As & Söder (2017), DSOs are considered to

As mentioned before, it is
important to identify, consider and analyze the negative impacts of DGs and
prosumers on DSOs in the tariff design process under different metering
systems, with different connection charging mechanisms. In the current work, we
focus on net metering system and two extreme cases of connection charges, deep
and shallow, to be charged to DG owners and prosumers as a fixed fee. We
closely follow a model proposed by Gautier et al. (2017) where they set up
consumers’ and prosumers’ utility functions. The model assumptions are
discusses in section 3.1. We then use these functions to show how “prosumption”
(the rate of consumers converting to prosumers) changes under the net metering
system while considering two types of connection charges alongside distribution
losses. The main contribution of this work is first of all to provide a
simplified model of energy losses due to DG integration to be considered as a
part of distribution costs. Second, to propose a new tariff mechanism (a two-part
tariff structure) to be assigned to DG owners and prosumers, based on shallow
and deep regulatory schemes.


3.1       Model Assumptions

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setting up the utility and profit functions of the grid users, we followed a
methodology which is closely aligned with a study previously done by Gautier
et. al (2017). The structure and components of this model are described below.


3.1.1    General assumptions

in Huang & Söder (2017), DSOs are considered to be under the unbundling
rule, meaning that they cannot own any DGs and their sole responsibility is to
manage the distribution grid. This assumption leaves DSOs as natural monopolies
to be regulated. The regulator sets up grid tariffs to cover DSO costs,
therefore the regulator’s problem will be as following:




the consumers’ utility from consuming electricity and

DSO’s profit.

types of consumers are present in the system: with and without distributed
generation facility. Total number of consumers is

 which is normalized to 1. Prosumers own only
one DG technology: solar panels. The total electricity consumption by both types
of consumers is homogeneous and equal to

 and can bring them a total amount of surplus
equal to

. The retail price of the imported
electricity is set as

 and is equal to marginal
cost of the centralized generation. The metering system to compensate renewable
energy resources (prosumers) is net metering.
Under the so called “third party access right” (European Commission, 2003),
DG owners/prosumers can have access to the grid and both import and export
electricity from/to the grid.


3.1.2    Decentralized Generation/Prosumers

 proportion of total number of consumers can
choose to install solar PV panels with a capacity equal to

 and become prosumers.

 is considered to be lower than

 since in general small-scale consumers which
eventually become prosumers do not have neither the financial assets nor the
physical ones to install large scale decentralized production units. Furthermore,
there are several jurisdictions which set limits for the amount of installed
capacity (Gautier et al., 2017).

a function of the installation cost,

, which
in turn depends on “exogenous” factors such as roof top space, angle of the PV
plates, etc. Therefore,  

, where

the distribution function of the installation cost

. Considering all of these factors, total
decentralized electricity generation equals to

 and total imported electricity from the centralized
generation equals to



defined to show the synchronization between consumption and production of the
prosumers. Consequently, prosumers will consume

of their own production and import the rest of their consumption from the grid,

. Accordingly, they will inject their
excess production equal to

the grid. Therefore, total amount of electricity injected to the grid equals to

Several factors can affect this self-consumption rate. For instance, recent
developments in storage technology can increase this rate which currently does
not exceed 0.5 (Gautier et al., 2017). However, grid tariffs can also act as a
nudge to promote self-consumption. An increased export tariff or a modified
tariff structure which charges prosumers for their network usage can also



3.1.3    Distribution Costs

distribution grid tariff,

, is set by the regulator at the
breakeven point for the DSO (

This tariff is set to cover distribution networks costs and is considered to be
between 18% to 35% of the final electricity bills (Ofgem, 2015; European
Commission, 2015; Gautier et al., 2017). The network cost of “providing” 1 MWh
of electricity to the users is

  and it
is the same for both consumers and prosumers. There is also a fixed
distribution cost burdened by DSOs which can be ignored for now since it will
not change the final results.

general, distribution costs can be either capital or operational expenditures
and both of these costs will be affected by integration of DGs into the grid.  DG integration can increase distribution costs
in two ways: i) operational expenditures: depending on the amount of integrated
capacity energy losses can increase in distribution networks; ii) capital
expenditures: DGs/prosumers impose extra costs on network managers to integrate
them into the grid, known as connection costs which is related to the capacity
and the number of connected DGs/prosumers.


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