 Methodology
 Open Access
Cost reduction of a hybrid energy storage system considering correlation between wind and PV power
 Lin Feng^{1}Email author,
 Jingning Zhang^{1},
 Guojie Li^{1} and
 Bangling Zhang^{2}
https://doi.org/10.1186/s4160101600211
© The Author(s) 2016
 Received: 13 May 2016
 Accepted: 16 May 2016
 Published: 6 July 2016
Abstract
A hybrid energy storage system (HESS) plays an important role in balancing the cost with the performance in terms of stabilizing the fluctuant power of wind farms and photovoltaic (PV) stations. To further bring down the cost and actually implement the dispatchability of wind/PV plants, there is a need to penetrate into the major factors that contribute to the cost of the any HESS. This paper first discusses hybrid energy storage systems, as well as chemical properties in different medium, deeming the ramp rate as one of the determinants that must be observed in the cost calculation. Then, a mathematical tool, Copula, is explained in details for the purpose of unscrambling the dependences between the power of wind and PV plants. To lower the cost, the basic rule for allocation of buffered power is also put forward, with the minimum energy capacities of the battery ESS(BESS) and the supercapacitor ESS(SCESS) simultaneously determined by integration. And the paper introduces the probability method to analyze how power and energy is compensated in certain confidence level. After that, two definitions of coefficients are set up, separately describing energy storage status and wind curtailment level. Finally, the paper gives a numerical example stemmed from real data acquired in wind farms and PV stations in Belgium. The conclusion presents that the cost of a hybrid energy storage system is greatly affected by ramprate and dependence between the power of wind farms and photovoltaic stations, in which dependence can easily be determined by Copulas.
Keywords
 Probability analysis
 Copula
 Correlation
 Capacity optimization
 Hybrid ESS
Introduction
Owing to the fact of the fast development of renewable energy and the increased concern of the environmental and sustainable impact of fossil fuels, wind farms and photovoltaic plants have been widely increasingly built around the world over past decades [1]. Wind farms and photovoltaic plants are currently not confined in the conventional offgrid generation systems. Those ongrid variable power sources, however, exert an adverse impact on the operation and control of conventional power grid [2]. The power of wind farms and PV plants is normally much more dependent upon the onsite landform, topography and climate. As a result, they inherently contain the congenital defects, including intermittency, fluctuation and undispatchablility. Hence, energy storage systems which nowadays have become less expensive are introduced in such systems to ease the instability tendency of grids, with the ability of compensating for intermitted and fluctuant outputs of wind/PV plants. As the cost gradually falls, energy storage systems have been put into use in grids on a larger scale. Single type energy storage systems cannot meet the demands in real applications, considering the power and energy requirement at different time scale. As a result, hybrid energy storage systems turn out to be the feasible choice. The most common hybrid energy storage system is composed of batteries, such as advanced leadacid or lithiumion batteries, and supercapacitors [3].
Refs. [4, 5] present a fundamental frame to analyze the cost in a hybrid energy storage system, pointing out the ramp rate is the principal factor that has effect on the cost. Copula functions are discussed in [6, 7]. The spacetime complementarities between wind farms and PV stations are emphasized in [8].
Ref. [9] cautiously explored the wind curtailment phenomenon in nations partly driven by wind power generation, such as America, Spain and Denmark. A new windESS combined control method for surpassing Wind curtailment are in detail discussed in [10].
To further bring down the cost and actually implement the dispatchability of wind/PV plants, hybrid energy storage systems will be increasingly pervasive in the foreseeable future. Therefore, there is a need to penetrate into the major factors that contribute to the cost of the any HESS.
In this study, based on the cost of HESS by considering the ramp rate mentioned in [4], Copulas functions are proposed to analyze the dependence between wind and PV power. Then the cost of HESS is analyzed considering the ramp rate as well as the dependence between wind and PV power. Simulation studies are carried out to verify the above analysis.
Hybrid energy storage system
A hybrid energy storage system often owns the merits of individual single energy storage system. A battery energy storage system, such as advanced leadacid batteries, has the advantages in pricing and largescale using. It, however, poorly performs in the situation where power soars dramatically, or on the contrary, drops instantly. So, it is supposed to accumulate massive less fluctuant energy. With the more costly price, a supercapacitor energy storage system is not equipped with possibility of extensive using, but it does well in the moments when power moves fast.
In Fig. 1, P _{v} represents the output power of photovoltaic stations. P _{w} represents the power of wind farms. P is the aggregated power of P _{v} and Pw. Buffered power is represented by P _{h}. P _{sc} is the power of the supercapacitor energy storage system. P _{b} is the power of the battery energy storage system. P _{d} represents the dispatched power into the grid.
Ramp rate
The limitation of ramprates in wind farms
Installed capacity  Maximum variation in 10 min(MW)  Maximum variation in 1 min(MW) 

<30  20  6 
30–150  capacity/1.5  capacity/5 
>150  100  30 
The limitation of ramprates in PV stations
Project scale  Maximum variation in 10 min(MW)  Maximum variation in 1 min(MW) 

small  capacity  0.2 
medium  capacity  capacity/5 
large  capacity/3  capacity/10 
Second, ramp rates also go for the energy storage system. Owing to the chemical properties and specifications by battery manufacturers, a battery energy storage system has the boundaries of maximum ramp rate as well. There is no limit to ramp rates in the supercapacitor energy storage system, which undoubtedly assumes the superiority of supercapacitor energy storage systems.
Method
By Copulas, the dependences, or correlations between random variables can be set up. On one hand, marginal distributions can easily be obtained with joint probability distribution. On the other hand, it is not easy to get the joint distribution when marginal distributions are known. The emergence and improvement of Copulas functions, to some extent, resolves the problem [6].
Definition
Common copulas
The measurement of correlation
There are several measurements of correlation, or dependency, between random variables. With regard to different usage, massive of them can be adopted, such as Pearson coefficient ρ, Kendall rank correlation coefficient τ, Spearman rank correlation coefficient ρ and tail dependence λ.
Results
Dispatchability
The allocation of P _{b} and P _{sc}
P _{h} is the aggregated power of P _{b} and P _{sc}. P _{h} is the power that buffers from/into hybrid energy storage system. Y is the ramp rate. P _{b} and P _{sc} are confirmed in (9) and (10) [4].
The determination of energy capacity
Cost function
Solving (9) and (10), every ramp rate Y corresponds to a set of P _{b}(t) and P _{sc}(t), from which E _{b}(t) and E _{sc}(t) can be gained. The fit value of P _{b} is the maximum of P _{b}(t); the same for P _{sc}. Note that the fit values of E _{b} and E _{sc} depend primarily on their difference between upper and lower bounds in Fig. 3.
Statistical observation
Definitions of coefficients
To make the problem more intuitive, here we separately define two types of coefficients, wind curtailment coefficient and energy storage coefficient. This approach will undoubtedly construct the connection between energy storage status and wind curtailment condition. The similar solar power abandonment is ignored for parallel approach.
The key to the problem is that we make a probabilistic modification to wind power output. In other words, P _{ w } is replaced by \( \left[1\xi \left({\mathrm{t}}_{\mathrm{i}}\right)\right]\cdot {P}_w^{\hbox{'}}; \) note that \( {P}_w^{\hbox{'}} \) is the original 100 % of wind power.

λ > 1, the cost of hybrid energy storage system goes up

λ = 1, the cost of hybrid energy storage system remains unchanged

λ < 1, the cost of hybrid energy storage system goes down
Procedure to determine the optimum BESS ramprates
Discussion
Here, the paper exhibits a numerical example. All the data are based on real historical scene. The installed capacities of wind farms and PV stations are 143.45 MW and 431.17 MW, respectively, which are located at Belgium (http://www.elia.be).
The dependence using copulas
The buffered power
Power and energy capacities
The essence of cost function
Conclusion
The paper concluded that the cost of a hybrid energy storage system is greatly affected by ramprate and dependence between the power of wind farms and photovoltaic stations, in which dependence can easily be determined by Copulas. A numerical example shows as the dependence between wind farms and PV stations goes up, the cost decreases. Moreover, the cost is also influenced by energy storage compensation coefficient.
Declarations
Acknowledgements
This work was supported by Shanghai Science and Technology Committee (13231204002) and National Key Technology R&D Program of China (2015BAA01B02).
Authors' contribution
LF and JNZ carried out the theoretic studies, calculated the numerical example and drafted the manuscript; GJL and BLZ participated in the theoretic studies. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
About the Authors
L. Feng She is now a lecturer in the Dept. of Electrical Engineering, Shanghai Jiao Tong Univ., Shanghai, China. Her research interests are the control and the integration of renewable energy, and Microgrid.
J. N. Zhang He is currently pursuing the Master Degree in SEIEE from Shanghai Jiao Tong University. His research interests are capacity optimization and energy storage systems.
G. J. Li He is now a professor in the Dept. of Electrical Engineering, Shanghai Jiao Tong Univ., Shanghai, China. His current research interests include power system analysis and control, wind and PV power control and integration, and Microgrid.
B. L. Zhang He is currently working for Shanghai Power & Energy Storage Battery System Engineering Tech. Co. Ltd.. His research interests are the electric power system design and the integration of new energy resources.
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Authors’ Affiliations
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