Locational Marginal Burden

Energy burden—the fraction of income spent on electricity—varies across communities due to how power systems are operated. This visualization demonstrates the Locational Marginal Burden (LMB) framework, which reveals how transmission congestion can create price disparities that disproportionately affect low-income communities.

The Three Communities

Consider a simple power network with three communities:

Label	Community Type	Income	Generator
High$	Wealthy suburb	$125,000	Expensive backup
Low$	Low-income area	$20,000	None
Cheap Gen	Power plant	N/A	Main generator

When the transmission line between High$ and Low$ becomes congested, Low$ is cut off from the cheap generator power. They must buy electricity from High$'s expensive generator—causing their electricity prices to spike.

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Interactive Visualization

Adjust the sliders below to explore how transmission capacity and demand affect electricity prices and energy burden.

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The Mathematics

Energy Burden

Energy burden at location $i$ is defined as:

$$b_i = \frac{\pi_i \cdot d_i}{s_i}$$

where:

• $\pi_i$ = locational marginal price (LMP) at bus $i$ ($/MWh)

• $d_i$ = electricity demand at bus $i$ (MW)

• $s_i$ = household income at bus $i$ ($/year)

Locational Marginal Burden (LMB)

The LMB matrix captures how changes in demand at one location affect energy burden everywhere:

$$K_{ij} = \frac{\partial b_i}{\partial d_j} = \frac{\text{change in burden at node}\hspace{0.5em} i}{\text{change in demand at node}\hspace{0.5em} j}$$

• Diagonal entries ($K_{ii}$): Self-sensitivity—how your own demand affects your burden

• Off-diagonal entries ($K_{ij}$, $i \neq j$): Spillover effects—how demand at location $j$ affects burden at location $i$ through network congestion

The off-diagonal terms are what make LMB different from simply looking at prices. They capture the network effects that propagate through congestion constraints.

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What the Visualization Shows

Component	Description
Network Diagram	The three-bus triangle with power flows. Red pulsing indicates congestion.
Controls	Adjust line capacity and demand at each community.
Metrics	LMP ($/MWh), energy burden (%), and system cost.
LMP Chart	How prices vary as transmission capacity changes.
Burden Chart	How energy burden varies with capacity. Notice the disparity under congestion!
LMB Matrix	The 2×2 sensitivity matrix (for the two communities with income). Off-diagonal entries show spillover effects.

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Citation

If you use this visualization or the LMB framework, please cite:

@inproceedings{talkington_west_haider_2024,
    author = {Talkington, Samuel and West, Amanda and Haider, Rabab},
    title = {Locational marginal burden: Quantifying the equity of optimal power flow solutions},
    year = {2024},
    isbn = {9798400704802},
    publisher = {Association for Computing Machinery},
    doi = {10.1145/3632775.3661947},
    booktitle = {Proceedings of the 15th ACM International Conference on Future and Sustainable Energy Systems},
    pages = {97–107},
    numpages = {11},
    location = {Singapore, Singapore},
    series = {e-Energy '24}
}

Paper (ACM DL) | arXiv

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Acknowledgments

This material is based upon work supported by the National Science Foundation Graduate Research Fellowship under Grant No. DGE-2039655. Any opinion, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.