Distribution Locational Marginal Prices Research Articles

Optimizing Peer-to-Peer Energy Transactions: Determining the Allowable Maximum Trading Power for Participants

This paper presents a comprehensive study on the impacts of peer-to-peer (P2P) energy markets on distribution systems, specifically focusing on voltage, power loss, and congestion. While P2P energy markets create opportunities for direct trading between prosumers and consumers, ensuring compliance with distribution system constraints remains a challenge. This paper proposes an iterative method and graphical interpretation in order to assess complex interactions, addressing the persistent issue of network constraints. Additionally, this paper proposes a method to determine distribution locational marginal prices (DLMPs) for real-time traditional energy markets. This ensures effective coordination among sellers, buyers, and the distribution system operator. The proposed method aims to prevent negative impacts on distribution system operation via the determination of the allowable maximum trading power (MTP), ensuring empirical validity and practical implementation via operating conditions and forecast errors, thus distinguishing it from prior studies. This paper also establishes a model for P2P energy market interactions, utilizing linear estimations for efficient DLMP updates. The contributions of this paper enhance the understanding and operation of P2P energy markets, and is supported by simulation results validating the proposed method.

Transactive energy trading in distribution systems via privacy-preserving distributed coordination

This paper presents an approach to the transactive energy (TE) market that aims to improve the network efficiency and fairness of electricity market in distribution systems. The TE market is designed to allow subscribers to trade electricity in real-time based-on their energy consumption and generation forecast. The proposed framework utilizes distribution locational marginal pricing (DLMP), which accurately reflects the costs of electricity transmission and distribution, to fairly allocate these costs among subscribers. The Small Neighborhood Search Optimal Points (SNSOP) algorithm is then introduced to solve the challenge of finding optimal points for all participants in the TE market, as the maximum financial gain for one participant comes at the maximum financial loss of another participant. The results of the case study show that the proposed framework leads to a more efficient and reliable electricity network, by enabling decentralized control and reducing losses through optimal trades in the TE market.

A risk-averse approach for distribution locational marginal price calculation in electrical distribution networks

As distributed generation (DG) systems continue reshaping power networks, optimizing pricing strategies at DG buses using the distribution locational marginal price (DLMP) concept becomes critical for economic efficiency and the optimal operation of the network. This paper proposes a novel approach that combines Information Gap Decision Theory (IGDT) and Particle Swarm Optimization (PSO) to address these challenges. IGDT offers a robust framework for optimizing pricing in the presence of uncertainties and incomplete information in the distribution network. It quantifies and models these uncertainties, enabling the creation of adaptable pricing strategies that respond effectively to changes in DG output and market conditions. To further refine pricing strategies, PSO is integrated into the IGDT framework. PSO's iterative approach allows for the discovery of optimal pricing parameters at DG buses, striking a balance between maximizing DG owner profits and ensuring system optimality. Extensive simulations on two realistic distribution network models validate the effectiveness of the proposed IGDT-PSO approach. It demonstrates that DG owners can reliably achieve their predefined profit targets while also adhering to the objectives of the distribution network.

Distribution Locational Marginal Price driven Reactive Demand Response from Electric Vehicle Aggregator

Distribution Locational Marginal Price driven Reactive Demand Response from Electric Vehicle Aggregator

Pricing Economic Dispatch With AC Power Flow Via Local Multipliers and Conic Relaxation

We analyze two locational marginal pricing schemes in electricity markets derived from an economic dispatch (ED) problem with AC power flow equations that define a non-convex feasible set. The first among these prices, termed AC-LMPs, are derived from Lagrange multipliers that satisfy Karush-Kuhn-Tucker conditions for stationarity/local optimality of the non-convex ED problem. The second, called SDP-LMPs, are derived from optimal dual multipliers of the semidefinite programming (SDP)-based convex relaxation of the ED problem. We establish that AC-LMPs and SDP-LMPs are derived from Lagrange dual-equivalent problems. Hence, they coincide under zero duality gap, but may not be equal when the gap is non-zero or the AC-LMPs are associated with a stationary/locally optimal, but not globally optimal, dispatch. SDP-LMPs share interesting parallels with convex hull prices (CHPs), being derived from the Lagrangian dual of the non-convex ED problem. However, there are important differences. For example, the epigraphs of the SDP relaxation of the ED problem and the latter, parameterized by the nodal power demands, may not enjoy the relationship that CHPs satisfy and derive their name from. Also, while CHPs minimize a form of side-payments, SDP-LMPs may not. We prove that AC-LMPs, (and SDP-LMPs under zero duality gap) guarantee revenue adequacy under a condition that is sufficient, but not necessary. Finally, the SDP-LMPs are shown to equal SOCP-DLMPs, that are distribution locational marginal prices derived with second-order cone programming-based relaxations of power flow equations over radial distribution networks. We illustrate our theoretical findings through numerical experiments.

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.

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.

A Price-Based Load Flow Algorithm in Decentralized Distribution Markets

With the addition of new elements such as distributed generation, demand response, and price-sensitive loads, as well as grid smartness, the operation and management of distribution networks have faced additional complexities. Hence, the electricity price has a vital role for all market participants and strongly affects the demand, generation, and subsequently, the load flow analysis in the network. In this situation, there is a need for a load flow algorithm in which price is integrated into load flow equations. Therefore, this paper seeks to present a suitable algorithm called price-based load flow which considers the electricity price as a state variable similar to technical variables. In this situation, the price is added to the load flow equations as a new state variable and the effect of location on the price is considered. Therefore, it is possible to use the radial structure of the distribution network and communication between adjacent buses in order to provide an effective and appropriate method to find the price simultaneously with technical variables. The numerical study on the IEEE 33-bus distribution network shows the performance of the proposed method. Unlike the centralized market structure, the method does not need all network information to calculate distribution locational marginal price using optimal power flow. In this method, each bus can perform its computation only by information exchange with adjacent buses.

Battery Swapping Station Pricing Optimization Considering Market Clearing and Electric Vehicles’ Driving Demand

With the development of the new energy vehicle market, the pricing of battery swapping stations (BSS) is becoming a concern. The pricing models of BSS usually only consider the interaction between the distribution system operator (DSO) and the BSS or between the BSS and electric vehicles (EVs). The impact of DSO and EVs on the pricing strategy of BSS has received less attention, which does not reflect the actual complex situation. Therefore, we propose a three-level BSS pricing method that includes market clearing and EV behaviors. Firstly, the distribution locational marginal price (DLMP) is modeled to determine the impact of the DSO on BSS. Secondly, the EV demand response is used to estimate the impact of EVs on BSS. Thirdly, to increase the adaptability of this model, an iteration algorithm with approximations and relaxations is used with mixed integer linear programming, effectively solving the pricing optimization. According to this optimization, it is evident that the BSS make decisions in the market environment by monitoring the quantity of batteries in various states and generate extra income by acting in response to price fluctuations in the electricity market. The model’s viability and applicability are confirmed.

Distribution Locational Marginal Pricing Under Uncertainty Considering Coordination of Distribution and Wholesale Markets

A rapidly growing amount of small-scale distributed energy resources (DERs) integrated into distribution systems call for an effective distribution electricity market to manage the uncertainty of DERs and remove barriers to the participation of DERs in wholesale electricity markets. To this end, this paper proposes an uncertainty-aware distribution locational marginal pricing (DLMP) mechanism based on robust optimization for day-ahead distribution markets within a transmission-distribution coordinated framework. The transmission-level model clears the wholesale market and forms transmission locational marginal prices (LMPs) to price energy, reserve, and uncertainty. At the distribution level, a robust optimization-based DLMP mechanism is proposed that internalizes uncertainties and coordinates with the wholesale market. Besides active and reactive power DLMPs, the uncertainty DLMP is introduced to reward reserve and charge uncertainties. The novel DLMP mechanism provides transparent and comprehensive price signals for managing voltage, congestion, loss, especially uncertainty. The coordinated model is solved in a decentralized manner by heterogeneous decomposition algorithm. Distribution and wholesale markets are integrated through the coordinated mechanism to fully utilize generation resources. Accordingly, DMLPs are highly correlated and consistent with transmission LMPs, and thus allow DERs to participate in wholesale markets. The effectiveness of the proposed method is verified via numerous case studies.

Profit-Oriented BESS Siting and Sizing in Deregulated Distribution Systems

Within the deregulation process of distribution systems, the distribution locational marginal price (DLMP) provides effective market signals for future unit investment. In that context, this paper proposes a two-stage stochastic bilevel programming (TS-SBP) model for investors to best allocate battery energy storage systems (BESSs). The first stage obtains the optimal siting and sizing of BESSs on a limited budget. The second stage, a bilevel BESS arbitrage model, maximizes the arbitrage revenue in the upper level and clears the distribution market in the lower level. Karush-Kuhn-Tucker (KKT) optimality conditions, strong duality theory, and the big-M method are utilized to transform the TS-SBP model into a tractable two-stage stochastic mixed-integer linear programming (TS-SMILP) model. A novel statistics-based scenario extraction algorithm is proposed to generate a series of typical operating scenarios. Then, scale reduction strategies for BESS candidate buses and inactive voltage constraints are proposed to reduce the scale of the TS-SMILP model. Finally, case studies on the IEEE 33-bus and 123-bus systems validate the effectiveness of the DLMP in incentivizing BESS planning and the efficiency of the two proposed scale reduction strategies.

Transactive Energy Market Operation Through Coordinated TSO-DSOs-DERs Interactions

This paper proposes a new decentralized transactive energy (TE) market strategy integrating wholesale and local energy markets through coordinated interactions between transmission system operator (TSO), distribution system operators (DSOs), and distributed energy resource (DER) owners. The overall market-clearing problem is formulated as an optimization problem with coupling variables between different market levels, decomposed into three sub-problems for each of them to solve for locational marginal prices (LMPs), distribution LMPs, and local dispatch commands, respectively, based on the optimal output of upper level utilizing the Alternating Direction Method of Multipliers (ADMM) algorithms in a decentralized manner. The effectiveness of the proposed approach is validated through software simulations by realizing it in interconnected transmission and distribution networks.

A Novel Loss Sensitivity Based Linearized OPF and LMP Calculations for Active Balanced Distribution Networks

The distribution system operator performs optimal power flow calculations for efficient and economical scheduling of the distributed energy resources (DERs) and congestion management of the active distribution network. A linearized version of the ac optimal power flow (ACOPF) model is more suitable for practical implementation due to its simplicity and fast convergence. Thus, this article proposes a linearized ACOPF framework and locational marginal price (LMP) calculations for a generalized (i.e., radial and meshed) active balanced distribution system. The proposed linearized ACOPF for the distribution level market is formulated based on novel active and reactive power loss sensitivities by considering the effects of high <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\boldsymbol{R/X}$</tex-math></inline-formula> ratio and network constraints. The distribution LMPs are mathematically derived for active and reactive power generations and loads. Different reactive power loads are represented as a function of active power loads using the concept of power-factors. Thus, the load portfolio consists of nominal active power demand and nominal power-factor. Different LMPs are calculated for loads with different power-factors. DERs submit a separate offer for active and reactive power generations. Thus, separate LMPs are derived for DERs. The efficacy and efficiency of the proposed ACOPF framework are illustrated and compared on different radial and meshed distribution systems.

Strategic active and reactive power scheduling of integrated community energy systems in day-ahead distribution electricity market

The increasing penetration of distributed energy resources (DERs) enable integrated community energy systems (ICESs) as emerging techno-economic energy entities at the end-user side. In the deregulated electricity market, the ICESs can actively participate in the distribution electricity market (DEM) to provide active and reactive power dispatched by ICES operator (ICESO). In this context, a strategic active and reactive power scheduling model for ICESs in the day-ahead DEM is proposed in this paper. A novel trading mechanism designed for ICESO and distribution system operator (DSO)’s interaction toward both active and reactive power is represented in the day-ahead DEM, where distribution locational marginal prices (DLMPs) for both active and reactive power are introduced as the market settlements. Then, the trading process is formulated as a bi-level programming problem. The upper level describes the combined cooling, heating, and power (CCHP)-dominated ICESO’s strategic active and reactive power dispatch, in which the DLMPs for active and reactive power, internal flexibility services, and optimal dispatch for inverter-based distributed generators are considered. The lower level performs a DEM clearing for both active and reactive power. Further, Karush–Kuhn–Tucker (KKT) conditions, Big-M approach, and duality theory are used to convert the bi-level model from a Mathematical Programing with Equilibrium Constraints (MPEC) model to a single-level mixed-integer second-order cone programming (MISOCP) model for efficient calculation. Finally, case studies on modified IEEE 33-node and IEEE 123-node distribution systems are adopted to evaluate the performance of the proposed scheduling method. The results show that the proposed scheduling approach can contribute to the renewable energy share and energy efficiency, reduce CCHP-dominated ICESs’ operation costs by 38.13% and 13.21% compared to the case where ICESO only acts as a price-taking consumer, and 6.64% and 3.44% compared to the case where ICESO does not consider reactive power bids/offers, respectively.

Distribution locational pricing mechanisms for flexible interconnected distribution system with variable renewable energy generation

Nowadays, distribution locational pricing mechanism has been widely used in the radial distribution network to guide the energy consumption and promote the renewables utilization. Aiming to explore the reasonable pricing policy which is applicable to the merging flexible interconnected distribution system (FIDS), this paper develops two different distribution locational pricing mechanisms for distribution lines interconnected by soft open points (SOPs). First, based on the Wasserstein ambiguity sets for uncertainties from the main grid and distribution network, a carbon-oriented distributionally robust economic dispatch model is constructed for FIDS considering different price and carbon signals from the main grid. Then, by leveraging the optimal scheme from economic scheduling model, distribution locational marginal prices (DLMPs) and equivalent DLMPs (EDLMPs) are presented to measure the marginal cost and actual cost for energy consumption in the FIDS respectively. The calculation and decomposition methods of these price signals are also developed. In case studies, a practical 63-node FIDS is chosen to verify the effectiveness of the proposed methods. Numerical results illustrate the characteristics of DLMPs and EDLMPs in FIDS under multiple uncertainties. Comparing to DLMPs, EDLMPs are more appropriate to FIDS because this pricing mechanism can reflect the lower generation cost of renewables for each consumer.

Network-aware energy management for microgrids in distribution market: A leader-followers approach

With the increasing penetration of distributed energy resources (DERs) into distribution systems, microgrids can participate in the market clearing of distribution-level electricity market. This paper proposes a leader-followers-type bi-level model for energy management and market clearing of distribution system with microgrids based on Stackelberg game. Distribution system operator (DSO) is considered as the leader, and microgrid operators (MOs) as followers. In the proposed model, market clearing problem of distribution system is modeled in the upper level, while the energy management problem of microgrids is modeled in the lower level. The distribution locational marginal price (DLMP) is obtained in the upper level model and then transmitted to the lower level model as price signals for microgrids. The model is then reformulated as a Mathematical Program with Equilibrium Constraints (MPEC) problem and the stochastic MPEC model is constructed with the uncertainty of PVs in microgrids. Existence of equilibrium of the proposed single leader multi-follower game is analyzed. Numerical results demonstrate the effectiveness of the proposed model.

Distribution locational marginal price based hierarchical scheduling framework for grid flexibility from virtual energy storage systems

• VESS's are modeled using residential air-conditioners for DSM. • Local ancillary services TSO-DSO coordination scheme for cooperative management in grids. • Hierarchical framework for scheduling aggregated VESS. • Network constrained optimal VESS participation in ancillary service markets. • DSM based practical market model for SOs, maximizing overall market benefits. Maintaining generation and demand equilibrium under large scale renewable energy integration is challenging. Conventional flexibility providers such as grid-scale Energy Storage Systems (ESS) have potential but are costly solutions. With evolving smart grid scenario, aggregated demand response from Thermostatically Controlled Loads (TCLs) is utilized as Virtual Energy Storage Systems (VESS) and considered as innovative and cost efficient solution to provide fast response reserves. VESS units are often scheduled and controlled in a centralized manner considering limited distribution system constraints. However, accurate operational flexibility potential of diversified VESS units for various grid services needs to consider distribution network constraints. It can be fully utilized when Distribution System Operators (DSO) coordinate with Transmission System Operators (TSO) to transfer grid services from VESS of its area. Local ancillary service TSO-DSO coordination scheme ensures in this perspective significant flexibility of TSO and allows both TSO and DSO to access VESS flexibility. For such controlling of diversified VESS units where DSO is responsible for aggregate flexibility and local area balancing, a hierarchical scheduling framework is more practical. In this context, this paper proposes a two-stage hierarchical approach for optimal scheduling of TCLs as VESS to optimize energy and provide grid flexibility. At the lower stage, TCLs are scheduled based on Distribution Locational Marginal Price (DLMP) provided by DSO, while ensuring consumers’ comfort. At the upper level, DSO provides additional flexibility to TSO through optimal scheduling of aggregated VESS considering local ancillary services TSO-DSO coordination scheme. The simulation results indicate that VESS scheduling improves system flexibility by maintaining a generation-demand balance.

Peer-to-Peer Joint Electricity and Carbon Trading Based on Carbon-Aware Distribution Locational Marginal Pricing

This paper proposes a novel Peer-to-Peer (P2P) joint electricity and carbon (E&C) trading model to co-optimize the energy and carbon emissions permit transactions considering the trading preferences in the distribution network. To realize the secure and low-carbon network operation, a decomposable carbon-aware distribution locational marginal pricing (CDLMP)-based operation service pricing scheme of the distribution system operator (DSO) is proposed to guide the P2P transactions among prosumers. In practice, the coordination between the P2P market and the DSO is cast as a bi-level optimization. In the upper level, the network operation optimization of the DSO is modeled as a carbon-aware optimal power flow (COPF) problem based on a carbon emission flow model to ensure the security of network operation and derive the CDLMP. In the lower level, a decentralized P2P joint E&C trading is modeled to simultaneously clear energy and carbon permit. Later, this paper develops an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">l</i> (p)-Box ADMM method to relax the binary variables originating from the peer-matching process of the carbon trading. Finally, a novel demurrage protocol is designed to facilitate the convergence of the bi-level interaction with an incentive for trading adjustments. Case studies illustrate the effectiveness of the proposed method in motivating “grid-friendly” and “low-carbon” P2P trading.

Distribution Locational Marginal Pricing Based Equilibrium Optimization Strategy for Data Center Park with Spatial-temporal Demand-side Resources

Distribution Locational Marginal Pricing Based Equilibrium Optimization Strategy for Data Center Park with Spatial-temporal Demand-side Resources

Enhanced deep neural networks with transfer learning for distribution LMP considering load and PV uncertainties

As the flexibility of generation and demand increases in distribution systems, the residential loads are emerging as a promising means to participate in demand response and the transactive energy market. Market pricing is an instrumental mechanism for the distribution system operator to exploit the full potential of the flexible resources. The distribution locational marginal price (DLMP) can be used to guide the residential load consumption. This type of market signal helps the distribution system operator to optimize the scheduling of all resources while satisfying related network constraints through a day-ahead market. However, solving the optimization problem for large-scale systems can be computationally expensive. To address the scalability and practicability limitations of the DLMP framework, a learning-based approach is proposed in this paper to complement the day-ahead distribution market framework. The proposed approach combines long short-term memory and transfer learning to develop deep neural network that can capture the spatial–temporal correlation of the input data. The model can determine the optimal DLMP for each node in a distribution system without the system parameters required to formulate the optimization problem. Testing results on IEEE 33-bus and 123-bus systems show that the proposed approach can generate a comparable DLMP against the optimization solutions.