Dispatchability
Generally, a generation plant bids against each other. It is common for bidders in several power trading markets to forecast its power (nowadays, more and more forecast data are purchased from thirdparty service providers) and to propose generation schedule N hours before the market begins every trading day, which can be exemplified with Nordic power exchange market. The mechanism is called Nhour rule. To simulate the operation of real world, a forecast example is given below, with the hypothesis that dispatched power is derived from hourly average of forecasting power. A forecast algorithm using historical power data can be found in Fig. 2.
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].
Supposing
$$ \begin{array}{l}{P}_{B,r}\left({t}_{i1}\right)+Y\cdot \varDelta t\ge {P}_{H,r}\left({t}_i\right)\hfill \\ {}{P}_{B,r}\left({t}_i\right)={P}_{H,r}\left({t}_i\right),{P}_{SC,r}\left({t}_i\right)=0\hfill \end{array} $$
(9)
Otherwise,
$$ \begin{array}{l}{P}_{B,r}\left({t}_i\right)={P}_{B,r}\left({t}_{i1}\right)+Y\cdot \varDelta t\hfill \\ {}{P}_{SC,r}\left({t}_i\right)={P}_{H,r}\left({t}_i\right){P}_{B,r}\left({t}_i\right)\hfill \end{array} $$
(10)
The determination of energy capacity
After integrating P
_{b} and P
_{sc} with time, E
_{b} and E
_{sc} can be achieved. E
_{b} and E
_{sc} display the energy variation, or the energy level, of the energy storage system [4]. In Fig. 3, the zerointerface represents the assumptive initial energy level. The energy storage system is charged when the curve goes up with system being discharged as the curve comes down. Thus, the minimum energy capacity of the BESS or the SCESS is based on its own moving range, respectively. This implies that the best energy capacity is no less than these least value.
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.
Then, the basic cost function is as follows [4].
$$ f={k}_1\times {E}_b+{k}_2\times {E}_{SC}+{k}_3\times {P}_b+{k}_3\times {P}_{SC} $$
(11)
where k
_{1}, k
_{2}, k
_{3} and k
_{4} are obtained in [11].
Statistical observation
To minimize the cost f, the proper ramp rate Y should be selected. Meanwhile, P
_{
b
}(t), P
_{
sc
}(t), E
_{
b
}(t) and E
_{
sc
}(t) are successively determined. It is natural that the Cumulative Distribution Function (CDF) of these capacities is obtained as shown in Fig. 4 to depict the complete spectacle in statistical manners [4].
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.
Now we choose ξ(t_{i}) to describe the level of wind curtailment and the definition of ξ(t_{i}) is as follows,
$$ \xi \left({\mathrm{t}}_{\mathrm{i}}\right)=\left\{\begin{array}{l}0,\hfill \\ {}0\sim 1,\hfill \\ {}1,\hfill \end{array}\begin{array}{c}\hfill zero\; wind\; curtailment\hfill \\ {}\hfill partly\; wind\; curtailment\hfill \\ {}\hfill complete\; wind\; curtailment\hfill \end{array}\right. $$
Then, the wind curtailment coefficient is denoted by,
$$ C=\frac{{\displaystyle \sum_i^{i+k}\xi \left({\mathrm{t}}_{\mathrm{i}}\right)}}{T/\varDelta t}\times 100\% $$
Finally, the energy storage compensation coefficient is represented,
$$ \lambda =\frac{{\displaystyle \sum_i^{i+k}\left\left[1\xi \left({\mathrm{t}}_{\mathrm{i}}\right)\right]{P}_w+{P}_v{P}_{H,r}\right.\left\cdot \varDelta t\right.}}{{\displaystyle \sum_i^{i+k}{P}_h\cdot \varDelta t}} $$
As a result, we obtain that

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
The MATLAB program is developed following the methods mentioned above. The flowchart is shown in Fig. 5.