This paper proposes a method to obtain the optimal placement of wind turbines (WTs) in an offshore wind farm (WF). The optimization objective is to minimize the levelized average cost per net electric power generated by a WF with a fixed number of WTs while the distance between WTs is not less than the allowed minimal distance in the far wake region. The WT wake losses have been taken into account, with the Frandsen-Gaussian (F-G) wake model and the optimization problem is subsequently solved by the Hybrid Grey Wolf Optimization (HGWO) algorithm. Synthesis methods which contain a special WT ranking strategy for multiple WTs are described in detail. Both the F-G model and Jensen's model are applied in the offshore WF optimization simulation platform for comparison. Simulation results demonstrate that the F-G model is more consistent with real wakes and thus the optimization result is more accurate than the commonly used Jensen's model.

Wind farms (WFs) are important components of smart grid. The modeling and optimal planning of the WF is preliminary before its construction. In this paper, a bi-level multi-objective optimization framework is presented, with the aim of simultaneously designing the configuration of wind turbines (WTs) as well as the topology of electrical collector system in an offshore WF. The installation capacity of the WF, the positioning of the WTs and the planning scheme of the electrical system are balanced to achieve a better performance of the WF. In this proposal, there is an outer layer along with two inner layers. The objectives of the outer-layer model are the maximization of the WF’s daily profit rate, the daily average capacity factor, and power quality. It is tackled by the Non-dominated Sorting Genetic Algorithm-III (NSGA-III). The objectives of the two inner layer models are to determine the topology of the electrical system and the generation schedule of other generators, and are solved by means of the Binary Particle Swarm Optimization (BPSO) algorithm and the quadratic programming (QP) method respectively. The WF is assumed to be connected to the IEEE-24 bus test system. The simulation results validate the adaptability and effectiveness of the proposed approach with the main factors that affect the WF layout being analyzed.

With the high penetration of renewable energy resources, energy prosumers and microgrids can trade energy directly with each other in a hierarchical way. This paper develops a nested market clearing algorithm that alternately produces optimal trading results in both inter- and intra-microgrid markets. The inter-microgrid market refers to the energy exchange among microgrids in distribution network. The intra-microgrid market is the energy sharing among prosumers inside microgrids. We use a distributionally robust optimization approach that is based on prospect theory (PT) to account for the complexity of prosumers’ behavior. The prosumers’ irrational behavior refers to the incomplete rationality in the market. The objective uncertainty and risk preference inside microgrids are modeled uniformly, based on which the alternating direction multiplier method (ADMM) algorithm is employed to solve this problem while preserving privacy. By filtering the marginal energy prosumers in each microgrid, the privacy of microgrids in the inter-microgrid market is preserved as well. Moreover, we prove that the proposed nested market clearing algorithm can reach the global Nash equilibrium. Numerical simulations demonstrate that the condensed equilibrium representation (CER) successfully selects energy prosumers from an intra-microgrid market to participate in an inter-microgrid market. The impact of risk preference parameters on the total utility is also analyzed.

Global changes in climate conditions and increasing number of weather-related disasters in the world have elevated the quest for better load restorations in power distribution systems. This paper proposes a distribution system restoration (DSR) model where non-exponential time-dependent cold load pickup (CLPU) characteristics and soft open point operations are simultaneously addressed. We develop a time-dependent CLPU model for attaining a more realistic and secure DSR in which we demonstrate that the traditional delayed exponential model (DEM) for a long outage duration is a special case of the adopted CLPU model. The current soft open point (SOP) models would typically relax the operation constraints without devising any tightening procedures, which might lead to inaccurate or even infeasible SOP states. In this paper, we analyze the reasons traditional SOP constraints would lead to unsecure operations and present a set of novel SOP operation constraints for recovering bindings. Also, we adopt the sequential second order cone programming (SSOCP) algorithm to establish the sequential framework of DSR and solve the proposed model effectively. Our presented case studies discuss the rationality of the proposed DSR model and algorithm.

Natural gas is the main energy source and carbon emission source of integrated energy systems (IES). In existing studies, the price of natural gas is generally fixed, and the impact of price fluctuation which may be brought by future liberalization of the terminal side of the natural gas market on the IES is rarely considered. This paper constructs a natural gas price fluctuation model based on particle swarm optimization (PSO) and Dynamic Bayesian networks (DBN) algorithms. It uses the improved epsilon constraint method and fuzzy multi-weight technology to solve the Pareto frontier set considering the system operation cost and carbon emission. The system operation cost is described using Latin Hypercube Sampling (LHS) to predict the stochastic output of the renewable energy source, and a penalty function based on the Predicted Mean Vote (PMV) model to describe the thermal comfort of the user. This is analyzed using the Grey Wolf Optimization (GWO) algorithm. Carbon emissions are calculated using the carbon accounting method, and a ladder penalty mechanism is introduced to define the carbon trading price. Results of the comparison illustrate that the Pareto optimal solution tends to choose less carbon emission, electricity is more economical, and gas is less carbon-intensive in a small IES for end-users when the price of natural gas fluctuates. The impacts of various extents of natural gas price fluctuation for the same load are also discussed.

Due to the coupling network constraints, the prosumers' trading strategies influence each other. This article analyzes the generalized Nash equilibrium (GNE) formulated by the prosumers and proposes a distribution locational marginal price (DLMP)-parametrized alternating direction method of multipliers (ADMM) algorithm to seek the GNE of peer-to-peer (P2P) transactive energy trading. We first present the prosumers' and distribution system operator's models in the P2P transactive energy market. To explicitly add the coupling network constraints to the prosumers' problems, we linearize the distribution network power flow model and project the linear constraints to the prosumers' feasible regions. We then analyze the GNE in the network-constrained P2P transactive energy market and reduce the original GNE to normalized Nash equilibrium (NNE). We relax the original model into a partial dual problem and employ DLMPs to depict the prosumers' heterogeneous influences on the distribution network operation. We modify the ADMM algorithm to decompose the prosumers' trading processes to protect their privacy. The algorithm convergence and market properties at NNE are finally listed and discussed. A four-bus toy model is introduced to illustrate the convergence and properties of our proposed method. We import a modified IEEE 69-bus system to further highlight the advantages of our model.