  The high penetration of photovoltaic (PV) is reshaping the electricity
net-load curve and has a significant impact on power system operation and
planning. The concept of duck curve is widely used to describe the timing
imbalance between peak demand and PV generation. The traditional duck curve is
deterministic and only shows a single extreme or typical scenario during a day.
Thus, it cannot capture both the probability of that scenario and the
uncertainty of PV generation and loads. These weaknesses limit the application
of the duck curve on power system planning under high PV penetration. To
address this issue, the novel concepts of probabilistic duck curve (PDC) and
probabilistic ramp curve (PRC) are proposed to accurately model the uncertainty
and variability of electricity net load and ramp under high PV penetration. An
efficient method is presented for modeling PDC and PRC using kernel density
estimation, copula function, and dependent discrete convolution. Several
indices are designed to quantify the characteristics of the PDC and PRC. For
the application, we demonstrate how the PDC and PRC will benefit flexible
resource planning. Finally, an empirical study on the Qinghai provincial power
system of China validates the effectiveness of the presented method. The
results of PDC and PRC intuitively illustrate that the ramp demand and the
valley of net load face considerable uncertainty under high PV penetration. The
results of flexible resource planning indicate that retrofitting coal-fired
units has remarkable performance on enhancing the power system flexibility in
Qinghai. In average, reducing the minimal output of coal-fired units by 1 MW
will increase PV accommodation by over 4 MWh each day.
