Locational Marginal Prices Research Articles

An electricity and carbon trading mechanism integrated with TSO-DSO-prosumer coordination

Due to the proliferation of distributed renewable energy, bidirectional electricity and carbon interaction appears in the coordinated transmission and distribution network and increases complexity in entities' decision-making. To address the issues, this paper develops a hierarchical market framework integrated with electricity and carbon trading. Specifically, an electricity market which combines locational marginal price (LMP) and peer-to-peer (P2P) trading is established considering transmission and distribution coordination. Meanwhile, based on carbon emission flow and P2P trading, a hierarchical coordinated carbon market is also designed to precisely measure and price carbon responsibility and contribution from prosumers. In addition, a hierarchical distributed algorithm is developed to clear the proposed market with privacy protection. Numerical results authenticate the necessity for transmission and distribution coordination, benefits of distribution electricity P2P trading as well as superiority in carbon measurement and pricing method.

Robust planning for distributed energy storage systems considering location marginal prices of distribution networks

Energy storage plays an important role in integrating renewable energy sources and power systems, thus how to deploy growing distributed energy storage systems (DESSs) while meeting technical requirements of distribution networks is a challenging problem. This paper proposes an area-to-bus planning path with network constraints for DESSs under uncertainty. First, a distribution location marginal price (DLMP) formulation with maximum fluctuation boundaries of uncertainties is designed to select vulnerable areas exceeding voltage limits and higher line losses that occur in distribution networks. Different from simple multi-scenario power flow calculation and sensitivity analysis, DLMP with time and regional characteristics could be more intuitive to reflect line losses and voltage limits of distribution networks through price signals. After that, a two-stage stochastic robust optimization based planning method is developed to determine locations and capacities of DESSs in vulnerable areas. To make the uncertainty problem more tractable, stochastic scenarios are used to portray upper and lower boundaries of uncertainties, which avoids too-conservative decisions for robust optimization. Finally, numerical tests are implemented to testify the reasonability and validity of the proposed area-to-bus planning path under uncertainty. Compared with the DESSs planning framework without DLMP, the costs of DESSs are observably reduced with DLMP. With same budgets of uncertainty, investment costs of DESSs for the stochastic robust optimization with 30 and 50 scenarios are 3.91% and 4.45% lower than classical adaptive robust optimization (ARO).

Incentive-compatibility auction and renewable energy pricing strategy based on incomplete Information game of price cost declaration

ABSTRACT The construction and development of the Electricity Spot Market (ESM) are beneficial to the fair distribution of power resources and the improvement of power system regulation ability. The original ESM was not designed to include renewable energy. Since there is almost no marginal cost for renewable energy, the renewable energy can not copy the thermal power unit price model after participating in ESM. The prevalent Locational Marginal Price (LMP) mechanism within the extant ESM structure encounters limitations wherein optimal benefits accrue to buyers and sellers only under specific conditions. This paper thus introduces an innovative electricity pricing model and trading settlement strategy tailored to the characteristics of wind turbine-generated power. To begin, we devise a novel electricity pricing model grounded in the construction expenses and predictive precision intrinsic to renewable energy sources. Subsequently, in synergy with the ESM framework, we formulate a Bayesian game model to compute benefits contingent upon bid success probabilities. A pricing strategy based on Vickrey – Clarke – Groves (VCG) is selected, which pays the other generating strategy as an incremental cost by removing itself. Empirical evaluations affirm the efficacy and rationality of the proposed approach. The outcomes of our study not only validate its applicability but also lay the groundwork for a fresh theoretical paradigm underpinning energy trading modalities in future ESM contexts.

Random block-coordinate methods for inconsistent convex optimisation problems

We develop a novel randomised block-coordinate primal-dual algorithm for a class of non-smooth ill-posed convex programs. Lying midway between the celebrated Chambolle–Pock primal-dual algorithm and Tseng’s accelerated proximal gradient method, we establish global convergence of the last iterate as well as optimal O(1/k) and O(1/k^{2}) complexity rates in the convex and strongly convex case, respectively, k being the iteration count. Motivated by the increased complexity in the control of distribution-level electric-power systems, we test the performance of our method on a second-order cone relaxation of an AC-OPF problem. Distributed control is achieved via the distributed locational marginal prices (DLMPs), which are obtained as dual variables in our optimisation framework.

Topology-Aware Graph Neural Networks for Learning Feasible and Adaptive AC-OPF Solutions

Solving the optimal power flow (OPF) problem is a fundamental task to ensure the system efficiency and reliability in real-time electricity grid operations. We develop a new topology-informed graph neural network (GNN) approach for predicting the optimal solutions of real-time ac-OPF problem. To incorporate grid topology to the NN model, the proposed GNN-for-OPF framework innovatively exploits the locality property of locational marginal prices and voltage magnitude. Furthermore, we develop a physics-aware (ac-)flow feasibility regularization approach for general OPF learning. The advantages of our proposed designs include reduced model complexity, improved generalizability and feasibility guarantees. By providing the analytical understanding on the graph subspace stability under grid topology contingency, we show the proposed GNN can quickly adapt to varying grid topology by an efficient re-training strategy. Numerical tests on various test systems of different sizes have validated the prediction accuracy, improved flow feasibility, and topology adaptivity capability of our proposed GNN-based learning framework.

Optimal Power Flow of Power System with Static VAR Compensator using Moth Flame Optimization with Locational Marginal Price

The determination of a generation unit's locational marginal price (LMP), which depends on our understanding of transmission line capacity and optimal power flow (OPF) based on reality, is crucial to evaluating the performance of the unit and determining its profit. Minimising the total cost of the generators will lower the price of electricity on the market. Since power flow equations are nonlinear, numerical and repetition-based approaches should be used to solve them. The equations in this paper are solved using a Moth Flame Optimization (MFO), and to enhance the performance of the MFO in its structure, for simultaneous calculations of power passing through in transmission lines so that by learning about the capacity of transmission lines, in addition to the optimal power flow becoming a reality, the price of electricity is determined using uniform market pricing, or LMP method. The FACTS device used for the problem is Static Var Compensator (SVC). Finally, values for bus voltages, line losses, power injected to buses, power travelling via lines, total generating costs, and generator profits would be included in the output of the proposed MFO algorithm. Additionally, the results of testing the proposed methodology on the IEEE 30-BUS network reveal improvements on the OPF problem.

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.

Opportunities for wave energy in bulk power system operations

Wave energy resources have high, yet largely untapped potential as candidate generation technology. In this paper, we perform a data-driven analysis to characterize the impact of wave energy integration on bulk-scale power systems and market operations. Through data-driven sensitivity studies centered on an optimization-based production cost modeling formulation, our work characterizes the inflection point beyond which wave integration starts impacting power system operations, considering present day transmission infrastructure. Furthermore, our analysis also considers the joint effects of wave energy integration and system-wide transmission expansion. Finally, potential resilience scenarios such as wildfire-driven transmission contingencies and heat wave events are investigated, whereby the contributions of grid-integrated wave energy in alleviating the effects of the resilience events are analyzed. As our demonstration test bed, we consider a reduced-order network topology for the U.S. Western Interconnection with wave energy generation integrated at carefully selected sites across the coastal areas of Washington, Oregon, and northern California. Our results indicate that over a representative year of operations, wave energy integration systematically reduces locational marginal prices (LMPs) of energy and price volatility, especially during periods of high wave resource availability (winter months for the U.S. west coast). Average, maximum, and minimum of hourly LMPs over a typical year of operation was reduced by 2.95, 51.28, and 1.13 $/MWh respectively (over a baseline scenario with no wave energy integration), when the selected network model had a total of 5000 MW wave power installed capacity during the representative year of study. The effects of wave energy integration can remain localized with existing transmission infrastructure (identified to be most pronounced in the Pacific Northwest region in the example we studied). However, with concurrent transmission expansion, the impacts of wave energy integration are likely to have a higher geographical spread. Our results also indicate that wave energy may be able to assist power system operations during resilience events such as major transmission contingencies and heat wave events, although such benefits might be dependent on factors such as proximity of affected area to wave resources, availability of adequate resource potential and adequate transmission capacity.

A Dataset for Electricity Market Studies on Western and Northeastern Power Grids in the United States

Efficient electricity market operations and cost-effective electricity generations are fundamental to a low-carbon energy future. The Western Electricity Coordinating Council (WECC) and Northeast Power Coordinating Council (NPCC) systems were built to provide efficient electrical grid simulation solutions for their respective U.S. regions. Data reuse for electricity economic studies remains a challenge due to the lack of credible and realistic economic data. This paper delivers a comprehensive dataset containing generator aggregations, generator costs, transmission limits, load distributions, and electricity prices for the WECC and NPCC systems based on real-world grid operation data at year 2020, including power plant geographic locations, generation profiles, regional power flow interchanges, and load distributions in both regions. The electricity price from the developed dataset is simulated based on the other items in the dataset, and we show that the variation of the simulated electricity price reasonably aligns with the real-world electricity price in both the WECC and NPCC regions. Overall, the developed dataset is of interest for various electricity market and economic studies, such as the economic dispatch and locational marginal price (LMP) analysis.

Profit Extension of a Wind-Integrated Competitive Power System by Vehicle-to-Grid Integration and UPFC Placement

Profit maximization is critical in the control of power system networks for both power providers and users. Electrical energy is freely accessible in the electrical grid during off-peak hours, with storage units helping to store excess energy and assist the electrical grid during high-demand situations. Such techniques promote grid stability and ensure safe operation. Because renewable resources are intermittent, energy storage technologies are especially significant in renewable-associated power systems. Vehicle-to-grid (V2G) technology has recently acquired popularity in preserving power grid stability in the presence of renewable resources.V2G technology employs automobiles as mobile storage devices and focuses on the efficient utilization of extra power available during off-peak hours. The goal of this work is to improve the functioning of a V2G system in a power network to reduce energy production costs while increasing system profitability. This study for deregulated power environments also depicts the influence of V2G mixing on system voltage profile and locational marginal pricing (LMP), as well as the performance of the Unified Power Flow Controller (UPFC) on system economics. The MiPower simulation program is used in the study to find the best placement of the power storage unit for the modified IEEE 14-bus system.

Simulating Generalised Locational Marginal Pricing for Power Markets in East Africa

There is an enormous opportunity for adopting a wholesale electricity market under locational marginal pricing. Besides ensuring competition and accounting for network congestion, the price signal reflects a space-time electricity economy. This paper examines the prospects of introducing a single East African electricity market in five selected partner states. It reports on a pioneering effort to simulate the coupling of power markets, estimate locational marginal prices, and determine the economic benefits of cross-border power trade and competition across these five countries. The nodes representing the primary power systems in these five countries are simulated in an optimal power flow model using optimisation software GAMS. The total welfare of electric power market integration is estimated at $ 4.8 million/hr, representing a welfare gain of $ 2.6 million/hr, thus, net total welfare increases by 118%. The simulation also investigates the implications for locational prices and power flows under constrained and unconstrained scenarios. To secure the benefits of an integrated electricity market, it is vital to pursue significant institutional restructuring, a robust transmission infrastructure, and the harmonisation of energy policies.

Robust Data-Driven Sparse Estimation of Distribution Factors Considering PMU Data Quality and Renewable Energy Uncertainty - Part II: Scalability and Applications

This two-part paper proposes a data-driven, robust, and scalable sparse estimation framework of distribution factors (DFs). Part I proposes a novel Adaptive <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> -Lasso estimator with theoretically guaranteed robustness. For solving this estimator, common algorithms are not scalable to large-scale systems since they often fail to converge under parallelism. This is addressed in Part II, where a novel Online Parallel Stochastic Coordinate Descent algorithm with theoretically guaranteed scalability is proposed. It can simultaneously update massive DF estimates by stochastic parallelism with fast convergence. It also works recursively under a multi-core setting and does not need step-size tuning, which is applicable for cloud-computing-based online parallel estimation. Convergence bounds of this algorithm are theoretically proven, and its speedup and maximum parallel core number are derived. These guide practical computational resource allocation for high efficiency. The benefits of the framework are showcased in real-time market operations under locational marginal pricing (LMP) and financial transmission right (FTR) mechanisms for congestion management. Thanks to its sparsity-promoting effect, robustness, and scalability, it allows for correctly and fast solving LMPs, congestion patterns, and FTR revenues against uncertainties. Test results on IEEE 300- and European 9241-bus systems via Alibaba Cloud validate the high scalability of this algorithm and benefits of the proposed framework to system applications.

Generalized Wardrop Equilibrium for Charging Station Selection and Route Choice of Electric Vehicles in Joint Power Distribution and Transportation Networks

This paper presents the equilibrium analysis of a game composed of heterogeneous electric vehicles (EVs) and a power distribution system operator (DSO) as the players, and charging station operators (CSOs) and a transportation network operator (TNO) as coordinators. Each EV tries to pick a charging station as its destination and a route to get there at the same time. However, the traffic and electrical load congestion on the roads and charging stations lead to the interdependencies between the optimal decisions of EVs. CSOs and the TNO need to apply some tolling to control such congestion. On the other hand, the pricing at charging stations depends on real-time distributional locational marginal pricing, which is determined by the DSO after solving the optimal power flow over the power distribution network. This paper also takes into account the local and the coupling/infrastructure constraints of EVs, transportation and distribution networks. This problem is modeled as a generalized aggregative game, and then a decentralized learning method is proposed to obtain an equilibrium point of the game, which is known as variational generalized Wardrop equilibrium. The existence of such an equilibrium point and the convergence of the proposed algorithm to it are proven. We undertake numerical studies on the Savannah city model and the IEEE 33-bus distribution network and investigate the impact of various characteristics on demand and prices.

Participation of strategic district heating networks in electricity markets: An arbitrage mechanism and its equilibrium analysis

Combined electricity-heat operation improves social welfare compared with the traditional heat-driven operation. However, it is left open how to achieve such an improvement in the current electricity market. Therefore, an arbitrage mechanism enabling strategic district heating networks (DHNs) to participate in electricity markets is designed, which settles the payment concerning the power deviation and the locational marginal price (LMP). Individual interests of both energy sectors are addressed via a bi-level model, while analytical results of the arbitrage equilibrium are proved theoretically. Although the mechanism intends to allow DHNs to profit selfishly from utilizing energy storage, it is strikingly guaranteed that electric power networks also benefit from this. A Pareto improvement is thus achieved by the mechanism with enhanced social welfare efficiency at the arbitrage equilibrium. The proposed mechanism is numerically compared with the traditional heat-driven operation, combined operation and existing cooperative and non-cooperative game approaches, while the merits are verified in two integrated electricity and heat systems with different scales.

Finding Nash equilibrium based on reinforcement learning for bidding strategy and distributed algorithm for ISO in imperfect electricity market

Finding Nash equilibrium in an imperfect market with active and strategic resources is key to the successful operation of the electricity market. A hierarchical Nash distributed reinforcement learning (HNDRL) framework is proposed to realize the interaction between the market participants and independent system operator (ISO). In the bidding stage, multi-agent Nash policy reinforcement learning is utilized to update the bidding strategies for market participants, i.e., generation company (GenCo) and distributed company (DisCo), which maximizes their own profit with imperfect information. The bidding action is updated by the probability iteration to deal with the continuous bidding strategy. And in the market clearing stage, the distributed dynamic-average consensus optimization algorithm is proposed at the ISO level to obtain the locational marginal price (LMP) and transaction quantities. With the participation of the demand-side in the electricity market, the proposed HNDRL framework can reach a Nash equilibrium with the optimal bidding strategy and handle global resource constraints in a distributed way. In addition, theoretical analysis is provided to ensure that the participants’ strategy exponentially converges to the Nash equilibrium for both convex and non-convex problems. Finally, the IEEE 30-bus system is employed to illustrate the efficiency. Compared with the existing method, the simulation results show that the proposed HNDRL framework has a faster convergence rate with the range of 2.667–3.333 times and can obtain higher profit with the range of 1.4286%–7.1429% at the Nash equilibrium point.

Planning distribution network using the multi-agent game and distribution system operators

When planning the distribution network, the income of each market entity is calculated by a fixed price. How to take the price of power into account while developing the planning strategy for each organization in the actual power market is an urgent issue that needs to be addressed imminently. To address this problem, considering the continuous change in the market price due to the change in the supply–demand relationship in the actual power market, this article proposes a distribution network planning method which considers the distribution system operator (DSO) and multi-agent game. First, the planning decision model of distribution network companies and power users with different interest subjects is constructed with grid planning and DG operation as decision variables. Second, DSO is introduced to the game framework. Based on the distribution locational marginal pricing (DLMP), a price accounting model is being developed. Then, the transfer relationships and game behavior among the distribution company, power users, and DSO are analyzed. Finally, an iterative search algorithm is used to solve a multi-agent game planning model of a distribution network that takes into account price signals in the power market. Examples based on IEEE 33-bus systems validate the suggested method’s validity and efficacy.

Low-carbon economic operation of integrated energy systems in consideration of demand-side management and carbon trading

Under the background of carbon emission abatement worldwide, carbon trading is becoming an important carbon financing policy to promote emission mitigation. Aiming at the emerging coupling among various energy sectors, this paper proposes a bi-level scheduling model to investigate the low-carbon operation of the electricity and natural gas integrated energy systems (IES). Firstly, an optimal energy flow model considering carbon trading is formulated at the upper level, in which carbon emission flow model is employed to track the carbon flows accompanying energy flows and identify the emission responsibility from the consumption-based perspective, and the locational marginal price is determined at the same time. Then at the lower level, a developed demand-side management strategy is introduced, which can manage demands in response to both the dynamic energy prices and the nodal carbon intensities, enabling the user side to participate in the joint energy and carbon trading. The bi-level model is solved iteratively and reaches an equilibrium. Finally, case studies based on the IEEE 39-bus system and the Belgium 20-node system illustrate the effectiveness of the proposed method in reducing carbon emissions and improving consumer surplus.

Price formation in short-term electricity market scheduling

Price formation is important for monitoring/development of an electricity market since the short/long-run efficiencies depend on the prices representing the economic signals. However, existing approaches cannot capture the contribution of suppliers’ bidding behavior to short-term price formation. As a result, regulators cannot evaluate these contributions. This can result in market monitoring failure/inefficient regulatory decisions that entail short-run market distortion or compromised investment respectively. This paper proposes a novel approach enabling regulators to retrace these contributions for every single non-zero shadow price formed in a dynamic security-constrained economic dispatch (SCED) problem. The decomposition of dual variables in a linear representation of SCED is adopted to evaluate the marginal contribution of the offered prices. The proposed theory yields explicit functions mapping the SCED shadow prices (i.e., locational marginal prices, and marginal values of (i) binding generation capacity limits, (ii) binding transmission capacity limits, and (iii) binding ramping limits) to the offered prices. Counterintuitively, the results show that increasing the offered prices will not necessarily leads to an increase in the shadow prices, especially the locational marginal prices. In addition, it is shown that the offered prices can pose long-run implications by contributing to the shadow prices associated with the marginal value of transmission/generation capacity.

A Market Framework for a 100% Renewable Energy Penetration Spot Market

The global installed capacity of renewable energy sources (RESs) is increasing rapidly. The 100% RESs power supply is being pursued. When renewable energy penetration tends to be 100%, the source-load coordination problem becomes extreme. The problems of market failure caused by the near-zero marginal cost of RESs and the scarcity pricing of flexible resources (FRs) participating in the rapid energy deviation balance need to be solved. Accordingly, a spot market framework including the day-ahead renewable energy temporal capacity market and the real-time energy sharing market is proposed in this paper. The RESs and FRs are decoupled to ensure that the homogenous commodities compete together. In the day-ahead stage, to obtain the locational marginal price with the guiding role of resource allocation, the fixed cost of the RESs is apportioned to obtain the spatial-temporal capacity price. In the real-time stage, a price-driven distributed energy sharing mechanism is proposed. It is proven that the sharing mechanism can achieve optimum social welfare and satisfy incentive compatibility. The simulation verifies that the new framework can solve market failure. The real value of FRs is discovered when a price consensus is reached.

DLMP of Competitive Markets in Active Distribution Networks: Models, Solutions, Applications, and Visions

Traditionally, the electric distribution system operates with uniform energy prices across all system nodes. However, as the adoption of distributed energy resources (DERs) propels a shift from passive to active distribution network (ADN) operation, a distribution-level electricity market has been proposed to manage new complexities efficiently. In addition, distribution locational marginal price (DLMP) has been established in the literature as the primary pricing mechanism. The DLMP inherits the LMP concept in the transmission-level wholesale market but incorporates characteristics of the distribution system, such as high <inline-formula> <tex-math notation="LaTeX">$R/X$</tex-math> </inline-formula> ratios and power losses, system imbalance, and voltage regulation needs. The DLMP provides a solution that can be essential for competitive market operation in future distribution systems. This article first provides an overview of the current distribution-level market architectures and their early implementations. Next, the general clearing model, model relaxations, and DLMP formulation are comprehensively reviewed. The state-of-the-art solution methods for distribution market clearing are summarized and categorized into centralized, distributed, and decentralized methods. Then, DLMP applications for the operation and planning of DERs and distribution system operators (DSOs) are discussed in detail. Finally, visions of future research directions and possible barriers and challenges are presented.