In this book, we have investigated distributed control and optimization technologies for MG systems. The obtained results are summarized as follows:

The problem of voltage and frequency restoration in islanded microgrid systems is considered in Chapter 3. A distributed secondary control scheme is proposed to solve this problem. Compared to the existing centralized control approach, our method is fully distributed. In order to design and analyze the voltage and frequency secondary restoration control separately, we first apply the distributed finite-time approach to design the voltage controller, which enables the voltage regulation within finite time. Then the frequency restoration is addressed while keeping the real power sharing accuracy. A sufficient local stability condition for the proposed controller is given. Simulation results show that the proposed controller can restore the voltage and frequency of the whole system to their reference values while keeping a good real power sharing accuracy, regardless of whether additional load is connected to or disconnected from the system.

In order to overcome some intrinsic disadvantages brought by the centralized control, we propose a distributed secondary control scheme for voltage unbalance compensation in Chapter 4. The main key here is to design a distributed control scheme which seeks global information by allowing each local controller to communicate with its neighboring controllers. The proposed control scheme has a distributed two-layer secondary compensation architecture. This 164architecture involves a finite time average-consensus algorithm and a newly developed graph discovery algorithm. The proposed control scheme is not only able to compensate well for the unbalanced voltage in SLB but also share the compensation effort dynamically in the distributed fashion. Also compared to the centralized control, this scheme has higher communication fault tolerance ability and has the plug-and-play property. A simulation test system is built in MATLAB ® $ ^{\textregistered } $ https://s3-euw1-ap-pe-df-pch-content-public-u.s3.eu-west-1.amazonaws.com/9781315109732/e7576b51-c0d6-4645-9b50-371cffac1bea/content/inline-math9_1.tif"/> and several case studies have validated the effectiveness of our proposed strategy. Future work may include VUC in more general cases, such as 1) SLB is located in an arbitrary bus in a mesh topology; 2) transmission line with unbalanced impedance.

In Chapter 5, a fully distributed ED algorithm based on finite-time average consensus and projected gradient is proposed for smart grid systems with random wind power. By allowing each agent to communicate with its neighbor agents, the total cost of the whole system can be minimized by the proposed distributed ED algorithm while satisfying both equality and inequality constraints. Compared to the existing methods, no private confidential gradient or incremental cost information exchange is needed and the objective function is not required to be quadratic. What’s more, the initial estimate values of our proposed method can be chosen arbitrarily by each agent individually. The effectiveness of the proposed scheme has been validated by several case studies including without generator constraints, with generator constraints, plug-and-play of generators and loads, and a large IEEE 30-bus test system. The results show good performance of the proposed method. As an alternative approach, how to develop a distributed ED strategy based on a stochastic programming method is an interesting topic worthy of consideration as a futurework.

In Chapter 6, a distributed optimization algorithm is proposed for the multi-agent system which consists of multi groups of agents. The goal for the agents is to cooperatively minimize the sum of all the local cost functions, each of which is only known by the local agent itself. Also, each agent is constrained by a global and a local constraint set. Our proposed algorithm allows the agents in the same group to estimate the optimal solution individually and communicate with their neighboring agents in parallel. Once their estimates reach consensus, the leader agent in the group sends the estimate to the leader agent in a neighboring group in a sequential way. Two kinds of communication strategies, i.e., deterministic and random, are designed for the leader agents. The convergence of the proposed algorithm is theoretically proved with the virtue of the virtual agent. We also apply this algorithm to solve the economic dispatch problem in multi-area power systems. The effectiveness of the proposed algorithm has been validated by several case studies on IEEE 30-bus power systems. In order to accelerate the convergence speed, future work may consider modifying our algorithm with a fast gradientmethod.

165In Chapter 7, we present a hierarchical decentralized optimization architecture for economic dispatch in smart grid. Different from conventional centralized ED methods, we decompose such problem into several sub-problems, which are solved by each local generator by using only its own information. In order to reduce the communication links, we divide the whole generator agents into clusters and assign a leader agent to each cluster. The leader agent gathers the whole cluster estimates and sends them to an extra coordinator agent. The main role of the coordinator agent is to handle the global demand and supply constraint as well as to coordinate among all the leader agents. It is theoretically shown that the proposed algorithm can ensure each local generator agent obtains the optimal power output when the chosen stepsizes are diminishing under certain conditions. The effectiveness of the proposed algorithm has been validated by several case studies implemented on IEEE 30-bus and IEEE 118-bus power systems. The results show good performance of the proposed method.

In Chapter 8, a distributed optimal energy scheduling strategy is proposed for a smart power system, which consists of a single energy provider, several loads and a regulatory authority. A novel real-time pricing strategy named PD pricing is proposed by adding an incremental term in the conventional P pricing. Two different distributed optimization methods are proposed to minimize the total social cost and they can be applied in different situations. The effectiveness of the proposed methods as well as the PD pricing strategy have been validated by case studies implemented on a HVAC system. It is worth noting that the proposed PD pricing strategy can be implemented in real applications with the development of big data technology [191]. Based on such technology, more information will be available for temporal and/or spatial integration of an ecosystem in practice. Subsequently, the overall performance of the ecosystem could be improved.