*3.3.2 Control of the DC/AC converter*

## *3.3.2.1 Standalone mode*

In standalone mode, the DC/AC converter control ensures that the LCL filter capacitor voltages are equal to their references. In that case, the converter control includes two cascade loops as shown in **Figure 7**. The external loop is based on a resonant controller *RC*<sup>1</sup> used to regulate the voltage across the LCL filter capacitor. This loop generates at its output the reference current *Ic-ref*. This current will be added to the current *I*<sup>2</sup> to provide the inner loop reference current *I*1-*ref*. The inner loop is based on a resonant controller, and in this work, it simplified to a simple gain *G*. In the following, the tuning of the parameters of the voltage external loop and the current inner loop will be presented and detailed.

*3.3.2.1.1 Tuning of the external loop resonant controller* RC*<sup>1</sup>*

*Control Analysis of Building-Integrated Photovoltaic System*

*DOI: http://dx.doi.org/10.5772/intechopen.91739*

as presented in **Figure 8**.

*Block diagram of the external voltage loop.*

**Figure 8.**

resonant controller *RC*<sup>1</sup> is given by Eq. (6):

*FCL*‐*Vc*ðÞ¼ *<sup>s</sup>*

defined by this criterion is expressed as follows:

For simplification reasons, it is assumed that the internal current loop is faster than the external voltage loop. Thus, it can be approximated equal to the unity by associating it with the PWM function. The following block diagram is then obtained for the determination of the external voltage loop resonant controller parameters

According to **Figure 4**, the open and closed-loop system transfer functions are expressed by Eqs. (7) and (8), respectively. Note that the transfer function of the

*c*2*cs*

*Vc Vc*‐*ref* � *Vc*

<sup>¼</sup> *<sup>c</sup>*2*cs*

generalized stability margin criterion [17, 18]. The reference polynomial *PGSMc*

where *λc*, *rc*, and *ωic* are the factorization coefficient, the abscissa, and the ordinate in the complex plane. On the other hand, the system characteristic

polynomial is deduced from Eq. (8), and it is expressed as follows:

<sup>3</sup> <sup>þ</sup> *<sup>c</sup>*2*cs*

system *Pc*(*s*) with the reference polynomial *PGSM*(*s*) as shown in Eq. (11):

loop resonant controller parameters as shown in the following equation:

*c*2*<sup>c</sup>* ¼ 3*rcλ<sup>c</sup> <sup>c</sup>*1*<sup>c</sup>* <sup>¼</sup> *<sup>λ</sup><sup>c</sup>* <sup>3</sup>*r*<sup>2</sup>

8 >>><

>>>:

**61**

*<sup>c</sup>*0*<sup>c</sup>* <sup>¼</sup> *<sup>λ</sup><sup>c</sup> <sup>r</sup>*<sup>3</sup>

*λ<sup>c</sup>* ¼ *Cf*

*Pc*ðÞ¼ *s Cf s*

<sup>2</sup> <sup>þ</sup> *<sup>c</sup>*1*cs* <sup>þ</sup> *<sup>c</sup>*0*<sup>c</sup> s*<sup>2</sup> þ *ω*<sup>2</sup> 0

> <sup>2</sup> <sup>þ</sup> *<sup>c</sup>*1*cs* <sup>þ</sup> *<sup>c</sup>*0*<sup>c</sup> Cf <sup>s</sup>*<sup>3</sup> <sup>þ</sup> *Cfω*<sup>2</sup>

<sup>2</sup> <sup>þ</sup> *<sup>c</sup>*1*cs* <sup>þ</sup> *<sup>c</sup>*0*<sup>c</sup>*

*PGSMc*ðÞ¼ *s λc*ð Þ *s* þ *rc* ð Þ *s* þ *rc* þ *jωic* ð Þ *s* þ *rc* � *jωic* (9)

<sup>0</sup> þ *c*1*<sup>c</sup>*

0*s*

� �*<sup>s</sup>* <sup>þ</sup> *<sup>c</sup>*0*<sup>c</sup>* (10)

*PGSMc*ðÞ¼ *s Pc*ð Þ*s* (11)

0

<sup>0</sup> þ *c*1*<sup>c</sup>* � �*<sup>s</sup>* <sup>þ</sup> *<sup>c</sup>*0*<sup>c</sup>*

<sup>¼</sup> *<sup>c</sup>*2*cs*

*Cf <sup>s</sup>*<sup>3</sup> <sup>þ</sup> *<sup>c</sup>*2*cs*<sup>2</sup> <sup>þ</sup> *Cfω*<sup>2</sup>

The method chosen for the resonant controller parameters tuning is based on the

<sup>2</sup> <sup>þ</sup> *Cfω*<sup>2</sup>

According to the generalized stability margin criterion, the resonant controller parameters are tuned by identifying the characteristic polynomial of the closed-loop

The identification of *PGSM*(*s*) and *Pc*(*s*) allows the deduction of the current inner

*<sup>c</sup>* <sup>þ</sup> *<sup>ω</sup>*<sup>2</sup> *ic* � � � *Cfω*<sup>2</sup>

*<sup>c</sup>* <sup>þ</sup> *rcω*<sup>2</sup> *ic* � � (6)

(7)

(8)

(12)

*FCR*1ðÞ¼ *s*

*FOL*‐*Vc*ðÞ¼ *<sup>s</sup>*

*Vc Vc*‐*ref*

**Figure 6.** *System filter block diagram.*

**Figure 7.** *Control strategy of DC/AC converter in the case of standalone mode.*

*Control Analysis of Building-Integrated Photovoltaic System DOI: http://dx.doi.org/10.5772/intechopen.91739*

**Figure 8.** *Block diagram of the external voltage loop.*

The transfer functions given by Eqs. (4) and (5) allow the deduction of the

In standalone mode, the DC/AC converter control ensures that the LCL filter capacitor voltages are equal to their references. In that case, the converter control includes two cascade loops as shown in **Figure 7**. The external loop is based on a resonant controller *RC*<sup>1</sup> used to regulate the voltage across the LCL filter capacitor. This loop generates at its output the reference current *Ic-ref*. This current will be added to the current *I*<sup>2</sup> to provide the inner loop reference current *I*1-*ref*. The inner loop is based on a resonant controller, and in this work, it simplified to a simple gain *G*. In the following, the tuning of the parameters of the voltage external loop and

system block diagram given by **Figure 6**.

*Numerical Modeling and Computer Simulation*

the current inner loop will be presented and detailed.

*Control strategy of DC/AC converter in the case of standalone mode.*

*3.3.2 Control of the DC/AC converter*

*3.3.2.1 Standalone mode*

**Figure 6.**

**Figure 7.**

**60**

*System filter block diagram.*
