Strategic Bidding Problem Research Articles

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.

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.

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.

Strategic bidding in electricity markets with convexified AC market-clearing process

This paper presents a framework to solve the strategic bidding problem of participants in an electricity market cleared by employing the full AC Optimal Power Flow (ACOPF) problem formulation. Traditionally, the Independent System Operators (ISOs) leveraged DC Optimal Power Flow (DCOPF) problem formulation to settle the electricity market. The main quest of this work is to find what would be the challenges and opportunities if ISOs leveraged the full ACOPF as the Market-Clearing Problem (MCP)? This paper presents tractable mathematical programming with equilibrium constraints for the convexified AC market-clearing problem. Market participants maximize their profit via strategic bidding while considering the reactive power dispatch of generation units. The equilibrium constraints are procured by presenting the dual form of the relaxed ACOPF problem. The strategic bidding problem with an ACOPF-based MCP improves the exactness of the Location Marginal Prices (LMPs) and profit of market participants compared to the one with DCOPF. It is shown that the strategic bidding problem with DCOFP-based MCP is unable to model the limitation of reactive power support. The presented results display cases where the proposed strategic bidding method renders 52.3% more profit for the Generation Company (GENCO) than the DCOPF-based MCP model. The proposed strategic bidding framework also addresses the challenges of coupling real and reactive power dispatch of generation constraints, ramping constraints, demand response implications with curtailable and time shiftable loads, and AC line flow constraints. Therefore, the presented method will help market participants leverage the more accurate ACOPF model in the strategic bidding problem.

Double‐sided bidding strategy for power suppliers and large buyers with amalgamation of wind and solar based generation in a modern energy market

The deployment of renewable energy sources has been rapidly increasing due to environmental constraints but renewable electricity suppliers face an inevitable problem of uncertainty which is caused by the intermittent nature of renewable sources. In real-time operation, compromises have been made in cost and power to balance the power which reduces supplier benefits. Therefore, the functions of Weibull and Beta distribution of probability are used to handle the adverse impact of wind speed uncertainty and solar irradiation, respectively, and scenarios are reduced using the forward-reduction algorithm. Moreover, to measure the deviation of renewable power, underestimation and overestimation cost functions are utilised. This study proposes a suitable double-sided strategic bidding problem as a multi-objective optimisation problem to maximise the profits of suppliers and buyers to minimise uncertainty of rivals and renewable power. The formulated problem is solved by Technique for Order of Preference by Similarity to Ideal Solution along with Gravitational Search Algorithm, and simulation results are obtained in absence and presence of both solar and wind power on IEEE standard 30-bus and 57-bus test systems. The obtained results prove the suitability of the proposed bidding strategy in the presence of uncertainty of solar and wind power.

A new redefined model of Firefly Algorithm with application to strategic bidding problem in Power Sector

Real-life optimization problems require an effective mechanism that completely utilizes the search space to obtain optimal solutions. A designer has always an opportunity to propose a new effective solution technique to address this issue. In this order, this paper presents a new upgraded redefined model of nature-inspired state of art meta-heuristic firefly algorithm (FA). FA is centered on swarm intelligence, which is motivated by the flashing pattern and behavior of fireflies. However, for a few instances, FA has a tendency to trap in local optima and it exhibits slow convergence. The proposed model is enabled through Time-varying Inertia Weight (TIW), Opposition Based Learning (OBL) and hybridized with sine cosine operators to get updated positions of search agents. A set of twenty-two classical benchmark function problems with numerous range and features are employed to prove the efficacy of the proposed model. Also, the effects of the above-mentioned modifications during the whole optimization routine are analyzed through different statistical and numerical analyses. The result analysis proves that the proposed modifications make FA more compatible. The proposed model is also tested on the strategic bidding problem of the power market of two different test systems with single and multi-trading hours. All the reported results confirm the supremacy of the proposed redefined model of FA.

Strategic Bidding of Private Information for Dynamic LQ Networks under Moral Hazard

This paper investigates the whole system behavior caused by the influence of the agents’ strategic behavior while utilizing their individual control and private information for a dynamic linear-quadratic (LQ) network in the presence of a principal-agent relationship. The principal aims at integrating agents’ behavior into the socially optimal one based on private information bid by the agents. To avoid a moral hazard on agents’ controls, the principal must give a reward to the agents. The reward induces the agents to choose their controls achieving the social objective under the true private information case, but the reward cannot prevent the strategic bidding of the agents’ private information. Under this situation, the case is considered that all the agents minimize their net cost composed of their own private cost and the reward from the principal, which is called the strategic bidding problem under moral hazard. Then, the strategic bidding problem is formulated and the optimal design of the problem is analytically derived. Their effectiveness and limitations are also discussed through a simulation.

Bidding strategy for generators considering ramp rates in a day-ahead electricity market

In a day-ahead electricity market, competitive bidding strategy plays a vital role for power suppliers to maximize their profit. In this type of market, each power supplier submits a set of hourly production prices and offers capacity for the next period. The market operator, after receiving this data along with forecasted hourly load from the demand side, allocates production output to each unit. Power suppliers face the problem in trading their offers in the market, due to the uncertain behavior of competitive power suppliers and power demand. Therefore, the power supplier requires a suitable bidding strategy for handling uncertainty in the market to maximize their profits. Moreover, the considerations of ramp rates are necessary for the precise representation of practical power system. Thus, in the present work, a modified gravitational search algorithm based on oppositional learning concept is used to solve strategic bidding problem for power suppliers considering six generators with ramp rates, 24-h load data and rivals behavior. The total hourly profits of generators with and without considering ramp rates have been compared.

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.

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.

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.

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.

Dynamic convexification within nested Benders decomposition using Lagrangian relaxation: An application to the strategic bidding problem

Many decomposition algorithms like Benders decomposition and stochastic dual dynamic programming are limited to convex optimization problems. In this paper, we utilize a dynamic convexification method that makes use of Lagrangian relaxation to overcome this limitation and enables the modeling of non-convex multi-stage problems using decomposition algorithms. Though the algorithm is confined by the duality gap of the problem being studied, the computed upper bounds (for maximization problems) are at least as good as those found via a linear programming relaxation approach. We apply the method to the strategic bidding problem for a hydroelectric producer, in which we ask: What is the revenue-maximizing production schedule for a single price-maker hydroelectric producer in a deregulated, bid-based market? Because the price-maker’s future revenue function has a sawtooth shape, we model it using mixed-integer linear programming. To remedy the non-concavity issues associated with modeling the future revenue function as a mixed-integer linear program, we model the price-maker’s bidding decision utilizing both Benders decomposition and Lagrangian relaxation. We demonstrate the utility of our algorithm through an illustrative example and through three case studies in which we model electricity markets in El Salvador, Honduras, and Nicaragua.

An application of genetic algorithm to a bidding problem in electricity markets

AbstractIn this paper, we present the problem of strategic bidding under uncertainty in a wholesale energy market, where the economic remuneration of each electricity generator depends on the ability of its own management to submit price and quantity bids. This stochastic problem is highly nonconvex, and due to its difficulty there has been an intensive search for efficient algorithms to solve it. We present a bilevel formulation for the problem and propose a genetic algorithm for its solution, where the individual of the population represents the choice of the upper‐level decision maker. For each individual, the linear programming formulation of the lower level problem is considered and its exact optimum solution is obtained in a very efficient way. Numerical experiments with instances of configurations derived from the Brazilian power system demonstrate the quality of the results obtained by the proposed algorithm. An analysis of the results is also presented for a case study comparing strategic bids to cost‐based bids.

Competitive Strategic Bidding Optimization in Electricity Markets Using Bilevel Programming and Swarm Technique

Competitive strategic bidding optimization is now a key issue in electricity generator markets. Digital ecosystems provide a powerful technological foundation and support for the implementation of the optimization. This paper presents a new strategic bidding optimization technique which applies bilevel programming and swarm intelligence. In this paper, we first propose a general multileader-one-follower nonlinear bilevel (MLNB) optimization concept and related definitions based on the generalized Nash equilibrium. By analyzing the strategic bidding behavior of generating companies, we create a specific MLNB decision model for day-ahead electricity markets. The MLNB decision model allows each generating company to choose its biddings to maximize its individual profit, and a market operator can find its minimized purchase electricity fare, which is determined by the output power of each unit and the uniform marginal prices. We then develop a particle-swarm-optimization-based algorithm to solve the problem defined in the MLNB decision model. The experiment results on a strategic bidding problem for a day-ahead electricity market have demonstrated the validity of the proposed decision model and algorithm.

Multi-objective bidding strategy for GenCo using non-dominated sorting particle swarm optimisation

This paper proposes a multi-objective bidding strategy for a generation company (GenCo) in a day-ahead uniform price spot market using non-dominated sorting particle swarm optimisation (NSPSO). NSPSO is introduced to solve the multi-objective strategic bidding problem considering expected profit maximisation and risk (profit variation) minimisation. Monte Carlo (MC) simulation is employed to simulate rivals' bidding behaviour. Test results indicate that the proposed approach can provide an efficient non-dominated solution front. In addition, it can be efficiently used as a decision-making tool for a GenCo compromising between expected profit and the risk of profit variation in a spot market.

Long-term optimal allocation of hydro generation for a price-maker company in a competitive market: latest developments and a stochastic dual dynamic programming approach

Since the liberalisation of the power industry, there has been a large amount of literature on the determination of optimal bidding decisions for price-maker energy producers. The vast majority of the work developed so far has focused on short-term horizons and may be viewed as successful approaches for systems whose operation is generally deterministic. In the case of price-maker hydro plants with significant storage capacity, however, the solution of the strategic bidding problem is more subtle. The reason is that hydro reservoirs allow the bidder to postpone energy production if future prices are expected to be higher than the current price. This demands the management of an energy-constrained resource and determines a time-coupling characteristic to the problem, implying that the bidding strategy should ideally take into account the following stages and consider the stochasticity of inflows. These aspects characterise the strategic bidding for price-maker hydro agents as a multi-stage stochastic programming problem, with significant computational challenges. The objective of this work is to present a new methodology for the strategic bidding problem of a price-maker hydropower-based company, taking into account several hydro plants, time-coupling and stochastic inflow scenarios. The proposed approach considers a deterministic residual demand curve and is based on stochastic dual dynamic programming (SDDP), which has been successfully applied to the least-cost hydrothermal scheduling problem. Since the technique requires the problem to be concave, a piecewise linear approximation of the expected future benefit function is proposed. The application of the methodology is exemplified with a real case study based on the hydrothermal system of El Salvador.

Bilevel optimization applied to strategic pricing in competitive electricity markets

In this paper, we present a bilevel programming formulation for the problem of strategic bidding under uncertainty in a wholesale energy market (WEM), where the economic remuneration of each generator depends on the ability of its own management to submit price and quantity bids. The leader of the bilevel problem consists of one among a group of competing generators and the follower is the electric system operator. The capability of the agent represented by the leader to affect the market price is considered by the model. We propose two solution approaches for this non-convex problem. The first one is a heuristic procedure whose efficiency is confirmed through comparisons with the optimal solutions for some instances of the problem. These optimal solutions are obtained by the second approach proposed, which consists of a mixed integer reformulation of the bilevel model. The heuristic proposed is also compared to standard solvers for nonlinearly constrained optimization problems. The application of the procedures is illustrated in case studies with configurations derived from the Brazilian power system.

Strategic Bidding Under Uncertainty: A Binary Expansion Approach

This work presents a binary expansion (BE) solution approach to the problem of strategic bidding under uncertainty in short-term electricity markets. The BE scheme is used to transform the products of variables in the nonlinear bidding problem into a mixed integer linear programming formulation, which can be solved by commercially available computational systems. The BE scheme is applicable to pure price, pure quantity, or joint price/quantity bidding models. It is also possible to represent transmission networks, uncertainties (scenarios for price, quantity, plant availability, and load), financial instruments, capacity reinforcement decisions, and unit commitment. The application of the methodology is illustrated in case studies, with configurations derived from the 80-GW Brazilian system.