Gibbs Sampling for Game-Theoretic Modeling of Private Network Upgrades with Distributed Generation

Renewable energy is increasingly being curtailed, due to oversupply or network constraints. Curtailment can be partially avoided by smart grid management, but the long term solution is network reinforcement. Network upgrades, however, can be costly, so recent interest has focused on incentivising private investors to participate in network investments. In this paper, we study settings where a private renewable investor constructs a power line, but also provides access to other generators that pay a transmission fee. The decisions on optimal (and interdependent) renewable capacities built by investors, affect the resulting curtailment and profitability of projects, and can be formulated as a Stackelberg game. Optimal capacities rely jointly on stochastic variables, such as the renewable resource at project location. In this paper, we show how Markov chain Monte Carlo (MCMC) and Gibbs sampling techniques, can be used to generate observations from historic resource data and simulate multiple future scenarios. Finally, we validate and apply our game-theoretic formulation of the investment decision, to a real network upgrade problem in the UK.Comment: Preprint of final submitted version. arXiv admin note: text overlap with arXiv:1908.1031

Strategic decision-making on low-carbon technology and network capacity investments using game theory

In recent years, renewable energy technologies have been increasingly adopted and seen as key to humanity’s efforts to reduce greenhouse gases emissions and combat climate change. Yet, a side effect is that renewables have reached high penetration rates in many areas, leading to undesired curtailment, especially if existing grid infrastructure is insufficient and renewable energy generated cannot be exported at areas of high energy demand. The issue of curtailment is compelling at remote areas, where renewable resources are abundant, such as in windy islands. Not only renewable production is wasted, but often curtailment comes with high costs for renewable energy developers and energy end-users. In fact, procedures on how generators access the grid and how curtailment is applied, are key factors that affect the decisions of investors about generation and grid capacity installed. Part of this thesis studies the properties of widely used curtailment rules, applied in several countries including the UK, and their effect on strategic interactions between self-interested and profit-maximising low-carbon technology investors. The work develops a game-theoretic framework to study the effects of curtailment on the profitability of existing renewable projects and future developments. More specifically, work presented in this thesis determines the upper bounds of tolerable curtailment at a given location that allows for profitable investments. Moreover, the work studies the effect of various curtailment strategies on the capacity factor of renewable generators and the effects of renewable resource spatial correlation on the resulting curtailment. In fact, power network operators face a significant knowledge gap about how to implement curtailment rules that achieve desired operational objectives, but at the same time minimise disruption and economic losses for renewable generators. In this context, this thesis shows that fairness and equal sharing of imposed curtailment among generators is important to achieve maximisation of the renewable generation capacity installed at a certain area. A new rule is proposed that minimises disruption and the number of curtailment events a generator needs to respond to, while achieving fair allocation of curtailment between generators of unequal ratings. While curtailment can be reduced by smart grid techniques, a long term solution is increasing the network capacity. Grid reinforcements, however, are expensive and costs weight to all energy consumers. For this reason, debate in the energy community has focused on ways to attract private investment in grid reinforcement. A key knowledge gap faced by regulators is how to incentivise such projects, that could prove beneficial, especially in cases where several distributed generators can use the same power line to access the main grid, against the payment of a transmission fee. This thesis develops methods from empirical and algorithmic game theory to provide solutions to this problem. Specifically, a two-location model is considered, where excess renewable generation and demand are not co-located, and where a private renewable investor constructs a power line, providing also access to other generators, against a charge for transmission. In other words, the privately developed line is shared among all generators, a principle known as ‘common access’ line rules. This formulation may be studied as a Stackelberg game between transmission and local generation capacity investors. Decisions on optimal (and interdependent) renewable capacities built by investors, affect the resulting curtailment and profitability of projects and can be determined in the equilibrium of the game. A first approach to study the behaviour of investors at the game equilibrium, assumed a simple model, based on average values of renewable production and demand over a larger time horizon. This assumption allowed for an initial examination of the Stackelberg game equilibrium, by achieving an analytical, closed-form solution of the equilibrium and the investigation of its properties for a wide range of cost parameters. Next, a refined model is developed, able to capture the stochastic nature of renewable production and variability of energy demand. A theoretical analysis of the game is presented along with an estimation of the equilibrium by utilisation of empirical game-theoretic techniques and production/demand data from a real network upgrade project in the UK. The proposed method is general, and can be applied to similar case studies, where there is excess of renewable generation capacity, and where sufficient data is available. In practice, however, available data may be erroneous or experience significant gaps. To deal with data issues, a method for generating time series data is developed, based on Gibbs sampling. This attains an iterative simulation analysis with different time series data as an input (Markov Chain Monte Carlo), thus achieving the exploration of the solution space for multiple future scenarios and leading to a reduction of the uncertainty with regards to the investment decisions taken. Energy storage can reduce curtailment or defer network upgrades. Hence, the last part of this thesis proposes a model consisted of a line investor, local generators and a third independent storage player, who can absorb renewable production, that would otherwise have been curtailed. The model estimates optimal transmission, generation and storage capacities for various financial parameters. The value of storage is determined by comparing the energy system operation with and without energy storage. All models proposed in this thesis, are validated and applied to a practical setting of a grid reinforcement project, in the UK, and a large dataset of real wind speed measurements and demand. In summary, the research work studies the interplay among self-interested and indepen dent low-carbon investors, at areas of excess renewable capacity with network constraints and high curtailment. The work proposes a mechanism for setting transmission charges that ensures that the transmission line gets built, but investors from the local community, can also benefit from investing in renewable energy and energy storage. Overall, the results of this work show how game-theoretic techniques can help energy system stakeholders to bridge the knowledge gap about setting optimal curtailment rules and determining appropriate transmission charges for privately developed network infrastructure.Engineering and Physical Sciences Research Council (EPSRC