3.3.2. Objective Function of the Converter Predictive Control

In order to realize fast regulation of the inner loop current of the converter, predictive control should aim for fast tracking of the reference current generated from the outer loop, as shown in Equation (9).

$$J \stackrel{\circ}{\cdot} = \left| i\_{\rm sto}(k+1) - I\_{\rm sto}^\* \right|. \tag{9}$$

On the basis of collecting the state information of the system at the current moment, the predicted values of the converter inductor current under different switching states can be calculated though the prediction model. The switch state with the smallest deviation between the predicted current and corresponding reference value is then selected as the system output to control the converter. As a result, fast current tracking can be achieved through active predictive control.

By combining the model predictive method of current inner loop with the adaptive droop control in the outer loop of the energy storage control system, fast power regulation of energy storage units under various working modes can be achieved, which stabilizes the DC voltage. The general control chart of the predictive method with adaptive droop control in the outer loop for different energy storage units is presented in Figure 6.

Figure 7.

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

**Figure 6.** Predictive control model of an energy storage system adopting adaptive droop control in the outer loop. **Figure 6.** Predictive control model of an energy storage system adopting adaptive droop control in the outer loop. **Figure 6.** Predictive control model of an energy storage system adopting adaptive droop control in the outer loop.

As mentioned before, the supercapacitor is appropriate for suppressing high frequency power fluctuations with small amplitude, which are hard for the biomass thermal unit or the battery to stabilize. On the contrary, the battery, which has large amount of stored energy and high energy density, is always utilized as a long-term power balance device to absorb or release power with low frequency. The reference current absorbed or released by the energy storage system is divided into two parts, namely, the low-frequency part and the high-frequency one, through the low pass filter LPF. The corresponding control block diagram of the hybrid energy storage system is shown in As mentioned before, the supercapacitor is appropriate for suppressing high frequency power fluctuations with small amplitude, which are hard for the biomass thermal unit or the battery to stabilize. On the contrary, the battery, which has large amount of stored energy and high energy density, is always utilized as a long-term power balance device to absorb or release power with low frequency. The reference current absorbed or released by the energy storage system is divided into two parts, namely, the low-frequency part and the high-frequency one, through the low pass filter LPF. The corresponding control block diagram of the hybrid energy storage system is shown in Figure 7. As mentioned before, the supercapacitor is appropriate for suppressing high frequency power fluctuations with small amplitude, which are hard for the biomass thermal unit or the battery to stabilize. On the contrary, the battery, which has large amount of stored energy and high energy density, is always utilized as a long-term power balance device to absorb or release power with low frequency. The reference current absorbed or released by the energy storage system is divided into two parts, namely, the low-frequency part and the high-frequency one, through the low pass filter LPF. The corresponding control block diagram of the hybrid energy storage system is shown in Figure 7.

**Figure 7.** Control block diagram of the hybrid energy storage system. **Figure 7.** Control block diagram of the hybrid energy storage system.

### **Figure 7.** Control block diagram of the hybrid energy storage system. *3.4. Control of the Energy Stored in the Wind Turbine*

capability of fault ride-through.

capability of fault ride-through.

*3.4. Control of the Energy Stored in the Wind Turbine*  In the wind power generation system, the wind turbine can store or release rotational kinetic energy through the change of its rotational speed, which makes it "the third energy storage unit" in the microgrid. However, in a converter-based microgrid, the direct connection between the disturbance in DC side and the change of rotational kinetic energy in the wind power system is isolated by the turbine-side converter. Generally, the wind power unit operates in maximum power point tracking (MPPT) mode, in which the output electric power is independent of the change of DC voltage. Therefore, auxiliary control is needed to establish the correlation between the kinetic energy of the wind turbine and the DC voltage, so that the mechanical rotation system can provide power support for the microgrid under conditions of significant change in DC voltage, to enhance its *3.4. Control of the Energy Stored in the Wind Turbine*  In the wind power generation system, the wind turbine can store or release rotational kinetic energy through the change of its rotational speed, which makes it "the third energy storage unit" in the microgrid. However, in a converter-based microgrid, the direct connection between the disturbance in DC side and the change of rotational kinetic energy in the wind power system is isolated by the turbine-side converter. Generally, the wind power unit operates in maximum power point tracking (MPPT) mode, in which the output electric power is independent of the change of DC voltage. Therefore, auxiliary control is needed to establish the correlation between the kinetic energy of the wind turbine and the DC voltage, so that the mechanical rotation system can provide power support for the microgrid under conditions of significant change in DC voltage, to enhance its In the wind power generation system, the wind turbine can store or release rotational kinetic energy through the change of its rotational speed, which makes it "the third energy storage unit" in the microgrid. However, in a converter-based microgrid, the direct connection between the disturbance in DC side and the change of rotational kinetic energy in the wind power system is isolated by the turbine-side converter. Generally, the wind power unit operates in maximum power point tracking (MPPT) mode, in which the output electric power is independent of the change of DC voltage. Therefore, auxiliary control is needed to establish the correlation between the kinetic energy of the wind turbine and the DC voltage, so that the mechanical rotation system can provide power support for the microgrid under conditions of significant change in DC voltage, to enhance its capability of fault ride-through.

capacitor in parallel with the wind power converter is calculated as follows.

When disturbance of DC bus voltage occurs, the charge or discharge power of the DC side

When disturbance of DC bus voltage occurs, the charge or discharge power of the DC side

When disturbance of DC bus voltage occurs, the charge or discharge power of the DC side capacitor in parallel with the wind power converter is calculated as follows.

$$
\Delta P\_{\rm dc} = \mathcal{C}\_{\rm w} \mathcal{U}\_{\rm dc} \frac{\mathbf{d} \mathcal{U}\_{\rm dc}}{\mathbf{d}t} \,, \tag{10}
$$

where *C*<sup>w</sup> is the DC side capacitor of the wind power system converter.

The variation of the output power caused by the change of the generator speed in the wind power unit is shown in Equation (11).

$$
\Delta P\_{\rm e} = \frac{\rm dE\_{\rm k}}{\rm dt} = J \omega\_{\rm r} \frac{\rm d\omega\_{\rm r}}{p^2 \rm dt} \tag{11}
$$

where ∆*P*<sup>e</sup> is the power variation of the wind power unit, *E*<sup>k</sup> is the rotating kinetic energy of the generator, *J* is the rotating inertia of the synchronous generator, ω<sup>r</sup> is the angular speed of the synchronous generator, and *p* is the number of pole pairs of the generator. As the wind turbine and the permanent magnet generator are directly coupled, the generator speed is equal to that of the wind turbine.

As the mechanical energy of the wind turbine is much larger than the energy stored in the capacitor, variation of the wind turbine speed is much smaller than that of the DC voltage when bearing the same amount of power disturbance. To quickly restrain the fluctuation of DC voltage with urgency, it is necessary to transform the power unbalance on the DC side into the change of rotational kinetic energy of the wind turbine through a control method. Therefore, fluctuation of DC bus voltage can be assumed by the wind turbine. The following equation is available by combining Equations (2) and (3).

$$J\omega\_{\rm r}\frac{d\omega\_{\rm r}}{p^{2}\rm dt} = \mathcal{C}\_{\rm w}U\_{\rm dc}\frac{\rm d}{\rm dt}\tag{12}$$

The relationship between the variation of the wind turbine speed and the change of DC voltage under the same power disturbance is obtained by integrating and normalizing both sides of Equation (12) simultaneously. It is assumed that the voltage is kept at its rated value *U*dc\_N before occurrence of the disturbance.

$$
\omega\_{\rm r1\\_pu}^2 - \omega\_{\rm r0\\_pu}^2 = \frac{\frac{1}{2}\mathcal{C}\_{\rm w}\mathcal{U}\_{\rm dc\\_N}^2}{\frac{1}{2p^2}\mathcal{I}\omega\_{\rm r\\_N}^2} (\mathcal{U}\_{\rm dc\\_pu}^2 - 1) = k\_{\rm r\\_g} (\mathcal{U}\_{\rm dc\\_pu}^2 - 1),
\tag{13}
$$

where ωr0\_pu and ωr1\_pu are the per-unit values of the angular speed of the generator before and after disturbance, respectively; *U*dc\_pu is the per-unit value of DC voltage after disturbance; ωr\_N is the rated speed of the generator. *k*reg is defined as the speed regulation coefficient, and varying degrees of regulation of the DC voltage can be achieved by setting different values of *k*reg to ensure smooth transition of the microgrid during major disturbances.

Figure 8 is the switching principle of the improved MPPT curve with speed response of the wind turbine when disturbance occurs in the DC voltage of the microgrid. As shown in this figure, *P*opt is the maximum power point tracking curve, which determines the output of wind power unit under normal conditions. In addition, the curves *P*opt\_max and *P*opt\_min are the upper and lower limits of the output power, respectively. Usually, the microgrid is stable and the wind power unit operates at point A, with the proportional coefficient of MPPT curve being *k*opt0. When a steep fall of the DC voltage occurs due to a sudden power vacancy, a large amount of energy is needed to reduce the change rate of DC voltage so that load shedding can be avoided. At this time, the curve switches to *P*opt\_max and the operating point moves from A to O, with the proportional coefficient rising to *k*opt\_max. The wind turbine, which connects directly to the generator, slows down due to the fact that the output electromagnetic power is larger than the mechanical power captured by the wind turbine, and the operation point decreases to B along *P*opt\_max. With the recovery of DC voltage, the proportional coefficient decreases gradually from *k*opt\_max to *k*opt0, with the power tracking curve cutting back

of the disturbance.

Equation (2) and (3).

turbine.

to *P*opt slowly and smoothly. Therefore, the wind turbine recovers and operates again at point A. Similarly, the switching process of the operation points can be analyzed when DC bus voltage surges. speed of the generator. *k*reg is defined as the speed regulation coefficient, and varying degrees of regulation of the DC voltage can be achieved by setting different values of *k*reg to ensure smooth transition of the microgrid during major disturbances. *Appl. Sci.* **2019**, *9*, 2523 11 of 19

− = −= −

*Appl. Sci.* **2019**, *9*, 2523 10 of 19

dc w dc

*<sup>E</sup> P J*

Δ= =

where Δ*P*e is the power variation of the wind power unit, *E*k is the rotating kinetic energy of the

synchronous generator, and *p* is the number of pole pairs of the generator. As the wind turbine and the permanent magnet generator are directly coupled, the generator speed is equal to that of the wind

As the mechanical energy of the wind turbine is much larger than the energy stored in the capacitor, variation of the wind turbine speed is much smaller than that of the DC voltage when bearing the same amount of power disturbance. To quickly restrain the fluctuation of DC voltage with urgency, it is necessary to transform the power unbalance on the DC side into the change of rotational kinetic energy of the wind turbine through a control method. Therefore, fluctuation of DC bus voltage can be assumed by the wind turbine. The following equation is available by combining

r dc

The relationship between the variation of the wind turbine speed and the change of DC voltage under the same power disturbance is obtained by integrating and normalizing both sides of Equation (12) simultaneously. It is assumed that the voltage is kept at its rated value *U*dc\_N before occurrence

<sup>2</sup> ( 1) ( 1) <sup>1</sup>

*U kU*

r1\_pu are the per-unit values of the angular speed of the generator before and after

*reg*

r w dc 2 d d d d *<sup>U</sup> J CU p t t*

ω

2 w dc\_N 22 2 2 r1\_pu r0\_pu dc\_pu dc\_pu <sup>2</sup> 2 r\_N

ω

*C U*

*J p*

disturbance, respectively; *U*dc\_pu is the per-unit value of DC voltage after disturbance;

ω

1

ω

 ω

2

where *C*w is the DC side capacitor of the wind power system converter.

generator, *J* is the rotating inertia of the synchronous generator,

power unit is shown in Equation (11).

*<sup>U</sup> P CU*

dc

ω

Δ = , (10)

ω

<sup>=</sup> . (12)

,

ω

(13)

r\_N is the rated

, (11)

r is the angular speed of the

*t*

d d

The variation of the output power caused by the change of the generator speed in the wind

k r e r 2 d d d d

ω

*t p t*

**Figure 8.** Switching principle of improved MPPT curve. **Figure 8.** Switching principle of improved MPPT curve. coefficient decreases gradually from *k*opt\_max to *k*opt0, with the power tracking curve cutting back to *P*opt slowly and smoothly. Therefore, the wind turbine recovers and operates again at point A. Similarly,

Point A and point B in Figure 8 correspond to the rotational speed ωr0\_pu and ωr1\_pu, respectively. When the range of speed regulation is not wide, the output power of point A and point B is approximately equal, as shown in Equation (14). the switching process of the operation points can be analyzed when DC bus voltage surges. Point A and point B in Figure 8 correspond to the rotational speed *ω*r0\_pu and *ω*r1\_pu, respectively. When the range of speed regulation is not wide, the output power of point A and point B is

$$k\_{\rm opt} \omega\_{r1\\_pu}^3 = k\_{\rm opt0} \omega\_{r0\\_pu}^3 \tag{14}$$

where *k*opt is the proportion coefficient of power tracking curve after adopting the improved speed control. *k*opt can be obtained by introducing Equation (13) into Equation (14). 3 3 opt opt0 r1\_pu r0\_pu *k k* ω ω = , (14) where *k*opt is the proportion coefficient of power tracking curve after adopting the improved speed

$$k\_{\rm opt} = \frac{\omega\_{\rm r0\\_pu}^3}{\left[\omega\_{\rm r0\\_pu}^2 + k\_{\rm reg}(\rm L)\_{\rm dc\\_pu}^2 - 1\right]^{3/2}} k\_{\rm op0\\_pu} \tag{15}$$

In order to adjust the inertia response of the wind power unit according to the change rate of DC voltage in microgrid, the speed regulation coefficient *k*reg is modified by the change rate signal to be *k*reg = *k*<sup>w</sup> |d*U*dc/d*t*|, where, *k*<sup>w</sup> is a constant. By utilizing the proportional coefficient *k*opt calculated in Equation (15) instead of the fixed proportional coefficient *k*opt0, adaptive speed response of the wind power system can be achieved to quickly adjust the output power by using the energy stored in wind turbines. The block diagram of the improved control strategy for the wind power system is shown in Figure 9, where *k*opt\_min and *k*opt\_max are the limit values of the proportional coefficient. In order to adjust the inertia response of the wind power unit according to the change rate of DC voltage in microgrid, the speed regulation coefficient *k*reg is modified by the change rate signal to be *k*reg= *k*w | d*U*dc/d*t* |, where, *k*w is a constant. By utilizing the proportional coefficient *k*opt calculated in Equation (15) instead of the fixed proportional coefficient *k*opt0, adaptive speed response of the wind power system can be achieved to quickly adjust the output power by using the energy stored in wind turbines. The block diagram of the improved control strategy for the wind power system is shown in Figure 9, where *k*opt\_min and *k*opt\_max are the limit values of the proportional coefficient.

**Figure 9.** Principle diagram of self-adaptive speed control of wind power system. **Figure 9.** Principle diagram of self-adaptive speed control of wind power system.
