[Paper Review] Economic Dispatch Considering Spatial and Temporal Correlations of Multiple Renewable Power Plants

Chenghui Tang, Yishen Wang+3 more|arXiv (Cornell University)|Jul 2, 2017

Electric Power System Optimization11 references3 citations

TL;DR

This paper proposes a Gibbs sampling-based dynamic scenario generation method that captures spatial and temporal correlations of multiple renewable power plants (RPPs) using Copula theory and historical probability histograms. By avoiding high-dimensional joint distributions, the method reduces computational complexity while accurately modeling uncertainties, spatial correlation, and variability. The study demonstrates that distribution-based and scenario-based economic dispatch (ED) methods incorporating these scenarios achieve lower system costs and better risk management than traditional approaches, with scenario-based ED approaching distribution-based performance when using 500–2000 scenarios.

ABSTRACT

The correlations of multiple renewable power plants (RPPs) should be fully considered in the power system with very high penetration renewable power integration. This paper models the uncertainties, spatial correlation of multiple RPPs based on Copula theory and actual probability historical histograms by one-dimension distributions for economic dispatch (ED) problem. An efficient dynamic renewable power scenario generation method based on Gibbs sampling is proposed to generate renewable power scenarios considering the uncertainties, spatial correlation and variability (temporal correlation) of multiple RPPs, in which the sampling space complexity do not increase with the number of RPPs. Distribution-based and scenario-based methods are proposed and compared to solve the real-time ED problem with multiple RPPs. Results show that the proposed dynamic scenario generation method is much more consist with the actual renewable power. The proposed ED methods show better understanding for the uncertainties, spatial and temporal correlations of renewable power and more economical compared with the traditional ones.

Motivation & Objective

• To address the challenge of modeling spatial and temporal correlations among multiple renewable power plants (RPPs) in high-penetration renewable power systems.
• To reduce computational complexity in generating correlated renewable power scenarios without relying on high-dimensional joint distributions.
• To develop and compare distribution-based and scenario-based economic dispatch (ED) methods that account for system reserve, load shedding, and renewable curtailment risks.
• To evaluate the impact of uncertainties, spatial correlation, and variability on system cost and operational risk in real-time ED.
• To determine the optimal balance between scenario count and dispatch performance for practical implementation.

Proposed method

• Employs Copula theory to model the joint dependence structure of multiple RPPs based on historical probability density histograms (PDHs), enabling accurate representation of spatial correlation.
• Introduces a dynamic scenario generation method using Gibbs sampling to sequentially sample from one-dimensional conditional distributions, avoiding the curse of dimensionality associated with high-dimensional joint distributions.
• Models temporal correlation (variability) across the scheduling horizon by iteratively sampling renewable power scenarios over time, preserving inter-temporal dependencies.
• Constructs conditional marginal distributions for total renewable power and power flows in transmission lines to assess system-wide risks of reserve deficiency and congestion.
• Develops two ED frameworks: a distribution-based method using analytical moment-matching and a scenario-based method using embedded scenarios, both incorporating penalties for load shedding (LS) and renewable curtailment (REC).
• Uses scenario reduction techniques to maintain computational efficiency while preserving statistical fidelity, with performance evaluated across 50, 500, and 2000 scenarios.

Experimental results

Research questions

• RQ1 How can the spatial and temporal correlations of multiple RPPs be efficiently modeled and simulated without incurring high computational costs?
• RQ2 What is the impact of neglecting spatial correlation and temporal variability on the accuracy and economy of economic dispatch in systems with high renewable penetration?
• RQ3 How do distribution-based and scenario-based ED methods compare in terms of system cost, reserve adequacy, and risk management under realistic RPP uncertainty?
• RQ4 What is the optimal number of scenarios required for scenario-based ED to achieve performance comparable to distribution-based ED while maintaining computational tractability?
• RQ5 How do varying penalty coefficients for load shedding and renewable curtailment affect the confidence level of sufficient downward reserve and overall system economy?

Key findings

• The proposed dynamic scenario generation method based on Gibbs sampling significantly reduces sampling space complexity and better reflects actual renewable power behavior compared to static or high-dimensional joint distribution methods.
• With 500 scenarios, the scenario-based RTED method achieves a total cost of $42,329, closely matching the distribution-based method’s $42,189 at 2,000 scenarios, indicating high fidelity with moderate scenario counts.
• The scenario-based method with 2,000 scenarios outperforms the distribution-based method by better capturing line-specific congestion risks, particularly in modeling REC penalties under transmission constraints.
• Compared to existing models, the proposed method reduces system costs by 10–15% due to better representation of uncertainties, spatial correlation, and temporal variability.
• When REC penalty increases from $40 to $200/MWh, the confidence level of sufficient downward reserve rises from 74.84% to 93.11%, demonstrating the model’s ability to adaptively adjust reserve levels based on risk preferences.
• The model in [19] incurs higher LS and REC penalties than the proposed method due to unmodeled transmission congestion, and the model in [4] has higher costs due to lack of temporal variability modeling.