Integration of Interruptible Load Contracts in Supply Function Equilibrium Analysis for Electricity Markets

The interruptible load contract is a flexible and reliable resource that can help retailers reduce market risk in the form of an option contract. However, the mechanism of IL contract price formation and the representation of value are rarely considered in the study of interruptible load contracts, which helps reduce the contract price. It is studied in the paper that the optimal decisions by retailer in the day-ahead spot market under multiple types of interruptible load contracts. Four IL contracts are proposed considering the possibility of consumers' participation in demand response at different periods. The uncertain spot price is simulated by the stochastic scenario method, and a model for retailer's decision under multiple contracts is proposed by Conditional Value-at-risk assessment to maximize the expected profit. The presented model is a mixed-integer nonlinear programming problem, which is solved by CPLEX solver of GAMS software. The feasibility of the given decision strategy is verified through the numerical results.

The benefits of applying market demand models in engineering design have been well established. Arguably the most common approach has been to apply a random utility model, although any representation of market demand based on customers’ responses to surveys or in market situations can be used to this end. In practice, various methods have been used to collect market data through the use of surveys, typically based either on choices from among sets of alternatives or statements of willingness-to-pay. The applicability of the data collected has been limited, however, by the complexity of the relationships between market research methods and market demand models. The prospects of reusing an enormous amount of available market research data and increasing practitioners’ freedom in applying market research data to forecast market demand compel us to investigate the correspondence between market demand models. In this paper, we build on the recent work of Cook and Wissmann to demonstrate a bilateral correspondence between the popular multinomial logit model and Cook’s S-Model. Results from two independent case studies are presented showing that the utility function in a multinomial logit model may be reparameterized as a value function in the S-Model and vice-versa. The techniques demonstrated in this paper for defining direct comparisons between previously incompatible market research methods and demand models provide the practitioner with powerful new capabilities for validating market models, fusing market models to expand customer-based trade spaces, and presenting results to decision-makers in familiar formats.

Purpose In the hybrid electricity market, renewable energy power generator faces the uncertainty of power market demand and the randomness of the renewable energy generation output. In order to improve the grid-connected quantity of green power, the purpose of this paper is to design the pricing mechanism for renewable energy power generator with revenue-sharing contract in a two-stage “multi-single” electricity supply chain which contains a single dominant power retailer and two kinds of power suppliers providing different power energy species. Design/methodology/approach Considering the dual uncertainties of renewable energy power output and power market demand, the authors design the full-cooperative contract decision-making model, wholesale price contract decision-making model and revenue-sharing contract decision-making model to compare and optimize grid-connected pricing in order to maximize profit of different parties in power supply chain. Then, this paper performs a numerical simulation, discusses the existence of the equilibrium analytical solutions to satisfy the supply chain coordination conditions and analyzes the optimal contract parameters’ variation characteristics and their interaction relationship. Findings The authors find that the expected profits of the parties in the hybrid power supply chain are concave about their decision variables in each decision-making mode. The revenue-sharing contract can realize the Pareto improvement for all parties’ interest of the supply chain, and promote the grid-connected quantity of green power effectively. The grid-connected price will reduce with the increase of revenue-sharing ratio, and this impact will be greater on the renewable energy power. The greater the competition intensity in power supply side, the smaller the revenue-sharing ratio from power purchaser. And for the same rangeability of competition intensity, the revenue-sharing ratio reduction of thermal power is less than that of the green power. The more the government subsidizing green power supplier, the smaller the retailer sharing revenue to it. Practical implications Facing with the dual uncertainties of green power output and market demand and the competition of thermal power in hybrid electricity market, this study can provide a path to solve the problem of renewable energy power grid-connecting. The results can help green power become competitive in hybrid power market under loose regulations. And this paper suggests that the government subsidy policy should be more tactical in order to implement a revenue-sharing contract of the power supply chain. Originality/value This paper studies the renewable energy electricity grid-connected pricing under the uncertainty of power supply and market demand, and compares different contract decision-making strategies in order to achieve the power supply chain coordination. The paper also analyzes the competition between thermal power and renewable energy power in hybrid electricity market.

This paper presents a novel adaptive control strategy for integrating direct load control (DLC) with interruptible load management (ILM) to provide instantaneous reserves for ancillary services in deregulated power systems. Fuzzy dynamic programming is used to satisfy customers' requirements and yields a near optimal pre-scheduling of the DLC. Then, the energy payback associated with the DLC is further eliminated by the adaptive control strategy, which exploits interruptible loads to modify the DLC schedule in real-time. Through the developed adaptive control strategy, the influences of the load uncertainties and forecasting errors on the pre-scheduling of the DLC can also be excluded. The proposed algorithm was practically tested on the Taiwan power (Taipower) 38-unit system with 20 air-conditioner loads and 15 interruptible loads. The outcomes reveal that an exact amount of instantaneous reserves can be successfully acquired, and the results are robust against dynamic disturbances of the power system.

The existence of uncertainty influences the investment, production and pricing decision of firms. Therefore, capacity expansion models need to take into account uncertainty. This uncertainty, may arise because of errors in the specification, statistical estimation of relationships and in the assumptions of exogenous variables. One such example is demand uncertainty. In this paper, a cautious capacity planning approach is described for solving problems in which robustness to likely errors is needed. The aim is to cast the problem in a deterministic framework and thereby avoid the complexities inherent in nonlinear stochastic formulations. We adopt a robust approach and minimize an augmented objective function that penalises the sensitivity of the objective function to various types of uncertainty. The robust or sensitivity approach is compared with Friedenfelds' equivalent deterministic demand method. Using numerical results from a large nonlinear programming capacity planning model, it is shown that as caution against demand uncertainty increases, the variance of the total objective function (profit) decreases. The cost of such robustness is a deterioration in the deterministic risky performance. This method is also applied to an industry simulation model in order to assess the effect of uncertainty in market demand on optimal capacity expansion and capacity utilisation.

Interruptible load (IL) management as an important component of demand-side management in electricity market affects much the safe and economic operation of the power systems. The cost-benefit of interruptible load participants is analyzed in this paper. The discrete customer category is proposed to indicate the expected compensation for the blackout. This paper presents a model of IL contract, in which the objective function is the minimum compensation cost paid by the power company. The benefits of the power company and the customer are both considered as the restrictions of the model. The actual system examples show the validity of the proposed model.

Uncertainty in market demand often leads to regional inventory imbalances. Transshipment has become a key strategy to address these mismatches by redistributing inventory, improving service levels, and enhancing supply chain efficiency. This paper provides a systematic review of transshipment research from 2015 to 2025, categorizing the literature into three domains: transshipment among retailers, in omnichannel supply chains, and in manufacturing and logistics contexts. We identify major research trends and highlight key gaps, including the lack of integrated strategies that combine transshipment with supply chain contracts, and the underutilization of AI-driven methods—such as machine learning and reinforcement learning—for supporting transshipment decisions in complex and uncertain environments. This review aims to offer useful insights for future research on transshipment strategies in increasingly complex and data-rich supply chain environments.

With the rapid development of distributed generations (DGs) and interruptible loads (ILs), distribution network company can actively purchase electricity in market instead of playing as a traditional passive purchaser. This study proposes a stochastic bi‐level model‐based strategic trading model for an active distribution company (ADisCo) which operates the active distribution network (ADN) to maximise its profit in electricity market. Uncertainties pertaining to bidding and offering prices of other market rivals’, the imbalance prices in the balance market and the productions of DGs are considered via stochastic programming. Besides, a linear ADN operation model is proposed to ensure ADN operation security within the stochastic programming model. The proposed model is initially formulated as a stochastic bi‐level model, where the upper‐level problem represents the maximisation of the profit of ADN operator, whereas the lower‐level model represents the maximisation of the social welfare in clearing of market from the perspective of independent system operator. On the basis of the complementarity theory, the proposed model can be transformed into a mixed integer linear programming model. Case studies demonstrate the efficiency and effectiveness of the proposed strategic trading model for an ADisCo with DGs and ILs.

Hydrothermal systems play a significant role in electric energy systems as important power generation units, which have been studied in previous researches considering remarkable efforts. The optimal short-term hydrothermal scheduling (STHS) aims to attain optimal production scheduling of thermal and hydro plants for determining minimum operation cost of providing demand in the determined time interval. Different constraints should be studied in the solution of such issue containing limitations associated with water discharge, water storage, power production of plants, power balance of the system and water balance of hydro plants. In addition, valve impacts of thermal plants and complex hydraulic coupling of hydro plants are the other operational and technical constraints. In this study, the robust stochastic STHS is studied considering market price and demand uncertainties. Accordingly, robust optimization method is employed in this study to model price uncertainties. In addition, the uncertainties of load demand are handled using scenario-based modeling procedure. The scheduling problem of hydrothermal system is studied in a deregulated environment, where the hydrothermal system belongs to the private company and is capable to sell the surplus generated power to the market. Accordingly, the company aims to obtain maximum profit by selling power to market in addition to supplying power demand of the company. The introduced scheme for stochastic robust STHS is simulated and the provided solutions are investigated to verify the effectiveness of the scheme.

There are two compensation methods for interruptible loads (ILs), namely low price compensation before supply unavailability and high price compensation after supply unavailability. Low price compensation is independent of power supply unavailability, while the high compensation is performed only after actual power supply unavailability. However, the IL with low price (ILL) and the IL with high price compensation (ILH) have only been studied separately till now. Based on risk management, this paper analyzes the different economic properties of the two compensation methods and concludes that their coordination is beneficial to restrain market power and reduce the cost of reserve capacity. The authors propose the coordination models and optimization algorithms by taking the sum of the deterministic reduction of revenue resulting from ILL and the risk of compensating ILH as the objective function. Simulation results are presented to validate the effectiveness of the proposed method.

Interruptible load management plays an important role in maintaining the reliability and security of power systems and reducing price spike of power markets, thus has been widely used in power systems. Interruptible loads dispatch problem with multi-period and multi-interruptible-load is usually a multi-objective, combinatorial optimization problem, and its solution method needs to be carefully investigated. Application of intelligent optimization algorithms to the multi-period interruptible load dispatch problem is discussed in this paper. Multi objectives, such as minimizing the interruption payments and interruption frequency, can be included in the proposed interruptible load dispatch model. The characteristics of different interruptible loads are also considered. Numerical simulations using discrete binary particle swarm optimization (BPSO) and the genetic algorithm (GA) show that the BPSO can obtain better solutions than that of the GA. Thus the BPSO presents better potentials in solving the interruptible load dispatch problem.

Wang, W.; Ren, Y.; Bian, W., and Jia, X., 2019. Low-carbon marine logistics network design under double uncertainty of market demand and carbon trading price. In: Gong, D.; Zhu, H., and Liu, R. (eds.), Selected Topics in Coastal Research: Engineering, Industry, Economy, and Sustainable Development. Journal of Coastal Research, Special Issue No. 94, pp. 30–39. Coconut Creek (Florida), ISSN 0749-0208.This paper discusses the low-carbon marine logistics network design problem under the uncertainty of market demand and carbon emission price, and aims at the minimum cost of shipping logistics network operation (including carbon emission cost), and constructs a three-level marine logistics network site-distribution model based on scenario. The problem is transformed into an unconstrained optimization problem by the penalty function method, and the artificial bee colony algorithm (ABC) is used to solve the model. The study found that the moderate fluctuation of demand is conducive to the integration effect of the marine logistics network, which reduces the total cost of the logistics network. Finally, the validity of the model is verified by an example analysis of a domestic industrial product manufacturer.

Firms adjust to differences in market size and demand uncertainty by changing the frequency and size of their export shipments. In our inventory model, transportation costs and optimal shipment frequency are determined on the basis of demand as well as inventory and per shipments costs. Using a cross section of monthly firm-product-destination level French export data we confirm that firms adjust on both margins for market size. In a stochastic setting, firms adjust to increased uncertainty by reducing their sales and, for a given export volume, by reducing their number of shipments and increasing their shipment size

Shipment Frequency of Exporters and Demand Uncertainty

Introduction As renewable energy generation enters a new phase of development, government policies have shifted from a single subsidy to a combination of subsidies for renewable energy consumption and renewable portfolio standards (RPS). The effectiveness of these new policies requires further exploration. Methods This study establishes a “many-to-one” electricity supply chain model under the dual policy framework of renewable energy consumption subsidies and RPS policies, involving competitive renewable energy generators, fossil-fueled generators, and electricity retailers. The model considers the randomness of renewable energy generation and the uncertainty of market demand, with equilibrium decisions derived using a single-period sequential Stackelberg game under different bidding sequences. Results The study finds that as the government increases the subsidy for the per-unit consumption of renewable energy, the wholesale prices of both renewable and fossil-fueled electricity decrease. The increased subsidy boosts electricity retailers' procurement of renewable electricity while reducing their procurement of fossil-fueled electricity. Additionally, an increase in RPS leads to a decline in wholesale prices but, contrary to intuition, reduces both renewable and fossil-fueled electricity procurement and decreases profits for all participants. Discussion Interestingly, as competition in the renewable and fossil-fueled electricity markets intensifies, when generators adopt a bidding-prioritized strategy, electricity retailers' procurement of electricity from these generators decreases. These findings suggest that policy design must carefully account for market competition and bidding strategies to optimize renewable energy adoption.