Distribution Locational Marginal Prices Research Articles

Strategic investments in mobile and stationary energy storage for low-carbon power systems

The main feature and trend of the distribution system is the integration of renewable energy with high penetration rates. The variability and zero marginal cost characteristics of renewable energy will lead to drastically fluctuating locational marginal prices. In the deregulated electricity market, merchants have incentives to utilize energy storage and price arbitrage. Mobile energy storage has a short capital payback period and is widely recognized for transferring energy in the temporal and spatial dimensions. This paper analyses the interaction between merchants and distribution system operators and presents a hybrid energy storage strategic investment framework using bi-level programming. In the upper-level problem, the merchant formulates the capacity, location, and operation strategy of different energy storage to maximize the market revenue of hybrid energy storage, which is paid for by the locational marginal price. In the lower-level problem, the distribution system operator develops an optimal dispatch strategy considering renewable energy and merchant investments. A joint energy and reserve market clearing procedure is performed to derive the locational marginal prices. In the lower-level problem, a data-driven solution strategy based on machine learning is introduced. It uses deep neural networks to approximate the mapping relationship between distribution system states and locational marginal prices. The presented methodology is implemented in an IEEE-33 node system. The results demonstrate that, compared to the basic case, the hybrid energy storage investment strategy has led to an 8.1 % increase in merchant profits and a 12.9 % reduction in the operational costs of the distribution network. The deep neural network approximator fully avoids the lower-level problem with less than 5 % optimality loss.

Framework design of distributed P2P2G energy transaction considering photovoltaic power and dispatch of manufacturing facilities

In this paper, a distributed peer-to-peer-to-grid (P2P2G) energy transaction framework considering photovoltaic generation and dispatch of manufacturing facilities is designed to increase the penetration of renewable energy resource. The factory with typical manufacturing assembly production task, photovoltaic panels and battery is regarded as a micro-grid (MG) to participate in the energy transaction market. The designed framework contains two levels. In the upper level, each MG determines the scheduling of manufacturing facilities and battery and the quantities of P2P2G energy transactions based on the given P2P energy transaction price and distribution locational marginal price (DLMP), in which the complex typical manufacturing assembly process is formulated as a kind of deferable load and the DLMP is updated according to the optimal power flow (OPF) of the network. In the lower level, peer-to-peer (P2P) energy transaction prices are updated by non-cooperative games and the homologous Rosen-Nash equilibrium points are obtained by using Nikaido-Isoda relaxation and alternating direction method of multipliers (ADMM) algorithm. The efficacy of the designed framework is demonstrated by a case study, and the results indicate the designed framework can improve the utilisation rate of renewable energy.

OPLEM: Open Platform for Local Energy Markets

Local Energy Markets (LEMs) have been proposed as an effective solution to coordinate distributed energy resources within emerging smart local energy systems. However, LEMs are still at an early stage of development and are not widely implemented yet. Extensible open-source software tools are needed to simulate different market designs and evaluate their feasibility and effectiveness. This paper presents OPLEM, an open-source Python package for modelling and testing LEM designs. It offers a modular and flexible framework to create and test market designs adapted for distribution networks. OPLEM integrates two distinct models—one for designing and simulating local energy markets, and another for network operation. Unlike existing tools, OPLEM platform offers a comprehensive solution that bridges the gap between market design and network operation assessment, enabling stakeholders to gain deeper insights into the interactions between market dynamics and grid performance. Additionally, the inclusion of participant and asset models further enhances the tool’s versatility, allowing for a holistic analysis. Thanks to its modular structure, OPLEM allows the development of customised LEM designs and initially incorporates four popular LEM designs: Time-of-Use pricing market, centralised dispatch with distribution locational marginal pricing, bilateral peer-to-peer market and auction market. By combining market design and network modelling functionalities, the tool empowers users to explore various scenarios and optimise market clearings to enhance both economic efficiency and grid reliability.

Optimizing local electricity markets: A bi-level primal-dual approach for integrating price-based demand response and distribution locational marginal pricing

This paper addresses the conundrum of optimizing electricity consumption patterns in response to fluctuations in demand and price, a task managed by both load aggregators and the distribution system operator (DSO). The conventional approaches in the literature to integrate demand response (DR) into optimal power flow (OPF) problems typically overlook the price responsiveness of consumers or simplify power flow equations to account for price-elastic demand.In this paper, we strive to close this gap by introducing a bi-level primal-dual optimization framework that incorporates aggregators' objectives into the market-clearing process while preserving the precision of the OPF equations. At the upper level, the model seeks to minimize both the total payment and peak load. The lower level, structured as a second-order conic (SOC) problem, aims to reduce overall generation costs subject to constraints of the second-order conic (SOC) branch flow model (BFM). The two levels interact through the optimal demand response and distribution locational marginal prices (DLMPs). The principles of convex duality principles together with the strong duality constraint are leveraged to transform the market-clearing problem into a single primal-dual problem. We also circumvent the non-linearity that stems from the DR payment term by incorporating discretizing loads and the big-M method, thus converting the problem into a mixed-integer SOC (MI-SOC) formulation. The merits of the proposed MI-SOC framework are validated through case studies conducted on the IEEE 33-bus test system, showcasing its potential to enforce price-elasticity demand response in distribution system's electricity markets.

Distribution network voltage control considering virtual power plants cooperative optimization with transactive energy

The integration of massive distributed energy resources (DERs) brings new challenges for the distribution networks (DNs) operation control. To control DERs effectively, virtual power plants (VPPs) are introduced into DNs. Conventionally, the control strategy of VPPs is formulated as an optimization model without considering voltage control and transactive energy (TE) in DNs. In this article, multiple VPPs cooperative optimization with TE is studied and cast as a nonlinear programming model. It aims to optimize the voltage control of DNs and the operation profits of VPPs. To dynamically capture the optimal operation state of VPPs in DNs, the distribution locational marginal pricing and DN partition are incorporated into the model. In general, this type of model is computationally challenging and mainly solved by approximate algorithms with low efficiency. Recently, multi-agent deep reinforcement learning (MADRL) is emerging as a scalable and promising data-driven approach. We propose an augmented MADRL solution to this problem. In the training stage, one soft actor-critic learning agent augmented by parameter sharing strategy is employed to simultaneously capture the state-action patterns of multiple VPPs. The prioritized experience replay technique is applied to improve learning efficiency and speed. Numerical test results demonstrate the superiority of the proposed method over benchmark methods.

Strategic trading equilibria in local community considering co-existence of pool-based and peer-to-peer energy markets with free-rider problem in network usage cost

The peer-to-peer (P2P) energy trading market is considered a promising method for allocating prosumers’ locally produced power in smart buildings. However, the existing literature overlooks the coexistence of P2P and pool-based energy markets. Therefore, this paper establishes a bi-level energy market model that incorporates both P2P and pool-based markets. The prosumers’ individual profit maximization model considering their network usage costs in the P2P energy trading network at the upper level is first developed. A hybrid market-clearing framework determining the optimal trading amounts with the prosumers’ strategic offers at the lower level is then exploited. The distribution network power flow model in the market clearing framework is then convexified. The lower-level problem is replaced with its strong duality conditions. This bi-level problem can be reformulated as an equilibrium problem with equilibrium constraints (EPEC). This EPEC is then solved after being transformed into an equivalent mixed integer linear programming (MILP) model. Finally, a fifteen-bus system is employed to illustrate the characteristics of the hybrid market equilibrium depicted by this EPEC model. The influences of the prosumers’ strategic offers on the distribution locational marginal prices (DLMPs) and network usage costs are highlighted. Since the prosumers can choose to transmit their energy in the pool-based or P2P markets, the emission and pollution costs caused by power transmission can be minimized. A cleaner energy production is thus guaranteed. The free-rider problem is verified by comparing the network usage charges in the strategic and perfect competition scenarios.

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.