Locational Marginal Price Calculation Research Articles

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.

A Two-Stage Algorithm of Locational Marginal Price Calculation Subject to Carbon Emission Allowance

To analyze the effect of carbon emission quota allocation on the locational marginal price (LMP) of day-ahead electricity markets, this paper proposes a two-stage algorithm. For the first stage of the algorithm, a multi-objective optimization model is established to simultaneously minimize the total costs and carbon emission costs of power systems. Hence, an evenly distributed Pareto optimal solution can be solved effectively by means of the normalized normal constraint method. For the second stage, a tracing model is built with the goal of minimizing the total costs of power systems and satisfying the constraints generated based on the Pareto optimal solution obtained from the first stage. Furthermore, the influence of carbon emission quota allocation on the LMP of electricity markets is analyzed, and different schemes to allocate carbon emission quotas are evaluated on a real 1560-bus and 52-unit system.

Investigation of Harmonic Effects in Locational Marginal Pricing and Developing a Framework for LMP Calculation

Locational Marginal Pricing (LMP) is arguably the most effective and commonly employed mechanism to provide the most reliable economic signal to market participants. Meanwhile, nodal prices depend on active power losses and transmission congestion which may be affected by harmonics pollution. In the conventional method, power system and loads are assumed linear and nodal prices are obtained by results of optimal power flow (OPF) at the power frequency. Harmonics lead to skin effect and increasing loss. Further, harmonic flowing in branches in a power network occupies transmission capacity. For providing more accurate signals to market participants and achieving more accurate nodal prices, harmonic effects on LMP are investigated and a framework is developed for LMP calculation in a harmonic polluted power system. In this framework, skin effect, losses, and congestion which can be arisen by harmonic pollution are modelled in optimal power flow (OPF) and are considered in LMP calculation. The proposed concept is implemented with 9-bus and 30-bus test systems while nodal price changes are also indicated.

Locational Marginal Price Calculation Implying Different System Uncertainties

This paper presents locational marginal price (LMP) calculation technique facing different operation conditions. Uncertainties in power systems such as loosing transmission line of load change could be consider a common case. In calculating LMP, the effect of line flow limits will affect the prices at each bus. Also, the effect of shifted the load from bus to another is investigated. LMP is a technique used in market to determine the cost of supplying the next incremental electrical energy at a specific bus. Four different case of LMP are discussed in this paper. Three and four simple bus networks are used to demonstrate different cases of LMP.

Loss minimization in distribution systems based on LMP calculation using honey bee mating optimization and point estimate method

Locational marginal price (LMP) calculation at distributed generation (DG) busses is an effective way for optimal operation of DG units. The aim of this study is presenting a new LMP formulation which includes distribution loss minimization. A Meta-heuristic modified honey bee mating optimization (MHBMO) algorithm is used to obtain optimal values of LMP and power factor of DG units so that the loss of network is minimized, and the benefit of DG units is maximized. Furthermore, a stochastic power flow based on the point estimate method (PEM) is located in MHBMO algorithm to capture uncertainty in the market price and load demand. The proposed policy is applied to a realistic distribution system for the various market prices at substation buses. The results of this study prove the accuracy and efficiency of the new method over the previous methods in terms of the DG units' benefit, loss minimization, and state estimation of the system.

Procurement of regulation services for a grid with high‐penetration wind generation resources: a case study of ERCOT

This study presents two enhancements at the Electric Reliability Council of Texas (ERCOT) for coping with the uncertainties and variations brought by high penetration of wind generation resources (GRs). The first enhancement is the incorporation of a novel short-term wind forecast algorithm into the look-ahead dispatch process to improve the calculation of locational marginal prices and generation schedules. The second enhancement is the development of a multi-time-scale method for quantifying regulation service requirements considering the combined impact of wind variations on governor response, automatic generation control, and economic dispatch results. A simulation model that is capable of simulating all relevant scheduling and operation processes from a few seconds to a few hours is developed to verify the performance of the proposed method. The ERCOT operational model and historical data are used to demonstrate that the derived regulation requirements can meet the ERCOT reliability needs by considering additional generation variations and uncertainties caused by wind GRs. The proposed methods are readily applicable to other regional power grids with high penetration of variable GRs.

Iterative DC Optimal Power Flow Considering Transmission Network Loss

In today's electricity market, DC optimal power flow and AC optimal power flow have become the main models to simulate generation dispatch and calculate locational marginal price. Although DC optimal power flow has the advantage of robustness, its result is not accurate compared to AC optimal power flow due to the neglect of transmission network loss. In this article, an iterative DC optimal power flow model with explicit consideration of accurate AC network loss is proposed. A general Newton–Raphson method is applied in this method to calculate AC transmission network loss, and iteration is used to minimize the error of calculated loss. The fictitious bus load is utilized to represent the loss, which is divided equally on each line. The proposed model is compared with basic DC optimal power flow and AC optimal power flow models on the calculation of locational marginal prices using PJM 5-bus and IEEE 30-bus systems at various load levels. The results show that the proposed model obtains better approximation of AC optimal power flow model on the simulation of generation dispatch and calculation of locational marginal prices.

Stochastic LMP (Locational marginal price) calculation method in distribution systems to minimize loss and emission based on Shapley value and two-point estimate method

LMP (Locational marginal price) calculation is a serious impediment in distribution operation when private DG (distributed generation) units are connected to the network. A novel policy is developed in this study to guide distribution company (DISCO) to exert its control over the private units when power loss and green-house gases emissions are minimized. LMP at each DG bus is calculated according to the contribution of the DG to the reduced amount of loss and emission. An iterative algorithm which is based on the Shapley value method is proposed to allocate loss and emission reduction. The proposed algorithm will provide a robust state estimation tool for DISCOs in the next step of operation. The state estimation tool provides the decision maker with the ability to exert its control over private DG units when loss and emission are minimized. Also, a stochastic approach based on the PEM (point estimate method) is employed to capture uncertainty in the market price and load demand. The proposed methodology is applied to a realistic distribution network, and efficiency and accuracy of the method are verified.

A Novel Policy for LMP Calculation in Distribution Networks Based on Loss and Emission Reduction Allocation Using Nucleolus Theory

This paper proposes a new policy to calculate the locational marginal price (LMP) in the distribution networks containing distributed generation (DG). The proposed policy is based on remunerating the DG units to reduce the loss and emission of the network. LMP at each DG bus is calculated according to the contribution of the DG to the reduced amount of loss and emission. An iterative algorithm which is based on the nucleolus theory is proposed to allocate the loss and emission reduction. The proposed algorithm will provide a robust state estimation tool for distribution companies (DISCOs) in the next step of operation. The state estimation tool provides the decision maker with the ability to exert its control over private DG units when the loss and emission are minimized. Also, the proposed pricing policy requires decision maker to simply apply its best response strategy to the LMP based on the priority of loss, emission and DISCO's extra benefit. The proposed methodology is applied to two realistic distribution networks, and efficiency and accuracy of the method are verified.

Stochastic locational marginal price calculation in distribution systems using game theory and point estimate method

This study presents a new stochastic method to estimate the locational marginal price (LMP) in the distribution networks containing distributed generation (DG). In the proposed method, LMP at each bus is calculated according to the contribution of the DG to the reduced amount of loss and emission. An iterative algorithm which is based on the game theory is proposed to allocate the loss and emission reduction among DG units. Also, a stochastic framework based on the point estimate method is considered to capture uncertainty in the market price and load demand. The proposed policy will provide a robust state estimation tool for distribution companies in the next step of operation. The state estimation tool provides the decision maker with the ability to exert its control over private DG units when loss and emission are minimised. The performance of the proposed algorithm is tested on a realistic distribution network in the deterministic and stochastic frameworks. The obtained results are encouraging.

A New Approach to Short-term Price Forecast Strategy with an Artificial Neural Network Approach: Application to the Nord Pool

In new deregulated electricity market, short-term price forecasting is key information for all market players. A better forecast of market-clearing price (MCP) helps market participants to strategically set up their bidding strategies for energy markets in the short-term. This paper presents a new prediction strategy to improve the need for more accurate short-term price forecasting tool at spot market using an artificial neural networks (ANNs). To build the forecasting ANN model, a three-layered feedforward neural network trained by the improved Levenberg-marquardt (LM) algorithm is used to forecast the locational marginal prices (LMPs). To accurately predict LMPs, actual power generation and load are considered as the input sets, and then the difference is used to predict price differences in the spot market. The proposed ANN model generalizes the relationship between the LMP in each area and the unconstrained MCP during the same period of time. The LMP calculation is iterated so that the capacity between the areas is maximized and the mechanism itself helps to relieve grid congestion. The addition of flow between the areas gives the LMPs a new equilibrium point, which is balanced when taking the transfer capacity into account, LMP forecasting is then possible. The proposed forecasting strategy is tested on the spot market of the Nord Pool. The validity, the efficiency, and effectiveness of the proposed approach are shown by comparing with time-series models

Performance Comparison of Optimal Power Flow Algorithms for LMP Calculations of the Full Scale Korean Power System

This paper proposes the comparison results of various optimal power flow algorithms (OPF) to calculate the locational marginal prices (LMP) of the unreduced full scale Korean transmission system. Five different types of optimal power flow models are employed: Full AC OPF, Cubic AC OPF, Quadratic AC OPF, Linear AC OPF and DC OPF. As the results, full AC OPF and cubic AC OPF model provides LMP calculation results very similar to each other while the calculation time of cubic AC OPF model is faster than that of the Full AC OPF. Other simplified OPF models, quadratic AC OPF, linear AC OPF and DC OPF offer erroneous results even though the calculation times are much faster than the Full AC OPF and the Cubic AC OPF. Given the condition that the OPF models sometimes fail to find the optimal solution due to the severe complexity of the Korean transmission power system, the Full AC OPF should be used as the primary OPF model while the Cubic AC OPF can be a promising backup OPF model for the LMP calculations and/or real-time operation.

A Study on Locational Marginal Prices Based on Single-Stage and Multi-Stage Optimization Models

Theoretically, there are two kinds of models to calculate Locational Marginal Price (LMP): single-stage optimization model and multi-stage optimization model. In the paper, two mathematical models were analyzed and compared. Economic concept of LMP was explained and LMPs calculation was derived based on optimization methods. Characteristics of LMPs for different optimization models and how marginal generators and non-marginal generators can affect LMPs were discussed. In case study, the PJM five buses system was adopted to calculate LMPs under single-stage and multi-stage optimization model. The study results show that multi-stage model can accomplish economic dispatch more effective than single-stage model. But single-stage optimization model is better competent for LMP based settlement.

A Novel Policy for Locational Marginal Price Calculation in Distribution Systems Based on Loss Reduction Allocation Using Game Theory

In this paper, a novel locational marginal price (LMP) policy for distribution system with significant penetration of distribution generation (DG) in competitive electricity market is presented. This new LMP method is based on remunerating DG units for their participation in reduced amount of energy losses in distribution systems brought about by participation of all DG units in supplying demand. Also, this method is combined with an iterative solution. This approach provides an efficient tool for distribution companies (DISCOs) to estimate the state of the system in the next step which other existing approaches of LMP fail to provide this system state estimation. Finally, in order to expand LMP method and provide effective prediction method for DISCOs to estimate the day-ahead state of the system, ANN tool is employed to predict the market price and demand for the next 24 h. This LMP prediction is a powerful operational tool for DISCO to exert its control over private DG units. However, prediction methods contain error. Therefore, uncertainty modeling is implemented for modeling the effect of error in prediction on the LMP calculation for the next day.

Locational Marginal Pricing (LMP) in Deregulated Electricity Market

The deregulation of electricity markets has a very large impact on almost all the power systems around the world. Competitive markets are complex systems with many participants who buy and sell electricity. Much of the complexity arises from the limitations of the underlying transmission systems and the fact that supply and demand must be in balance at all times. Generally the Locational marginal pricing (LMP) is obtained by solving a linear programming formulation. Network losses are considered through the preset loss factor based on historical operational information. This usually brings error in the calculated loss under different new scenarios. In this paper a new iterative LMP calculation method is proposed to overcome the aforementioned drawbacks associated with the traditional LMP calculations. At each iteration, a linear programming problem for market clearing is solved first .Losses on branches are considered as fictitious nodal demand at their terminal buses .Secondly the AC power flow calculated according to the dispatch results. Loss factors and fictitious nodal demand are then updated according to the AC power flow solution. The effectiveness of the proposed method is illustrated on PJM 5 bus

An Iterative LMP Calculation Method Considering Loss Distributions

Generally, the locational marginal price (LMP) is obtained by solving a linear programming formulation. Network losses are considered through the preset loss factors based on historical operation information. This usually brings errors in the calculated loss under different new scenarios. Further, the congestion component of an LMP is dependent on the choice of the reference bus. In this paper, a new iterative LMP calculation method is proposed to overcome the aforementioned two drawbacks associated with the traditional LMP calculations. At each iteration, a linear programming problem for market clearing is solved first. Losses on branches are considered as fictitious nodal demands at their terminal buses. Secondly, the AC power flow is calculated according to the dispatch results. Loss factors and fictitious nodal demands are then updated according to the AC power flow solution, thus removing the need and dependence on presetting loss factors. Another important merit is that LMP and its congestion component obtained from the proposed iterative LMP calculation method are independent of choice of the reference bus. The effectiveness of the proposed method is illustrated on two benchmark systems. The importance of obtaining accurate losses and LMPs is also demonstrated.

Independent marginal losses with application to locational marginal price calculation

A new kind of power system marginal loss (or loss sensitivity) for nodal MW/Mvar is developed. First the electricity transmission loss is expressed in terms of source currents. It is thus an analytical function. Then the marginal loss with respect to source current is derived based on calculus and vector algebra. Using each source/load power represents its nodal injection current, the marginal loss with respect to source current is then transformed into the marginal loss with respect to source/load power. The new kind of marginal loss is based on load flow solution. It is exact in algorithm and independent of reference bus, thus called independent marginal loss (IML). The IML exactly leads to double collection of actual system loss. It makes loss components of locational marginal price small in spatial fluctuation compared to the existing marginal losses. Numerical examples including the IEEE 118-bus and PJM [Note 1] 5-bus systems are presented to demonstrate the calculation and effectiveness of the IML.

Admissible Locational Marginal Prices via Laplacian Structure in Network Constraints

Standard computations reveal that locational marginal prices (LMPs), being Lagrange multipliers in an optimization problem, must lie in the null space of a Jacobian matrix evaluated at the optimal power flow solution, augmented by columns associated with active line flow limits. The impact of network power flow and active line limit constraints is to confine the LMPs in a subspace that satisfies necessary conditions for optimality. Optimal market clearing can then proceed as a minimization over offer curves confined to admissible LMPs in this subspace. When no line limits are active and losses neglected (e.g. in a dc power flow representation), the matrix in question has a generalized Laplacian structure, and admits only a vector of all equal elements in its null space (verifying the well-known equal incremental cost condition). As line flow limits become active, the null space grows in dimension. Among the phenomena of interest as the dimension of admissible LMPs grows is that of ldquoload pocketsrdquo; that is, admissible LMP vectors that can show patterns in which buses partition into zones of approximately equal LMPs, with significant differences between zones. This paper explores an approach to admissible LMP calculation that isolates the topological role of active line flow constraints, independent of offer curve prices. Identification of this admissible subspace can then greatly facilitate computations such as clustering to identify potential zones of differentiated LMPs.

Locational Marginal Price with Demand-Side Bidding in a Competitive Electricity Market

This paper presents a new approach for the evaluation of locational marginal prices (LMPs) considering demand-side bidding (DSB) in a competitive electricity market. The stabilization of the electric power supply and demand balance is one of the major important activities in electric power industry. In this paper, we present an analytical method for calculation of LMPs considering DSB, which has opportunity to compete with generating units, as England & Wales Pool's DSB scheme Also, we propose a new approach that the LMP with DSB is divided into three components. The proposed approach can be used for evaluation of DSB in the electricity market and for assessment of the influence of DSB on total production costs and LMPs.

Applications of Ellipsoidal Approximations to Polyhedral Sets in Power System Optimization

The paper presents a computational method that approximates feasible sets specified by linear or convex inequalities. This numerically efficient approach to power system optimization is based on computational geometry of multidimensional ellipsoids and is potentially applicable to problems with high dimensions, as it builds on recent advances in convex optimization. In an important application, it provides ranges in which nodal (generator) injections can vary without violating operational constraints in security analysis. The model is applied to two important problems in deregulated power systems: optimal economic dispatch (OED) and calculation of locational marginal prices (LMPs) in a day-ahead power market. Optimization problem with convex (ellipsoid-based) constraints is solved by a linear matrix inequality (LMI)-based procedure. The method is verified on the benchmark example with 68 buses, 16 generators, and 86 lines.