Bidding Problem Research Articles

Risk-aware microgrid operation and participation in the day-ahead electricity market

This work examines the daily bidding problem of a grid-connected microgrid with locally deployed resources for electricity generation, storage and its own electricity demand. Trading electricity in energy markets may offer economic incentives but exposes the microgrid to financial risk caused by market commitments. Hence, a multi-objective, two-stage stochastic mixed integer linear programming (MILP) model is formulated, extending prior work of a risk-neutral microgrid bidding approach. The multi-objective model minimises both expected total cost of day-ahead microgrid operations and financial risk from bidding measured by conditional value-at-risk (CVaR). Bidding curves derived as first stage decisions are always feasible under present market rules – including a limitation on the number of break points per submitted curve – while being near optimal for the microgrid’s day-ahead recourse schedule. The proposed optimisation model is embedded in a variant of the ɛ-constrained method to generate bidding curve candidates with different trade-offs between the two conflicting objectives. Moreover, scenario reduction is used to compromise accuracy of the uncertainty set for better computational performance. Particularly, the marginal relative probability distance between initial and reduced scenario set is suggested to make a decision on the extent of scenario reduction. The proposed solution procedure is tested in a computational study to demonstrate its applicability to generate optimal microgrid bidding curve candidates with different emphasis between total cost and CVaR in reasonable computational time.

Convexity in Real-time Bidding and Related Problems

We study problems arising in real-time auction markets, common in e-commerce and computational advertising, where bidders face the problem of calculating optimal bids. We focus upon a contract management problem where a demand aggregator is subject to multiple contractual obligations requiring them to acquire items of heterogeneous types at a specified rate and where they will seek to fulfill these obligations at minimum cost. Our main results show that, through a transformation of variables, this problem can be formulated as a convex optimization problem, for both first and second price auctions. The resulting duality theory admits rich structure and interpretations. Additionally, we show that the transformation of variables can be used to guarantee the convexity of optimal bidding problems studied by other authors, who did not leverage convexity in their analysis. The main point of our work is to emphasize that the natural convexity properties arising in first and second price auctions are not being fully exploited. Finally, we show direct analogies to problems in financial markets: the expected cost of bidding in second price auctions is formally identical to certain transaction costs when submitting market orders, and that a related conjugate function arises in dark pool financial markets.

Continuous auction mechanism model for safety electric energy market transaction

With the rapid development of microgrid in the electric power industry, the microgrid electric energy transaction has begun to be marketized, and the research on the microgrid electric energy trusted transaction has important theoretical research value and social value. The existing blockchain-based microgrid electric energy trusted transaction models mostly focus on energy management and scheduling control between microgrids when conducting electric energy transactions, and do not fully consider the bidding problems in the market-based transaction of microgrid electric energy, resulting in trading strategies are difficult to adapt to new market changes. In response to this problem, this paper proposes a reliable transaction approach for microgrid electric energy based on a continuous two-way auction mechanism. The proposed strategy accounts for the volatility of electricity prices in the microgrid trading market and employs the continuous two-way auction mechanism to evaluate the microgrid electricity trading tactics. In the microgrid electric energy transaction, the self-adaptive learning theory is applied to adjust the quotations of both parties, so that both parties can make reasonable quotations according to the market environment. By simulating experimental data, the findings indicate that the continuous two-way auction mechanism transaction strategy enables both parties to modify their quotations based on market transaction information, thereby displaying a high degree of flexibility in microgrid electricity’s market-oriented trading.

A sample robust optimal bidding model for a virtual power plant

In many energy markets, the trade amount of electricity must be committed to before the actual supply. This study explores one consecutive operational challenge for a virtual power plant—the optimal bidding for highly uncertain distributed energy resources in a day-ahead electricity market. The optimal bidding problem is formulated as a scenario-based multi-stage stochastic optimization model. However, the scenario-tree approach raises two consequent issues—scenario overfitting and massive computation cost. This study addresses the issues by deploying a sample robust optimization approach with linear decision rules. A tractable robust counterpart is derived from the model where the uncertainty appears in a nonlinear objective and constraints. By applying the decision rules to the balancing policy, the original model can be reduced to a two-stage stochastic mixed-integer programming model and then efficiently solved by adopting a dual decomposition method combined with heuristics. Based on real-world business data, a numerical experiment is conducted with several benchmark models. The results verify the superior performance of our proposed approach based on increased out-of-sample profits and decreased overestimation of in-sample profits.

Wind Power Bidding Based on an Ensemble Differential Evolution Algorithm with a Problem-Specific Constraint-Handling Technique

The intermittent nature of wind power generation induces great challenges for power bidding in the electricity market. The deployment of battery energy storage can improve flexibility for power bidding. This paper investigates an optimal power bidding strategy for a wind–storage hybrid power plant in the day-ahead electricity market. To handle the challenges of the uncertainties of wind power generation and electricity prices, the optimal bidding problem is formulated as a risk-aware scenario-based stochastic programming, in which a number of scenarios are generated using a copula-based approach to represent the uncertainties. These scenarios consider the temporal correlation of wind power generation and electricity prices between consecutive time intervals. In the stochastic programming, a more practical but nonlinear battery operation cost function is considered, which leads to a nonlinear constrained optimization problem. To solve the nonlinear constrained optimization problem, an ensemble differential evolution (EDE) algorithm is proposed, which makes use of the merits of an ensemble of mutant operators to generate mutant vectors. Moreover, a problem-specific constraint-handling technique is developed. To validate the effectiveness of the proposed EDE algorithm, it is compared with state-of-the-art DE-based algorithms for constrained optimization problems, including a constrained composite DE (C2oDE) algorithm and a novel DE (NDE) algorithm. The experimental results demonstrate that the EDE algorithm is much more reliable and much faster in finding a better bidding strategy against benchmarking algorithms. More precisely, the average values of the success rate are 0.893, 0.667, and 0.96 for C2oDE, NDE, and EDE, respectively. Compared to C2oDE and NDE, the average value of the mean number of function evaluations to succeed with EDE is reduced by 76% and 59%, respectively.

Co-Optimizing Bidding and Power Allocation of an EV Aggregator Providing Real-Time Frequency Regulation Service

The rapidly expanding scale of electric vehicle (EV) fleets and continuously decreasing battery costs are making vehicle-to-grid services a reality. In this paper, we study the interaction between the problems of an EV aggregator’s bidding in the regulation market and power allocation (i.e., determining the (dis)charging powers of the EVs in regulation deployment). Although the two problems are coupled, they are often regarded as decoupled and optimized separately for complexity issues. However, failing to consider the coupling of bidding and power allocation can lead to a decline in the profit of the EV aggregator (EVA). In this paper, we propose a framework for co-optimizing EVA bidding and power allocation in the regulation market. The bidding model is formulated as a stochastic programming problem with embedded power allocation in discretized regulation signal scenarios. To meet the solution time requirement for regulation deployment, we further propose a power allocation model that can be solved online. It utilizes the Lagrange multipliers from the bidding problem to ensure that the allocation results correspond to the optimal solution of the bidding problem. The effect of the proposed framework on improving EVA profits and reducing degradation costs is verified in the case study.

Analysis of selected reinforcement learning applications in contract bridge

This paper presents an overview of four selected solutions addressing problem of bidding in card game of contract bridge. In the beginning the basic rules are presented along with basic problem size estimation. Brief description of collected work is presented in chronological order, tracking evolution of approaches to the problem. While presenting solution a short description of mathematical base is attached. In the end a comparison of solution is made, followed by an attempt to estimate future development of techniques.

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.

Day-Ahead Bidding Strategy of a Virtual Power Plant with Multi-Level Electric Energy Interaction in China

Effective aggregation and rational allocation of flexible resources are the fundamental methods for solving the problem of an insufficient flexibility adjustment ability of a power system. The flexible scheduling resources of a distribution system are often small in scale and distributed mostly by different stakeholders. A virtual power plant (VPP) gathers small resources to participate in the day-ahead electricity market, but, due to the scale and characteristics of a VPP’s internal flexible resources, it cannot reach the access threshold of a peak shaving market in some periods due to small differences. In order to solve the market bidding problem of a VPP limited by capacity, and to achieve economic goals, a virtual power plant operator (VPPO) not only needs to interact with internal subjects but also needs to interact with other subjects with flexible resources in the distribution network. In this study, an electric vehicle (EV) cluster is taken as the interactive object, and a day-ahead bidding strategy of a VPP with multi-level electric energy interaction is proposed. The VPP not only makes full-time game pricing for internal participants but also makes time-sharing bargaining with an EV operator. The validity and the rationality of the proposed strategy are verified by an example.

Two-stage dispatch optimal model of virtual power plant considering pumped storage

When virtual power plant (VPP) participates in power grid dispatch, it not only faces the problem of market bidding but also has the security and stability problems of voltage, frequency, power flow, and so on. The optimal dispatch strategy of VPP, which participates in a hybrid market, is proposed. The two-stage optimal model is established. An economic dispatch optimal model based on robust control and stochastic linear programming is established to maximize the profit of VPP. Aiming to minimize the difference between the output power of each distribution energy resource and the optimal results of economic dispatch, a safety dispatch optimal model based on a particle swarm optimization algorithm is established. The simulation results with the measured data of the Ningxia power grid show that the two-stage optimal dispatch model is effective.

Cooperative Power Bidding of Smart Community Grids With an Aggregator-Prosumer-Based Hierarchical Framework

The progressive development of electricity markets envisions the participation of smart community grids in energy trading, but it is still challenging to guarantee global optimality for uncertain power management of multiple entities under a hierarchical framework. To tackle the cooperative strategic bid-ding problem with uncertainties, this paper proposes a hierar-chical three-stage robust optimization (HTS-RO) method. With respect to the bilayer coordination framework involving an ag-gregator gathering multiple prosumers, a novel HTS-RO bidding model is firstly established relying on the canonical centralized two-stage RO model. In the first stage, the aggregator performs power bidding in the upper layer according to the derived power flow information of the shared buses from the lower-layer prosumers. Considering renewable-load uncertainties and pri-vacy preservation, each prosumer conducts its own robust scheduling via the second and third stages based on the bidding prices from the aggregator and submits its optimal results of the shared bus back to the aggregator. For the robust scheduling model of each prosumer, the second stage identifies the basic plans of the nominal scenario, and the third stage checks the fea-sibility of the basic plans under uncertainties. To solve the re-sulting intractable multi-level mixed-integer nonlinear pro-gramming, a tri-loop decomposition-based iterative algorithm is tailored to ensure that the distributed computation converges to the optimal solution with the overall profit, thereby achieving the equivalent split of the centralized optimization into a hierarchical manner. Numerical tests on generic smart community grids with multiple prosumers validate the applicability and superiority of the proposed HTS-RO method for power bidding.

Solving Bilevel Optimal Bidding Problems Using Deep Convolutional Neural Networks

Current state-of-the-art solution techniques for solving bilevel optimization problems either assume strong problem regularity criteria or are computationally intractable. In this article, we address power system problems of bilevel structure, commonly arising after the deregulation of the power industry. Such problems are predominantly solved by converting the lower level problem into a set of equivalent constraints using the Karush–Kuhn–Tucker optimality conditions at an expense of binary variables. Furthermore, in case the lower level problem is nonconvex, the strong duality does not hold rendering the single-level reduction techniques inapplicable. To overcome this, we propose an effective numerical scheme based on bypassing the lower level completely using an approximation function that replicates the relevant lower level effect on the upper level. The approximation function is constructed by training a deep convolutional neural network. The numerical procedure is run iteratively to enhance the accuracy. As a case study, the proposed method is applied to a price-maker energy storage optimal bidding problem that considers an ac power flow-based market clearing in the lower level. The results indicate that greater actual profits are achieved as compared to the less accurate dc market representation.

Risk-Aware Battery Bidding With a Novel Benchmark Selection Under Second-Order Stochastic Dominance

This paper studies the risk management of a battery bidding in both day-ahead and intraday markets arising from the uncertain nature of electricity prices. To this end, a coherent risk measure, Second-order Stochastic Dominance (SSD), which is capable of expressing battery preferences in the form of a preset fixed benchmark (profit), is incorporated into the bidding model. The SSD serves the decision-maker as a risk-averse optimizer exploring for profit distribution members greater than a preset fixed benchmark. The most challenging facet of SSD-constrained methodologies is how to effectually define the preset fixed benchmark. In this regard, first, a generic approach is offered to find the feasible region for benchmark selection in SSD-constrained optimization problems. Then, a novel benchmark selection technique considering both the decision-maker's regret and out-of-sample profit, leverages the VIKOR method to get the ranking of different solutions and find the compromise benchmark in the risk-aware environment. Consequently, two decisive criteria from both ex- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ante</i> and ex- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">post</i> tests are involved in the benchmark selection procedure, making the bidding problem regret- and consequence-aware. The numerical results of the developed methodology against risk-neutral and deterministic approaches show the efficiency of the proposed model.

Learning Active Constraints to Efficiently Solve Linear Bilevel Problems: Application to the Generator Strategic Bidding Problem

Bilevel programming can be used to formulate many problems in the field of power systems, such as strategic bidding. However, common reformulations of bilevel problems to mixed-integer linear programs make solving such problems hard, which impedes their implementation in real-life. In this paper, we significantly improve solution speed and tractability by introducing decision trees to learn the active constraints of the lower-level problem, while avoiding to introduce binaries and big-M constants. The application of machine learning reduces the online solving time, by moving the selection of active constraints to an offline process, and becomes particularly beneficial when the same problem has to be solved multiple times. We apply our approach to the strategic bidding of generators in electricity markets, where generators solve the same problem many times for varying load demand or renewable production. Three methods are developed and applied to the problem of a strategic generator, with a DCOPF in the lower-level. These methods are heuristic and as so, do not provide guarantees of optimality or solution quality. Yet, we show that for networks of varying sizes, the computational burden is significantly reduced, while we also manage to find solutions for strategic bidding problems that were previously intractable.

Research on Intelligent Verification Technology of Bid Evaluation Results

Bidding is an important procurement method. By giving full play to the advantages of bidding enterprises and carrying out open and fair competition, it has realized the effective optimization of the market economic environment and significantly improved the benefits of engineering projects. The bidding of power engineering project is to realize the fair and transparent competition among bidding units. In order to improve the standardization and fairness of bid evaluation results and solve the final control problem of power bidding, it is particularly important to do a good job in the intelligent verification of bid evaluation results. This paper mainly studies the intelligent verification technology of bidding and bid evaluation results. By studying the bidding and bid evaluation process and standards, and using information intelligent technology, this project summarizes some standard laws and models for verifying the bid evaluation results, and develops the intelligent verification tool of bid evaluation results.

Design of a Structured Parsing Model for Corporate Bidding Documents Based on Bi-LSTM and Conditional Random Field (CRF)

International projects are often realized through the bidding process, but the existence of information exchange barriers in different countries leads to a complex and tedious bidding process. In this paper, the authors study the complex problem of reading bidding documents, combine the artificial intelligence to analyze them in a structured way, and realize the intelligent analysis of bidding documents. Firstly, through the CRF model, the structured analysis of the tender document is carried out according to the title of the tender document, and the extraction of quoted price, technology and commercial part is realized. Secondly, the detailed analysis of quoted price and technology is completed using the Bi-LSTM method, and the main five key feature extraction and analysis are completed. Finally, based on the CRF-Bi-LSTM method, the actual test is carried out, and the correlation coefficient is as high as 0.965. The results show that the structured parsing model proposed has good application prospects.

Provision of multiple services with controllable loads as multi-area thermal energy storage

Power systems are experiencing a decrease of synchronous generation along with increased penetration of inverter based renewable generation leading to reduced system inertia and a need for flexible resources. Non-generating resources such as thermostatically controlled loads (TCLs) are flexible due to their thermal energy storage capacity. When aggregated, TCLs can arbitrage energy prices and provide reserves to the power system. We approach the operational flexibility of the TCLs by modeling a risk-averse aggregator that controls decentralized TCLs and aims to maximize its own profit. The high number and low power rating of residential TCLs makes it difficult to model and assess their flexibility potential on national level. Thus, we make use of a high-level thermal energy storage model for aggregations of TCLs to quantify their flexibility potential. We present a method to aggregate temperature, TCL parameters, and building stock data into a thermal battery equivalent. We propose a multi-period multi-market multi-zonal two-stage chance constrained rolling horizon optimization problem formulation for the risk-averse day-ahead self-scheduling problem of a price-taker TCL aggregator bidding in energy and reserve markets under uncertainty and recast the problem as a linear program. We perform several case studies in the Swedish power system based on a survey of single- and two-family dwellings with electric heating and assess the flexibility potential. Additionally, a sensitivity analysis provides insights regarding market design and policy implications.

A Data-Driven Joint Chance-Constrained Game for Renewable Energy Aggregators in the Local Market

The local market can promote more self-generated electricity consumed locally. However, the unstable and intermittent generation of renewable energy sources brings uncertainty and overbidding risk to the local market. We proposed a competitive local energy market (LEM) where renewable energy aggregators (REAs) can submit bids instead of acting as price takers. A data-driven joint chance-constrained game of REAs is proposed for the optimal bidding problem under the network constraints and the risk-averse chance constraint. We consider the case that the maximum outputs of REAs are random variables whose probability distributions are unknown, but the decision-maker has access to finite samples. Each player’s strategy set is defined in a data-driven distributionally robust framework with the Wasserstein ambiguity set. The exact reformulation of the distributionally robust chance constraint and the corresponding inner approximation version are derived. We prove the existence of the Nash equilibrium in the proposed distributionally robust chance-constrained game. Finally, an efficient best response seeking algorithm is developed to find the normalized Nash equilibrium, and the convergence proof of the proposed algorithm is also provided. Numerical simulations demonstrate that the proposed game model can effectively increase the revenue of reliable players and reduce the overbidding rate of REAs.

Production Planning of Cascaded Hydropower Stations using Approximate Dynamic Programming

We formulate the day-ahead bidding problem for a hydropower producer having several hydropower plants residing in a river basin. We present a novel approach inspired by Dynamic programming with approximations in value and policy space by neural networks. This allows for more accurate modeling of the problem by avoiding linear approximations of the production function and bidding. Stochastic programming is a method frequently used in literature to solve the hydropower production planning problem. Stochastic programming is used on linearized systems and under assumptions of known distributions of the involved stochastic processes. We test the proposed algorithm on a simplified system, suitable for Stochastic Programming and compare the obtained policy with the results from Stochastic Programming. The results show that the algorithm obtains a policy similar to that of Stochastic Programming.

Optimal Bidding Strategy Considering Bilevel Approach and Multistage Process for a Renewable Energy Portfolio Manager Managing RESs With ESS

This article presents a bilevel and multistage framework in whicha renewable energy portfolio manager (REPM) manages renewable energy sources (RESs) integrated with an energy storage system (ESS) to reduce imbalances and joins in the day-ahead market and the balancing market, including bilateral contracts. The total REPM gain is maximized in the upper level, whereas the loss of income of each portfolio participant in the lower level is minimized taking into account the specified income value. In the multistage structure, different decisions are taken regarding energy trade according to the hours of the day. Generations and price uncertainties that need to be addressed in optimum bidding problems are eliminated with a stochastic approach. Besides, risk management is evaluated through the conditional value-at-risk method. Besides, the test is carried out using real data from Spain in order to verify the effectiveness of the proposed model. According to the results obtained from the study, it can be stated that RESs with ESS increase the portfolio profit by 2%, and even in the case of expected generation, it is 4.1%, by better managing the energy imbalance of participants.