорослинного потенціалу (32,04 %). Втрата від інших факторів є незначною і не перевищує 1 % від загального запасу деревини.

How nonrandom habitat loss affects nature reserve planning strategies

The SLOSS (single large or several small reserves) debate is central to species conservation, and habitat loss is the primary cause of species extinction. As a result, habitat loss is crucial for exploring the debate. This study investigates the effect of nonrandom habitat loss and its interactions with individual migration and disturbance. The results suggest that (1) if the spatial distribution of lost habitats is dispersed, a few large reserves are optimal for the protected species; and if it is clustered, many small reserves are optimal. (2) The effects of the spatial distribution of lost habitats on the debate depends on individual migration, and if there are more individuals migrating among reserves, the spatial distribution of lost habitats has greater impacts. (3) If disturbance rate is low, many small reserves are optimal; and increasing disturbance rate tends to favor the implementation of few large reserves. And the spatial distribution of lost habitats exhibits a threshold above which the response of the optimal reserve number to disturbance rate is amplified. This study facilitates improving the nature reserve planning strategies.

Determination of optimal reserve contribution of thermal units to afford the wind power uncertainty

Due to unforeseen variations in wind speed profiles, wind farm integrations are recognized as intermittent and uncertain energy contributors. More specifically, integration of such renewable energy resources aligned with the conventional thermal units although reduces the emissions and brings about a clean environment, it introduces serious problems in assigning optimal and reliable level of these units in load supplying and spinning reserve provision. This situation is more intensified considering the uncertainties arisen by the power system loading demand. To facilitate such operational hurdles, the ongoing study puts forward an efficient model for assigning the optimal spinning reserve which accommodates the uncertainties in both the wind speed and load profiles. Stochastic behavior of these parameters is simulated by generating a proper number of scenarios through the Monte Carlo simulation (MCS) approach. Then, each of these scenarios is evaluated based on the established linear mixed integer approach in a deterministic fashion. Accordingly, a computationally efficient approach is obtained paving the way for real-world implementations and assuring the global optimum results. The proposed approach is applied to a 12-unit test system including 10 thermal units and 2 wind farms. Results are reflected in terms of the commitment status, energy dispatches, and reserve contributions of each committed unit. A comprehensive discussion is conducted to disclose the possible improvements.

Optimal harvest strategy for even‐aged stands with price uncertainty and risk of natural disturbances

AbstractWe present a reservation price model to examine the joint impacts of natural disturbances and stumpage price uncertainty on the optimal harvesting decision for even‐aged forest stands. We consider a landowner who manages a loblolly pine stand to produce timber and amenities, under age‐dependent risk of wildfires and uncertainty in future timber prices. We show that the incorporation of risk of wildfires decreases the optimal reservation prices. The inclusion of risk of wildfires leads to lower land values and reduces the mean harvest age compared with the case of no‐risk of wildfires. Higher economic gains are obtained with the reservation price strategy compared with the deterministic rotation age model—a difference in the land value of $2,326 ha−1 (21%) between the two approaches.Recommendations for Resource Managers Our adaptive harvest strategy shows that the incorporation of risk of wildfires decreases the optimal reservation prices compared with the case of no‐risk of wildfires. Low reservation prices—a price that makes the landowner indifferent between harvesting or waiting longer—result in lower economic benefits for landowners and potential conversions of lands to nonforest use. Forest management practices oriented to reduce the effects of catastrophic disturbances, for example, creating a more complex forest structure with different stand densities, become imperative to ensure the sustainability of forestlands in the US South. Our analysis also suggests that the valuation of forestry investments should consider not only the risk of catastrophic events but also uncertainty in future timber prices. Higher appraisals of land value are obtained when timber price uncertainty is explicitly recognized, providing financial incentives for landowners to invest in forestry.

Robust Inference in First-Price Auctions: Experimental Findings as Identifying Restrictions

In laboratory experiments bidding in first-price auctions is more aggressive than predicted by the risk-neutral Bayesian Nash Equilibrium (RNBNE) - a finding known as the overbidding puzzle. Several models have been proposed to explain the overbidding puzzle, but no canonical alternative to RNBNE has emerged, and RNBNE remains the basis of the structural auction literature. Instead of estimating a particular model of overbidding, we use the overbidding restriction itself for identification, which allows us to bound the valuation distribution, the seller's payoff function, and the optimal reserve price. These bounds are consistent with RNBNE and all models of overbidding and remain valid if different bidders employ different bidding strategies. We propose simple estimators and evaluate the validity of the bounds numerically and in experimental data.

The bidder exclusion effect

AbstractWe introduce a new, simple‐to‐compute test of independence of valuations and the number of bidders for ascending button auctions with symmetric, conditionally independent private values. The test involves estimating the expected revenue drop from excluding a bidder at random, which can be computed as a scaled sample average of a difference of order statistics. This object also provides a bound on counterfactual revenue changes from optimal reserve pricing or bidder mergers. We illustrate the approach using data from timber auctions, where we find some evidence that bidder valuations and the number of participants are not independent.

Optimal reserve inventory from output of one machine to input of two machines when inter-arrival breakdown is a random variable

In this paper, a two stage production process is considered such that there is only one machine M1 in the first stage and two machines M2′, M2″ in the second stage. It is assumed that the output of M1 is the input for M2′, M2″. During the breakdown time of M1, a reserve inventory is suggested for M2′, M2″, to prevent the idle time, which is costlier. An inventory model is derived here based on certain assumptions to find the optimum size of the reserve inventory of the semi-finished product of the machine M1 to supply the machines M2′, M2″ till M1 resumes the function. Numerical illustrations are provided.

Robust Reserve Pricing in Auctions Under Mean Constraints

We study a seller who sets a reserve price in a second price auction with uncertainty over the joint distribution of bidders' valuations. The seller only knows the mean of the marginal distribution of each bidder's valuation and the range, and an adversarial Nature chooses the worst-case distribution within this ambiguity set. We use a dual characterization to solve for this distribution. We find that the seller's optimal reserve price tends to be low and converges to zero in probability as the number of bidders increases.

Optimal reserve inventory from output of one machine to input of two machines when inter-arrival breakdown is a random variable

In this paper, a two stage production process is considered such that there is only one machine M1 in the first stage and two machines M2′, M2″ in the second stage. It is assumed that the output of M1 is the input for M2′, M2″. During the breakdown time of M1, a reserve inventory is suggested for M2′, M2″, to prevent the idle time, which is costlier. An inventory model is derived here based on certain assumptions to find the optimum size of the reserve inventory of the semi-finished product of the machine M1 to supply the machines M2′, M2″ till M1 resumes the function. Numerical illustrations are provided.

The formulation and solution of the task of the optimum reservation in the system of residual classes

The formulation and solution of the task of the optimum reservation in the system of residual classes

An Energy Management System With Optimum Reserve Power Procurement Function for Microgrid Resilience Improvement

Power system decentralization has been an emerging topic for the past decade in an effort to improve power quality and environment protection via the increased integration of renewable energy sources. Toward these objectives, decentralized microgrids have been proposed and thoroughly investigated in terms of technical capabilities and economic performance. In fact, the planning and actual operation of small-scale, decentralized microgrids have started in countries, such as Canada, Japan, USA, U.K., and other countries. It is expected that the research in this area will progress and eventually take over the existing paradigm of large-scale power generation in the future. These small-size decentralized microgrids could be connected with nearby microgrids under normal operating conditions, but under special events, such as natural or man-made disasters, they would be disconnected and run in an islanded mode. Under such a high impact, low probability events, the microgrid must have the resiliency to successfully re-connect with other microgrids and the main grid. In this paper, an energy management system (EMS) for a microgrid having a resiliency function, allowing to operate under the islanded mode after an accident, is proposed. The proposed tool, called Resilient Energy Management System (ResEMS), aims at procuring reserve power into the microgrid's battery energy storage system (BESS) effectively, by importing it from the nearby connected power system. The quantity of power to be imported is decided considering the value of the load, photovoltaic device generation, and the state of charge (SOC) of BESS. The accident is assumed to be a predictable natural disaster, which means that the accident occurrence date or time period can be estimated. The proposed ResEMS has been applied to a microgrid comprising of a BESS, a diesel generator, and several photovoltaic devices. The simulation results verify its beneficial operation.

Information disclosure in optimal auctions

This paper analyzes a situation in which the seller controls the accuracy of what potential buyers learn about their valuation of a good to be sold. This setting is related to many real situations such as home sales, antique auctions, and digital platforms such as Google and Facebook selling online advertising slots. Two important questions arise: what is the optimal selling mechanism, and what is the optimal disclosure policy of the seller. Under the assumption of private values, a simple auction with a reserve price is the optimal mechanism. What we show is that the amount of (costly) information provided increases with the number of potential bidders when using the optimal mechanism and is greater than when the object is always sold. Because information changes the distribution of a bidder’s expected valuations, the optimal reserve price also changes, so that the number of bidders (indirectly) affects the reserve price. We show that as the number of bidders increases, the optimal reserve price becomes more restrictive.