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Hao Bai
State Key Laboratory of Advanced Electromagnetic Engineering and Technology, Huazhong University of Science and Technology, Wuhan 430074, China

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Journal article
Published: 24 February 2016 in Energies
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In this study, a novel intentional island model of a distribution system with distributed generations (DGs) is presented and the improved Dijkstra algorithm is used to solve this model. This paper abstracts the distribution network with DGs to the layered directed tree according to its radial structure and power restoration process. In consideration of grade, controllability, capacity, level and electrical betweenness of load, the model weights load and maximizes total load weight in the island. The proposed model considers power balance, node voltage, phase angle and transmission capability of the branch, and network connectivity to meet practical engineering requirements. The improved Dijkstra algorithm formulates a search rule to select the load that can be divided into an island in descending order of the shortest path between the load node and DG node. An optimal island partition scheme is achieved through three stages: origin island, baby island and mature island. Meanwhile, scheme adjustment and constraint checking are used alternately to balance objective functions and constraints. The improved IEEE 43-bus distribution network is applied to verify the validity of the algorithm. A comparison of two island methods shows that the proposed algorithm can generate a reasonable scheme for island partitioning.

ACS Style

Jian Su; Hao Bai; Pipei Zhang; Haitao Liu; Shihong Miao. Intentional Islanding Algorithm for Distribution Network Based on Layered Directed Tree Model. Energies 2016, 9, 124 .

AMA Style

Jian Su, Hao Bai, Pipei Zhang, Haitao Liu, Shihong Miao. Intentional Islanding Algorithm for Distribution Network Based on Layered Directed Tree Model. Energies. 2016; 9 (3):124.

Chicago/Turabian Style

Jian Su; Hao Bai; Pipei Zhang; Haitao Liu; Shihong Miao. 2016. "Intentional Islanding Algorithm for Distribution Network Based on Layered Directed Tree Model." Energies 9, no. 3: 124.

Research article
Published: 03 November 2015 in Mathematical Problems in Engineering
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With the increasing penetration of wind power, the randomness and volatility of wind power output would have a greater impact on safety and steady operation of power system. In allusion to the uncertainty of wind speed and load demand, this paper applied box set robust optimization theory in determining the maximum allowable installed capacity of wind farm, while constraints of node voltage and line capacity are considered. Optimized duality theory is used to simplify the model and convert uncertainty quantities in constraints into certainty quantities. Under the condition of multi wind farms, a bilevel optimization model to calculate penetration capacity is proposed. The result of IEEE 30-bus system shows that the robust optimization model proposed in the paper is correct and effective and indicates that the fluctuation range of wind speed and load and the importance degree of grid connection point of wind farm and load point have impact on the allowable capacity of wind farm.1. IntroductionWith unceasing increase of grid-connected wind power, the fluctuation and randomness of wind power output bring aggravated negative influence to power grid such as overvoltage and overloads [1–3]. The operating state of power system will be worse when the allowable capacity of wind farm is high. The basic method to solve the problem is to redesign network structure and improve electrical equipment, but it is undoubtedly uneconomic considering the high investment and long construction time. Therefore, the feasible measure at present is to research on maximum allowable capacity of wind farm on condition of ensuring the system can operate safely and steadily with unchanged network structure and original electrical device.The allowable capacity refers to the maximum installed capacity of wind farms connected into the distribution network on the premise of guaranteeing safety and steady operation of power grid. Many factors can determine the allowable capacity, such as voltage regulation, harmonic distortion, short-circuit current, and transient stability. It will be a very complicated problem to calculate allowable capacity if all the factors are considered, and the result may not be universal either. The existing methods usually regard wind power as distributed generation (DG) to calculate the allowable capacity from one or several aspects [4–12].Based on the voltage sensitivities related to active and reactive power injections, [4] directly determines the maximum power of distributed generation (DG) without leading to steady-state voltage violations. The maximum voltage deviation of customers, cables current limits, and transformer nominal value can be defined as three main criteria to determine allowable capacity of photovoltaics [5]. Reference [6] analyzes sensitivity of bus voltage and lines current to determine the maximum capacity that can be injected in a specific bus and then searches all buses to find the minimum acceptable allowable capacity. Due to the nonlinear current injected by inverter-based DG units, the DG penetration level could be limited by harmonic distortion constraint [7, 8]. In [9], the maximum allowable capacity of the distributed generator in the distribution network is analyzed for meeting the requirements of relay protection and limiting the impact to short-circuit current characteristics. Reference [10] deliberates the influence of DG’s allowable capacity on traditional three-stage current protection and then builds four constraints to determine the penetration level of DG. Reference [11] uses dynamic studies to investigate the behavior of the system at different penetration level of DG, the frequency, and voltage stability of all () contingencies. With the help of an improved transient energy function, the transient energy margin can be calculated to quantify transient stability of power grid integrated with wind generation and analyze penetration level of wind generation furthermore [12].The existing methods suppose that wind farm has a stable power output and ignores the uncertainty and fluctuation of wind speed; moreover the load demand in distribution network is in fluctuation condition. The coupled uncertainty of wind speed and load demand increases dimension of uncertain factors and complexity of the analysis. Without considering the effect of these uncertain variables, the conventional method for determining allowable capability of wind farm cannot ensure that power grid operates safely and steadily in a variety of conditions. The stochastic approach uses Weibull distribution to express the probability of wind speed and develops a chance constrained model to calculate the allowable capacity of wind farm [13], but the work has some limitations in application. First, it is difficult to identify an accurate probability distribution of the uncertainty. A large number of scenarios should be collected to get relatively accurate shape parameter and scale parameter in Weibull distribution [14, 15], which increases complexity of analysis procedure and deviation of evaluation result. Second, it is not easy to represent the wind power “ramp” events in the scenarios [16], which refer to the situations where wind power output increases or decreases significantly during a short period of time due to fast-moving weather phenomena.Robust optimization has recently gained substantial popularity as a powerful tool to solve problems in power system with uncertainty parameter. Instead of making assumption on specific probability distribution, the robust optimization approach replaces the random parameters by predetermined uncertainty sets in the deterministic formulation [17]. The uncertainty set can be easily constructed from the historical data, such as the mean value and range of uncertainty data. The robust model immunizes against all realizations of the uncertain data within uncertainty set containing worst-case scenario, so power system can have normal operation in all uncertainty scenarios [18]. Combining robust optimization theory with fast decoupling PQ method, the paper proposes a method for determining the maximum allowable capacity of wind farm with the uncertainty of wind speed and load demand taken into consideration. The method uses box set to formulate the uncertainty data and make constraints for node voltage and line capacity. To solve the proposed model conveniently, duality theory is applied to convert uncertainty quantities in constraints to certainty quantities as well as the proposed model into linear programming model. Under the condition of multi wind farms, the paper further builds a bilevel optimization model to calculate penetration capacity. The result of IEEE 30-bus system analyzes the influence on allowable capacity of wind farm caused by fluctuation range of wind speed and load as well as the importance degree of grid connection point of wind farm and load point.The paper is organized as follows. Section 2 introduces allowable capacity model based on linear programming. Section 3 describes robust linear optimization model and box set. Section 4 shows allowable capacity model of single wind farm based on robust linear optimization and bilevel optimization model for allowable capacity of multi wind farms. Section 5 performs a set of computational studies and reports numerical results. Section 6 concludes the paper.2. Allowable Capacity Model Based on Linear Programming 2.1. Mathematical ModelThe allowable capacity of wind farm connection to gird is the maximum allowable capacity of wind farm with some constraints. The mathematical model based on linear programming can be expressed as where is allowable capacity of single wind farm; and are numbers of conventional generators and wind farms; is network loss; is total load demand; is active power output of conventional generator ; , are upper and lower limit for active power output of conventional generator ; is active power transferred in line ; is maximum active power transferred in line ; is voltage of node ; is nominal voltage; is allowable voltage deviation.2.2. Load Flow CalculationPower flow calculation has two basic calculation methods: DC model and AC model. The DC power flow model is an imprecise method and cannot calculate node voltage, so the paper adopts AC power flow model. According to physical characteristics of power grid, many decoupling flow algorithms have been introduced. The fast decoupling PQ method adjusts phase angle and voltage amplitude based on active power and reactive power, respectively:where and are increment of active power and reactive power at node; , are increment of phase angle and voltage amplitude at node. and are sensitivity matrix.Considering some small electrical parameter, modified equation of fast decoupling PQ method can be expressed as [19]Suppose the voltage is per unit value; the simplified equation can be written as where , are node admittance matrix; the nondiagonal and diagonal elements in , can be formulated aswhere and are resistance and inductance of branch ; is grounding branch susceptance of node .The incremental expression of phase angle and voltage amplitude can be derived from (8) and expressed aswhere , are increment of active power output for generator and active power demand for load; are power factor of generator and load; , are corresponding submatrix for generator and load in ; , are corresponding submatrix for generator and load in .The power flow in branch can be expressed as [20]where and are active power and reactive power transferred in branch , and are node voltage on both ends of branch ; is phase-angle difference between nodes of branch ; , are susceptance and conductance of branch .Based on theoretical basis and simplified method of decoupling method, formulation (11) can be expressed with the same form of formulation (8):where are increment of active power and reactive power at branch; are sensitivity matrix between phase angle, voltage amplitude, and branch

ACS Style

Lihui Guo; Hao Bai. Method for Determining the Maximum Allowable Capacity of Wind Farm Based on Box Set Robust Optimization. Mathematical Problems in Engineering 2015, 2015, 1 -11.

AMA Style

Lihui Guo, Hao Bai. Method for Determining the Maximum Allowable Capacity of Wind Farm Based on Box Set Robust Optimization. Mathematical Problems in Engineering. 2015; 2015 ():1-11.

Chicago/Turabian Style

Lihui Guo; Hao Bai. 2015. "Method for Determining the Maximum Allowable Capacity of Wind Farm Based on Box Set Robust Optimization." Mathematical Problems in Engineering 2015, no. : 1-11.

Journal article
Published: 23 March 2015 in Energies
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A virtual power plant takes advantage of interactive communication and energy management systems to optimize and coordinate the dispatch of distributed generation, interruptible loads, energy storage systems and battery switch stations, so as to integrate them as an entity to exchange energy with the power market. This paper studies the optimal dispatch strategy of a virtual power plant, based on a unified electricity market combining day-ahead trading with real-time trading. The operation models of interruptible loads, energy storage systems and battery switch stations are specifically described in the paper. The virtual power plant applies an optimal dispatch strategy to earn the maximal expected profit under some fluctuating parameters, including market price, retail price and load demand. The presented model is a nonlinear mixed-integer programming with inter-temporal constraints and is solved by the fruit fly algorithm.

ACS Style

Hao Bai; Shihong Miao; Xiaohong Ran; Chang Ye. Optimal Dispatch Strategy of a Virtual Power Plant Containing Battery Switch Stations in a Unified Electricity Market. Energies 2015, 8, 2268 -2289.

AMA Style

Hao Bai, Shihong Miao, Xiaohong Ran, Chang Ye. Optimal Dispatch Strategy of a Virtual Power Plant Containing Battery Switch Stations in a Unified Electricity Market. Energies. 2015; 8 (3):2268-2289.

Chicago/Turabian Style

Hao Bai; Shihong Miao; Xiaohong Ran; Chang Ye. 2015. "Optimal Dispatch Strategy of a Virtual Power Plant Containing Battery Switch Stations in a Unified Electricity Market." Energies 8, no. 3: 2268-2289.

Journal article
Published: 04 February 2015 in Energies
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Distributed generation (DG), battery storage (BS) and electric vehicles (EVs) in a microgrid constitute the combined power generation system (CPGS). A CPGS can be applied to achieve a reliable evaluation of a distribution network with microgrids. To model charging load and discharging capacity, respectively, the EVs in a CPGS can be divided into regular EVs and ruleless EVs, according to their driving behavior. Based on statistical data of gasoline-fueled vehicles and the probability distribution of charging start instant and charging time, a statistical model can be built to describe the charging load and discharging capacity of ruleless EVs. The charge and discharge curves of regular EVs can also be drawn on the basis of a daily dispatch table. The CPGS takes the charge and discharge curves of EVs, daily load and DG power generation into consideration to calculate its power supply time during islanding. Combined with fault duration, the power supply time during islanding will be used to analyze and determine the interruption times and interruption duration of loads in islands. Then the Sequential Monte Carlo method is applied to complete the reliability evaluation of the distribution system. The RBTS Bus 4 test system is utilized to illustrate the proposed technique. The effects on the system reliability of BS capacity and V2G technology, driving behavior, recharging mode and penetration of EVs are all investigated.

ACS Style

Hao Bai; Shihong Miao; Pipei Zhang; Zhan Bai. Reliability Evaluation of a Distribution Network with Microgrid Based on a Combined Power Generation System. Energies 2015, 8, 1216 -1241.

AMA Style

Hao Bai, Shihong Miao, Pipei Zhang, Zhan Bai. Reliability Evaluation of a Distribution Network with Microgrid Based on a Combined Power Generation System. Energies. 2015; 8 (2):1216-1241.

Chicago/Turabian Style

Hao Bai; Shihong Miao; Pipei Zhang; Zhan Bai. 2015. "Reliability Evaluation of a Distribution Network with Microgrid Based on a Combined Power Generation System." Energies 8, no. 2: 1216-1241.