Stakeholder Perspectives on Energy Auctions: A Case Study in Roraima, Brazil

: Energy auctions are commonly used to contract energy projects and are extensively studied from the regulator’s perspective. However, analyzing auctions from the stakeholders’ perspective is critical to determine the impact of regulatory details on the bidder’s revenues. In this study, we analyze a public energy auction in Roraima, a Brazilian state with a significant energy deficit and no grid connection, where many projects were successful in the non-intermittent Power Product category, typically unfavorable for biomass. Using Linear Programming to maximize bidders’ revenues, we examine the regulatory formulas that contributed to the success of these projects and compare the optimization results to actual revenues. Our analysis shows that certain regulatory elements can benefit stakeholders by allowing them to make unconventional project design decisions. In addition, we identify a possible loophole in the formula that can have the opposite effect of the regulator’s intent in the renewable Power Product category. Our findings can help bidders increase profits through optimization and regulators to change formulas if objectives are not met. This study brings the often-overlooked perspective of stakeholders to energy auctions, adding to the literature on this topic.


Background of the Study
Auctions have been studied extensively in auction theory [1], with different types and contexts depending on the number of buyers and sellers [2][3][4], and with many different formats. The 2020 Nobel Prize in Economic Sciences was awarded to Paul R. Milgrom and Robert B. Wilson "for improvements in auction theory and the invention of new auction formats" [5], showing the importance of these formats and the rules of auctions.
Auctions are considered part of the theory of Mechanism Design (MD), and the secondprice auction is the type of auction in which bidders with independent private values reveal their choices without incentive to lie [6].
Far beyond the lessons of economic theory, auctions evolve according to the intertwining between the need for a price reference and policy goals [7].
Irene [8] and Del Rio and Kiefer [9] present the essential elements of an auction that can be adjusted by the regulator: (a) the remuneration, which allows bidders to win depending on policy incentives, such as long-term power purchase agreements (PPA), feed-in tariffs, or feed-in premiums; (b) the auction format and type, e.g., single or multiparty auction; (c) the pricing rules, i.e., post-bid pricing or uniform pricing; (d) the rules that limit bid prices or require projects to be delivered by a certain date. Del Rio and Kiefer [9] list the variables that distinguish auctions (considering a sample of energy auctions): (a) quantity setting and disclosure metrics; (b) timing, i.e., whether there is a commitment to start an auction at regular intervals; (c) diversity of technologies, focusing on technology-neutral as opposed to technology-specific, but also considering whether renewable energy sources are involved or not; (d) rules related to policy objectives, such as current local rules or some limits to avoid future market concentrations.
For the above reasons, the design of auctions has also been studied in detail [10][11][12]. As Klemperer [13] points out, "What really matters in auction design are the same issues that any industry regulator would recognize as key concerns: discouraging collusive, entry-deterring and predatory behavior. In short, good auction design is mostly good elementary economics".
There is consensus in the literature that auction design has a major impact on the tradeoff between efficiency and effectiveness [14,15] and on the energy transition toward decarbonization [9]. The choice of design elements may determine whether these benefits actually affect outcomes [16,17], although some authors argue that the most important effects on various criteria and objectives come from the structural features of the auctions as a whole and not necessarily from the design elements [18].
One of these structural features is the geographic component, which in many cases leads to outcomes that are less efficient than expected by "pure" economic theory. Analysis of auctions in the PJM system has shown that auctions whose rules divide a region "into smaller Location Delivery Areas" make it easier for bidders to predict certain supply curves and increase the influence of specific companies [12]. The case of energy islands (In the context of energy, an island or energy island can also mean an artificial island or an island on a platform that serves as a hub for power generation from surrounding offshore sources to interconnect them and distribute the power) presents this type of challenge to the formulation of auction rules.

Economic Theory-Auctions as Design Mechanism
The theme of this paper is to combine the discussion of energy security in an energy island (Da Ponte et al., 2021 [19]) and the role of algorithms reflecting policy decisions of the regulator with an original look at the position of the bidder. It is not easy to find a theoretical reference point that covers all these aspects together. However, the economic theory underpinning the rationality of auctions is part of the study of economic mechanism design and could be a starting point. Hurwick and Reiter (2006) [20] present a systematic method for designing decentralized economic mechanisms whose performance achieves specific goals. Addressing economic adjustments based on the "Walrasian Tatonnement" is insufficient when competitive equilibria are inefficient. The authors point out that in cases where the "tatonnement process" fails to converge, other desiderata fail: fairness or ensuring a minimum standard of living for a portion of the population.
In more direct language, the design process (DP) consists of (a) an adaptation process with a message exchange; (b) decentralized information; and (c) the realization of a certain desirability criterion. The minimum degree of decentralization depends on the preservation of private information (PPI). For example, the idea of PPI links DP to two concepts: the direct mechanism and the Revelation Principle (Cowell, 2018, Ch. 12, [21]). The direct mechanism occurs when it makes agents declare their preferences and generates the condition for implementing a social choice function in the dominant strategy directly by the agency so that the social process in dominant methods can be implemented truthfully with the direct tool. (Cowell, 2018, Ch. 12 [21]) (In the form of the game as the Principal-Agent, asymmetric information is a guarantee against the principal's complete exploitation of the Agent (Jehle and Reny, 2011 [6])).
Designing mechanisms provides an advanced view of how to combine (a) those that apply to the intended outcomes of the mechanism and (b) the people associated with operating a mechanism. Information and communication processing costs are relevant.
Nevertheless, incentive compatibility and the costs of enforcing the rules of the game are central to the evaluation of outcomes by an independent objective function. Hurwick and Reiter (2006) [20] point out the key role of the environment. The elements that constrain the situation, in the case of this paper the technological capabilities and some geographical features (energy island), are beyond the control or influence of the designer of the economic organization. The number of parameters of the model is finite and "the environment is represented by the parameters that characterize the actors" (Hurwick and Reiter, 2006, p. 25 [20]).
In envisioning the mechanism, the designer knows the environmental space Θ and the objective function F, taking into account the environment for which the mechanism is designed and a desirability criterion. F: Θ -> Z gives the result space, which can be measured in numbers, F = R (Hurwick and Reiter, 2006 [20]).
To verify the criterion, the processes of message exchange must be carried out in the form of a game, assuming that the agents have strategies. In the state of the game of interest to this paper, there is a one-shot with a "specified message space" in which the player's movement selects a message depending on its information, where it is possible that a set of notes exists that perform a solution based on a convention (which could be strong, such as Nash's). A game from G can realize an objective function F if there is a corresponding mechanism π that realizes F. The transfer from the ambient space to a message space M implies the application of h that leads to the result Z. The correspondence between Θ and Z represents the idea of a direct mechanism (Cowell, 2018 [21]).
An important aspect is privacy (PP): "the verification performed by an agent", according to Hurwick and Reiter, 2006: p. 30 [20] requires only the knowledge of its own characteristics θ' in θ as an argument: an agent's strategy depends only on this private information.
Quite consistent with this paper's view of the auction case, DP is concerned with finding a mechanism in which the objective function is the most important specification, the opposite of traditional economic theory, which is devoted to studying the performance of a particular mechanism.
Policies can be formulated on the basis of market failures, as outlined by Stiglitz, 1989 [22]. Some suggestions are the use of marginal cost prices in the presence of increased returns, Lindahl prices in the presence of public goods (a direct DP), and closer to energy problems, taxes, and carbon taxation. Criticisms of many of these solutions are the following: (a) increased bureaucratization and centralization of decision making; (b) high costs of information and enforcement rules, both discussed in McCoullogh et al., 2019 [12]; and (c) incentive compatibility problems caused by high costs of enforcing rules of conduct and fees to enforce the rules of the game.
If we take a step back, auctioning is one of the ways to contract energy. Free energy markets based on bilateral relations, on the one hand, and vertical integration, on the other, are forms that are alternatives but do not fit the environmental conditions. These remarks make it clear that the choice of a particular form of auction, the reverse auction, is to propose a mechanism that can be verified in its implementation. The idea is to complete the evaluation of DPs with the least amount of information processing. These points are relevant to the analysis of the "excess" in the definition of the formulas used in energy auctions as presented in this paper.
In the wake of climate change, the idea of promoting electricity from renewable sources (Held et al., 2013 [23]; Tol, 2023 [24]) leads to a complexification of the design process that interferes with F once the multidimensional goal of providing energy security, lowering prices, and promoting clean energy can be a burden on the mechanism. This paper has taken all these considerations into account in describing the case of the energy auction in Roraima. Nevertheless, it is postulated to focus on the µ-component of DP (Figure 1), i.e., the way agents take the message, assuming that each agent is looking for an individual equilibrium message correspondence, denoted by µ i in Hurwick and Reiter, 2006: p. 30 [20], where µ i : θ -> M, such that µ(θ) = ∩ N i−1 µ (θ ). This "group message" contains messages that satisfy the agent's equilibrium equation (in the sense that no one wants a change at the end of the process) and, again following Hurwick and Reiter, 2006 [20], that the equations of the agent have only components θ as arguments.
Energies 2023, 16, x FOR PEER REVIEW 4 of 20 of DP (Figure 1), i.e., the way agents take the message, assuming that each agent is looking for an individual equilibrium message correspondence, denoted by μi in Hurwick and Reiter, 2006: p. 30 [20], where μi: θ -> M, such that μ(θ) This "group message" contains messages that satisfy the agent's equilibrium equation (in the sense that no one wants a change at the end of the process) and, again following Hurwick and Reiter, 2006 [20], that the equations of the agent have only components θ′ as arguments.

Importance of the Stakeholder's Perspective
Energy auctions themselves have also been studied extensively. A quick search of the ScienceDirect database [25] since 2020 reveals more than 4500 research articles on this topic. So far, there is broad agreement in this literature that all of the design elements of auctions have a major impact on the trade-off between efficiency and effectiveness [14,15] and on the energy transition toward decarbonization [9]. There is agreement that the choice of design elements can determine whether these benefits will actually impact the results [9,17].
These studies take the point of view of the regulator who sets up the auction, and they analyze the results of the auction.
However, in an energy auction, there are two sides: that of the regulator and that of the bidder.
When the ScienceDirect database is searched again using the argument ("stakeholder perspective" energy auction) since 1999, it shows only 72 results among the more than 4500 previously cited.
The importance of the indicated articles is that they are very few, considering the importance of the subject. Among these results, we could not find any reference that adopts the stakeholder perspective instead of using it to better design auctions.
One of the articles we found [26] studies auctions based on stakeholder opinions, but the authors only use them to improve auction design without adopting the stakeholder perspective. This is very important because it is extremely difficult to prove the absence of references-you can only search in reliable databases with appropriate search arguments, check what is found, and then count the number of results.
Even considering other options for similar searches and other databases such as ResearchGate or Google Scholar, the search results always show that the number of studies taking the regulator's perspective is orders of magnitude greater than the number of studies taking the stakeholder's perspective, especially if we consider auctions as an economic game with sellers and buyers as parts whose perspectives should be equally considered.
A notable exception is the work of McCullough et al. [12]. They analyze PJM's Reliability Pricing Model for auctions in the context of current reform proposals aimed at dispelling the perception that government subsidies for zero-carbon generation put downward pressure on capacity prices. They show how PJM's clearing algorithm departs from economic theory and conclude that the capacity market construct drives prices up rather than depressing them.
Why is this study important and how is it similar to our study?

Importance of the Stakeholder's Perspective
Energy auctions themselves have also been studied extensively. A quick search of the ScienceDirect database [25] since 2020 reveals more than 4500 research articles on this topic. So far, there is broad agreement in this literature that all of the design elements of auctions have a major impact on the trade-off between efficiency and effectiveness [14,15] and on the energy transition toward decarbonization [9]. There is agreement that the choice of design elements can determine whether these benefits will actually impact the results [9,17].
These studies take the point of view of the regulator who sets up the auction, and they analyze the results of the auction.
However, in an energy auction, there are two sides: that of the regulator and that of the bidder.
When the ScienceDirect database is searched again using the argument ("stakeholder perspective" energy auction) since 1999, it shows only 72 results among the more than 4500 previously cited.
The importance of the indicated articles is that they are very few, considering the importance of the subject. Among these results, we could not find any reference that adopts the stakeholder perspective instead of using it to better design auctions.
One of the articles we found [26] studies auctions based on stakeholder opinions, but the authors only use them to improve auction design without adopting the stakeholder perspective. This is very important because it is extremely difficult to prove the absence of references-you can only search in reliable databases with appropriate search arguments, check what is found, and then count the number of results.
Even considering other options for similar searches and other databases such as ResearchGate or Google Scholar, the search results always show that the number of studies taking the regulator's perspective is orders of magnitude greater than the number of studies taking the stakeholder's perspective, especially if we consider auctions as an economic game with sellers and buyers as parts whose perspectives should be equally considered.
A notable exception is the work of McCullough et al. [12]. They analyze PJM's Reliability Pricing Model for auctions in the context of current reform proposals aimed at dispelling the perception that government subsidies for zero-carbon generation put downward pressure on capacity prices. They show how PJM's clearing algorithm departs from economic theory and conclude that the capacity market construct drives prices up rather than depressing them.
Why is this study important and how is it similar to our study? First, it is important because PJM is a regional transmission organization (RTO) that regulates auctions in one of the largest energy markets in the world. Following the deregulation of wholesale electricity markets in the United States in 1991, seven "organized" markets have developed in the United States where prices are set through independent auctions. PJM is the largest of these markets, providing 178,563 MW of capacity for thirteen states and the District of Columbia [12]. Therefore, their study can hardly be considered as a small or too local case study. Although the authors do not explicitly adopt the stakeholder perspective, they show a similar result to our case study, i.e., mathematical algorithms or formulas set by the regulator can always be "beaten" by bidders, or at least they can find the equilibrium point that may not have been anticipated by the regulator and that is contrary to their intentions.
This raises an important question: "What would the analyses and outcomes of the auction rules look like from the perspective of the stakeholder rather than the regulator, and what design would the stakeholder choose"?
To explore this question, we take the perspective of a stakeholder in a particular auction where the analysis of the auction rules and subsequent design were based on the profitability of the project for the bidding project prior to the auction.

Overview of the Public Energy Auction
We focus on the 2019 energy auction in Roraima, a Brazilian state isolated from the national energy grid and with a significant energy deficit. As of 2021, there are about 250 isolated systems in Brazil, concentrated in the northern region, accounting for only 1% of the country's total electricity consumption but covering 40% of the territory [19].
The auction was mediated and regulated by a government agency, and its purpose was to replace and supplement the existing thermoelectric diesel power plants, which are expensive and polluting, with cleaner energy projects that can be called only when needed. To this end, certain special provisions were established to promote projects that provide energy only on demand, while allowing projects that require a fixed minimum consumption of fuel to participate via an inflexibility (In the context of energy auctions, inflexibility refers to the value of mandatory minimum electricity generation from a thermoelectric power plant that is not subject to the National Electricity System Operator's (ONS) rules for on-demand energy) declaration.
The government agency established a formula for what was called the "Reference Price" (equivalent to the Benefit-Cost Ratio-BCR (Only in the context of energy auctions, BCR is measured in R$/MWh and in this paper we use it in the same meaning as Reference Price)), with some constants set by the regulator and some variables to be determined by the bidder. The formula aimed to equalize the prices of projects with and without inflexibility and to determine which projects would win the auction.
Among the projects that won the auction, we analyze those that won in the "Power Product" (better known as "Reserve Capacity") category, where the bidder assumes a contract for variable operation with a guaranteed minimum amount of non-intermittent generation. This category is generally unfavorable for biomass projects because the generation is not intermittent.
Four of these projects (the biomass cogeneration ones) stand out because they won the auction with projects that apparently declared some unrealistic costs and where the bidder was the owner of a renewable reforestation that was used as a woodchip generator for the project.

Objectives and Research Questions
Since the formula was the key element in determining the winning bids, our objective was to analyze in detail the variables that must be determined to maximize the profit for the bidder and then examine the consequences of these decisions.
Our research question is what details of the regulator's rules and formulas enabled the bidders to win the auction.

Auction
The context of this study is the northern region of Brazil, where 250 isolated systems account for about 1% of national energy consumption. Historically, these systems have been supplied by diesel power plants, which are expensive and responsible for high greenhouse gas emissions. Although renewable energy is already a cost-effective solution for such isolated systems, conventional power generation is still the main source of electricity, even in newer projects.
Isolated systems are places that, for technical or economic reasons, are not connected to the national power grid [27,28] and are supplied by local power generation. Most of these isolated grids with local power generation are located on islands, in rural areas, or in remote regions with strong economic activities such as mining or onshore oil and gas exploration. In areas far from main power grids, regional isolated grids powered by expensive diesel fuel are often the main source of electricity for industry and households. Islands, in particular, are vulnerable in terms of energy security, as they often have limited capacity for energy sources and are not connected to the energy grid. Renewable energy is often sought in isolated systems as a solution to minimize dependence on fossil fuel energy production [29,30]. However, conventional power generation is still the main source of electricity for isolated systems, even in newer projects.
From the article by Moges [31], it is clear that the Roraima project faces all the challenges that can occur in the energy islands, such as political (auction with particularly high BCR), technological (cogeneration project with "on-demand" supply), operational (lack of experienced labor and eucalyptus production), economic (first auction of its kind), infrastructural (transmission line constraints), and environmental (no time for environmental licensing and no incentives for renewable generation).
In developing countries, whose energy matrix is mainly based on hydropower, the increasing energy demand requires an exponential growth of reservoirs, which is not feasible. The construction of hydropower plants with insufficient reservoirs to meet current storage needs, along with the volatility of renewable energy sources, has increased the demand for distributed renewable energy sources. Distributed renewable energy sources are not only about transitioning to a green energy supply but also about supplying certain regions and enabling the necessary expansion of the economy and a reduction in prices. Therefore, the design of an energy auction by the regulator is critical to encourage an increase in energy production and the production of more renewable energy as a state energy and environmental policy.
Brazil has traditionally relied on hydropower plants, which use large reservoirs to minimize energy fluctuations caused by natural factors. However, thermoelectric power plants have played a supporting role in the country's electricity generation portfolio, typically activated during peak demand or severe drought. Unfortunately, these power plants incurred high maintenance costs due to frequent outages, even when not needed.
In 2001, an energy supply-demand imbalance led to a rationing decree in Brazil [32]. The country's historical energy pattern shows signs of depletion due to the challenge of developing new power plants with storage capacity to meet increasing demand and the expansion of intermittent renewable energy sources.
Biomass is a renewable energy source that can be replenished relatively quickly and is environmentally friendly. Sustainable management of trees and crops can offset carbon emissions by absorbing carbon dioxide through respiration. In some bioenergy processes, the amount of carbon that is reabsorbed exceeds the carbon emissions released during fuel processing and use.
Various types of biomass, including sugarcane, biogas, wood, beets, charcoal, and vegetable oils, can be used in Combined Heat and Power (CHP) plants to generate electricity from the same primary source of mechanical and thermoelectric energy. CHP plants are highly efficient and ecological alternatives, and they are becoming increasingly popular in the Brazilian economy. CHP plants have the potential to complement the Brazilian hydroelectric park and can be a promising addition to the country's energy mix.
The energy auction in Roraima aimed to supply locally generated electricity, as there is a significant imbalance between the consumption and generation of internal electricity in the state [33]. The auction allowed power plants with renewable biomass, although no restrictions were set in terms of greenhouse gas emissions. This auction is similar to one studied by Abbas et al. [34] in terms of being isolated and based on steam turbine systems, but it focuses on a chip cogeneration plant based on wood burning. Fossil energy is compared to biomass energy in this context (Marchenko et al. [35]. Tillman and Jamison [36] demonstrate that this cogeneration type is feasible and can be generalized to other regions of Brazil, as demonstrated by Nzotcha and Kenfack [37] in Cameroon and sub-Saharan regions, and Madlener and Vogtli in Basel [38] and other Switzerland regions, as well as other cases where government barriers to inflexibility play an unnecessary negative role, such as in Espinoza et al. [39]. Currently, only 9 out of 156 biomass cogeneration projects (1.618 MW average contracted) in Brazil incorporate woodchips (202 MW average contracted), indicating that woodchip usage accounts for only 5.7% of biomass projects or 12.5% of total energy contracted. It is worth noting that Brazil lacks an effective policy for biomass power generation, even though cogeneration is a byproduct of sugar and ethanol production.
In addition, isolated systems pose a risk to bidders, as their power plants could become obsolete in the future due to a lack of demand if or when these systems are integrated into the power grid. On the other hand, they represent opportunities-Roraima has many renewable reforestations that are underutilized, and winning such auctions encourages other projects. Even if Roraima is connected to the power grid, the plants can still be used as a small part of the power supply and the remaining wood can be sold. This same reasoning applies to other places that are isolated systems where renewable forests are underutilized or could be created.

Historical Context
Energy auctions in Brazil are regulated by the National Electric Energy Agency (ANEEL) and occur within the framework of the Regulated Contracting Environment (ACR). The energy auction in Roraima was primarily aimed at energy supply, but it also aimed to encourage renewable biomass power plants by establishing a "Reference Price" that would determine winning bids. However, inflexibility was one of the variables specified by the bidder, and a high degree of inflexibility may occur to secure a minimum quantity of raw materials and to be technically viable in providing the anticipated quantity of energy in the shortest time possible (On power product the energy generator should be able to start producing energy on demand when requested by National System Operator (ONS). For woodchip cogeneration projects, the start of operation of the boiler, when it is stopped is at least 24 h (ramp-up). When the boiler is already in operation, even if it is only partially in operation (inflexibility), the response to the increase of energy production occurs within a few minutes). This inflexibility can have a negative effect on the price that the bidder can offer.
The majority of the energy auctioned in these processes is allocated to distributors. However, these auctions ultimately benefit fossil-based initiatives at the expense of environmentally viable ventures such as biomass facilities. In particular, restrictions imposed on the level of inflexibility allowed in auctions for biomass proposals, especially woodchips, appear to hinder the potential of biomass projects to compete with fossil projects.
Brazil's electricity expansion was centralized before 2001, but after demand increased, the state-owned generation companies promoted energy supply. However, the energy supply and demand imbalance resulted in a rationing decree in 2001. This led to the creation of the Electric Energy Crisis Management Chamber (GCE), which established the Committee for the Revitalization of the Electric Sector Model to propose a model and to correct current dysfunctions.
This Committee suggested contracting reserve thermoelectric generation capacity to protect the National Interconnected System (SIN) from potential shortages caused by higher-than-expected increases in demand, delays in the construction of already contracted plants, and delays in transmission reinforcement, among others. Furthermore, the reserve energy would boost thermoelectric improvement in the system, thus reducing hydrological noise and price volatility.
The recommendations of the Committee defined the Brazilian thermoelectric park as mostly composed of flexible units or reserve or emergency plants to complement hydraulic generation and no mandatory minimum generation. The dominance of hydraulics, the broad National Interconnected System (SIN), and the configuration of water reservoirs influenced the choices for electrical system expansion. Much of the thermoelectric complementation was designed to be flexible, operating as a backup to hydro generation [40].
Thermoelectric inflexibility refers to the percentage of contracted availability that the power plant must always generate, regardless of any dispatch (Dispatch means sending energy above the inflexibility level on request from ONS) and merit order (The Order of Dispatch or Order of Merit is a procedure established by the regulatory authority to determine the order in which the power generators that have won the auction are called to dispatch when needed). Thus, a thermoelectric power plant with 50% inflexibility creates half of its availability at all times, while a thermoelectric power plant that is 100% flexible only generates when sent in order of merit.
A flexible thermoelectric power plant is a variable fuel source, the availability of which is associated with a high degree of uncertainty about the time period and level of dispatch. Dispatchable sources are those whose generation time is independent of local weather conditions. Because they generate energy at a constant rate, thermal and hydroelectric plants are examples of dispatchable sources.
As Romeiro makes clear, since 2005 [41], 18 auctions have been held in Brazil using the Benefit-Cost Ratio (BCR (Only in the context of energy auctions, BCR is measured in R$/MWh and in this paper we use it in the same meaning as Reference Price)) mechanism to select product availability, contracting an average of more than 22 GW. However, due to the considerable challenges in acquiring an environmental license for hydropower plants, only 22% of the contracted energy came from hydropower, with 16% from wind and 62% from thermoelectric sources. In the early auctions, less competitive sources were contracted, and coal-fired thermoelectric plants sold more electricity than all biomass-powered projects combined.
By 2010, wind energy became the most competitive source, but oil, diesel, and natural gas thermoelectric plants dominated the auctions, accounting for more than 5 GW of winning bids. Despite the low fixed costs of all flexible power plants when dispatched, they result in significant variable operating costs, which are overestimated in the BCR since it assumes flexible thermoelectric power plants will only be used irregularly, overestimating low fixed costs.
Romeiro's research also showed that additional flexible thermoelectric plants have been dispatched, increasing the share of thermoelectric generation in satisfying the System of Electric Power Operations (SIN) load, from less than 10% to 25% in 2012, and now accounting for approximately 30% of the total load. This has skewed options in favor of dispatchable thermoelectric power plants with high variable unit prices.
Energy auctions in Brazil can be classified into two categories: "quantity contracts" and "availability contracts". The former is based on the provision of a fixed amount of energy at a fixed price, while the latter ensures the efficiency of the national hydrothermal system by establishing a fixed payment for the electricity producer, regardless of the amount of energy supplied.
In 2019, an energy auction was held in the state of Roraima, the only Brazilian state not integrated into the National Interconnected System (SIN). Roraima relies mainly on thermoelectric plants for its energy needs, and all energy consumed in the state is generated locally or imported from other countries. The auction aimed to address the significant imbalance between the consumption and generation of internal electricity in Roraima, where electricity generated locally was insufficient to meet demand.
The Boa Vista Auction was conducted based on the guidelines established by the Ministry of Mines and Energy (MME) in MME Ordinance No. 512/2018, which was later The Power Product corresponds to solutions that provide load modulation and flexibility for variable operation to supply the maximum power required by the system. The Power Product is further divided into sub-products, namely Gas and Renewables, and Other Sources. On the other hand, the Energy Product is exclusively for renewable sources, whose supply obligation is based on an annual energy output approved by the Energy Research Company (EPE).
This auction is the first of its kind for an isolated system that behaves like an interconnected system. Therefore, renewable and other sources are distinguished. Biomass cogeneration plants were usually a participant in the Energy Product auctions because biomass is not suitable for competing as a Power Product. In the Power Product modality, EPE refers to solar plants with batteries, not woodchip cogeneration plants that cannot be turned on and off and are always on.
The Energy Product frequently deals with intermittent generation, especially when renewable sources are considered. The Power Product, on the other hand, deals with non-intermittent generation that occurs on demand. For instance, solar energy is usually an Energy Product since it is intermittent, but when batteries are used, it becomes nonintermittent and can be a Power Product. This distinction is crucial in ensuring energy security. Therefore, the Power Product is auctioned first in the auction, followed by the Energy Product.
For the Energy Product, the price of energy generation is substantially lower than the price of the Power Product. However, suppliers of the Energy Product are not compelled to generate on demand but to supply an annual quantity of energy. There are no penalties in the BCR formula related to an inflexible part. Therefore, a supplier as an Energy Product does not need to generate when the agent demands it, but when it can.

Results of the Auction
A total of 156 proposals were submitted, out of which 124 were eligible, representing a capacity of 4.2 GW.
Of the eligible proposals, 53 projects with a total capacity of 3.0 GW were eligible for the electricity product, while 71 projects with a capacity of 1.2 GW were eligible for the energy product. In the subsequent phase, nine projects were selected as winners, out of which seven were renewables under the Power Product scope, with a total installed capacity of 294 MW.
Two of the winners in the Roraima region produce liquid biofuels on site, one also with photovoltaics and the other with biomass. A hybrid project with biofuels, photovoltaics, and batteries has also won in Boa Vista. In addition, a thermoelectric natural gas power plant is being built in Boa Vista, with fuel produced in the Amazon and completely flexible power generation.
Four projects based on biomass (woodchip) have been installed in Boa Vista and Bonfim, with a total of 40 MW, all coming from the same renewable reforestation owned by the stakeholder of this case study. This was the first time that a biomass cogeneration project won an auction under the Power Product scope. The steady production of the declared capacity required some modifications to the existing boilers to make the project viable. The stakeholder analyzed and designed a woodchip power plant project that won the Roraima Auction with an unfavorable reference price formula by avoiding its drawbacks to investigate whether the underlying ideas can be applied to similar projects.
The estimated investment of the winners was R$ 1.62 billion, with an average discount per MW/h of 22.7% compared to the government prospect of R$ 1078 MW/h. Roraima will generate 42.0% clean energy and 43.0% from natural gas. The Energy Product winners based on natural gas or renewable sources have 15-year power trading contracts in isolated systems, while the other winners have 7-year contracts.

Methods
First, we describe the formula for the reference price that determines which bids win. We then divide the variables and constants in the formula into elements that can be freely determined by project stakeholders, e.g., those that are not constants set by the regulator and those that are not constrained by pre-existing operating conditions for the stakeholder's project.
Then, we use Linear Programming to obtain revenues higher than those that the bidders obtained.
Finally, we compare the results of the optimization to the actual results of these projects, using the numbers declared in these projects. The data of these projects are in Table 2.
This method is the authors' own development, but the underlying idea of optimization in favor of the bidder has already been used independently [12].
In terms of Mathematical Programming, this problem can be stated as Linear Programming Program (LP), a very traditional and widely used tool in optimization.
Linear Programming is a mathematical optimization technique used to find the best possible solution to a problem with linear constraints and a linear objective function. It is a tool that allows decision makers to allocate limited resources as efficiently as possible. Linear Programming is widely used in fields such as economics, engineering, and operations research to solve problems involving the optimal allocation of resources.
The basic idea of Linear Programming is to represent a problem in terms of a set of linear equations and inequalities, and then find the optimal solution by maximizing or minimizing a linear objective function given these constraints. The constraints and the objective function can be represented graphically as a system of linear equations and inequalities, and the optimal solution can be found by identifying the intersection of the feasible region with the objective function.
The advantages of Linear Programming include the ability to solve complex problems with many variables, the ability to optimize solutions in a systematic and quantitative manner, and the ability to incorporate various constraints and restrictions into the problem formulation. Linear Programming is also an important tool for decision making in the presence of uncertainty, as it allows decision makers to evaluate different scenarios and determine the best course of action.
The Reference Price, set by the Ministry of Mines and Energy [46] as a mediator of the auction, is as follows. We quote: Equation (1)-Reference Price where P REF = Reference Price in R$/MWh; C other = Cost of Other Items, expressed in Reals per year (R$/year); Pd max = power availability of the supply solution in MW; F INFLEX = Under the Guidelines, the annual inflexibility factor associated with the inflexible energy amount, as defined by the proponent in the technical qualification process, which is limited to 50% (fifty percent); f c = 0.7; α = 0.2 × f c ; O&M var = Operation and Maintenance Cost of the Variable Portion, or Variable O&M, expressed in R$/MWh; C Fuel = Fuel Cost, applicable both to inflexible generation and to generation above the declared Inflexibility, expressed in R$/MWh, with specific formulation for each type of fuel, that was presented in a Technical Report by EPE [26]. f c and α are constants set by the regulatory authority that mediates the auction; all other items are set by the bidder before the auction begins and cannot be changed, except for item C other , which can be changed, but only during the auction.
A first look at Equation (1) indicates that the inflexibility F INFLEX penalizes the fuel cost C Fuel and favors O&M var , because F INFLEX is multiplied by a positive number and the result then multiplies C Fuel , i.e., it contributes to increase the resulting Reference Price, an undesired effect for the bidder. On the other hand, F INFLEX is multiplied by a negative number and the result then multiplies O&M var , i.e., it contributes to decrease the resulting Reference Price, a desired effect for the bidder.
Let us model the best choice of the variables involved, making a few assumptions. Of all the variables and constants in the Reference Price formula, a bidder would consider Pd max a variable previously decided in the project for reasons such as risk assessment and operating conditions, f c and α as constants set by the regulator, and O&M var and C Fuel as variables that can be freely specified. The value of C other is usually fixed by the bidder as it represents some unavoidable costs and must be guaranteed, so it will not be considered as a control variable.
Another factor that probably influences the bidder's choices is the order of dispatch, which is the order that the government agency uses to select additional energy among the plants in the Power Product category that won the auction. This order is decreasingly established by the variable cost, which we will call V C = O&M var + C Fuel .

Results
In a first approach, a bidder would choose to decrease the declared fuel cost well below its estimated value because inflexibility penalizes this cost while increasing the stated O&M var well above the estimated cost because inflexibility favors a higher O&M var . The idea is that these costs can offset each other, which is quite true, as we will see, but C other was not considered in this naïve approach.
This intuitive approach could be extended to three variables and even obtain the optimal solution, but this would not be the case in a new formula by the regulator in some other auction if there were many more control variables.
For this reason, we wanted to deepen this intuitive approach to evaluate which would be the best choice to optimize the bidder's profit. For this purpose, we need to isolate the F INFLEX variable in the formula.
After rearranging the formula to isolate inflexibility and assess its impact, the formula becomes: Now it is possible to see that F INFLEX can have a positive (decreasing) or negative (increasing) impact on the Reference Price, depending on the sign of (O&M var − α × C Fuel ). As mentioned before, C Fuel could also be chosen, so the best decision is not evident.
A way to find the optimal choice for the control variables C Fuel and O&M var is to model this decision problem as a Linear Programming problem.
In our model, we want to keep the same P REF and the same dispatch order V C that won the auction and maximize the bidder's total revenue when operating at 50% inflexibility. The total revenue can be expressed as This LP problem can now be stated as where s.t. stands for "subject to", i.e., the constraints of our maximization. We will examine some of the projects that won in the Power Product category with a non-zero inflexibility.
We first examine Uniagro's projects, as it appears that the bidder had already taken the naïve approach described earlier.
We substitute the numbers of these projects, leaving only the control variables so that the problem is equivalent to Since there are only three variables C other , C Fuel , and O&M var , we can use the Simplex method (This method is available in Excel and many other solvers), and the optimal results for Bonfim and Canta (Bonfim) are C other = 34,509,702.89, O&M = 387, and C Fuel = 0 (zero!), and the total revenue is T REV = 34,509,702.89, equal to C other .
Replacing these values in the formula, we obtain exactly the desired value of 800 for P REF and V C = 387.
The results for Pau Rainha and Santa Luz (Boa Vista) are C other = 32,207,149.15, O&M = 387, and C Fuel = 0 (zero!), and the total revenue is T REV = 32,207,149.15, equal to C other .
Replacing these values in the formula, we obtain exactly the desired value of 754 for P REF and V C = 387.
Note that the additional gain for all Uniagro's projects in the total revenue is relatively small, 425,471.89, indicating that the bidder already applied some optimization. Now we apply the same ideas to BBF Hibrido São Joaquim, another winning project that has much higher power availability. Its data are also in Table 2.
Again, we substitute the numbers of this project, leaving only the control variables, so that the problem is equivalent to Using again the Simplex method, the optimal results are C other = 191,805,119.27, O&M = 758.41, and C Fuel = 0 (zero!), and the total revenue is T REV = 191,805,119.27, equal to C other .
Note the additional gain in the total revenue per year is now much greater, 22,809,655.53, suggesting that the bidder did not apply any optimization. Now we apply for the last winning project with inflexibility, BBF Baliza. Its data are also in Table 2.
Using again the Simplex method, the optimal results are C other = 40,449,811.93, O&M = 610.38, and C Fuel = 0 (zero!), and the total revenue is T REV = 40,449,811.93, equal to C other .
Note the additional gain in the total revenue per year is now 4,665,794.47, which means a 13% increase in the previously fixed revenue.
These results indicate that the bidders could have presented very different projects, with the same Reference Price, which would make them win, and the same Variable Cost, which would keep them in the same Order of Dispatch. As far as the auction is concerned, nothing would have changed.
However, the bidders' profits would have been much higher, with this difference ultimately paid by the consumer. This is a loophole in the regulator's rules and formulas. Regardless of what rules and formulas the regulator establishes, it should always take the perspective of the other side and optimize its profits and then check whether this runs counter to the regulator's objectives. Other auctions will have other regulators' objectives, but this basic principle will apply. Game theory can be used to study auctions, as evidenced by almost 1000 articles on ScienceDirect since 2020.
The optimizations performed are shown in Table 3 below.

Discussion
There is a lot of discussion on designing auctions [26] to make renewable energy resources (RES) available, and one key factor is emission reductions, which both biomass and biofuel can perform.
The design of most RES auctions attempts to create a suitable environment for this type of source while keeping prices as low as possible [11].
When we look at isolated systems or islands such as Roraima, where the nonintermittent generation (Power Product) has such a huge importance, the regulator should consider all types of technologies which can produce the outcome expected while taking RES into account.
The decision to introduce reserve energy/electricity should involve consideration of not only the financial social cost of the flexibility gain but also the social cost of replacing a renewable energy source with a fossil one when both can solve the same problem.
From the regulator's point of view, it is clear that the option of inflexible generation can be beneficial for the power producer, as it provides greater predictability in the management of fuels and power generation when greater inflexibility is declared. As a result, inflexibility can translate to lower electricity generation prices, primarily due to lower fuel costs.
On the other hand, inflexible generation may penalize generation when the order of economic merit is applied by the regulator, which aims to match supply to demand through the sequential dispatch of plants with lower operating costs. Now from the operator's point of view, the less inflexible the thermoelectric plants are, the more robust the optimization of system operation with the objective of minimizing the total cost to the electricity consumer.
Qualitatively, it is possible that a thermoelectric power plant with less inflexibility, even if it has higher fuel costs (which directly affects the higher price of its electricity generation), enables the system operator to generate more economically overall due to greater autonomy in portfolio management over a given period.
In addition, the regulator's argument for the Roraima auction [20] was that it must be taken into account that contracting inflexible generation has an impact on the maximum amount contracted in the Energy Product, i.e., the more inflexible generation contracted in the Power Product, the less energy can be contracted in the Energy Product to avoid overproduction, which would lead to additional costs for the consumer.
Although the intent of the regulator was to create a P REF equation that would optimize the flexibility, they ended up with a completely different result. Expectations regarding future energy use, hydropower development, or even a future connection to the power grid were all wrong.
Another important flaw is that as long as the bidder can freely declare the costs O&M var and C Fuel , with no upper limitation to O&M var , the reference price can be adjusted to any number, subject only to the price that the bidder estimates that can win the bid.
Inflexibility is essential for the development of woodchip cogeneration and biodiesel projects to ensure the flow and availability of biomass.
The regulator can establish affirmative policies that allow for avoiding the penalty formula. The future challenge is to review the technical and economic parameters when and if the isolated system of Roraima is connected to the National Interconnected System and to perform a similar analysis for connected systems with renewable eucalyptus and biodiesel.

Conclusions
The regulator has chosen to favor flexible generation. He did this through the reference price when it inserted the alpha factor into the equation.
We understand that the motivation is based on three points:

1.
Flexible systems can be better optimized through dispatch order (run the cheapest sources first) and also through portfolio management (choose the preferred sources to dispatch);

2.
The possibility to connect the isolated system of Roraima to the Brazilian interconnected grid; 3.
The possibility to contract cheaper energy sources in the energy auction (at the end of the capacity auction).
The challenge is that the regulator appears to be making very strong assumptions that ultimately cannot be proven.
Notwithstanding the potential benefit of flexibility, Roraima's isolated system is still not connected to the integrated system after 2 years of operation, and although the transmission line that would make this connection has been auctioned for over 10 years, there is no forecast for its installation due to environmental permitting issues. In addition, after the end of Phase 1 of the auction, in which the capacity projects were awarded, Phase 2, in which the energy projects were to be awarded, was canceled. Therefore, Roraima is only counting on the capacity projects that were auctioned.
One lesson from the process the regulator used to set the reference price based on the BCR is that it complicated a formula that should have been simple.
Instead of simply defining what the variable costs of generating electricity are and penalizing them in the P REF equation, it has attempted to refine the formula by splitting variable costs into variable fuel costs and variable O&M costs within the price.
This equation might even make sense for costs that involve commodities such as natural gas, but it is extremely complex when we think of costs that are simply declaratory.
That is, if the bidder is allowed to set its prices arbitrarily, the regulator should be more careful with formulas.
The lesson is that a complicated formula can end up creating loopholes. In theory, the loophole could have been solved if the bidder had room to question the rules proposed by the regulator. However, in fact, this did not happen as there were no questions on the auction about inflexibility or the formula [43].
The question that arises is how it can be that those who do not use the possibilities opened by the formula (BBF) do not recognize the open possibilities or do not follow the rules.
A difficult but important question is if the regulator was actually aware of the loophole or even created it for some particular reason.
Would the regulator have opened a space for some agents (bidders) to explore a space that was not strictly due to their characteristics? For example, those who have bioenergy need to provide a potential part of the parameters of the formula. This is a feature that conditions decisions, and it was only a fact for bioenergy. It creates room to manipulate the formula in relation to operating costs.
Questions still to be answered are the following: