November 4, 2026
Two Ways, Two Bills: How to Separate Consumption and Injection in Grid Cost Allocation
Series “Cost Allocation in the Era of Prosumers” – Article 2 of 3
Abstract
This is the second article in a series of three. In Article 1 we saw that the official method for dividing grid costs assumes that power flows in a single direction, which no longer reflects reality now that distributed generation is widespread. Here we explain, in accessible language, how the TR Soluções study rebuilds the calculation in four steps: closing the energy balance, separating consumption from injection, identifying who uses which part of the grid, and turning that use into cost. Article 3 will present the results.
In Part 1
We saw that the grid is sized for peak demand, that its cost (the Fio B tariff component) is divided according to the Marginal Capacity Cost (CMC), and that the official model assumes one-way flow. With 112 of the 228 load curves of the distribution company analyzed representing prosumers, that assumption no longer holds.
1. The Method in Six Phases
The study starts from the same ingredients as the methodology of the Brazilian Electricity Regulatory Agency (Aneel): typical curves, reference market, grid topology, losses and marginal expansion costs. It organizes them into six phases. This article covers phases 2 to 5; phase 6 is left for Article 3.
Figure 1 – The six phases of the method; the highlighted phases are covered in this article
Source: prepared by the authors. Illustrative diagram.
2. Step 1: Closing the Energy Balance
Before talking about cost, we must make sure the curves describe a consistent system. Think of reconciling a condominium’s accounts: what came into the cash box has to match what was spent. On the grid, the energy entering each voltage level must equal the energy leaving it, plus losses. In the raw data of the distribution company analyzed, this was not the case: input energy totaled 52.5 TWh per year, while the consumption curves accounted for 47.8 TWh.
The difference, called the residual, is absorbed by an explicit and traceable adjustment rule that preserves billing data and the offsets under the Electric Energy Compensation System (SCEE). The adjustment is concentrated in the A4/BT (medium-to-low voltage) curve, which goes from 11.13 to 23.73 TWh (+113%). The cause of this difference was not identified, and the report itself lists it among its limitations.
Figure 2 – Energy balance of the distribution company analyzed: the residual and the adjustment to the A4/BT curve
Source: TR Soluções report, ESTRUTURA platform, Aneel data for Cemig, 2023.
3. Step 2: The Orthogonal Decomposition
This is the core of the proposal. A prosumer’s curve is a net profile: positive values indicate consumption and negative values indicate injection. The study splits it into two curves that never take values at the same time: Forward Flow (consumption) and Reverse Flow (injection). The net profile is the difference between the two. Since only one of them is nonzero in any given hour, the separation is said to be orthogonal: one does not offset the other.
Figure 3 – Decomposition of a net profile into Forward Flow and Reverse Flow
Source: prepared by the authors. Illustrative diagram.
Why does this matter? Because the grid does not charge for the “balance.” Think of a two-way avenue: the morning rush in one direction and the evening rush in the other do not cancel each other out. Likewise, a transformer is stressed by midday injection and by evening consumption, even if the prosumer’s net balance is zero. The separation also eliminates the divisions by zero that used to break the traditional model.
Figure 4 – Why the balance is misleading: two moments of stress on the grid hide behind a near-zero balance
Source: prepared by the authors. Illustrative diagram.
4. Step 3: Who Uses What (β and π Matrices)
With the two environments separated, the next task is to find out which part of the grid serves which load. The study uses two complementary matrices, linked by Bayes’ theorem:
- β: indicates what fraction of the energy of each Typical Network is delivered to each Typical Load (“where the energy goes”).
- π: works the other way around and indicates what share of each load’s demand originates in each network (“where the demand comes from”).
Figure 5 – The β and π matrices: two ways of reading the same relationship between networks and loads
Source: prepared by the authors. Illustrative diagram.
The results for the distribution company analyzed clearly illustrate the difference between the two environments. At the consumption peak, at 8 p.m., 96.10% of the low-voltage load is supplied by the medium-voltage grid, the classic hierarchical pattern. At the injection peak, at 11 a.m., only 20.19% of the surplus generated at low voltage flows up to medium voltage; according to the model, the remaining 79.81% is consumed by neighbors at the low-voltage level itself. Reverse flow is therefore a predominantly local phenomenon. This percentage results from closing the model and was not measured.
Figure 6 – Where the energy goes at the two peaks of the distribution company analyzed
Source: TR Soluções report, ESTRUTURA platform, Aneel data for Cemig, 2023.
5. Step 4: From Use to Cost
The Marginal Capacity Cost (CMC) of each load, in each hour, combines four elements: the load’s responsibility for each network (π), the marginal expansion cost of each voltage level, losses, and the question “is the grid at peak right now?”, which the model answers by comparing grid loading with a threshold close to its maximum. The calculation is performed twice, producing the forward CMC, for load, and the reverse CMC, for generation.
Figure 7 – The ingredients of the Marginal Capacity Cost
Source: prepared by the authors. Illustrative diagram.
Three consequences are worth highlighting:
- Causality: the reverse CMC rises when injection actually reverses the flow and increases the need for expansion. Injection that does not stress the grid is not charged for the costs of networks upstream of the injection point.
- Relief recognized: generation consumed locally reduces consumers’ responsibility in the Forward Flow, which benefits all of them.
- No curves discarded: the approach processed 100% of the available curves, including those with reverse flow.
6. A Bonus: Simulating the Effect of Batteries and Electric Vehicles
Because the matrices relate networks and loads, it is possible to apply a load modulation (ΔY) and see how the marginal cost changes. For example, a battery that shifts consumption from late afternoon to midday reduces the evening peak. This turns the calculation, which today is static and performed once per cycle, into a sensitivity indicator. The simulation is linear, works as a regulatory and economic approximation, and does not replace a power flow study.
Figure 8 – Effect of a load modulation (for example, a battery) on the evening peak
Source: prepared by the authors. Illustrative diagram.
7. In Summary
| Current model | Proposed method | |
|---|---|---|
| Flow direction | One direction only (from substation to consumer) | Two environments: Forward Flow and Reverse Flow |
| Curves with reverse flow | Discarded | Included (100% of curves processed) |
| Calculation output | Load CMC | Forward CMC (load) and reverse CMC (generation) |
| Use of the calculation | Static, at each tariff review | Also as a simulation of load modulations (ΔY) |
In the next article, we will see what these calculations reveal about the most expensive hours for the grid, which price signals follow from them, and how the values compare with Aneel’s.
* About this series. The three articles summarize the technical report “Alocação de custos na era dos prosumidores: separação de sinais de preço para carga e geração” [Cost Allocation in the Era of Prosumers: Separating Price Signals for Load and Generation] (TR Soluções, version 3.8, 2026), available at https://doi.org/10.5281/zenodo.23439480.