*3.2. Improvement in Traditional Control of Batteries and Supercapacitors*

The reference current absorbed or released by the energy storage system is divided into a low frequency part and a high frequency part through the low pass filter (LPF). As batteries boast high energy density and large energy storage, they are used as long-term devices for power balance by absorbing or releasing low frequency power, while supercapacitors are utilized for suppressing high frequency disturbances.

The power disturbances that lead the system to emergency mode always give rise to large change rates of DC voltage (d*U*dc/d*t*). Therefore, d*U*dc/d*t* can be utilized to adaptively modify the droop coefficient of the energy storage converter. When it exceeds the preset threshold *C*, the droop coefficient *k*<sup>i</sup> varies adaptively to improve the response speed, as shown in Equation (1).

$$k\_{\rm i} = \begin{cases} \left. k\_{\rm n\_{\rm -i}} - m\_1 ( \left| \frac{\text{dI} I\_{\rm dc}}{\text{dI}} \right| ) \right|^{m\_2} & \text{, for} \left| \frac{\text{dI} I\_{\rm dc}}{\text{dI}} \right| \ge \text{C} \\\left. k\_{\rm n\_{\rm -i}} \right| & \text{, for} \left| \frac{\text{dI} I\_{\rm dc}}{\text{dI}} \right| < \text{C} \end{cases} \tag{1}$$

where *k*n\_i is the droop coefficient of the converter in the original control method. Constants *m*<sup>1</sup> and *m*<sup>2</sup> are based on the rated capacity of microgrid converter and the maximum allowable deviation of DC voltage. *m*<sup>1</sup> is determined by the following Equations.

$$m\_1 = \frac{k\_{\rm n\\_i} - k\_{\rm i\\_min}}{\left(\left|\frac{\rm dJ\_{dc}}{\rm df}\right|\_{\rm max}\right)^{m\_2}}\tag{2}$$

$$k\_{\rm i\\_min} = \frac{\Delta U\_{\rm dci}}{\Delta I\_{\rm i\\_max}},\tag{3}$$

where *k*i\_min is the minimum droop gain, the selection of which is to prevent the output power of the converter from exceeding its maximum limit. ∆*U*dci is the variation of DC voltage corresponding to the maximum current limit (∆*I*i\_max) of the convertor, and is intended for setting the allowable voltage variation corresponding to a specific converter.

The value of *m*<sup>1</sup> depends on the output capacity of the converter represented by the maximum voltage change rate |d*U*dc/d*t*|max and *k*i\_min. The power support capability of the energy storage converter increases in the same direction with *m*1. A small *m*<sup>1</sup> may result in transient overshoot of DC voltage, while a large one may cause power oscillation of the system. Therefore, it is critical to select an appropriate *m*1. Similarly, a smaller *m*<sup>2</sup> corresponds to smaller droop coefficient of the converter, variation corresponding to a specific converter.

variation corresponding to a specific converter.

which implies more power available at the instant of disturbance, providing reliable energy support for the system. an appropriate *m*1. Similarly, a smaller *m*2 corresponds to smaller droop coefficient of the converter, which implies more power available at the instant of disturbance, providing reliable energy support an appropriate *m*1. Similarly, a smaller *m*2 corresponds to smaller droop coefficient of the converter, which implies more power available at the instant of disturbance, providing reliable energy support for the system.

voltage, while a large one may cause power oscillation of the system. Therefore, it is critical to select

voltage, while a large one may cause power oscillation of the system. Therefore, it is critical to select

*Appl. Sci.* **2019**, *9*, 2523 7 of 19

*Appl. Sci.* **2019**, *9*, 2523 7 of 19

the maximum current limit (Δ*I*i\_max) of the convertor, and is intended for setting the allowable voltage

the maximum current limit (Δ*I*i\_max) of the convertor, and is intended for setting the allowable voltage

The value of *m*1 depends on the output capacity of the converter represented by the maximum

The value of *m*1 depends on the output capacity of the converter represented by the maximum voltage change rate |d*U*dc/d*t*|max and *k*i\_min. The power support capability of the energy storage

The generation procedure of the reference value of the energy storage converter with an adaptive droop coefficient is shown in Figure 4. When the system operates steadily, the change rate of DC voltage is less than the set threshold *C*<sup>i</sup> . Therefore, the output of the comparator is 0, and the converter operates with the original droop coefficient. When the system is disturbed rapidly with large amplitudes, which leads the system to emergency mode, the change rate of DC voltage may exceed the set threshold. Under this circumstance, the output of the comparator is 1 and the dynamic droop coefficient of the converter is adopted, which smooths the DC voltage. for the system. The generation procedure of the reference value of the energy storage converter with an adaptive droop coefficient is shown in Figure 4. When the system operates steadily, the change rate of DC voltage is less than the set threshold *C*i. Therefore, the output of the comparator is 0, and the converter operates with the original droop coefficient. When the system is disturbed rapidly with large amplitudes, which leads the system to emergency mode, the change rate of DC voltage may exceed the set threshold. Under this circumstance, the output of the comparator is 1 and the dynamic The generation procedure of the reference value of the energy storage converter with an adaptive droop coefficient is shown in Figure 4. When the system operates steadily, the change rate of DC voltage is less than the set threshold *C*i. Therefore, the output of the comparator is 0, and the converter operates with the original droop coefficient. When the system is disturbed rapidly with large amplitudes, which leads the system to emergency mode, the change rate of DC voltage may exceed the set threshold. Under this circumstance, the output of the comparator is 1 and the dynamic droop coefficient of the converter is adopted, which smooths the DC voltage.

droop coefficient of the converter is adopted, which smooths the DC voltage.

**Figure 4.** Principle diagram of self-adaptive inertia droop control. **Figure 4.** Principle diagram of self-adaptive inertia droop control. **Figure 4.** Principle diagram of self-adaptive inertia droop control.

## *3.3. Predictive Converter Control Method 3.3. Predictive Converter Control Method*

needs to be charged, the converter switches to Buck mode.

Conduction period of V2; (**b**) Shutdown period of V2.

*3.3. Predictive Converter Control Method*  Achieving fast smoothing of the system power requires fast converter control, whereas adopting the routine method based on real time value of DC/DC converters may weaken the effect of the selfadaptive droop control due to the lag regulation of current. Therefore, a predictive control method is proposed for the hybrid energy storage system to improve corresponding regulation speed. The converters of the supercapacitor and battery adopt the same Buck/Boost topology, as shown in Figure 5, with the switches V1 and V2 operating complementarily [27]. When the DC voltage in the microgrid is lower than the switching threshold, the energy storage unit discharges, in which condition the converter works in Boost mode. Contrarily, when there is power surplus and the energy storage unit Achieving fast smoothing of the system power requires fast converter control, whereas adopting the routine method based on real time value of DC/DC converters may weaken the effect of the self-adaptive droop control due to the lag regulation of current. Therefore, a predictive control method is proposed for the hybrid energy storage system to improve corresponding regulation speed. The converters of the supercapacitor and battery adopt the same Buck/Boost topology, as shown in Figure 5, with the switches V<sup>1</sup> and V<sup>2</sup> operating complementarily [27]. When the DC voltage in the microgrid is lower than the switching threshold, the energy storage unit discharges, in which condition the converter works in Boost mode. Contrarily, when there is power surplus and the energy storage unit needs to be charged, the converter switches to Buck mode. Achieving fast smoothing of the system power requires fast converter control, whereas adopting the routine method based on real time value of DC/DC converters may weaken the effect of the selfadaptive droop control due to the lag regulation of current. Therefore, a predictive control method is proposed for the hybrid energy storage system to improve corresponding regulation speed. The converters of the supercapacitor and battery adopt the same Buck/Boost topology, as shown in Figure 5, with the switches V1 and V2 operating complementarily [27]. When the DC voltage in the microgrid is lower than the switching threshold, the energy storage unit discharges, in which condition the converter works in Boost mode. Contrarily, when there is power surplus and the energy storage unit needs to be charged, the converter switches to Buck mode.

**Figure 5.** Topology and working mode of bi-directional DC/DC converter in Boost mode: (**a**) **Figure 5.** Topology and working mode of bi-directional DC/DC converter in Boost mode: (**a**) Conduction period of V2; (**b**) Shutdown period of V2. **Figure 5.** Topology and working mode of bi-directional DC/DC converter in Boost mode: (**a**) Conduction period of V<sup>2</sup> ; (**b**) Shutdown period of V<sup>2</sup> .

The converter of the energy storage system usually adopts a double closed-loop control structure, with the outer-loop being voltage control and the inner loop current control. Being different from the commonly used PI control method, the predictive control method based on converter model collects the current state variables of the system and calculates the predictive current value at the next moment through the predictive model. The switching action of the converter is then chosen by The converter of the energy storage system usually adopts a double closed-loop control structure, with the outer-loop being voltage control and the inner loop current control. Being different from the commonly used PI control method, the predictive control method based on converter model collects the current state variables of the system and calculates the predictive current value at the next moment through the predictive model. The switching action of the converter is then chosen by The converter of the energy storage system usually adopts a double closed-loop control structure, with the outer-loop being voltage control and the inner loop current control. Being different from the commonly used PI control method, the predictive control method based on converter model collects the current state variables of the system and calculates the predictive current value at the next moment through the predictive model. The switching action of the converter is then chosen by minimizing the deviation between the predicted current value and the reference one [28]. This method adopts active predictive control instead of passive feedback regulation, which effectively avoids the time lag in traditional PI-based current regulation within the inner loop. Therefore, the predictive method is suitable for the occasion of voltage regulation, which requires high control speed.
