Bidding Problem Research Articles

An opposition theory enabled moth flame optimizer for strategic bidding in uniform spot energy market

Power generating companies have an opportunity to maximize their profit in electricity market by selling the energy at competitive prices under incomplete information of other rivals behavior. In a day-ahead energy market, Generating Company (GENCOs) sells the energy at optimal bid prices. To calculate the bid prices optimally and for maximizing the profit of generating company, this paper presents a solution for strategic bidding problem which is based on opposition theory enabled moth flame optimizer (OB-MFO).In this work, a new opposition theory enabled moth flame optimizer is proposed which have the additional concept of oppositional feature. First OB-MFO algorithm is tested on 22 benchmark and Congress on Evolutionary Computation (CEC-2017) functions, then it is applied to bidding problem of standard IEEE-14 bus (Test Case-1) and 7 generator power system (Test Case-2). The strategic bidding scheme for a generating company for single and multi hour trading duration in a day-ahead market is formulated. The major findings of the proposed approach are market clearing price (MCP), load dispatch and bid prices of five different blocks of different capacities. The meaningful comparison of the bidding results of other optimization techniques are presented. In addition to that price volatility analysis and exercise of market power analysis are also presented. The results confirm the effectiveness of proposed technique.

Market bidding strategy of the microgrids considering demand response and energy storage potential flexibilities

Volatile impact of intermittent renewable energy sources (RESs) on the one hand and the uncertainties of loads and market prices, on the other hand, make the bidding strategy of microgrids (MGs) too risky and high-computational problem. To cope with these challenges, the bidding problem of MGs based on a three-stage hybrid stochastic/interval optimisation (HSIO) is devised in this study, which provides a trade-off between covering the volatilities by means of the MG potential flexibilities resources or by means of the energy provision from the real-time market (RTM). To tackle the uncertainties of the day-ahead market prices, the cost-effective stochastic programming (SP) is applied to maximise the profit of MG in the day-ahead stage of decision-making. In order to handle the volatilities of RESs production and uncertainties of RTM prices, a flexibility scheme based on the robust and low-computational interval optimisation (IO) approach is designed to minimise the balancing cost of MG in the real-time stages. Comprehensive numerical results are provided to compare the effectiveness, robustness, and computational complexity of the proposed model. Results show that the HSIO model takes advantage of the cost-effective solution from the SP model, and the robust solution with computational simplicity from the IO model.

Skew to win, not to profit – unbalanced bidding among informed bidders

PurposeSeveral sectors, especially the construction industry, use unit price contracting (UPC). This contracting form provides agents, ex ante, with estimated quantities of the work to be done. Competing agents then offer corresponding unit prices i.e. the bid is a price vectors, and most often the lowest vector sum is awarded the contract. This way of procuring is not only transparent but also entails a potential problem of unbalanced bidding. Unbalanced bidding occurs when an informed agent skews unit prices to win the ex ante bid. The concept is not new topic in research, but theoretical models from an economics perspective are not extensive.Design/methodology/approachThis paper will focus on how competition among informed bidders will affect the optimal solution.FindingsIt is shown that skewing is still a dominating strategy under competition. However, competition will decrease, but not necessarily eliminate, information rents.Originality/valueIn this setting, unbalanced bidding could mainly be seen as a way to win the contract and not to extract information rents. Thus, it would not constitute an efficiency problem for the client.

Algorithmic Bidding for Virtual Trading in Electricity Markets

We consider the problem of optimal bidding for virtual trading in two-settlement electricity markets. A virtual trader aims to arbitrage on differences between day-ahead and real-time market prices that are random and unknown to market participants. An online learning algorithm is proposed to maximize the cumulative payoff over a finite number of trading sessions by allocating the trader's budget among his bids for K options in each session. It is shown that the expected payoff of the proposed algorithm converges, with an almost optimal convergence rate, to the expected payoff of the global optimal corresponding to the case when the underlying price distribution is known. The proposed algorithm is also generalized for trading strategies with a risk measure. By using both cumulative payoff and Sharpe ratio as performance metrics, evaluations were performed based on the historical data spanning ten year period of NYISO and PJM markets. It was shown that the proposed strategy outperforms standard benchmarks and the S&P 500 index over the same period.

Two-Stage Stochastic Optimization for the Strategic Bidding of a Generation Company Considering Wind Power Uncertainty

With the deregulation of electricity market, generation companies must take part in strategic bidding by offering its bidding quantity and bidding price in a day-ahead electricity wholesale market to sell their electricity. This paper studies the strategic bidding of a generation company with thermal power units and wind farms. This company is assumed to be a price-maker, which indicates that its installed capacity is high enough to affect the market-clearing price in the electricity wholesale market. The relationship between the bidding quantity of the generation company and market-clearing price is then studied. The uncertainty of wind power is considered and modeled through a set of discrete scenarios. A scenario-based two-stage stochastic bidding model is then provided. In the first stage, the decision-maker determines the bidding quantity in each time period. In the second stage, the decision-maker optimizes the unit commitment in each wind power scenario based on the bidding quantity in the first stage. The proposed two-stage stochastic optimization model is an NP-hard problem with high dimensions. To tackle the problem of “curses-of-dimensionality” caused by the coupling scenarios and improve the computation efficiency, a modified Benders decomposition algorithm is used to solve the model. The computational results show the following: (1) When wind power uncertainty is considered, generation companies prefer higher bidding quantities since the loss of wind power curtailment is much higher than the cost of additional power purchases in the current policy environment. (2) The wind power volatility has a strong negative effect on generation companies. The higher the power volatility is, the lower the profits, the bidding quantities, and the wind power curtailment of generation companies are. (3) The thermal power units play an important role in dealing with the wind power uncertainty in the strategic bidding problem, by shaving peak and filling valley probabilistic scheduling.

Model-based bidding strategies on the primary balancing market for energy-intense processes

Energy-intense enterprises that flexibilize their electricity consumption can market this either at electricity spot markets or by offering ancillary services on demand, such as balancing power. We formulate optimization of the balancing power bidding strategy as a mixed-integer nonlinear program considering both price forecasts for the ancillary service market and hourly varying spot market prices. We solve this two-stage approach by decomposition into a nonlinear bidding problem and a mixed-integer linear scheduling problem. We consider aluminum electrolysis participating in the German primary balancing market. We show savings in weekly production costs of 5–20% compared to stationary operation. The savings due to the optimal bidding strategy are up to twice the savings from pure exploitation of electricity spot market price spreads. We thus demonstrate that energy-intense processes can systematically take advantage of highly profitable demand-side management measures beyond a spot market price adjusted production.

Economic Advantages of Office Buildings Providing Ancillary Services With Intraday Participation

Controlling the consumption profile of office buildings can be used to provide balancing services to the power grid at a financial benefit without violating its thermal comfort constraints. The economic advantage of such a service is a reduction in the total operating cost, but also an increase in average occupants' comfort when using our control scheme. We study these effects for the case of participating in the secondary frequency control market of Switzerland. Moreover, we examine the advantages of engaging in the intraday energy market. We propose a method for solving the flexibility bidding problem for a building in order to partake in the ancillary services (AS) market. The proposed solution is based on the combination of a new intraday control policy and two-stage stochastic programming. We also study the sensitivity of this economic benefit to electricity pricing. Our findings are based on extensive simulations with real data for energy prices, AS bids, meteorological records, and the frequency control signals for the year 2014 as transmitted by Swissgrid.

A Bidding Strategy for Virtual Power Plants With the Intraday Demand Response Exchange Market Using the Stochastic Programming

This paper presents a mathematical model for the energy bidding problem of a virtual power plant (VPP) that participates in the regular electricity market and the intraday demand response exchange (DRX) market. Different system uncertainties due to the intermittent renewable energy sources, retail customers’ demand, and electricity prices are considered in the model. The DRX market enables a VPP to purchase demand response services, which can be treated as “virtual energy resources,” from several demand response providers to reduce the penalty cost on the deviation between the day-head bidding and the real-time dispatch. This could increase the expected profit and the renewable energy utilization of the VPP. The overall energy bidding problem is modeled as a three-stage stochastic program, which can be solved efficiently by the scenario-based optimization approach. Extensive numerical results show that the DRX market participation can improve the VPP's energy management.

Hydropower bidding in a multi-market setting

We present a literature survey and research gap analysis of mathematical and statistical methods used in the context of optimizing bids in electricity markets. Particularly, we are interested in methods for hydropower producers that participate in multiple, sequential markets for short-term delivery of physical power. As most of the literature focus on day-ahead bidding and thermal energy producers, there are important research gaps for hydropower, which require specialized methods due to the fact that electricity may be stored as water in reservoirs. Our opinion is that multi-market participation, although reportedly having a limited profit potential, can provide gains in flexibility and system stability for hydro producers. We argue that managing uncertainty is of key importance for making good decision support tools for the multi-market bidding problem. Considering uncertainty calls for some form of stochastic programming, and we define a modelling process that consists of three interconnected tasks; mathematical modelling, electricity price forecasting and scenario generation. We survey research investigating these tasks and point out areas that are not covered by existing literature.

Optimal Joint Bidding and Pricing of Profit-Seeking Load Serving Entity

The demand response provides an opportunity for load serving entities (LSEs) that operate retail electricity markets (REMs) to strategically purchase energy and provide reserves in wholesale electricity markets (WEMs). This paper concerns with the problem of simultaneously determining the optimal energy bids and reserve offers an LSE submits to the WEM as well as the optimal energy and reserve prices it sets in the REM so as to maximize its profit. To this end, we explicitly model the trilayer market structure that consists of a WEM, a REM, and a set of end user customers, so as to capture the coupling between the bidding problem and the pricing problem. Based on the trilayer market model, we then formulate the joint bidding and pricing problem as a bilevel programming problem and further transform it into a single-level mixed integer linear programming problem, which can be solved efficiently. Numerical studies using the IEEE test cases are presented to illustrate the application of the proposed methodology as well as to reveal several interesting characteristics of the LSE's profit-seeking behavior..

Robust Profit Maximization in Multiperiod Energy Markets with Interval Prediction of Photovoltaics

Abstract In this paper, we formulate an optimal bidding problem in a multiperiod electricity market with the consideration of the uncertain PV output. Based on the proposed strategy, the aggregator of interest operates his dispatchable assets to pursue the largest profit by submitting one optimal prosumption curve to the day-ahead market. To deal with a non-convexity issue stemming from the robust optimization problem, we reformulate the problem as its Lagrange dual counterpart. Then, we describe the uncertain range of the PV output by one polyhedral set, with which a new decision variable is introduced. We implement a constraints-generation method to solve the newly formulated problem by splitting it into another two subproblems. Based on one iterative scheme, the two subproblems are solved in sequence, and the solution of the robust optimization problem is obtained when the optimal results of the two subproblems are equal. In the numerical simulation, the profits under different PV lower bounds are presented.

Sto2Auc: A Stochastic Optimal Bidding Strategy for Microgrids

Microgrids (MGs) have attracted growing attention due to self-sufficiency and self-healing properties. Nonetheless, the intermittent nature and uncertainty of distributed energy resources and load demands remain challenging issues in balancing demands and managing energy resources in MGs. Existing research efforts mainly focus on developing techniques to enable interactions between local MGs and the utility grid, which leads to high line power losses and operation costs. In this paper, we present the Sto2Auc framework to address the issue of stochastic optimal bidding problem for a system with MGs. First, the optimal bidding problem is formulated as a two-stage stochastic programming process, which aims to minimize the system operation cost and obtain optimal energy capacity of MGs by the MG center controller (MGCC). Uncertainties arise from both energy supply and demand, which are considered in the stochastic model, and random parameters representing those uncertainties are captured by using the Monte Carlo method. Second, to enable optimal electricity trading between the insufficient and surplus MGs, we propose a distributed double auction (DDA)-based scheme, which is proven to converge to the optimal social welfare of the system with MGs, and achieves the economical properties of being strategy-proof, individually rational, and (weak) budget balanced. Extensive experiments on an MG system composed of IEEE-33 buses demonstrate the effectiveness of proposed scheme. The experimental results show that Sto2Auc framework is capable of reducing the operational cost of MG systems, while the implemented DDA scheme achieves good performance with respect to social welfare, demand insufficiency, and MGCC profit.

Hydroassets portfolio management for intraday electricity trading from a discrete time stochastic optimization perspective

Hydro storage system optimization is becoming one of the most challenging tasks in energy finance. While currently the state-of-the-art of the commercial software in the industry implements mainly linear models, we would like to introduce risk aversion and a generic utility function. At the same time, we aim to develop and implement a computational efficient algorithm, which is not affected by the curse of dimensionality and does not utilize subjective heuristics to prevent it. For the short term power market we propose a simultaneous solution for both dispatch and bidding problems. Following the Blomvall and Lindberg (Eur J Oper Res 143(2):452–461, 2002) interior point model, we set up a stochastic multiperiod optimization procedure by means of a “bushy”recombining tree that provides fast computational results. Inequality constraints are packed into the objective function by the logarithmic barrier approach and the utility function is approximated by its second order Taylor polynomial. The optimal solution for the original problem is obtained as a diagonal sequence where the first diagonal dimension is the parameter controlling the logarithmic penalty and the second one is the parameter for the Newton step in the construction of the approximated solution. Optimal intraday electricity trading and water values for hydroassets as shadow prices are computed. The algorithm is implemented in Mathematica.

Game Theory Analysis of Bidding for A Construction Contract

The authors are concerned with a bidding problem. There are two companies (P1 and P2) bidding for a highway construction project. In order to be more competitive, P1 considers buying a new gravel pit near the construction site. The basic cost of the pit is known to both companies. However, there is also an additional, hidden, cost (C) known only to P1. P2 is uncertain whether the hidden cost is C = 0 or C = x. P1 plans to bid for the job, but has to decide whether to buy the gravel pit. P2, not having a complete knowledge about C, thus not knowing the strategy choice of P1, has to decide if to bid for the job. In effect we have two payoff matrices, one for the additional cost C = 0, and the other one for C = x. If the probability of P2 bidding for the project can be estimated by propagating intelligence information through a Bayesian Belief Network, the best strategy for P1 can be readily determined.Otherwise, the solution calls for changing this game of incomplete information (players may or may not know some information about the other players, e.g., their “type,” their strategies, payoffs) into a game of imperfect information (players are simply unaware of the actions chosen by other players).This is achieved by introducing an additional “Nature” node which for this problem determines with some probability “p” the additional cost C= 0 (thus, C = x with probability 1-p). The solution of this game turns out to depend on the probability “p”. For some values of p the game is solved with pure strategies, whereas for other values the game is in equilibrium when the players randomly mix their strategies.

Strategic Bidding for Producers in Nodal Electricity Markets: A Convex Relaxation Approach

Strategic bidding problems in electricity markets are widely studied in power systems, often by formulating complex bi-level optimization problems that are hard to solve. The state-of-the-art approach to solve such problems is to reformulate them as mixed-integer linear programs (MILPs). However, the computational time of such MILP reformulations grows dramatically, once the network size increases, scheduling horizon increases, or randomness is taken into consideration. In this paper, we take a fundamentally different approach and propose effective and customized convex programming tools to solve the strategic bidding problem for producers in nodal electricity markets. Our approach is inspired by the Schmudgen's Positivstellensatz Theorem in semialgebraic geometry; but then we go through several steps based upon both convex optimization and mixed-integer programming that results in obtaining close to optimal bidding solutions, as evidenced by several numerical case studies, besides having a huge advantage on reducing computation time. While the computation time of the state-of-the-art MILP approach grows exponentially when we increase the scheduling horizon or the number of random scenarios, the computation time of our approach increases rather linearly.

Optimal Bidding in Performance-Based Regulation Markets: An MPEC Analysis With System Dynamics

In this paper, we address the problem of optimal bidding in performance-based regulation markets for a large price-maker regulation resource. Focusing on the case of the California Independent System Operator (ISO), detailed market components are considered, such as regulation capacity payment, regulation mileage payment, performance accuracy adjustment, automatic generation control dispatch, and participation factor. Our analysis also incorporates system dynamics of the regulation resource for different resource types and technologies. In principle, our problem formulation is a mathematical program with equilibrium constraints (MPEC). However, our fundamentally new formulations introduce several new challenges in solving the MPEC problem in the context of performance-based regulation markets that are not previously addressed. In fact, global optimization techniques fail to solve the original nonlinear program due to its complexity. Therefore, we undergo several innovative steps to transform the problem into a mixed-integer linear program which is solved with accuracy, reliability, and computational efficiency. Insightful case studies are presented using data from a California ISO regulation market project.

Modelling contractor’s bidding decision

Abstract The authors aim to provide a set of tools to facilitate the main stages of the competitive bidding process for construction contractors. These involve 1) deciding whether to bid, 2) calculating the total price, and 3) breaking down the total price into the items of the bill of quantities or the schedule of payments to optimise contractor cash flows. To define factors that affect the decision to bid, the authors rely upon literature on the subject and put forward that multi-criteria methods are applied to calculate a single measure of contract attractiveness (utility value). An attractive contract implies that the contractor is likely to offer a lower price to increase chances of winning the competition. The total bid price is thus to be interpolated between the lowest acceptable and the highest justifiable price based on the contract attractiveness. With the total bid price established, the next step is to split it between the items of the schedule of payments. A linear programming model is proposed for this purpose. The application of the models is illustrated with a numerical example. The model produces an economically justified bid price together with its breakdown, maintaining the logical proportion between unit prices of particular items of the schedule of payment. Contrary to most methods presented in the literature, the method does not focus on the trade-off between probability of winning and the price but is solely devoted to defining the most reasonable price under project-specific circumstances. The approach proposed in the paper promotes a systematic approach to real-life bidding problems. It integrates practices observed in operation of construction enterprises and uses directly available input. It may facilitate establishing the contractor’s in-house procedures and managerial decision support systems for the pricing process.

A Study of Compact Reserve Pricing Languages

Online advertising allows advertisers to implement fine-tuned targeting of users. While such precise targeting leads to more effective advertising, it introduces challenging multidimensional pricing and bidding problems for publishers and advertisers. In this context, advertisers and publishers need to deal with an exponential number of possibilities. As a result, designing efficient and compact multidimensional bidding and pricing systems and algorithms are practically important for online advertisement. Compact bidding languages have already been studied in the context of multiplicative bidding. In this paper, we study the compact pricing problem.

Agent-Based Modeling in Electrical Energy Markets Using Dynamic Bayesian Networks

Due to uncertainties in generation and load, optimal decision making in electrical energy markets is a complicated and challenging task. Participating agents in the market have to estimate optimal bidding strategies based on incomplete public information and private assessment of the future state of the market, to maximize their expected profit at different time scales. In this paper, we present an agent-based model to address the problem of short-term strategic bidding of conventional generation companies (GenCos) in a power pool. Based on the proposed model, each GenCo agent develops a private probabilistic model of the market (using dynamic Bayesian networks), employs an online learning algorithm to train the model (sparse Bayesian learning), and infers the future state of the market to estimate the optimal bidding function. We show that by using this multiagent framework, the agents will be able to predict and adapt to approximate Nash equilibrium of the market through time using local reasoning and incomplete publicly available data. The model is implemented in MATLAB and is tested on four test case systems: two generic systems with 5 and 15 GenCo agents, and two IEEE benchmarks (9-bus and 30-bus systems). Both the day-ahead (DA) and hour-ahead (HA) bidding schemes are implemented. The results show a drop in market power in the 15-agent system compared to 5-agent system, along with a Pareto superior equilibrium in the HA scheme compared to the DA scheme, which corroborates the validity of the proposed decision making model. Also, the simulations show that introduction of an HA decision making stage as an uncertainty containment tool, leads to a more stable and less volatile price signal in the market, which consequently results in flatter and improved profit curves for the GenCos.

Estimating the number of new and repeated bidders in construction auctions

The number of new bidders – bidders from whom there is no previous registered participation – is an important variable in most bid tender forecasting models, since the unknown competitive profile of the former strongly limits the predictive accuracy of the latter. Analogously, when a bidder considers entering a bid or when an auctioneer is handling a procurement auction, assessing the likely proportion of experienced bidders is considered an important aspect, as some strategic decisions or even the awarding criteria might differ. However, estimating the number of bidders in a future auction that have not submitted a single bid yet is difficult, since there is no data at all linking their potential participation, an essential requirement for the implementation of any forecasting or estimation method. A practical approach is derived for determining the expected proportion of new bidders to frequent bidders as a function of the population of potential bidders. A multinomial model useful for selective and Open tendering is proposed and its performance is validated with a dataset of actual construction auctions. Final remarks concern the valuable information provided by the model to an enduring unsolved bidding problem and the prospects for new research continuations.