# Probabilistic duck curve in high PV penetration power system: Concept, modeling, and empirical analysis in China

arXiv: https://arxiv.org/abs/1909.11711 · HTML: https://mlsanity.com/paper/1909.11711/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Sep 2019.

## Built on by (most cited first, 5 of 5)

- [Learning and Fast Adaptation for Grid Emergency Control via Deep Meta Reinforcement Learning](https://mlsanity.com/paper/2101.05317/) (2021)
- [Distributed solar generation forecasting using attention-based deep neural networks for cloud movement prediction](https://mlsanity.com/paper/2411.10921/) (2024)
- [A generalised multi-factor deep learning electricity load forecasting model for wildfire-prone areas](https://mlsanity.com/paper/2304.10686/) (2023)
- [Anomaly Detection in California Electricity Price Forecasting: Enhancing Accuracy and Reliability Using Principal Component Analysis](https://mlsanity.com/paper/2412.07787/) (2024)
- [Optimizing a domestic battery and solar photovoltaic system with deep reinforcement learning](https://mlsanity.com/paper/2109.05024/) (2021)

## Abstract (arXiv)

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.