In this chapter, we developed a hierarchical interactive architecture the Utility and the distributed smart-homes in a smart grid while ensuring grid-stability and Quality-of-Service (QoS). With an abstract model consisting of one controller and multiple smart-homes developed, we formulated a two-step decision framework for the real-time scheduling. The two-step decision framework consisted of (1) centralized con-troller sequential decisions and (2) distributed smart-home decisions. We developed a hidden mode Markov decision process (HM-MDP) model for customer real-time
deci-sion making. We first proposed a value iteration (VI) based exact solution algorithm, with the Baum-Welch and the incremental pruning (IP) algorithms adopted to learn the non-stationary dynamics and to iterate the representation sets, respectively. We further discussed the Q-learning based approximate dynamic programming (ADP) algorithm with relatively low computational complexity. Compared to greedy or ran-dom decision strategies, the Q-learning algorithm offered much more flexibility and adaptiveness with relatively good performance.
With the solution algorithm design for the HM-MDP model well developed, we then focused on the Vickrey auction design for distributed smart-homes. The solu-tion set of the Vickrey aucsolu-tioning game was divided into two categories and detailed analysis on the Bayesian Nash equilibria were presented, which showed that the truthful bidding strategy was a weakly dominant Bayesian Nash equilibrium. To overcome the vulnerability of the Vickrey auction against collusion by selling-mode smart-homes, the developed Vickrey auction was extended by introducing a reserve price, which guaranteed robustness of the auction and the convergence of the auc-tioning game to the unique truthful bidding equilibrium.
Summary of the Dissertation and Research Directions
In this dissertation, we have developed a hierarchical interactive architecture for future smart grids. In the followings, we summarize the main aspects and contribu-tions of this dissertation. We also propose possible research direccontribu-tions that can be addressed in the near future.
6.1 Summary of the Dissertation
In Chapter 2, we proposed two types of approaches to model the uncertainty in cus-tomer load demand. The first approach was based on a first order non-stationary Markov chain. A maximum likelihood estimator (MLE) was derived to estimate the time variant transition matrix of the Markov chain. The second approach was based on time series analysis techniques. We presented linear prediction models such as standard autoregressive (AR) process and time varying autoregressive (TVAR) pro-cess, according to different assumptions on the stationarity of customer load profile:
piecewise stationarity, local stationarity and cyclo-stationarity. Prediction perfor-mances of different models were analyzed and compared, advantages and disadvan-tages were discussed.
In Chapter 3, we designed a DR scheduling scheme based on the Utility cost minimization with different customer clustering sizes. A convex optimization prob-lem was formulated and the optimal demand response profile was in the form of a two-dimensional water-filling solution either with flat water levels or different water levels for different customers. Price of Anarchy (PoA) analysis was presented to balance both the centralized and distributed competing objectives.
In Chapter 4, an optimal stochastic tracking scheme was proposed in an inter-active smart grid infrastructure. Optimal stochastic control schemes for the inter-active power control (primary frequency control) were designed, in the presence of uncer-tainties arising from customer load demands and distributed renewable generations, to stabilize frequency and maintain a balance between generation and consump-tion within the distributed synchronous area. We proposed two stochastic tracking schemes based on the state-space representation of a synchronous generator: (1) ref-erence dynamics-based tracking and (2) refref-erence statistics-based tracking. We fur-ther extended the proposed optimal controllers by considering the realistic scenario of asynchronous load demand signals from different households. To compensate for different delays seen by different household signals, a Kalman filter (KF) based pre-diction scheme was proposed to generate the correct reference signal and we showed that the centralized reference prediction could equivalently be implemented distribu-tively. Simulation results were presented to show the performances of the proposed prediction and tracking schemes.
In Chapter 5, we developed a hierarchical interactive architecture the Utility and the distributed smart-homes in a smart grid while ensuring grid-stability and Quality-of-Service (QoS). With an abstract model consisting of one controller and
multiple smart-homes developed, we formulated a two-step decision framework for the real-time scheduling. The two-step decision framework consisted of (1) central-ized controller sequential decisions and (2) distributed smart-home decisions. We developed a hidden mode Markov decision process (HM-MDP) model for customer real-time decision making. We first proposed a value iteration (VI) based exact solution algorithm, with the Baum-Welch and the incremental pruning (IP) algo-rithms adopted to learn the non-stationary dynamics and to iterate the represen-tation sets, respectively. We further discussed the Q-learning based approximate dynamic programming (ADP) algorithm with relatively low computational complex-ity. Compared to greedy or random decision strategies, the Q-learning algorithm offered much more flexibility and adaptiveness with relatively good performance.
With the solution algorithm design for the HM-MDP model well developed, we then focused on the Vickrey auction design for distributed smart-homes. The solution set of the Vickrey auctioning game was divided into two categories and detailed analysis on the Bayesian Nash equilibria were presented, which showed that the truthful bid-ding strategy was a weakly dominant Bayesian Nash equilibrium. To overcome the vulnerability of the Vickrey auction against collusion by selling-mode smart-homes, the developed Vickrey auction was extended by introducing a reserve price, which guaranteed robustness of the auction and the convergence of the auctioning game to the unique truthful bidding equilibrium.