[orcid=0000-0001-9857-2223]

[orcid=0000-0002-0735-1597]

[orcid=0000-0002-9810-948X]

[cor1]Corresponding author: Le Xie
Disclaimer: The views expressed in this paper are solely those of the authors
and do not necessarily represent those of ComEd or MISO.

# A Smart Meter Data-driven Distribution Utility Rate Model for Networks with
Prosumers

Athindra Venkatraman  Commonwealth Edison Company, 2 Lincoln Center, Oakbrook
Terrace, IL 60181, USA  Anupam A. Thatte  Midcontinent Independent System
Operator, 720 City Center Drive, Carmel, IN 46032, USA  Le Xie  Department of
Electrical and Computer Engineering, Texas A&M University, College Station, TX
77843, USA

###### Abstract

Distribution grids across the world are undergoing profound changes due to
advances in energy technologies. Electrification of the transportation sector
and the integration of Distributed Energy Resources (DERs), such as photo-
voltaic panels and energy storage devices, have gained substantial momentum,
especially at the grid edge. Transformation in the technological aspects of
the grid could directly conflict with existing distribution utility retail
tariff structures. We propose a smart meter data-driven rate model to recover
distribution network-related charges, where the implementation of these grid-
edge technologies is aligned with the interest of the various stakeholders in
the electricity ecosystem. The model envisions a shift from charging end-users
based on their KWh volumetric consumption, towards charging them a grid access
fee that approximates the impact of end-users’ time-varying demand on their
local distribution network. The proposed rate incorporates two cost metrics
affecting distribution utilities (DUs), namely magnitude and variability of
customer demand. The proposed rate can be applied to prosumers and
conventional consumers without DERs.

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contain the abstract and keywords respectively.

Each keyword shall be separated by a `\sep` command.

###### keywords:

Rate design; Distributed Energy Resources; Solar PV; Behind-The-Meter storage;
Utility Cost Recovery

##  1 Introduction

Distributed energy resources (DERs) have been integrated to the electric grid
edge at an accelerated pace over the past decade. The levelized costs of
photo-voltaic (PV) panels and energy storage have dropped significantly and
are projected to continue this trend [21]. Behind-The-Meter (BTM) technologies
are estimated to make up over 50% of the US energy storage market by 2021,
with the deployed energy storage expected to reach 2 GW by then [33].

Although end-use demand is projected to increase in the next few decades both
in the residential and commercial sectors, there is a significant projected
reduction in energy intensity [25]. Further, projections indicate that the
growth rate of electricity sales will be diminished due to the significant
increase in generation from rooftop PV systems, from both residential and
commercial buildings [42]. The adoption of Electric Vehicles (EVs) is also on
the rise, with the number of EVs on the road in the US reaching 1.1 million by
the end of 2018 [27]. With increased installation of these technologies many
consumers are turning into DER prosumers, thus eroding the revenue stream of
the utilities [29].

The rise in DER penetration in markets around the globe makes the following
question extremely relevant - are the existing distribution utility rate
models poised to handle the accelerated pace of DER deployment at the grid
edge? This study addresses customer rate models of Distribution Utilities
(DUs) i.e., how they recover their costs from customers. DUs need to be
compensated for their investments and the grid maintenance costs they incur to
ensure reliable power supply to all customers. Their compensation is akin to a
toll fee for using the DU’s grid infrastructure. We focus on the proper
determination and allocation of grid access costs to retail customers, and do
not deal with the variable production costs for delivered power (the 'Energy
Charge') 111Here we consider a scenario in which the variable production costs
(Energy Charges) are passed through to the customer, and these are separate
from the proposed grid-access fee. [40] states that ”a comprehensive system of
prices and charges consists of four core elements: (1) a price for electric
energy; (2) prices or charges for other energy-related services, such as
operating reserves or firm capacity; (3) charges for network-related services;
and (4) charges to recover policy costs.” Our paper focuses on (3) network-
related services..

Existing DU charges are a combination of a small fixed charge, coupled with a
larger volumetric ¢/kWh charge. The dotted line in Fig. 1 represents the cost
curve to consumers of this rate structure [38]. The revenue earned by DUs is
directly proportional to the volume of electricity in kWh that is consumed by
the end-users. This rate structure incentivizes DUs to maximize sales and
makes them dependent on the volumetric charge for the bulk of their revenue
[19]. With increasing deployment of grid-edge DERs the current rate design
could be insufficient since it does not fully account for the rising fixed
costs faced by the DUs [26]. Grid-edge DERs pose a threat to the revenue
stream of utility companies in a few different ways. First, the increase in
solar PV penetration directly results in reduction of the kWh demand from the
grid. This reduction lowers the customer’s utility bill, even though the
utility offers the service of access to the grid at all times, which the PV
customer will require when sunlight is not available. Second, the expansion of
participation in net metering has resulted in utilities providing financial
compensation for injections of PV power to the grid [31].

Costello [13] argues that net metering is inefficient and results in cross-
subsidy, and Brown et al. [10, 9] show that net metering is often not optimal.
Gautier et al. [23] show that net metering may lead to an uneconomic level of
DER prosumption, with the lower bills for the DER prosumers compensated by
higher bills for regular non-DER consumers. This form of cross-subsidy could
lead to the utility death spiral [8].

Various case studies have been devoted to examining the impact of high DER
penetration on the distribution grid and related technological, economic, and
regulatory aspects. The resulting need for utilities to update their business
models, and a rebalancing of costs on the electricity value chain from the
grid side to behind the meter has been discussed in Woodhouse et al. [43] and
Smith et al. [41] respectively. Baak [3] and Alvarez Pelegry [37] explore the
regulatory framework in different parts of the world, and the restructuring
that may be required to enable an accelerated transformation towards grid
modernization, while Gellings [24] argues that the existing regulatory
measures may be adequate to accommodate even a transformed grid. Laws et al.
[30] indicates that residential PV penetration could reach a substantial
number over the next decade. But, they argue that utilities have ample time to
change their business model in order to avoid the death spiral. Darghouth et
al. [14] shows how various rate design choices can impact the long term
cumulative distributed PV deployment.

Gautier et al. [23] build a model to compare net metering and net purchasing,
concluding that net purchasing is a better rate model for a network with
prosumers. Cambini et al. [11] observe that net metering remains the mechanism
most compatible with existing metering technologies, and propose a multi-part
tariff for DER prosumers, with explicit components for connection costs,
distribution costs, and energy losses. However, the proliferation of Advanced
Metering Infrastructure (AMI) technologies provides an enabling platform for
retail rate innovations that could improve upon the current volumetric
delivery rate structure.

In Bharatkumar [6], a Distribution Network Use-of-System (DNUoS) charge has
been proposed, which aids in the accurate recovery of distribution utility
costs, by capturing the contribution of each user on the network to the
system’s costs. This study applies a similar line of thought, by billing
customers based on a novel measure of their individual impact on distribution
system costs.

The difference in our approach is the consideration of the granular inter-
temporal impact factor, i.e., when the customers impact the grid. This
approach is akin to the idea of coincident-peak capacity charges, discussed in
[40, 1, 4, 35, 32]. We aim to use higher granularity AMI data to more
accurately allocate the cost incurred by distribution utilities to their
customers. The overall goal is to design rates that are more reflective of the
cost drivers, thereby better aligning the incentives for both infrastructure
owners and technological innovation at the grid edge.

Both Gautier et al. [23] and Cambini et al. [11] base their respective models
on the assumption of a fixed retail volumetric kWh unit price for energy. Our
model is a departure from the conventional volumetric unit price for network-
related costs, and proposes a data-driven approach to approximately estimate
the contribution of customers to system costs. Our model applies to all end-
users, including DER prosumers and non-DER consumers, unlike the model
proposed by Cambini et al. [11], which only applies to DER prosumers.

In view of the above, the key contributions of this research are as follows:

  * •

We propose new metrics to quantify the impact of customers on the grid, based
on demand magnitude and variability.

  * •

We introduce an alternative billing determinant that calculates DU grid-access
charges for customers based on the proposed demand metrics.

  * •

We conduct realistic numerical case studies to illustrate the efficacy of the
proposed rate structure, especially for customers solar PV and electric
vehicles.

  * •

We simulate and analyze the deployment of battery storage in the new rate
structure to illustrate its major impact on the grid and on the customers.

The rest of the article is organized as follows: Section 2 highlights the
drawbacks of the existing distribution utility rate model, and describes the
design details and mathematical formulation of the proposed rate model.
Section 3 is a critical comparison of the existing and proposed distribution
utility rate models, supported by a case study using real residential customer
data. Section 4 summarizes the key lessons and the most significant policy
implications of the proposed distribution utility rate model.

##  2 Methodology and Data

###  2.1 Proposed Distribution Utility Rate Model

The proposed DU charge features the introduction of a grid-access fee,
replacing the existing distribution utility charges, which are typically
structured as a small flat access charge combined with a large volumetric
($/kWh) charge (see footnote 1). Fig. 1 presents a graphical comparison of the
existing and proposed utility rate models. The uniqueness of this idea lies in
how these grid-access fees would be calculated, by taking into account some
key parameters that define the impact of customers to the grid. This impact is
quantified through a combination of cost metrics called Grid Impact Factors.

This concept is analogous to an insurance rate model or a credit score, where
each customer’s rate or credit limit is considered to accurately reflect the
risk level taken up by the insurance company or bank by entering into business
with said customer. An example of providing incentives in wholesale
electricity markets is FERC Order 755 [20]. Prior to the adoption of the
order, most ISO markets in the US had a single capacity payment for
regulation. Payments from ISOs to generators compensating them for frequency
regulation service were not tied to the performance of the resource. As a
result of this rule a two-part payment was enacted, which added a mileage-
based component that accounts for the performance of the resource, in addition
to the capacity based payment.

In the following case study, we describe an idealized setup where the grid-
access fees are tailored to individual customers. Recognizing the limitations
of the approach, we propose a practical implementation mechanism in Section
3.7.5.

Figure 1: Existing vs. Proposed DU charges: Consumer Cost Curve

As is evident from Fig. 1, the DU does not have revenue assurance i.e., they
have to hope that consumers use more kWh, thus driving up their revenue.
However, under the proposed approach the DU has a steady and assured income
from each consumer via the fixed Grid Access Fees. In the figure, Customer 2
has a lower grid impact than Customer 1, and thus is charged a lower Grid
Access Fee.

###  2.2 Cost Drivers for Distribution Utilities

In the context of a distribution grid, the installed capacity of the system is
a key parameter; it determines how much load can be served. Depending on
changing load patterns this limit also dictates the need for capital
investment. System capacity requirements are directly dependent on the system
Peak Demand to be supplied to the customers. Thus, the "Peak Demand Time
Slots" are a critical time for the system. To account for this, a Demand
Magnitude Impact Factor $W$ is introduced, that measures the demand impact
factor of each home during the peak demand time slots.

$\displaystyle\text{Demand Impact Factor of Home $i$ }(W_{i})$ (1)
$\displaystyle=\text{Total Demand of Home }i\text{ during Peak Slots}$

Another key concern for the distribution grid is the health of the existing
infrastructure, directly impacting the capital investment and maintenance
costs that the DU incurs. McBee [34] describes how a high penetration of PV,
EV charging, and energy storage causes a significant increase in transformer
aging due to higher total harmonic distortion, and almost constant energy
demand over long periods. Awadallah et. al. [2] quantify the harmonic
distortion caused by PV on distribution transformers, and find that with high
penetration of PV, transformer life expectancy could decrease by 8.3%. Various
studies have shown that for higher penetrations of PV in the distribution
system, the number of transformer tap changes increase rapidly even for small
levels of variability [17, 45], sometimes up to a sixfold increase on high
variability days [22]. Dubey et al. [18] provide a comprehensive study on the
impact of EV charging on residential distribution systems, where voltage
variations at EV load locations is identified as a key issue.

Thus, the health of grid infrastructure is correlated to its loading
conditions and the fluctuations in demand. These fluctuations are measured
using the Demand Variability Impact Factor $V$, which quantifies customer
usage contribution to system variability by computing the normalized
correlation between the variability of customers demand and the variability of
total system demand.

$\displaystyle\text{Variability Impact Factor of Home $i$ }(V_{i})$ (2)
$\displaystyle=\text{Normalized Correlation between}$
$\displaystyle\text{Variability of Home }i\text{ and Total System
Variability}$

The inclusion of the Variability Impact Factor $V$ is a novel concept. We
build upon this concept to propose a compatible distribution utility rate
model to reflect this time-varying impact on the network-related cost.

###  2.3 Peak Demand Indicator Function

To make the rate structure as flexible and general as possible, a Peak
Indicator Function for Demand has been introduced. This function takes as
input the present system conditions, the peak threshold for the system
conditions, and a strictness parameter $k$, to deliver an indication of
whether the system condition at that time $t$ is considered to be a peak slot
or not. When the value of $k$ is very low, the Peak is considered based on a
stringent cut-off, whereas if the value of $k$ is larger, the function also
begins to consider those time slots where System Demand ($S^{t}$) is almost
equal to the peak threshold, thus reducing the importance and emphasis placed
on an inherently arbitrary definition of peak threshold.

Distribution grids have diverse load profiles, even between different feeders
within the same DU service territory. The proposed mechanism provides the DU
with the option to select peak thresholds and $k$ values that are best suited
for their system conditions. Optimal peak thresholds can be determined through
engineering analysis performed by the DU, with oversight of the regulator.

The Peak Indicator Function has been defined for Peak Demand Magnitude as
$\mu$. This function is described below.

####  2.3.1 Peak Demand Indicator Function $\mu$

This function is designed similar to a logistic function, and is centered
around the System Peak Threshold value $S_{\text{PeakTh}}$.
$S_{\text{PeakTh}}$ is calculated based on a percentile value that is set by
the DU. If the peak threshold percentage is set as $15\%$, then
$S_{\text{PeakTh}}=85^{th}$ percentile of the system load curve. This means
that a given time slot $t$ is defined as a peak demand time slot when
$S^{t}\geq S_{\text{PeakTh}}$. In essence, this function returns $1$ if it is
a peak slot, and $0$ if not (Fig. 2). For a given time $t$, $\mu$ is described
as follows:

$\mu^{t}=\frac{1}{1+e^{\frac{-(S^{t}-S_{\text{PeakTh}})}{k}}}$ (3)

Figure 2: Peak Demand Indicator Function $\mu$

####  2.3.2 Peak Demand Variability Indicator $\lambda$

The Variability indicator has the additional unique property of being
unbounded, thus it not only indicates that a given slot is a peak slot, but it
also captures how big the peak is, i.e., it quantifies the peak.

Similar to $S_{\text{PeakTh}}$, $\beta_{\text{PeakTh}}$ is calculated based on
a percentile value that can be set by the DU. A given time slot $t$ is defined
as a peak variability time slot when $\beta^{t}\geq\beta_{\text{PeakTh}}$. For
a given time $t$, $\lambda$ is defined as follows:

$\lambda^{t}=k\ln(1+e^{\frac{(\beta^{t}-\beta_{\text{PeakTh}})}{k}})$

Figure 3: Peak Demand Variability Indicator Function $\lambda$

###  2.4 Calculating the Grid Impact Factors $W$ and $V$

Let $X_{i}^{t}=$ Demand of user $i$ at time $t$
$dX_{i}^{t}=$ Change in Demand (Variability) of user $i$ between time $t$ and
$t-1$
i.e., $dX_{i}^{t}=X_{i}^{t}-X_{i}^{t-1}$

####  2.4.1 Element-Wise Multiplication

$\begin{aligned} W^{t}_{i}&=X_{i}^{t}\cdot\mu^{t}\\\
W_{i}&=\sum_{t}{W_{i}^{t}}\\\ \end{aligned}\qquad\begin{aligned}
V^{t}_{i}&=dX_{i}^{t}\cdot\lambda^{t}\\\ V_{i}&=\sum_{t}{V_{i}^{t}}\\\
\end{aligned}$ (4)

####  2.4.2 Demand Magnitude Impact Factor $W$

Demand Magnitude Impact Factor for Customer $i$ ($W_{i}$) is the total demand
of Customer $i$ during peak demand time slots (defined in Section 2.3). The
Peak Indicator Function $\mu$ is used to determine whether time-step $t$ is a
peak or not.

##### Element-Wise Multiplication

$W^{t}_{i}=X_{i}^{t}\cdot\mu^{t}\\\ W_{i}=\sum_{t}{W_{i}^{t}}$ (5)

##### Matrix Multiplication

$W_{N\times 1}=X_{N\times T}\cdot\mu_{T\times 1}\\\ N\text{ homes},T\text{
timesteps}\\\ $ (6)

####  2.4.3 Demand Variability Impact Factor $V$

The Demand Variability Impact Factor for customer $i$ ($V_{i}$) is the
normalized correlation between the variability of customer $i$ ($dX_{i}$) and
the variability of total system demand $\beta$.

$\displaystyle V_{i}$
$\displaystyle=\frac{\sum_{t}(dX_{i}^{t}-\overline{dX_{i}})(\beta^{t}-\overline{\beta})}{\sqrt{\sum_{t}{(dX_{i}^{t}-\overline{dX_{i}})}\sum_{t}{(\beta^{t}-\overline{\beta})}}}$
(7)

####  2.4.4 Relative Factor (% allocation) for each Customer $i$

$\begin{aligned} W_{\text{share }i}=\frac{W_{i}}{\sum_{j=1}^{N}W_{j}}\\\
\end{aligned}\qquad\qquad\begin{aligned} V_{\text{share
}i}=\frac{V_{i}}{\sum_{j=1}^{N}V_{j}}\\\ \end{aligned}$ (8)

###  2.5 Calculating the Final Bills

Let $B_{i\text{ total}}^{\text{old}}\rightarrow$ Total DU charge of home $i$
calculated in the current method, and $B_{i\text{
total}}^{\text{new}}\rightarrow$ Total DU charge of home $i$ calculated in the
proposed method.

To calculate DU charges for each home under the current mechanism, we consider
a standard volumetric rate formula for DU charges defined below (5¢ per kWh)
($X_{i}^{t}>0$):

$B_{i}^{t\text{ old}}=\$0.05\times X_{i}^{t}$ (9)

In case a home generates more than it consumes at any point in time, i.e.,
$X_{i}^{t}<0$, the excess electricity is sold back to the grid at a discounted
rate of 2¢ per kWh (Net Metering).

$B_{i}^{t\text{ old}}=-\$0.02\times X_{i}^{t}$ (10)

So, the total DU charges in the current mechanism for the full 2 year period
is calculated as follows.

$B_{i\text{ total}}^{\text{old}}=\sum_{t}(B_{i}^{t\text{ old}})$ (11)

In the proposed distribution utility rate model, customers are charged a
cumulative grid access charge (e.g. on a monthly basis), based on their Grid
Impact Factors. This access charge is calculated by starting from the total
target revenue for the DU, and dividing this total among customers based on
their contribution to grid impact.

The access charge for customers remains the same during one assessment period,
and is updated at the end of each assessment period based on usage data
collected to-date.

It is assumed that the $/kWh rate is derived from the total target revenue of
the system, which is obtained as a result of the current rate case process.

For simplicity, the analysis operates under the assumption that the total
target revenue is calculated for the full period of assessment. In our case
study, this period of assessment is two years. Further, to make a fair and
direct comparison of the current and proposed rate models, this total target
revenue for the DU has been fixed as the $B_{i\text{ total}}^{\text{old}}$
value, i.e.,

$\sum_{i=1}^{N}B_{i\text{ total}}^{\text{old}}=\sum_{i=1}^{N}B_{i\text{
total}}^{\text{new}}$ (12)

The result is essentially a redistribution of the same final cost among the
customers. This assumption is a fair one to make because the total target
revenue for the current mechanism is calculated through the rate case process,
which is assumed to be an accurate reflection of system costs.

Since the proposed mechanism has to account for two contributing grid impact
factors $W$ and $V$, the importance of these respective weighting factors are
determined by the allocation percentage parameters $\Pi_{V}$ and $\Pi_{W}$
(also determined by the DU and regulator), defined as follows:

$\Pi_{W}=\%$ allocation of Total Target Revenue for $W$
$\Pi_{V}=\%$ allocation of Total Target Revenue for $V$

And so, finally, the total DU charges for each home $i$ as per the proposed
scheme is calculated as a linear combination of the weighting factors scaled
with their respective allocation percentage parameters, as follows:

$B_{i\text{ total}}^{\text{new}}=W_{\text{share
}i}\times\Pi_{W}+V_{\text{share }i}\times\Pi_{V}$ (13)

###  2.6 Data and Case Study System Description

The data used for the results discussed in Section 3 is the instantaneous kW
demand for 200 residential customers, measured at a resolution of 1-minute.
The dataset spanning two years (from 01-01-2016 to 12-31-2017) was obtained
from Pecan Street Dataport [36].

##  3 Results and Discussion

To thoroughly examine the effects of the proposed distribution utility rate
model, we calculate the DU charges for each home in a system of 200
residential demand profiles, with 25% penetration of EVs and PVs each, i.e.,
50 EV homes and 50 PV homes among the 200 total homes.

For the purpose of this example, we set the $S_{\text{PeakTh}}$ at the 75th
percentile of total system demand. Also, the % allocations of Total Target
Revenue $\Pi_{W}$ and $\Pi_{V}$ are set as 75% and 25% respectively.

###  3.1 Comparing the Performance of Two Homes in the Proposed Mechanism

Figure 4: System Demand Curve and Comparison of Demand between two homes over
one week during Peak Time Slots

To illustrate the effects of the proposed scheme, we examine two homes which
have a similar DU charge in the existing scheme but a significant difference
in DU charges in the proposed scheme.

In Fig. 4 (top), the system demand curve has been plotted along with the Peak
Threshold line (red), indicating which intervals are considered to be peak
time slots. Fig. 4 (bottom) depicts the individual demand of the higher impact
and lower impact homes during the system peak time slots, and is assumed to be
zero for non-peak time slots.

Despite having a few spikes of demand, the demand of Home 1 during the peak
time slots is, for the most part, less than that of Home 2. Furthermore, Home
2 has a negative demand for several periods each day i.e., it is generating
more power than it consumes, indicating that it is a solar PV home. The fact
that this home is a higher impact home can be attributed to the benefit given
to solar PV homes in the existing mechanism due to net metering. In the
proposed mechanism, such demand variability is penalized through the $V$
parameter.

###  3.2 Comparing the Current and Proposed Distribution Utility Rate Models

Figure 5: Comparison of Proposed and Existing Distribution Utility Rate Models
for Homes

Fig. 5 describes the effect of the proposed rate model for each subset of
homes. This effect is quantified by evaluating the percentage change between
the proposed bill and the current bill, i.e., $B_{i\text{
total}}^{\text{new}}-B_{i\text{ total}}^{\text{old}}$ for each home. The
distribution of this range has been plotted, categorized based on the type of
home: EV Homes, PV Homes, and non-DER Homes.

In the case of EV homes, most homes have a negative % change of $B_{i\text{
total}}^{\text{new}}-B_{i\text{ total}}^{\text{old}}$. Thus, almost all homes
have a lower DU charge in the proposed mechanism than they do in the current
mechanism. As a result, it seems that the proposed rate model is favorable for
EVs. This observation follows intuition, because under the current rate model,
all that matters for billing is the kWh volumetric consumption by the home.
Whereas in the proposed billing algorithm, the impact of the user is
calculated during the peak time slots of demand, where the distribution system
is under the most stress. Thus, under the proposed rate model, there is great
potential for smart scheduling of EV charging during the non-peak periods,
which could lead to significant savings for those homes. As a result, the
interests of both the DU and the user are aligned.

When we observe the trend for PV homes, most homes have a positive % change of
$B_{i\text{ total}}^{\text{new}}-B_{i\text{ total}}^{\text{old}}$, which means
that almost all PV homes have a significant increase in their DU charge when
evaluated under the proposed mechanism. While this observation seems to
suggest that the proposed mechanism is unfavorable to PV homes, it can be
argued that the proposed mechanism is capturing the actual costs of PV that
were previously (unfairly) being borne by non-PV homes. Although the kWh
volume of consumption for PV homes is relatively lower, the sudden ramping of
PV during the late evening causes significant strain on the distribution grid.
This aspect is captured in the proposed billing scheme through the Variability
impact factor $V$.

Let us now consider the case of non-DER homes. Most homes have a negative
percentage change value for $B_{i\text{ total}}^{\text{new}}-B_{i\text{
total}}^{\text{old}}$. More specifically, of the 100 non-DER homes, over 80
have a negative $B_{i\text{ total}}^{\text{new}}-B_{i\text{
total}}^{\text{old}}$, with almost 70 homes having a slightly negative change
(0-20% reduction in the bill). This indicates that the proposed rate model is
benefiting most non-DER homes. This addresses one of the key drawbacks of the
existing billing scheme, where, in many cases, costs incurred by the DUs in
their PV-incentive programs such as net metering or other subsidies would be
recovered from the non-PV customers via an increase in access charges. With
the proposed mechanism, the trend of penalizing non-PV customers is reversed,
bringing the distribution of DU charges back to balance.

###  3.3 The Effect of DER Penetration on DU charges Calculated under the
Proposed Mechanism

Figure 6: % Change in DU charges before and after 25% DER Penetration
(Calculated under the Proposed Mechanism)

Fig. 6 describes the effect of penetration of individual DERs (EV and PV) on
each subset of homes. In the default system, there is a DER penetration of 25%
EV and 25% PV (50 homes each). In the system without EV, the DER penetration
is 0% EV (0 homes) and 25% PV (50 homes). Similarly, in the system without PV,
the DER penetration is 25% EV (50 EV homes) and 0% PV (0 PV Homes). In the
system without DERs, the DER penetration is 0%, i.e., 0% EV and 0% PV. The
left figure compares the DU charges of the EV Homes calculated in the default
system vs the system without EVs. The middle figure compares DU charges of PV
homes calculated in the default system vs the system without PV generation.
The right figure shows the effect on DU charges of non-DER homes due to DER
penetration in the system, by comparing the DU charges calculated in the
default system vs the system with 0% DER penetration.

When considering the effect of EV penetration on EV homes, it is observed that
most homes have a positive % change between with and without EV cases, thus
following the expected trend of having higher electricity bills due to the
presence of an EV.

With PV however, the story is different. Some PV homes seem to benefit with
the introduction of PV (around 30 homes), but the rest have a higher DU charge
with the introduction of PV. One factor could be explained by the variability
index $V$ accounting for 25% of the total revenue, and that the PV homes have
the highest variability impact factors. Another issue could be that PVs are
pulling down the system conditions below peak threshold when the sun is
shining, and shifting peak slots to different times. Thus, the application of
solar + storage technology combined with smart scheduling for maximizing usage
during system non-peak conditions could be the optimal strategy in the
proposed billing scheme. This has been explored in the case study discussed in
Section 3.4.

Figure 7: % Change in DU charges (Proposed Mechanism) after introducing
Battery Storage in 25 PV Homes

Looking at the effect of DER penetration on non-DER homes, it is noted that
every single non-DER home has seen a reduction in their DU charges due to the
penetration of DER. While this seems like the proposed mechanism rewards
customers for not investing in DER, it is more accurate to view this as
evidence that a fair cost recovery from DER homes is happening because of DER
homes having an increase in their grid impact, due to the penetration of DERs.

###  3.4 Effect of Battery Storage on DU charges calculated under the Proposed
Mechanism

Fig. 7 shows the effect of penetration of battery storage in the system on the
DU charges calculated under the proposed rate mechanism. In this case study,
half of the PV homes (25 out of 50) are given a battery storage unit, that
operates under a brute force algorithm, charging during typical non-peak hours
(1 am to 3 am), and discharging during typical peak hours (5 pm to 7 pm), with
a rate of 2 kW for both charge and discharge cycles. Essentially, this is
meant to reduce the impact on the grid by discharging during peak time slots,
and charging during non-peak time slots.

Fig. 7 (top-right) shows that every single ’PV+battery’ home has experienced a
reduction in DU charge due to the introduction of battery storage. This
reduction has been observed even though a brute force charging-discharging
schedule was implemented. This result could be further improved if the battery
storage devices are operated under a smart-scheduling algorithm, that not only
reduces impact during peak time slots, but also counteracts spikes in the
variability of the system, thus earning rewards for positive contributions to
grid conditions.

The other three sub-figures in Fig. 7 show the effects of the introduction of
battery systems in 25 PV homes on the other categories of homes. Homes in all
of these categories see minor increases in their bills, so it could be argued
that the proposed mechanism provides the most rewards for customers having PV
+ battery storage, who are more likely to be wealthier customers, at the
expense of non-DER customers, who may be less affluent and cannot afford PVs
and battery storage. However, when comparing the DU charges of these non-DER
customers under the proposed and current schemes, it is clear that these homes
will still be better off than they are under the current scheme.

###  3.5 Effect of Customer Aggregation on DU charges calculated under the
Proposed Mechanism

Figure 8: Case Study: Aggregating a low-$V_{i}$ EV customer and a high-$V_{i}$
PV customer

Consider the case of customer aggregation, where a group of customers come
together to form an aggregated customer group, which is essentially treated as
a singular customer entity by the DU. It is desirable for customers within
this group to complement each other’s variability $V_{i}^{t}$ such that there
is a reduction in the net variability impact of the aggregated customer group.
If net variability impact of a group reduces, the total impact on the system
reduces. Such aggregated customer groups could potentially be governed by an
internal smart control algorithm such that the group minimizes their net
impact on the system. An efficient rate model should reflect rewards for a
desirable reduction in system impact.

In the existing rate model, there would be no change in the total DU charge of
these aggregated customers, since the total kWh consumption remains the same.
However, the proposed mechanism considers variability of power demand as a key
parameter for evaluating the impact of customers. Thus, such aggregated
customer groups will have a net reduction in aggregate customer bill, compared
to the sum of DU charges of the same customers treated as individuals.

Fig. 8 is a case study performed with two customers to illustrate the effect
of aggregation on DU charges calculated in the proposed mechanism. Here, a
low-$V_{i}$ EV customer is aggregated with a high-$V_{i}$ PV customer. No
smart control algorithm has been implemented to change the behavior of either
customer; this case study is conducted to illustrate the potential of customer
aggregation for DU charge reduction. Fig. 8 shows the demands of the system,
the EV customer, and the PV customer over one week. These homes oppose each
other’s variability quite regularly, especially when the EV customer’s EV is
charging and the PV customer’s solar panel is generating power (note the
multiple 6.6 kW spikes seen in the EV customer’s demand curve and the
intermittent spiking of the PV customer’s demand curve). We expect a net
reduction in variability impact when these customers are aggregated, thus
resulting in a lower DU charge for the aggregated customer group compared to
the sum of the two individual bills. The results of this case study are shown
in Table 1.

We observe that customer aggregation could have the desired effect of further
incentivizing variability impact reductions, which can be harnessed by smart
control algorithms governing the behavior of customers within such aggregated
customer groups.

Evaluation Metric | Individual Customers | If same customers were Aggregated
---|---|---
PV Customer | EV Customer
% Share of Variability Impact using Normalized Correlation | 2.11% | 0.27% | 1.85%
Total Bill over full 2-year period ($) | $1913 | $622 |  $2234 $301 (11.87%) saved through aggregation
Total = $2535
Table 1: Case Study: Comparing Impact and Total DU charges before and after
Aggregation

###  3.6 Pros and Cons of the Proposed Mechanism

####  3.6.1 Pros

##### Revenue Decoupling

The mechanism introduced in this work effectively decouples utility revenue
and customer bills from volumetric consumption. Revenue decoupling is
important to the long-term stability of utility revenues, since due to the
growing penetration of DERs, volumetric based revenue could decline in the
future.

##### Recovers Utility Costs Accurately and Effectively

The proposed mechanism is more representative of the actual costs inflicted
upon the distribution grid by the customers, due to the usage of kW rather
than kWh as a defining metric. The major driver for investment costs in
equipment is the consumer demand during peak periods. Thus, the proposed
approach provides better alignment between the revenue and costs as compared
to the volumetric charge. The introduction of ’Variability’ is also a novel
approach. The variable nature of renewable resources adversely impacts the
efficient operation of the grid and as such should be accounted for in the
cost recovery mechanism.

##### Utility Revenue Targets are Assured to Be Met

There is a key and prominent distinction between the proposed mechanism and
the current model: rather than expecting a total revenue for the DU depending
on several variables, the proposed mechanism offers the DU the opportunity to
ensure a stable and assured revenue. The total target revenue is first set,
then the proposed mechanism allocates the costs to all customers. Another
advantage is that this form of rate-making could require less frequent rate
cases, which is a time-consuming and expensive process.

##### Reduces Unfair Cross-Subsidy

Both the current volumetric charge and the net-metering policies result in DUs
over-recovering costs from non-PV customers while under-recovering them from
PV customers. Further, there is a high likelihood that non-PV customers fall
in the low-income category, while PV customers fall in the high-income
category, as observed by De Groote et al. [15]. Thus the proposed mechanism
mitigates against the existing unfair and regressive cross-subsidy. Further,
the proposed approach is consistent for all types of DERs. This consistency is
relevant to incentivize technologies such as energy storage.

##### Retains Efficiency Incentive

Under the current volumetric mechanism increasing efficiency reduces
electricity sales and therefore profits [28]. The proposed rate model retains
the incentive for the DU to be efficient. Since the total revenue target is
controlled under this structure, the DU is incentivized to take action to
improve system efficiency to get higher profits.

##### Rewards Smart Customer Aggregation

The proposed rate structure could incentivize aggregation of customers with
consumption patterns that are negatively correlated with each other. As
illustrated in Section 3.5 and Fig. 8, such groups of customers could reduce
their aggregate impact on the grid, thus reducing their DU charge when part of
a group, compared to their DU charge when considered individually.

Smarter scheduling and real-time adaptive consumption patterns could be
leveraged in such aggregation mechanisms to negate the spikes introduced by
other customers in the group. This also opens up the market for customer
aggregation as an electricity service. Providers of customer aggregation could
run local energy markets, create demand response-based incentive programs, and
perform smart automatic control of their customer groups to minimize group
impact.

Further, the effect of smarter scheduling of distributed energy resources
should be tested. Applying this on the aggregation of solar and storage could
be transformative.

####  3.6.2 Cons

##### Peak Threshold Calculation Unfair to Solar PV?

As mentioned earlier, the introduction of PV could cause the total system
demand to go below the peak threshold in some time slots, thus converting
those time slots from peak slots to non-peak slots. However, this also shifts
the peak slots to a different time, because peak slots are defined on a
percentile basis, rather than absolute. There will always be a top $x$% set of
values; it does not matter whether that range is small or large. As a result,
the new system peaks would be those times when sunlight is not available. The
appliance usage of a PV home is not offset when the sun is not shining. These
shifted peak slots could be when the PV homes stop generating, and demand
power from the grid, thus contributing to increase in the system demand. These
slots are now the peak slots, and PV homes, along with all other homes,
contribute to their $W$ and $V$ impact factors significantly during this time.
Thus, it could lead to the situation where non-PV homes get away with highly
variable or inefficient usage patterns when the sun is shining because PV
homes are generating enough power to reduce the stress on the system below the
system peak threshold. Essentially, some non-PV homes escape penalization due
to their behavior being covered or compensated for by the PV homes.

This problem could be easily dealt with when rolling out the proposed
mechanism in practice: peak thresholds could potentially be selected by DUs
based on distribution feeder capacity, for the feeders on which this algorithm
is being implemented. Thus, the peak thresholds would become absolute, rather
than relative.

##### Solar PV Ancillary Benefits

It could be argued that Solar PV is not being rewarded for the various
benefits it brings to the grid or indeed its societal benefit in terms of
reducing pollution. Distributed PV systems likely provide ancillary benefits
such as reducing distribution system losses by generating close to the point
of consumption, and in the future also might offer frequency and voltage
support services through the use of smart inverters [16].

##### Rate Simplicity

Clarity and simplicity is a consideration for rate design. In this respect the
volumetric rate has an advantage since customers have become accustomed to it.
On the other hand it could be argued that customers are also familiar with the
concept of credit scores, and paying different interest rates relative to
other customers, based on their individual risk to the lender.

##### High Grid Access Charges

As mentioned in [7, 5], the peak-coincident charges could be too high and
hence send inefficient signals to end-customers. Low income customers may not
be able to respond easily to such a price signal since they have limited
ability to invest in demand management technologies. Residential customers
also might not have too much flexibility in their consumption schedules, due
to work and school timings [12].

###  3.7 Implementation Considerations

Our case study is a proof of concept that uses real-world data to instantiate
the paradigm shift from a one-size-fits-all volumetric rate model to a
customer-specific grid access fee based on cost causation. A practical
implementation of a utility rate model based on this paradigm shift will
require adaptation and modification to suit the existing cost-of-service
regulatory framework already in place. The model would still be subject to
rigorous regulatory review in the ratemaking process for the distribution
utility.

In this subsection, we propose some specific practical recommendations that
could be applied to make the proposed rate mechanism more implementable in the
General Rate Case environment.

####  3.7.1 Calculation and Periodic Update of Key Parameters

The proposed rate mechanism employs a few key parameters which, in the study,
rely on engineering judgment. When this proposed mechanism is being
implemented, these parameters need to be carefully calculated because they
strongly influence the final bills for all customers in the system. Critical
metrics including the peak threshold ($S_{\text{PeakTh}}$), Strictness of Peak
Demand Percentile Cut-off ($k$), Allocation % of Total Target Revenue to Grid
Impact Factors $\Pi_{V}$ and $\Pi_{W}$ all need to be defined clearly through
rigorous studies. These studies to calculate key parameters can be conducted
periodically as a regulatory requirement, with the engineering analysis
performed by the DU, with oversight of the regulator. These parameters could
remain fixed for a certain period (e.g. the duration of the rate period or
year), and are revised based on periodic studies.

####  3.7.2 Feeder-Specific Peak Threshold Design

We propose calculating feeder-specific peak thresholds, so that the impact of
a customer during the critical “grid stress” conditions on the feeder is
captured more accurately. The utility company can conduct studies to determine
the peak thresholds by considering various parameters, including typical
feeder loading conditions, time of operation under increased loading
conditions, and line losses, to name a few.

####  3.7.3 Feeder-Specific Total Target Revenue

We propose calculating total target revenue on a feeder-specific basis.
Utility companies typically have most of the pertinent information such as
capital and maintenance costs of grid infrastructure assets (such as
transformers, capacitor banks and poles) already categorized by feeder. Thus,
a feeder-specific approach will make the implementation of a cost-causation
based rate mechanism more accurate and straightforward, compared to a system-
wide approach. The responsibility to carry out such studies could easily be
subsumed into the traditional roles of distribution utilities.

####  3.7.4 Feeder-Specific Smart Customer Aggregation

The objective of smart customer aggregation is to reward reductions in demand
and variability impact on the grid. In other words, customers must be
aggregated such that there is a physical manifestation of the desired
reduction in grid impact. Therefore, we propose that each customer in an
aggregated group must be on the same physical network, i.e., the same feeder.

####  3.7.5 Mechanism for Implementation

Implementing this proposed rate structure is data-intensive, requiring timely
data at customer-level granularity. A practical approach to implementation
might be to categorize customers based on two key factors: type of customer
(DER or non-DER) and the level of their impact on the grid (low, medium, and
high based on the proposed metric). For each customer subgroup, the grid
access fee could be the same.

####  3.7.6 Determination of More Cost-Causing Grid Factors

At present, the proposed rate mechanism involves two cost-causing Grid
Factors: demand magnitude $W_{i}$ and demand variability $V_{i}$. While these
two factors are impacted by several drivers of cost, such as voltage and
frequency fluctuations, capacity, line losses, and age of existing equipment,
this is not an exhaustive list. Further studies need to be conducted to
determine more parameters that drive cost incurred by utilities when providing
service to their customers.

The Relationship between the Utility, Regulator, and third-party Experts The
studies mentioned in this section will need to be designed as a cooperative
effort of the utility company and independent third-party experts, then
approved by regulators. The regulatory process of reasonably determining these
parameters should have similar rigor as that for the existing distribution
utility rate model when formulating the rate case.

####  3.7.7 Ex-Post Review

The existing rate mechanism is ex-ante. Utility companies can thus determine
the rate charged per kWh, which is revised in every rate case. Given that the
proposed rate mechanism is ex-post, and evaluates the impact of a customer
based on cost-causation at the end of the observation period, traditional
monthly billing needs to be adapted. This can be achieved by using historical
smart meter data to evaluate customer behavior. Before the transition to the
proposed rate model, customers can be notified in advance (say one year), and
customer education programs can be initiated to inform the customers how the
new rate model works. Further, a “grid friendliness score” can be calculated
and reported to customers, similar to a credit score, which will enable
customers to understand how their consumption pattern impacts their bill. A
moving-window based evaluation should be adopted, so that this grid
friendliness score can be evaluated and updated periodically (say monthly).
These recommendations would provide adequate notice as well as evaluate
customers over a substantial period to ensure fairness.

####  3.7.8 Other Charges

While we have discussed a mechanism to charge customers for some grid costs
based on cost-causation principles, these do not account for all costs. Other
charges include residual network costs as well as policy-related costs, which
can be recovered in a minimally distortive fashion [40, 7, 5, 39]. Utilities
may be allowed to charge customers for some variable costs using riders or
surcharges for specific purposes, including costs of new power plants, costs
of energy efficiency programs, costs of renewable energy standards, or cross-
subsidies for low-income customers [44].

Further research is required to substantiate the details needed for
implementation.

e developed a framework for a complete restructuring of existing policy. The
above points are only an initial consideration of how the proposed utility
rate model can be implemented. Further follow-up research would be required to
substantiate the details of such studies so that this policy could be
implemented effectively.

###  3.8 Policy Implications

The current volumetric rate structure has apparent drawbacks, the first being
that the DU is not assured of sufficient revenues, and the second that there
is effectively an unfair cross-subsidy from non-PV customers to PV customers.
With declining revenues, the DU would be forced to raise the rates for
everyone, so the proposed approach provides long-term stability to the DU. PV
customers could face higher bills, but this might be considered justified
given that the energy they contribute may not be coincident with peak demand,
which is a large driver of distribution system costs. Moreover, if such
customers also had optimally operating storage, their DU charges could be
reduced.

With the introduction of metrics such as peak thresholds and % allocation, the
DU has far greater flexibility to modify the rate model based on the actual
costs they incur, customized for their system conditions.

The regulatory framework plays a crucial role in implementing any rate design
reform. For privately-owned and some publicly-owned distribution utilities,
rates are regulated by the state commissions. Regulators should be careful not
to favor any particular technology and rate design should be based on the
actual value of energy provided by DER assets.

##  4 Concluding Remarks

With the increasing penetration of DER technologies, utilities are likely to
face challenges associated with the current volumetric rate design. Rate
design and cost allocation are imprecise, and involve both judgment and policy
goals. That being said, regulators should be open to considering alternative
rate designs that allocate costs that are more directly aligned with the
drivers of that cost.

The process of establishing cost allocation and rate design methods in the
real world is a complex technical and policy issue. This paper aims at
providing conceptual clarity and a methodological, smart meter data-driven
approach to a fair and sustainable rate structure that would provide clearer
signals to different end users based on their impact on distribution grid
operations. This impact is quantified by a "grid friendliness score", which
calculates the customers’ normalized correlation of their consumption pattern
with the net power demand of the distribution system.

Future work will investigate some key questions: further insight needs to be
gained on how to calculate the actual Total Target Revenue, such that it
recovers the costs incurred by utilities under different system conditions. In
addition to magnitude and variability of consumption, several factors may
contribute to costs, such as line losses, locational congestion, and ageing of
equipment. Our proposed framework allows for the addition of such contributors
as individual parameters.

### Acknowledgments

This work is supported in part by Power Systems Engineering Research Center,
and in part by National Science Foundation Grants OAC-1636772 and
ECCS-1839616.

The authors are grateful to Dr. Leigh Tesfatsion and Editor-in-Chief Dr.
Janice Beecher for comments that helped improve the manuscript.

here are various bibliography styles available. You can select the style of
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Here are two sample references: [Fortunato2010] [Fortunato2010,
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##  5 Floats

Figures may be included using the command,`\includegraphics` in combination
with or without its several options to further control graphic.
`\includegraphics` is provided by graphic[s,x].sty which is part of any
standard LaTeX distribution. graphicx.sty is loaded by default. LaTeX accepts
figures in the postscript format while pdfLaTeX accepts *.pdf, *.mps
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Figure 9: The evanescent light - $1S$ quadrupole coupling ($g_{1,l}$) scaled
to the bulk exciton-photon coupling ($g_{1,2}$). The size parameter $kr_{0}$
is denoted as $x$ and the pms is placed directly on the cuprous oxide sample
($\delta r=0$, See also Table 2).

The `table` environment is handy for marking up tabular material. If users
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Table 2: This is a test caption. This is a test caption. This is a test caption. This is a test caption. Col 1 | Col 2 | Col 3 | Col4
---|---|---|---
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##  6 Theorem and theorem like environments

cas-dc.cls provides a few shortcuts to format theorems and theorem-like
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         \begin{eqnarray}\label{10}
         ....
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###### Theorem 1

For system (8), consensus can be achieved with $\|T_{\omega z}$ …

$\displaystyle....$ (14)

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##  7 Enumerated and Itemized Lists

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##  8 Cross-references

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