## 1 Introduction
### Active Power Ramp Rate Control/Power Smoothing
#### 3.1.2 Measurement and Quantification  
Attempting to define a methodology for the measurement and quantification of the limitation of electrical active power ramp rate, active power ramp rate at the Point of Common Coupling (PCC) of a DRES is firstly defined by,  
\[ramp=\frac{\Delta P_{\text{el}}(t)}{\Delta t} \tag{1}\]  
with:  
\[\Delta P_{\text{el}}(t)=\frac{P_{\text{el}}(t)-P_{\text{el}}(t-\Delta t)}{P_{ \text{N,DRES}}} \tag{2}\]  
where, \(\Delta P_{\text{el}}(t)\) is the per-unit (pu) variation of the electrical active power, \(P_{\text{el}}(t)\), during the time interval, \(\Delta t\), while \(P_{\text{N,DRES}}\), is the rated power of the DRES. In order to better clarify our approach for the definition of the measurement and quantification of the ramp limitation we will use the following example: Measurements of the electrical power of a 239 kW\({}_{\text{P}}\) PVPP in the region of Sencur (Slovenia) were taken for several hours with 1 s resolution [28]. Figure 4 shows the power (expressed in pu) during a 40-min period. The shaded area in Figure 4 is enlarged in Figure 5 where the PV power is shown in red, while the smoothed electrical power in green. The PV power is the power determined by the maximum power point tracking (MPPT) algorithm of the PVPP. The smoothed electrical power is achieved by using a FSS (an ultracapacitor bank) in the DC link of the PV converter and by implementing the smoothing algorithm developed in [28] that limits the ramp rate to \(\pm\)20%-\(P_{\text{N,DRES}}/\min\). Figure 4: Output power (red: actual; green: smoothed) of a 239 kW\({}_{\text{P}}\) PVPP with 1 s resolution [28]. The ramp rates are shown in Figure 6, where it is evident that, the ramp rate would be as high as \(-30\%\cdot P_{\text{N,DRES}}/\min\) or \(+25\%\cdot P_{\text{N,DRES}}/\min\). The achieved ramp rate limitation (\(RRL\)) can be quantified on the basis of the difference between the actual electrical power, \(P_{\text{el}}(t)\) and the active power generated by the primary source \(P_{g}(t)\). \[RRL=\int\limits_{t_{1}}^{t_{2}}\big{|}P_{\text{el}}(t)-P_{g}(t)\big{|}dt \tag{3}\]  
with the time interval \(t_{2}-t_{1}\) is defined as the period over which the \(RRL\) needs to be quantified, e.g., one hour or one day, etc. The resulting \(RRL\) can be seen as the sum of the shaded areas A1 and A2 in Figure 5. It is important that the control algorithm regularly (e.g., every some seconds) returns the state of charge of the FSS to its original state so the DRES is able to achieve the next ramp limitation. This prerequisite will finally yield  
\[\int\limits_{t_{1}}^{t_{2}}\big{(}P_{\text{el}}(t)-P_{g}(t)\big{)}dt=0 \tag{4}\]  
Figure 5: Actual (red) and smoothed (green) electrical power of the \(239\)\(\text{kW}_{\text{P}}\) PVPP during a 4-min interval [28]. Figure 6: Evaluation of ramp-rates without (red curve) or with (green curve) power smoothing. if the losses in the FSS and the associated DC/DC converter as well as the losses in the DC/AC converter are ignored. In case these losses are evaluated [21], then the integral in (4) should be equal to the aggregated losses over the period \(t_{2}-t_{1}\). Another way for the evaluation of \(RRL\) could be based on the measurement of the work performed by the FSS associated with the DRES as shown in Figure 3. In this case,  
\[RRL=\int_{t_{1}}^{t_{2}}\bigl{|}P_{\text{FSS}}(t)\bigr{|}dt=\int_{0}^{T}\bigl{|} V_{\text{DC}}(t)\cdot I_{\text{FSS}}(t)\bigr{|}dt\,\,\,\bigr{\}}RRL_{\text{NET}}=RRL-E_{ \text{Loss\_Tot}} \tag{5}\]  
where \(RRL\) is the total energy absorbed or released by the FSS within the time interval \(t_{2}-t_{1}\), \(I_{\text{FSS}}\) is the current flowing to the FSS, \(V_{\text{DC}}\) is the DC-Link voltage level and \(E_{\text{Loss\_DC/AC}}\) are the energy losses on the DC/AC converter of the DRES. Equation (3) can be applied not only to DRES but also to a BESS. In the latter case, \(P_{\text{el}}(t)\) is the electrical power upstream of the BESS, while \(P_{g}(t)\) is the electrical power downstream of the BESS.