The scheme of wind-storage combined system capacity configuration based on random fuzzy chance constrained bi-level programming

A random fuzzy chance constrained bilevel programming scheme for distributed wind-storage combined system is proposed. The random fuzzy simulation is used to describe the uncertainty of distributed wind power output. The reliability of randomness and ambiguity is taken as the index to evaluate the capacity allocation scheme of the distributed wind-storage combined system. Considering system power balance, opportunity measurement constraint of static security index and active management (AM) measures, the random fuzzy expectation value of maximum annual profit is set as the upper optimization goal, and the minimum random fuzzy expectation value of the distributed wind power active reduction is set as the lower optimization target. The scheme is constructed by judging whether the static security index of the upper goal satisfies the confidence level of the random fuzzy chance constraint and the coordination of the upper and lower goals. Finally, the random fuzzy simulation, the forward pushback power flow calculation and the genetic algorithm (GA) are applied to solve the model. The simulation result of IEEE 14-bus example shows the effectiveness and superiority of the model and scheme.


Introduction
With a flexible power regulation ability, energy storage equipments can greatly improve the access characteristics of wind turbines. However, the existing schemes of grid configuration can not be applied to the system with wind energy storage system. It is urgent to establish a grid configuration scheme considering the characteristics of wind turbine and energy storage.
Nowadays, the researches on the configuration of distributed wind power and energy storage are usually separate. L. Li et al. propose a multi-stage programming modeland discretize and couple DG output and load data [1]. On the basis of considering wind power and load, A. Soroudi et al. add electricity price factor to construct different stages [2]. Based on chance constrained programming, the randomness of wind power and load is considered for reactive compensation configuration and distributed wind power location by S. Zhang, et al [3]. Based on fuzzy mathematics theory, the random fuzzy variables can be applied to obtain more uncertain information in configuration [4][5]. At present, there is no reserches of wind-storage combined system configuration based on random fuzzy chance constrained bilevel programming.
Generally, the paper is organized as follows: i) A random fuzzy chance constrained bilevel programming scheme for combined wind-storage system is proposed. ii) Presenting a method Combined with the random fuzzy simulation, the forward pushback power flow calculation and the genetic algorithm (GA) to solve the model. iii) Showing the the effectiveness and superiority of the model and algorithm with simulation of IEEE 14-bus example.
2 Random fuzzy modeling of distributed wind-storage combined system output and static security 2.1 The sequential random fuzzy model of distributed wind power output.
In the work, we choose some typical days form four seasons and divide each day into 24 hours to conduct random fuzzy simulation of wind power output respectively; The shape parameter k in Weibull distribution is represented by triangular fuzzy variable      ; The membership function can be described as follows: Wind speed is represented by random fuzzy variable v  . Its chance-constrained distribution function of weibull distribution can be described as bellow: The random fuzzy wind speed value as follows is obtained by inverse transformation of Eq. (4): The probability of the wind speed above is equal to the probability of the current k and c, which is marked as Pos{ } kc  . According to the uncertainty theory, , which is the smaller value in the membership of k and c.

Modeling of the wind-storage combined system
Adjusting charging and discharging power in storage configuration to stabilize the fluctuation of wind power: where, P ess,t is the planned value of energy storage charging power for a given t-period, and the negative value represents discharge; P w,t represents wind power generated by random fuzzy simulation at t-time; P up,t and P down,t are the maximum and minimum random fuzzy expectation values of wind power within a certain range of confidence in t-period.

Random fuzzy chance measure of static security index
A method to solve the random fuzzy power flow of wind-storage combined system is proposed, in order to acquire the static security indexes such as node voltage, branch power and the limit of backward power. The specific steps are as follows: 1) Obtain the wind power output of each period by random fuzzy simulation, and simulate the load by adding random numbers of normal distribution on the basis of typical daily load data.
2) Calculate the power flow by the forward and backward substitution method.
3) Calculate the probability measure and its parameter membership function of the static security index which matches the static security range in the random simulated samples under each possibility. The expressions of the random fuzzy chance measure with node voltage, branch power and backward power in normal interval are as follows: where node voltage U % , branch power l P % and B P % are random fuzzy variables; Ch{}( )   is the chance for random fuzzy events; Pr is a probability measure; ,  ,  ,  ,  ,  are the given confidence levels; is a random fuzzy event with branch power satisfying boundary conditions; And { 0} B P  % is a random fuzzy event when the input power, sent by the low voltage side of distribution substation to the active distribution network, is greater than zero.
3 The scheme of wind-storage combined system capacity configuration based on random fuzzy chance constrained bilevel programming

Objective function
The upper-level optimization is to maximize the random fuzzy expected value of annual profit under the confidence level of chance measure. The objective function is as follows:

Constraint conditions
Chance constraint conditions for objective functions can be described as: and, where, x is a decision variable, representing the number of wind turbines connected; k is the kth random fuzzy variable;  and  are the given confidence levels; where, m N is the number of days in each season; NDG is the number of wind turbine nodes installed in the system; In addition, the constraints should include equality constraints of node power, node voltage, branch power and random fuzzy chance constraints of backward power, wind power penetration, inequality constraints of DG amount, energy storage state and power capacity constraints. and,

The lower-level optimization model
Based on the upper level optimization, the lower-level optimization is to optimize the wind power output in different periods. Its objective function is as follows:

Objective function
where, c u r

Constraint conditions
The equality constraints are shown in Eq.(18).

Solution of the model
We combine random fuzzy simulation, forward and backward substitution method and genetic algorithm to solve the model. The process of random fuzzy modeling of distributed wind power output and static security index is metioned above. Mixed integer coding operator is used to solve the initial individual, and mixed integer mutation operator is used to solve the mutation individual. The number of wind turbines and energy storage configuration is set as the upper chromosome, and the three AM measures are set as the lower chromosome.

Random fuzzy simulation of wind speed and static security index
The DG output and active load obtained from timing simulation are as follows:  Table 1. As is shown in Table 1, for one thing, the annual profit of wind-storage configuration decreased by 5.1%, for the restrictions on optimization by the cost of energy storage, which result in a profits reduction. For another thing, the penetration of wind power increased from 7.1% to 9.2%. Through the analysis of the expressions, the load of the two models is nearly equal. The main reason causing the increase of penetration is that, the wind will be abandoned without considering the limitation of the maximum fluctuation of the wind-storage system when in a sharp fluctuation period. The wind-storage combined system can use the energy storage to improve the uncertainty by peak-load shifting. Hence, the supply and the penetration of wind power are increased.

5.3
Influence of confidence level on configuration In random fuzzy chance constrained programming, the confidence level represents the trustworthiness of results. Setting the confidence level of 0.95 indicates that the random fuzzy chance constrained scheme is established when the lower limit of the chance measure, satisfying the static security index, is greater than 95%. The random fuzzy expectations of profit are shown in Table 2 when the confidence level of static security indicators is respectively 0.90, 0.92, 0.94, 0.96 and 0.98. As is shown in Table 2, the higher the confidence level is, the lower the annual profit and the wind power penetration are. Therefore, in the proposed optimal configuration of distributed power based on random fuzzy chance constrained programming, the planners can achieve the maximum annual profit by setting different confidence levels of chance measure within an allowed risk range according to the requirement.

Conclusion
In this paper, A random fuzzy chance constrained bilevel programming scheme for distributed wind power and energy storage combined system is proposed. The results can be summarized as follows: i) The scheme comprehensively takes the objective temporal characteristics of the wind speed and the random fuzzy uncertainties into consideration and describes the static security index with random fuzzy chance measure, which will enrich uncertain information of configuration.
ii) The capacity of wind turbine and energy storage is planned jointly in the proposed scheme, for improving the fluctuation characteristics of wind power output. The scheme is able to fully consider the peak load shifting of energy storage to improve the operation of distribution networks. The capacity allocation scheme of distributed wind has stronger adaptability under the precondition of improving DG acceptance.
iii) The scheme considers different confidence levels of the system static security index, provides economic benefits evaluation such as annual profit under the premise of feasibility, which allows planners allocate distributed wind capacity flexibly considering both technical and economic perspectives.