Following the current corona regulations in place, the maximum capacity of the auditorium is limited. You are more than welcome to participate in online (via a conference invitation that will be sent later). Please send a mail to email@example.com if you wish to participate.
The distribution system is one of the key components of the power system. In the past several decades, the centralized power generation of power plants promoted the transmission system's development, while the distribution system was regarded as a collection set of ``feeders''. Most of the advanced control and monitoring techniques were developed and implemented for the transmission system. With the development of distributed energy resources, the distribution system is expected to be the small distributed energy sources' integrator. Especially the low voltage distribution networks have to manage more and more multifarious users. On the one hand, this development trend has created quite a few opportunities to implement new smart grid application to improve energy efficiency; on the other hand, it calls for innovative approaches to implement active control to the ``last mile'' of the power system.
To help the modern low voltage distribution network face the new challenges, this dissertation proposed three distributed algorithms to optimize the users' active power consumption in a given low voltage distribution network while ensuring the voltage constraints and additional objectives. All three distributed optimization algorithms are model-free, computationally tractable, and communication-friendly. The first algorithm leverages statistic methods and game theory to make individual users in LVDN achieve local optimum autonomously. A variant of the log-linear trial and error learning process is applied in a novel "suggest-convince" mechanism, which guarantees the convergence to Nash Equilibrium (NE) and uses player compatible relations to form a specific equilibrium. The second algorithm employs Bernoulli trials to imitate the searching process in the classical gradient descent approach. The player-compatible relationship is employed to play the role of gradients to indicate the direction of the search. Working in a model-free manner without relying on iterations, this algorithm offers an approximate optimization to minimize the accumulated compensation of reshaping/deferring the shapeable energy resources in a given LVDN while respecting the system constraints. The third algorithm uses the mean-filed theory. By solving individual Hamilton-Jacobi-Bellman-Flemming function with public information, users can compute a good approximation to their optimal control trajectory and take uncertainties into account in a distributed manner. A detailed mathematical framework is provided, accompanied by a discussion on the different entries of uncertainties. The corresponding control scheme uses a broadcast signal to indicate the probability distribution in mean-field theory and streamline the demand on Fokker-Planck-Kolmogorov PDE or Mc-Kean Vlasov SDE, which relieves the computational burden.
Besides the distributed optimization algorithms, to address the dilemma where a user is not able/willing to follow the control signal, a real-time peer to peer flexibility trading scheme is proposed. The scheme offers a way to let users trade their flexibility, making the control more flexible and practical. The scheme consists of flexibility allocation and trading. In the flexibility allocation, player compatibility equilibrium and Bernoulli trials are employed to approximate the Pareto optimality. At the same time, consensus and voltage reference is used to provide real-time offers for flexibility trading. Inconsistent with the optimization algorithms, the trading scheme is computationally tractable and can work with limited communication in a decentralized manner; all the user data is used locally; therefore, privacy is guaranteed.
A 103 nodes test network based on a realistic Belgian semiurban distribution network is used for validation for all the proposed algorithms. Different profiles and special cases of various failures are used for test purpose depends on the specific algorithm characteristics. Moreover, a classical AC optimal power flow algorithm is implemented for further validated and benchmark. The results of the case studies prove the effectiveness and robustness of the proposed algorithms.
A conceptual comparison of the three proposed algorithms is given in the conclusion section of this dissertation. Their corresponding advantages and disadvantages are discussed in control accuracy, communication demand, computational burden, robustness, and scalability. For each algorithm, a typical application scenario is given and discussed respectively. Besides, the compatibility with other optimization approaches of the proposed flexibility trading scheme is discussed case by case. A general outlook to future research is given at the end of this dissertation as a complement to the specific discussions on future research in each chapter.