Marginal Pricing Scheme Research Articles

An optimization-based partial marginal pricing method to reduce excessive consumer payment in electricity markets

Among the pricing schemes, locational marginal pricing is the most widely adopted scheme in current electricity markets. Despite the nice properties, theoretical study and practical experience have shown that considering the strategic bidding behaviors of market participants, locational marginal pricing may result in excessive consumer payment and prejudices market efficiency. In this paper, we propose an optimization-based partial marginal pricing method to reduce consumer payment under strategic bidding. The advantages of the locational marginal pricing method are reserved to the best extent while the remaining problems are delicately handled. To achieve this, we first analyze the characteristics and problems of the locational marginal pricing scheme and present a partial marginal pricing structure. Second, we establish an optimization-based partial marginal pricing model, in which discriminatory price components are introduced in price formulation and the pricing properties including competitive equilibrium and revenue adequacy are formulated as constraints. Third, to verify the performance of the proposed pricing scheme considering the strategic bidding, a bi-level strategic bidding problem of the generator under the proposed pricing method is established and transformed into a mixed integer linear programming problem. The numerical results indicate that under the conventional pricing methods, the consumer payments under strategic bidding can be up to 16.67 times higher than those under truthful bidding, while the proposed method can effectively reduce excessive consumer payments by 92.1% while maintaining the desired pricing properties.

Load Shifting Demand Response in Energy Scheduling Based on Payment Cost Minimization Auction Mechanism

Demand response (DR) is proven to be very efficacious for load mitigation especially in peak time period. On the other hand, DR facilitates both consumers, system operator as well as producers to moderate their payments while reducing system operating costs. Offer cost minimization is currently used as the clearing mechanism associated with locational marginal pricing scheme to determine the consumers’ payments. Such clearing and pricing mechanisms are inconsistent as the system costs is being minimized, while the payments are calculated based upon marginal prices. Payment cost minimization auction as a price-based clearing mechanism is envisaged to be an effective alternative to solve such a crucial issue. This paper shows how to include DR in PCM mechanism to further reduce the consumers’ payment. It facilitates utilizing price responsive consumers for load shifting DR in a PCM auction. The optimization problem is modeled as a mixed-integer nonlinear bi-level programming. Duality theorem, KKT conditions and integer algebra are used to convert such a complicated optimization problem to a single level MILP problem. This problem is then solved by CPLEX in GAMS. The impacts are studied by implementing the proposed formulation to solve the clearing problem in the case studies deriving promising numerical results.

A Unified Approach to Pricing Under Nonconvexity

Nonconvexity in electricity markets creates difficulties in the pricing of electricity today. Equilibrium prices often do not exist, and some forms of side payments are required to provide revenue adequacy for cleared offers and bids in markets. To improve market efficiency and transparency, academia and industry have proposed different pricing schemes, each of that emphasizes only a certain aspect of the desired price. In this paper, we summarize the existing pricing objectives and propose a unified model for pricing under nonconvexity. The tradeoff among competing objectives can be modeled. A specific example of the unified nonconvexity pricing model is presented, which can be regarded as a general representation of the convex hull pricing method and the commonly adopted locational marginal pricing scheme. The primal formulation of this model is derived. The economic insight of the convex hull pricing method is illustrated based on this model. An extreme-point-based solution method is presented. The proposed pricing model establishes a framework for analyzing the tradeoff among different objectives for pricing under nonconvexity and provides an opportunity to construct more economically justifiable prices through a modification of the objective function and constraints of the proposed pricing model.

A community microgrid architecture with an internal local market

This work fits in the context of community microgrids, where members of a community can exchange energy and services among themselves, without going through the usual channels of the public electricity grid. We introduce and analyze a framework to operate a community microgrid, and to share the resulting revenues and costs among its members. A market-oriented pricing of energy exchanges within the community is obtained by implementing an internal local market based on the marginal pricing scheme. The market aims at maximizing the social welfare of the community, thanks to the more efficient allocation of resources, the reduction of the peak power to be paid, and the increased amount of reserve, achieved at an aggregate level. A community microgrid operator, acting as a benevolent planner, redistributes revenues and costs among the members, in such a way that the solution achieved by each member within the community is not worse than the solution it would achieve by acting individually. In this way, each member is incentivized to participate in the community on a voluntary basis. The overall framework is formulated in the form of a bilevel model, where the lower level problem clears the market, while the upper level problem plays the role of the community microgrid operator. Numerical results obtained on a real test case implemented in Belgium show around 54% cost savings on a yearly scale for the community, as compared to the case when its members act individually.

Stochastic Market Clearing With Revenue Sufficiency Constraints

Revenue insufficiency is a major problem in market designs built on unit commitment and marginal pricing based remuneration schemes. Varied financial mechanisms and market clearing procedures have been adopted by different electricity markets to address this problem. But these schemes are based on deterministic market clearing algorithms. To the best of the authors’ knowledge, there has been no work done in ensuring revenue sufficiency in stochastic market clearing algorithms in the manner adopted in the proposed work. With the increasing penetration of renewable sources of energy, it has become imperative to adopt market equilibrium solutions that consider the dynamism of renewable sources of energy along with a guarantee of revenue sufficiency. This paper presents a novel stochastic market clearing procedure wherein the mathematical formulation explicitly includes the marginal pricing scheme into its modeling features. Recourse approach has been adopted to include the uncertainties associated with renewable sources of the system into the market clearing strategy. The entire problem has been formulated as a mixed integer linear programming (MILP) problem with marginal pricing being a part of the unknown decision variables. Dual variables of a security constrained economic dispatch problem is used for implementing revenue constrained stochastic market clearing model. The proposed model is validated using a three bus network with wind penetration that has wind forecast presented as scenarios over a time horizon of four hours.

Economic valuation of smart grid investments on electricity markets

Abstract Many countries are establishing regulatory guidelines to promote the integration of smart grid technologies with the aim of improving the efficiency of the power system. This paper analyzes how the investment costs of the different smart grid applications installed by network operators can be recovered in the short-term when a locational marginal pricing scheme is applied. This issue has been previously addressed in literature with simple economic models where the multilevel structure of the smart grid is not considered. As a key contribution, this paper presents a new social welfare optimization model considering implementation strategies with different expenditure levels in smart grid technologies where specific applications as renewable distributed generation, network automation, demand–response and reactive power management are explicitly considered. The proposed model has been implemented using a 3-node illustrative example and a 149000-node network under real-world conditions. Results show how a progressive implementation of smart grid applications can produce increased system efficiency and social welfare, in particular when demand–response is enabled. Results also show how the costs of demand–response applications applied in weak power systems are suitable to be recovered in the short-term with marginal revenues of the network provider.

Marginal cost pricing for system optimal traffic assignment with recourse under supply-side uncertainty

Transportation networks are often subject to fluctuations in supply-side parameters such as capacity and free-flow travel time due to factors such as incidents, poor weather, and bottlenecks. In such scenarios, assuming that network arcs exist in a finite number of states with different delay functions with different probabilities, a marginal cost pricing scheme that leads to a socially optimal outcome is proposed. The suggested framework makes the behavioral assumption that travelers do not just choose paths but follow routing policies that respond to en route information. Specifically, it is assumed that travelers are fully-rational and that they compute the optimal online shortest path assuming full-reset. However, such policies may involve cycling, which is unrealistic in practice. Hence, a network transformation that helps restrict cycles up to a certain length is devised and the problem is reformulated as a convex optimization problem with symmetric delay functions. The results of numerical tests on the Sioux Falls test network are presented using the Frank–Wolfe algorithm.

On the Solution of Revenue- and Network-Constrained Day-Ahead Market Clearing Under Marginal Pricing—Part II: Case Studies

This paper presents the numerical analysis of the bilevel programming approach for revenue- and network-constrained market clearing developed in its companion paper. The impact of minimum revenue conditions and minimum declared profits on generation and consumption levels as well as on locational marginal prices for energy is examined in detail through three case studies. First, the results from an illustrative example including minimum revenue conditions are comprehensively analyzed. The second case study is based on the IEEE Reliability Test System and considers minimum declared profits. In the third case study, a modified version of the IEEE 118-bus system is tested while accounting for minimum revenue conditions. In addition, the computational behavior of the proposed approach is illustrated with several case studies including the IEEE 300-bus system. Numerical results show the effectiveness of the proposed approach to handle revenue constraints as well as its superiority over the heuristic currently implemented in the Iberian electricity market. Moreover, simulations reveal that, unlike previous works in the literature, generation revenue constraints can be precisely incorporated in day-ahead market clearing while explicitly considering the standard economic-dispatch-based marginal pricing scheme and without requiring price uplifts.

Value‐based reserve market settlement

The main focus of this study is on reserve market settlement in an electricity market with marginal pricing scheme as the pricing mechanism. Following a day-ahead market clearing, the marginal prices are found using the appropriate Lagrange multipliers as the bi-products of the optimisation process. The payments to energy and reserve providers can then be found based on these prices. However, it is hard to find an appropriate settlement scheme that provides the fair and justifiable consumer payments based on marginal pricing scheme considering the actual reserve functions in power systems. In this study, a reserve marginal pricing that is based on a proper reserve marginal price definition and considers the free market requirements and accounts for the lost opportunity of selling the convertible products is proposed. Also, a value-based reserve market settlement scheme is proposed in this study that is justifiable for customers and best suits the actual reserve functions in the system. In the proposed settlement scheme, the reserves are eliminated one after the other and the loss of load (LL) and generation is then calculated for market participants in different contingencies via a novel optimal power flow that finds the fair and optimal LLs and generations. The reserve market is then settled based on the LLs and generations in different contingencies. The proposed reserve pricing and settlement schemes are tested on a 3-bus system, a 6-bus system, and the 24-bus reliability test system to show the effectiveness of the proposed method.

Incorporating Price-Responsive Demand in Energy Scheduling Based on Consumer Payment Minimization

In the restructured power industry, demand responsiveness is a key factor whose importance will be boosted due to the impetus provided by the development of smart grids. Within the context of pool-based electricity markets, this paper addresses the incorporation of price-responsive demand in multiperiod energy scheduling driven by consumer payment minimization. Although consumer payment minimization has drawn considerable attention mainly in an operational setting and also recently under a planning framework, available models and solution approaches typically neglect demand-side participation. The proposed scheduling model considers a marginal pricing scheme as well as the effects of both network constraints and intertemporal constraints associated with generation operation. Modeling demand-side participation leads to bilinear payment terms that significantly increase the mathematical complexity of the optimization process. The resulting problem is formulated as a mixed-integer nonlinear bilevel program for which no exact solution technique is currently available. This paper presents a novel methodology by which the original bilevel and bilinear problem is converted into an equivalent single-level mixed-integer linear program suitable for efficient off-the-shelf software. This transformation is based on the application of duality theory of linear programming, integer algebra, and Karush–Kuhn–Tucker optimality conditions. The proposed approach has been successfully applied to the IEEE 118-bus system.

Evolutionary Marginal Cost Pricing Scheme Implementation Based on Stochastic Traffic Flow Information

Traditionally, to implement the first-best marginal cost pricing scheme in a traffic network requires the information on the exact demand function or true origin-destination demand, which, however, is rarely available in practice. To overcome this dilemma, the trial-and-error method has been proposed to find the marginal cost toll through an iterative process using the observed traffic volumes. This method guarantees the convergence of tolls and flows to the system optimal state under the assumption of deterministic traffic conditions. However, in reality, the uncertainty of transportation network has been recognized well that induces the variability of link flow and travel time. Therefore, this paper proposes an evolutionary implementation method that iteratively finds the first-best marginal cost toll pattern according to the observed stochastic link flow information and the known travel time functions. The proof of the convergence of the iterative algorithm is presented. The paper also analyzes the effect of the sampling error of the link flow data on the convergence of the algorithm and shows that the biases from the flow observation will not affect the convergence. The numerical tests are provided for the illustration of the algorithm.

Dynamic Strategies and Management of Focusing Devices

This paper examines how dynamic strategies and underlying focusing devices lead to dynamic competitive advantage. Our methodology is an analysis based on the simple mode of focusing device and innovation. We show that quality-improving and cost-reducing strategies are facilitated under a productivity-based pricingscheme, while a hybrid strategy is favoured by having a marginal productivity-based pricing scheme as the underlying focusing device of innovation. We also argue that a hybrid strategy achieves dynamic efficiency, so that cost-reducing and quality-improving strategies should converge towards ahybrid strategy over time, to attain dynamic competitive advantage. The implications of these results are threefold. First, the firm should determine the appropriate direction of innovationtrajectories, rather than a competitive position. Second, the firm should identify its current focusing device and examine whether it is congruent with the desired dynamic strategy. Third, over the long term, the firm should adopt a hybrid strategy. The value of this paper is significant as it provides the formal model of dynamic strategies.

Active Participation of Demand Through a Secondary Ancillary Services Market in a Smart Grid Environment

An optimization model that incorporates demand in the paradigm of smart grids and distributed generation is formulated. The objective is to transform the demand into an active agent that helps minimizing costs incurred by a distribution company for energy purchases and capacity payments, in a cost based marginal pricing scheme, also extrapolated to market based bids. The development of a secondary market for ancillary services offered by demand is proposed, with local intelligence and distributed generation, operating in a similar way to a day ahead market. Existing resources from the demand-side are provided to allow hourly market adjustments. The demand uncertain future is modeled via preference models using discrete choice methods. Portfolios of incentives, tailored to demand needs and preferences, are built. Consumption profiles of users are identified from synthetic curves and real consumption profiles, associated to large customers. NYISO time series data are used to illustrate the mechanism operation. The optimization model may be easily integrated into any management model of a market operator or within electricity distribution and traders. The only requirement for proper incorporation is the use of two-way communications for coordinating with the customers in the smart-grid and distributed generation paradigm.

Toll pricing framework under logit‐based stochastic user equilibrium constraints

SUMMARYThis paper addresses the toll pricing framework for the first‐best pricing with logit‐based stochastic user equilibrium (SUE) constraints. The first‐best pricing is usually known as marginal‐cost toll, which can be obtained by solving a traffic assignment problem based on the marginal cost functions. The marginal‐cost toll, however, has rarely been implemented in practice, because it requires every specific link on the network to be charged. Thus, it is necessary to search for a substitute of the marginal cost pricing scheme, which can reduce the toll locations but still minimize the total travel time. The toll pricing framework is the set of all the substitute toll patterns of the marginal cost pricing. Assuming the users' route choice behavior following the logit‐based SUE principle, this paper has first derived a mathematical expression for the toll pricing framework. Then, by proposing an origin‐based variational inequality model for the logit‐based SUE problem, another toll pricing framework is built, which avoids path enumeration/storage. Finally, the numerical test shows that many alternative pricing patterns can inherently reduce the charging locations and total toll collected, while achieving the same equilibrium link flow pattern. Copyright © 2013 John Wiley & Sons, Ltd.

Bisection-based trial-and-error implementation of marginal cost pricing and tradable credit scheme

The purpose of this paper is three fold: First, it demonstrates the non-convergence of the bisection method proposed in the literature for the trial-and-error implementation of the marginal-cost pricing in the absence of a demand function. Second, it provides a modified version of the bisection method and establishes its convergence. Third, it adapts the modified bisection method for the trial-and-error implementation of the tradable credit scheme proposed recently, which can emulate a congestion pricing system in a revenue-neutral manner.

A Unified Bilevel Programming Framework for Price-Based Market Clearing Under Marginal Pricing

Market clearing in restructured power systems is mostly implemented through an offer-based setting with the goal of maximizing social welfare. This approach leads to sound results from an economic viewpoint when generation offers reflect true production costs. However, offers may significantly differ from actual costs in practice, thus yielding undesired distortion. Under a marginal pricing scheme, this paper presents a general bilevel programming framework for alternative market-clearing procedures dependent on market-clearing prices rather than on offers. The resulting nonlinear mixed-integer bilevel programming formulation is transformed into an equivalent single-level mixed-integer linear program suitable for efficient off-the-shelf software. The bilevel formulation is investigated through a particular instance of price-based market clearing driven by consumer payment minimization. This problem has recently received considerable attention due to the open challenges posed from both modeling and computational perspectives. Numerical results are provided to illustrate the performance of the proposed approach.

On the Effects of Central Japan Expressway's Commuter Toll Discount Policy in Nagoya Area

Road pricing policies have two equally important objectives that have to be considered: the optimal use of the road network and the fiscal sustainability for the management of the network. The aim of this work is to examine the effects on these two objectives of a recent pricing policy implemented in Japan's expressway networks. Recently the Nippon (Japan) Expressway Companies (NEXCO, operators of Japan's nation wide expressway network) have implemented several toll discount policies for users equipped with electronic toll collectors (ETCs). One of the policies is the commuter discount policy that discounts 50% for a journey on the NEXCO expressway no longer than 100 km during the commuting peak hours. This paper examines its effect on congestion reduction in the road network of Nagoya area and its influence on the use of expressways operated by another major local public expressway company in Nagoya. The congestion easing effect of this policy is compared with a potential marginal cost pricing scheme. These observations suggest that policy coordination regarding toll levels is needed for expressway corporations and transportation authorities for improving transportation efficiency of utilization of the whole network.

A comparison of Nash equilibria analysis and agent-based modelling for power markets

In this paper we compare Nash equilibria analysis and agent-based modelling for assessing the market dynamics of network-constrained pool markets. Power suppliers submit their bids to the market place in order to maximize their payoffs, where we apply reinforcement learning as a behavioral agent model. The market clearing mechanism is based on the locational marginal pricing scheme. Simulations are carried out on a benchmark power system. We show how the evolution of the agent-based approach relates to the existence of a unique Nash equilibrium or multiple equilibria in the system. Additionally, the parameter sensitivity of the results is discussed.

Placement and Penetration of Distributed Generation under Standard Market Design

Distributed Generation (DG) can help in reducing the cost of electricity to the costumer, relieve network congestion and provide environmentally friendly energy close to load centers. Its capacity is also scalable and it provides voltage support at distribution level. Hence, DG placement and penetration level is an important problem for both the utility and DG owner. The cost of electricity as a commodity depends upon market model. The restructured power markets are slowly maturing with standardizations like Standard Market Design (SMD). The key feature of SMD is the Locational Marginal Pricing (LMP) scheme. This paper examines placement and penetration level of the DGs under the SMD framework. The proposed approach is illustrated by case studies on MATPOWER 30 bus and IEEE 118 bus systems.

Airport marginal cost pricing: discussion and an application to Swedish airport

In this paper, an optimal airport-pricing model is derived, both with and without a constraint on the revenues, that includes all relevant external marginal costs. Given the results of the model, the implications on the profit of airports are discussed. It was found that, given that proceeds of the environmental charges are seen as revenue for the airport, it is not obvious that a marginal cost-pricing scheme would result in financial deficits for the airports, despite the reasonable assumption of increasing returns to scale in airport capacity. Using relatively crude estimates of the marginal costs, the current pricing scheme is compared with a marginal cost pricing scheme. Findings show that the effect on revenues of moving towards a marginal cost pricing scheme may not be so dramatic; especially not if the marginal external costs include estimated marginal costs of carbon dioxide emissions.