From Zonal to Nodal Capacity Expansion Planning: Spatial Aggregation Impacts on a Realistic Test-Case

TL;DR

The paper challenges the widespread use of zonal CEP by showing that spatial aggregation can distort investment decisions on a realistic, large-scale network. It introduces a geography-based network reduction approach (KITTENS) that creates collapsed networks while preserving key electrical characteristics, enabling direct comparison with nodal CEP. Across deterministic and stochastic CEP experiments on a California-like system, coarser zonal models exhibit large errors and under-investment, whereas tightened, distance-based reduced networks can match full-resolution results within tight tolerances in many scenarios. The findings advocate for nodal, high-fidelity CEP in practice and offer practical reduction-and-mapping strategies to improve tractability without sacrificing solution quality.

Abstract

Solving power system capacity expansion planning (CEP) problems at realistic spatial resolutions is computationally challenging. Thus, a common practice is to solve CEP over zonal models with low spatial resolution rather than over full-scale nodal power networks. Due to improvements in solving large-scale stochastic mixed integer programs, these computational limitations are becoming less relevant, and the assumption that zonal models are realistic and useful approximations of nodal CEP is worth revisiting. This work is the first to conduct a systematic computational study on the assumption that spatial aggregation can reasonably be used for ISO- and interconnect-scale CEP. By considering a realistic, large-scale test network based on the state of California with over 8,000 buses and 10,000 transmission lines, we demonstrate that well-designed small spatial aggregations can yield good approximations but that coarser zonal models result in large distortions of investment decisions.

Figures (4)

• Figure 1: Proposed network reduction method on a simple example. Transmission line parameters of resistance $r$, reactance $x$, and line rating $\overline{P}$ are shown. The original 4-bus network is shown in (a). First, short radial lines are eliminated, as shown in (b). Then, the remaining bus within the given distance threshold (i.e., bus 2) is merged, as shown in (c).
• Figure 2: Overall solution time to solve the CEP problem on CATS, with a two-step approach for reduced networks. Each boxplot corresponds to 360 scenarios of single-day CEP problems. The top figure includes the KITTENS variations with meshed lines collapsed, and the bottom figure includes the KITTENS variations with only radial lines collapsed.
• Figure 3: Quality of solutions to reduced KITTENS models when mapped backed to CATS, as measured by the error metric ERMM given in (\ref{['eqn:error']}). Each boxplot corresponds to 360 scenarios of single-day CEP problems. We see that the majority of reduced models result in median errors greater than 5%.
• Figure 4: Overall solution times (top figure) and ERMM error metric (bottom figure) for a selection of the best performing models, as determined by the median error over all 360 single-day CEP scenarios. We can see that several of these reduced models obtain median error values below the 1% optimality tolerance.