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energies
Article
Demand Price Elasticity of Residential Electricity
Consumers with Zonal TariffSettlement Based
on Their Load Profiles
Jerzy Andruszkiewicz , Józef Lorenc and Agnieszka Weychan *
Institute of Electric Power Engineering, Poznan University of Technology, 60-965 Poznan, Poland;
jerzy.andruszkiewicz@put.poznan.pl (J.A.); jozef.lorenc@put.poznan.pl (J.L.)
*Correspondence: agnieszka.weychan@put.poznan.pl
Received: 18 October 2019; Accepted: 8 November 2019; Published: 13 November 2019
Abstract:
The concept of price elasticity of demand has been widely used for the assessment of the
consumers’ behavior in the electricity market. As the residential consumers represent a significant
percentage of the total load, price elasticity of their demand may be used to design desirable demand
side response programs in order to manage peak load in a power system. The method presented in this
study proposes an alternative approach towards price elasticity determination for zonal tariffusers,
based on comparisons of load profiles of consumers settled according to flat and time-of-use electricity
tariffs. A detailed explanation of the proposed method is presented, followed by a case-study of
price elasticity determination for residential electricity consumers in Poland. The forecasted values
of price elasticity of demand for the Polish households using time-of-use (TOU) tariffvary between
−
1.7 and
−
2.3, depending on the consumers’ annual electricity consumption. Moreover, an efficiency
study of residential zonal tariffis performed to assess the operation of currently applicable electricity
tariffs. Presented analysis is based on load profiles published by Distribution System Operators and
statistical data, but the method can be applied to the real-life measurements from the smart metering
systems as well when such systems are accessible for residential consumers.
Keywords: price elasticity of demand; residential load; tariffprograms; demand response
1. Introduction
Over the recent years, increasing problems with ensuring reliable and stable supply of energy in
the global aspect may be observed due to rapidly increasing peak electricity demand and hindered
development of generating units with sufficient peak capacities. These problems generate growing
interest in alternative ways of managing power systems, such as demand side response (DSR), because
the electricity suppliers are given a choice between investing in new, costly peak capacities at generation
side and using less risky means, related to load management, pay significant attention to using these less
radical methods being more environmentally friendly as well. Demand response is a vital component
of smart grid technologies. DSR can be properly used only based on smart metering systems ensuring
the detailed knowledge of the demand, helping to explain the relationship between DSR and energy
prices and demonstrate the flexibility of electricity demand.
An application of demand side response price based programs includes applying various pricing
schemes to be chosen by the consumers in the form of electricity tariffs [
1
]. An appropriate electricity
tariffdesign requires one to know the price elasticity of electricity demand of the considered consumers,
which describes a possible change in the electricity demand as a result of electricity price change or
other events, such as price change of different energy carriers, which may act as substitute for electricity,
consumer’s change of income, etc. [2].
Energies 2019,12, 4317; doi:10.3390/en12224317 www.mdpi.com/journal/energies
Energies 2019,12, 4317 2 of 22
That is why price elasticity of demand is a key indicator characterizing electricity market and the
consumer acting on this market [
3
]. A specific group of consumers are residential consumers, which,
in the case of Poland, are settled according to electricity tariffs set by energy supplying companies and
distribution system operators (DSOs). These residential consumers, in the Polish conditions, are given
a choice between a flat tariffand a time-of-use tariff. In Poland, such consumers generate over 20%
of the total electricity demand, 80% of which are settled according to the flat tariff[
4
]. Therefore,
knowledge of their behavior in the energy market is extremely important, as they create a significant
potential for load management. The proper design of low voltage customers’ tariffs analyzed in [
5
]
can ensure savings for customers from the cost of electricity use and at the same time it may allow
electricity providers to balance the demand better with less instability in the system. The problems how
to optimize the power purchase portfolio decision of electricity sales companies offering time-of-use
tariffs taking into account load uncertainties and electricity prices is dealt with in [6].
As price elasticity of demand values are used as input data for an electricity tariff design [
7
] and
determining possible consumers’ reactions for price changes in DSR programs [
1
,
8
,
9
], which are influencing
the management of generating capacities at the competitive market [
10
], they are vital to be precisely
determined. Studies published up to now base the price elasticity of electricity calculation on historic data,
i.e., comparing the electricity consumption and prices in corresponding time periods (months, seasons,
years). However, the power industry has undergone massive restructuring and numerous merging
processes within power companies in previous years in order to implement energy market and to create
large entities able to undertake important development tasks. Introduced energy market rules changed
the operation conditions of supply companies while the newly created regulation authorities influenced
the tariff building process of distribution system operators. All these changes distorted the possibility of
using the historic data to determine the precise price elasticity of demand values.
The aim of the presented research is to propose a new method of determining price elasticity of
electricity demand, not on the basis of historical data comparison in series of years (as it is presented
extensively in the literature), but on the basis of comparison of load profiles of customers settled
according to flat and time-of-use tariffs. Thus, a current customers’ response to market conditions
is explored. A primary motivation for this research is providing a novel method for determining
price elasticity of demand, so that it may be used by electricity suppliers to forecast the consumers’
behavior at the electricity market based on the experience from actually applied time-of-use (TOU)
tariffs. The main goals of this paper are as follows: a) Propose an alternative method of determining
the price elasticity of electricity demand for residential customers using zonal tariffs, b) determine
the annual price elasticity of electricity demand for residential customers using zonal tariffs for the
selected distribution area in Poland based on the introduced methodology, c) evaluate the efficiency of
zonal tariffs for residential customers changing their load profile.
The article is organized in sections presenting the following issues: Section 2—literature review,
Section 3—data used and method applied for price elasticity of demand determination, consisting of
subsections concerning background information on demand management using electricity tariffs in
Poland, source data on customers’ load profiles used for analysis, analysis of changes in load profile,
and yearly electricity consumption in result of TOU tariffapplication, and, finally, the methodology
for determining the price elasticity of demand using the comparative load profiles method. Section 4
presents the results of calculations of annual elasticity values for the analyzed distribution area, Section 5
presents the proposed efficiency estimation of time-of-use tariffs, and Section 6presents the discussion
of the obtained results. Finally, a summary of the research is presented in the conclusion section.
2. Literature Review
Methods of determining the price elasticity of demand vary significantly in the literature,
depending on applied load model, settlement system of the consumers, econometric estimation
methods, and number of other factors taken into account, such as consumers’ income or spending,
climate conditions, or household appliances’ energy efficiency.
Energies 2019,12, 4317 3 of 22
Variations concerning values of price elasticity of electricity demand provided by different studies
are significant and they are influenced by a number of factors specific to a given country, consumers’
group, pricing schemes and regulations, etc. Comparison of the results of price elasticity of electricity
demand analyses described in the literature is presented in Table 1. It acknowledges the variety of the
research conducted and the variety of the obtained results of price elasticity of demand at the global
level. Both self elasticity values and cross elasticity values concerning other energy carriers or other
time zones during the day are considered.
Table 1. Price elasticity of demand studies’ review (if one value is not specified, minimum/maximum
values determined in a given study are presented).
Author Country Elasticity Short-term Elasticity Long-term Elasticity
Aalami et al. [1]Iran Self −0.10 -
Cross
(peak/off-peak) 0.016 -
Alberini et al. [11] USA Self −0.08/−0.15 −0.45/−0.75
Arthur et al. [12] Mozambique Self −0.6043 -
Boogen et al. [13] Switzerland Self −0.54/−0.59 −0.56/−0.68
Boogen et al. [14] Switzerland Self −0.30 −0.58
Boonekamp [15] The Netherlands Self −0.124 -
Burke et al. [16] USA Self −0.06/−0.24 −0.95/−1.01
Campbell [17] Jamaica Self - −0.82
Chindakar et al. [18] India Self −0.39 -
Espey et al. [19] USA mainly Self average −0.35
(−0.004 to −2.01)
average −0.85
(−0.04 to −2.25)
Filippini [20]Switzerland Self - peak: −0.778/−0.835
- off-peak:
−
0.652/
−
0.758
- peak: −1.608/−2.266
- off-peak: −1.273/−1.652
Cross
(peak/off-peak)
- peak: 0.793/0.917
- off-peak: 0.363/0.407
- peak: 1.767/2.311
- off-peak: 0.684/0.919
Gautam et al. [21]USA Self −0.0523 −0.110
Cross (natural gas) - 0.0952
Ishaque [22] Pakistan Self −0.10 −0.462
Kwon et al. [23] South Korea Self −0.051 −0.207
Labandeira et al. [
24
]
Various Self −0.126 −0.365
Lijesen [25] The Netherlands Self −0.0014/−0.0043 -
Loi et al. [26] Singapore Self −0.050/−0.368 -
Matar [27] Saudi Arabia Self
- double progressive
tariff:−0.45
- flat tariff:−0.09
- time-of-use (TOU) tariff:
−0.05
-
Okajima et al. [28] Japan Self −0.397 −0.487
Rai et al. [29]Australia Self −0.447 −0.748
Cross (natural gas) 0.121 0.273
Schulte [30] Germany Self −0.4310 -
Shaik et al. [31] USA Self average −0.4145 (max. 0.247, min. −1.409)
Shi et al. [32] China Self −2.477 -
Silva et al. [33]Portugal Self −0.585/−0.673 (urban);
−0.652/−0.897 (rural): -
Cross (other
carriers)
0.244 (urban),
0.374 (rural) -
Tambe et al. [34] India Self −0.47 -
Volland et al. [35] Switzerland Self average −0.3394 (max.
−0.2631, min. −0.3810)
average −1.853 (max.
−0.990, min. −2.417)
Wolak [36] GB Self
- real-time pricing (RTP)
tariff:−0.030
- critical peak pricing
(CPP) tariff:−0.090
-
Woo et al. [37]USA Self −0.0351 −0.0997
Cross (natural gas) 0.2709 0.6841
Analyses regarding customer responses using different pricing schemes have already started
in the second half of the previous century, beginning with the identification of problems related to
determining the price elasticity of demand [38] and attempts to determine the response of customers
Energies 2019,12, 4317 4 of 22
using multi-zone tariffs for price changes [
39
,
40
]. More detailed analyses of electricity demand in
multi-zone tariffs, determining price elasticity of demand, were later carried out for time-of-use (TOU)
tariffs [
20
,
27
,
41
], for progressive tariffs [
27
], for tariffs with a critical peak pricing (CPP) [
36
,
42
], and for
real-time pricing (RTP) tariffs [
36
]. In [
43
,
44
], the customers’ flexibility to price changes in dynamic
tariffs was determined empirically, based on real energy consumption measurements, depending on
the household appliances used. The interesting method of demand elasticity learning and estimation
algorithm is presented in [45] for future smart energy systems.
Researches on price elasticity of demand also include other, non-economic factors affecting
the consumption of electricity. The methodologies proposed in [
27
,
46
,
47
] combine preferences of
consumer behavior and energy prices with physical factors, such as external weather conditions or
temperature and humidity in a household. In [
48
], the most significant drivers for price responsiveness
were determined using machine learning techniques. The most meaningful drivers turned out to be
the previous electricity consumption, revenues, and number of inhabitants in a household and the
possession of specific household appliances, such as dishwashers or water boilers. In [
31
], elasticity is
determined for various areas of the USA to determine the impact of climatic conditions on electricity
consumer’s behavior (self and cross price elasticity), whereas in [
35
], price elasticity of demand is
needed to create strategies for sustainable energy development.
Source data for price analyses of electricity demand elasticity are often panel data at the household
level [
35
,
49
,
50
], that is multi-dimensional data including measurements and observations of various
phenomena over time for the same individuals. Basing the analyses on such data sets allows for a very
accurate analysis, but the results become very susceptible to regional factors and require very high
detail of household data. In the absence of full panel data, some studies create pseudo-panels and
base their analyses on a series of independent data [
33
,
51
]. Another approach to the price elasticity of
demand research focuses on aggregate data, which is summary data based on multiple measurements,
often made available by energy suppliers [
34
,
52
]. Research based on aggregate data is characterized by
high repeatability. However, some of the relevant household data may be lost in this way.
Part of the reported research assumes that the price elasticity of demand is constant [
53
], especially
in the long-term perspective [
54
]. However, in the latest research, more and more attention is being paid
to the fact that the price elasticity of demand is a variable in time feature [
27
] and should be determined
individually for individual cases. In [
52
], the hourly variability of the customer’s responsiveness for
price change for the 24-hour period is presented, according to which the greatest elasticity of residential
consumers occurs early in the morning and in the afternoon, while the smallest one is around midnight.
In [
25
], the author also determines the volatility of the real-time price elasticity of the demand values
in order to determine the potential for introducing RTP tariffs.
Research on price elasticity of demand also differs in terms of the properties of the considered
elasticity. One can distinguish between long-term and short-term elasticity, as well as self and cross elasticity.
The research conducted worldwide focuses more often on short-term elasticity, since the determination of
long-term elasticity requires much more data [
20
]. However, it has been found that short-term elasticity
values are much lower than of the long-term elasticity, because in the long term the customer may react to
the price increases by, for example, buying more energy-efficient equipment or improving the insulation
conditions of the building [
20
,
51
]. In a short term, the customer may react to a price change only by reducing
electricity consumption or shifting this consumption to off-peak periods [3,20].
The methods of determining price elasticity of demand also differ in terms of the applied model
of energy demand and the customer’s response to price changes. The basic models are the Quadratic
Benefit Function [
1
,
53
] and power, exponential, and logarithmic models [
54
], which present the
customer’s response to price changes in real time. However, these models have been extended
using double logarithmic forms [
19
,
20
] or log-linear models [
52
], making the demand for electricity
dependent on its price, the household’s income, and socio-economic factors, such as household size,
age, or number of the inhabitants. Furthermore, the energy demand can also be modeled through the
Generalised Leontief (GL) system [37] or using neural networks [48].
Energies 2019,12, 4317 5 of 22
Due to complex load models used in various studies, it is necessary to use sophisticated methods
of econometric estimation to determine the price elasticity of demand. In [
17
], the OLS (Ordinary
Least Squares) method is used, in [
19
,
20
], the LSDV (Least Squares Dummy Variable) and LSDVC
(Least Squares Dummy Variable Corrected) approaches are used, in [
42
], the methods of robust
statistics (robust regression) is adopted, [
33
] proposes two specifications: FE (Fixed Effects) and
RE (Random Effects) models, while in [
16
] the author confronts the OLS, FE, and LSDVC methods.
In addition, the improved AIC (Akaike’s Information Criterion) can be used to find the most appropriate
specifications in the load models under consideration [
52
]. Furthermore, when using the panel data,
it is possible to use the PMG (Pooled Mean Group) method to determine price elasticity of demand [
21
].
A different approach to the estimation of results is presented in [
37
], where the ITSUR (Iterated
Seemingly Unrelated Regression) method is used. An alternative methodology to assess consumer
elasticity for price incentives was proposed in [
55
], assuming that the average elasticity values are
burdened with a very large error, so the probabilistic Quantile Regression (QR) method can be used to
model human behavior more appropriately.
3. Data and Methods Used for Price Elasticity of Demand Determination
To reach the aim of the study the data reflecting the conditions of demand side response in
one of Polish distribution system operators’ area supplying above two millions of customers was
used. Beyond the prices of energy and distribution services in the chosen area in the years 2016 and
2017, crucial were average annual electricity consumptions and the average load profiles with hourly
resolution. Details concerning the applied method for price elasticity of demand determination and
the data used are presented in the following subsections. The detailed list of symbols used for the
method of price elasticity of demand determination is presented in Table A1 in Appendix A.
3.1. Demand Side Management Using Zonal Electricity Tariffs
Demand control programs applying zonal tariffs are widely used in Poland. The set of tariffs
available to the customer depends on the voltage level to which the customer is connected and the
contracted capacity of the customer. DSOs in Poland offer the possibility of settling their services in
accordance with the following tariffs:
•From flat tariffA21 to four zone tariffA24 for HV (110 kV) connected customers;
•
From single-zone tariffs B11 and B21 to three-zone tariffB23 for medium voltage
connected customers;
•
From single-zone tariffs C11 and C21 to three-zone tariffC23 for commercial and industrial
customers, and from single-zone tariffG11 to three-zone tariffG13 for residential customers
connected to low voltage grid. Residential customers’ tariffs considered later are related to as Gxx
tariffs in general, where “xx” stands for its digital designation being “11” for flat tariffand “12”
for TOU tariff, whichever is appropriate.
The number of price zones in the distribution tariffis determined by the last digit in the tariff
symbol and varies between 1 for flat tariffs to a maximum of 4 for TOU tariffs in the case of Poland.
The first digit in the tariffsymbol (1 or 2) stands for the contracted capacity of the customer and means
the customer up to 40 kW of ordered power (number 1) or over 40 kW of ordered power (number 2).
The duration periods of individual zones are also approved in the tariffs of DSOs and are generally
correlated with peak load periods in winter, and they are shifted to corresponding peak periods in
other seasons of the year, but only for customers connected at high and medium voltage levels. Energy
suppliers use their own tariffs, which are compatible in terms of duration of time zones with the offer
of DSOs for the case of residential customers.
The amount of energy supplied within zonal tariffs accounted for 64% of total electricity
consumption in Poland in 2016 and for 65% in 2017 [
56
]. These values indicate a significant influence
of tariffdemand side management on the power system load curve.
Energies 2019,12, 4317 6 of 22
Figure 1presents a comparison of the percentage share of electricity settlements in zonal tariffs in
terms of energy supply and distribution service in Poland for the years 2016 and 2017 [
56
]. It can be
concluded that zonal settlements dominate at higher voltage levels for tariffgroups B and A reaching
85% in distribution agreements. At the low voltage level in supply and distribution service contracts
of industrial and commercial customers, this share drops to 45–56%, while at the low voltage level for
households it reaches only 21–22%.
Energies 2019, 12, x FOR PEER REVIEW 6 of 24
contracted capacity of the customer. DSOs in Poland offer the possibility of settling their services in
accordance with the following tariffs:
• From flat tariff A21 to four zone tariff A24 for HV (110 kV) connected customers;
• From single-zone tariffs B11 and B21 to three-zone tariff B23 for medium voltage connected
customers;
• From single-zone tariffs C11 and C21 to three-zone tariff C23 for commercial and industrial
customers, and from single-zone tariff G11 to three-zone tariff G13 for residential customers
connected to low voltage grid. Residential customers’ tariffs considered later are related to as
Gxx tariffs in general, where “xx” stands for its digital designation being “11” for flat tariff and
“12” for TOU tariff, whichever is appropriate.
The number of price zones in the distribution tariff is determined by the last digit in the tariff
symbol and varies between 1 for flat tariffs to a maximum of 4 for TOU tariffs in the case of Poland.
The first digit in the tariff symbol (1 or 2) stands for the contracted capacity of the customer and
means the customer up to 40 kW of ordered power (number 1) or over 40 kW of ordered power
(number 2). The duration periods of individual zones are also approved in the tariffs of DSOs and
are generally correlated with peak load periods in winter, and they are shifted to corresponding peak
periods in other seasons of the year, but only for customers connected at high and medium voltage
levels. Energy suppliers use their own tariffs, which are compatible in terms of duration of time zones
with the offer of DSOs for the case of residential customers.
The amount of energy supplied within zonal tariffs accounted for 64% of total electricity
consumption in Poland in 2016 and for 65% in 2017 [56]. These values indicate a significant influence
of tariff demand side management on the power system load curve.
Figure 1 presents a comparison of the percentage share of electricity settlements in zonal tariffs
in terms of energy supply and distribution service in Poland for the years 2016 and 2017 [56]. It can
be concluded that zonal settlements dominate at higher voltage levels for tariff groups B and A
reaching 85% in distribution agreements. At the low voltage level in supply and distribution service
contracts of industrial and commercial customers, this share drops to 45–56%, while at the low
voltage level for households it reaches only 21–22%.
Figure 1. Shares of energy supply and distribution service under zonal contracts in Poland for
individual tariff groups in 2016 and 2017.
Figure 1.
Shares of energy supply and distribution service under zonal contracts in Poland for individual
tariffgroups in 2016 and 2017.
The energy consumption in the G tariffgroup subject to demand management using zonal tariffs
reaches over 6000 GWh, which is over 20% of the total energy supplied to this group of customers.
The development of smart metering systems creates new opportunities for this group of customers who,
knowing their own hourly consumption profiles, can make rational choices regarding participation
in the offered tariffdemand response programs. On the other hand, energy suppliers and network
operators may be interested in designing tariffs for this group of customers, which will allow for
limiting the costs of energy supply and decreasing expenditures necessary for technical infrastructure
construction enabling such supplies. In order to effectively create such tariffs, it is essential to know the
price elasticity of demand of residential consumers using zonal settlement for electricity consumption.
3.2. Load Profiles of Households Using Flat and TOU Tariffs
The introduction of the electricity market resulted in the need to settle purchases of wholesale
energy suppliers in hourly periods. Due to the small availability of smart metering systems allowing
to obtain such hourly data of consumers’ electricity consumption in households, which is necessary
to settle electricity suppliers on the market, hourly consumption levels are determined by applying
standard load profiles (Supplementary Materials) for individual tariffgroups. Standard load profiles
illustrate the replacement profile characterizing the average consumption profile of a given customers’
group for a given area settled for electricity in accordance with a specific tariffplan and are determined
on the basis of measurements of a group of 500 customers settled according to a given tariffin Poland.
Profiles have the form of data sets for individual Gxx tariffs, containing the values of relative energy
consumption H
Gxxi
in the i
th
hour of the year of a representative customer expressed in relation to its
annual consumption EaGxx.
Energies 2019,12, 4317 7 of 22
Standard load profiles are published by DSOs for their operation areas and are an approximation
of the electricity consumption profiles of consumer groups settled according to various tariffs. In the
future, when the smart metering devices in households become widespread, the load profiles can be
obtained by aggregating and averaging the loads of individual customers settled according to the
same tariffand they can then be considered as accurate. At present, familiarity with the course of
the standard load profiles may form the basis for energy purchases for this group of customers by
retailers and for the implementation of demand response programs in order to avoid overloading
power system infrastructure components during peak loads and energy purchases during periods of
high market prices.
In this paper, standard load profiles for residential customers using flat and TOU tariffs were
used as a basis for a practical assessment of the effectiveness of the already implemented demand
response tariffprograms and for determination of price elasticity of demand of customer groups settled
according to their conditions. In the future, the presented method may be used with more accurate
profiles collected using data from smart metering systems.
The impact of dual-zone tarifffor households on changing the load profile is presented in Figure 2.
Introduction of reduced energy prices and rates of distribution fees in the off-peak zone, covering
eight hours in the night from 22:00 to 6:00 and two hours during the day between 13:00 and 15:00,
encourages consumers to consider electricity as an energy carrier for space heating purposes. In fact,
the customer deciding to settle the electricity supply according to the dual-zone tariffuses the reduction
of energy prices due to the use of electricity in the off-peak period. Due to the off-peak period during
the afternoon hours, a significant load peak may be observed during the day, which may in some cases
correspond with the peak load of the country power system.
Energies 2019, 12, x FOR PEER REVIEW 8 of 24
Figure 2. Exemplary hourly energy consumption of G11 and G12 tariffs customers on 18 January 2017
according to Enea Operator load profiles and hourly tariff prices.
The impact of dual-zone tariff for households on changing the load profile is presented in Figure
2. Introduction of reduced energy prices and rates of distribution fees in the off-peak zone, covering
eight hours in the night from 22:00 to 6:00 and two hours during the day between 13:00 and 15:00,
encourages consumers to consider electricity as an energy carrier for space heating purposes. In fact,
the customer deciding to settle the electricity supply according to the dual-zone tariff uses the
reduction of energy prices due to the use of electricity in the off-peak period. Due to the off-peak
period during the afternoon hours, a significant load peak may be observed during the day, which
may in some cases correspond with the peak load of the country power system.
3.3. Analysis of Changes in Load Profile and Yearly Consumption in Result of TOU Tariff
The purpose of introducing zonal tariffs is to use the elasticity of the demand of the customers
to induce a change in the profile of electricity consumption by customers due to the increase in off-
peak sales and its reduction in the peak periods. The price elasticity of demand, binding the change
of the settlement price for purchase and supply of energy ΔP and the following change in energy
consumption ΔE with the assumed initial price P
1
and the initial consumption E
1
is defined by the
following equation:
11
ΔΔ
P
P
/
E
E
ε= (1)
Price elasticity of demand is usually negative and the higher its absolute value is, the more
effectively demand can be controlled using the energy price and distribution fees change.
Below, the method of determining the price elasticity of the demand of customers of the dual-
zone G12 tariff group will be presented. In order to obtain data for determining the price elasticity of
demand for this group of tariff customers in households, standard load profiles for tariff groups G11
and G12 will be used. The introduced procedure for determining elasticity includes two stages:
Figure 2.
Exemplary hourly energy consumption of G11 and G12 tariffs customers on 18 January 2017
according to Enea Operator load profiles and hourly tariffprices.
3.3. Analysis of Changes in Load Profile and Yearly Consumption in Result of TOU Tariff
The purpose of introducing zonal tariffs is to use the elasticity of the demand of the customers
to induce a change in the profile of electricity consumption by customers due to the increase in
Energies 2019,12, 4317 8 of 22
off-peak sales and its reduction in the peak periods. The price elasticity of demand, binding the change
of the settlement price for purchase and supply of energy
∆
Pand the following change in energy
consumption
∆
Ewith the assumed initial price P
1
and the initial consumption E
1
is defined by the
following equation:
ε=∆E
E1
/∆P
P1
(1)
Price elasticity of demand is usually negative and the higher its absolute value is, the more
effectively demand can be controlled using the energy price and distribution fees change.
Below, the method of determining the price elasticity of the demand of customers of the dual-zone
G12 tariffgroup will be presented. In order to obtain data for determining the price elasticity of
demand for this group of tariffcustomers in households, standard load profiles for tariffgroups G11
and G12 will be used. The introduced procedure for determining elasticity includes two stages:
•
Determining, based on the analysis of load profiles, the changes in annual energy consumption
in tariffprice zones when transitioning from G11 to G12 tariff; for this purpose we set, for the
G12 customer with the assumed annual consumption of the output energy, the value of energy,
which was consumed under G11 tariffbefore his/her decision to change the tariff;
•Determining the average elasticity of the G12 customer for the annual period.
Therefore, the determined elasticity values concern a customer choosing G12 tariffwith
the intention of increasing the consumption in the off-peak zone in consequence of purchasing
energy-consuming appliances to be utilized in that zone, such as electric heaters. The remaining
electricity demand stays approximately unchanged with the exception of shifting some appliances to
the off-peak to generate savings.
Figure 3presents levels of daily energy consumption in the course of a year for representative
consumers settled for electricity in G11 and G12 tariffs divided into consumption in peak and off-peak
settlement periods of the G12 tariffmarked in Figure 2. Energy consumption settled in G11 tariff
reflects a natural satisfaction of the customer’s needs within a day. In the case of settlements in the G12
tariff, the consumer tries to shift consumption from peak to off-peak periods in order to obtain lower
costs of electricity use. Analysis of the energy consumption ratio of a representative customer settled
according to G11 tariffand consumption of a representative customer settled according to G12 tariffin
a year allows for determining the impact of prices on the behavior of customers settled according to
zonal tariffs expressed by the concept of price elasticity of demand.
On the basis of the presented graphs, it can be stated that the energy consumption is significantly
higher in off-peak periods (o) of the G12 zonal tariffcustomers in relation to the G11 flat tariffcustomers.
In addition, a greater use of energy in peak periods (p) outside the heating season by customers of
the G11 group may be observed. During the heating season, an increasing use of energy in the peak
period in the G12 profile in relation to the G11 profile is noted for the periods of short winter days
in which low outside temperatures are usually encountered. In order to describe these observation
quantitatively, the following assumptions were made:
a.
The starting days D
s
and the ending days D
e
of the non-heating season are the days designated
as points of intersection of the downward trend line of off-peak energy consumption E
aG12o
in the
spring season and the increase in off-peak energy consumption E
aG12o
in autumn with the average
off-peak electricity consumption E
aG12o
beyond the heating season, which is approximately
constant value;
b.
In the non-heating season, the reduction of energy consumption in the peak zone of G12 tariff
consumers in relation to consumption of G11 tariffconsumers is offset by the increase in G12
consumption in relation to G11 consumers in the off-peak zone—this phenomenon is caused by
the transfer of household appliances use by G12 tariffconsumers to the off-peak zone and occurs
uniformly to the same extent on all days of the year;
Energies 2019,12, 4317 9 of 22
c.
The main increase in the load of consumers in the G12 tariffin relation to the G11 tariffis the
increase caused by the use of electricity for residential space heating purposes in the off-peak
zone during the heating season;
d.
During the heating season in the G12 tariff, a slight increase in energy use for heating purposes
may be noted also during the peak period, which offsets to a certain extent the transfer of
household appliances usage to the off-peak zone during this period—this is due to the occurrence
of cold days and, at the same time, the possible use of already installed easily accessible sources
of additional heat using electricity during peak periods of the G12 tariff.
Energies 2019, 12, x FOR PEER REVIEW 10 of 24
Figure 3. The levels of daily electricity consumption broken down by tariff and peak/off-peak zone,
for the G12 tariff consumer with an annual consumption of 2526 kWh (based on statistical data [56])
and for the G11 tariff consumer with annual consumption of 2236 kWh (resulting from Equation (3)),
according to the standard load profiles of the Enea Operator distribution system operator (DSO) from
2017.
An exemplary analysis of the electricity consumption trend line in the off-peak zone of G12
customers for 2017 profiles allows for setting the beginning of the non-heating season at D
s
= 125
th
day of the year, i.e., 5 May 2017. Analogical analysis for the consumption increase in G12 off-peak
period for heating in the autumn–winter period allows to determine the end of the non-heating
season at D
e
= 265
th
day of the year, i.e., 22 September 2017.
The annual energy consumption of the G11 tariff consumer is assumed at E
aG11
level and the
consumption of the G12 tariff consumer at E
aG12
level. Based on the analysis of standard load profiles
for these tariff groups in the non-heating season, on the example of 2017 shown in Figure 3, using the
assumption (b) presented above, an equation can be formulated to determine the relation of annual
E
aG12
consumption of a representative G12 tariff consumer and annual E
aG11
consumption of a
representative G11 tariff consumer. The shift in energy consumption of G12 customers in this period
is due to their transition from settlements according to G11 tariff to settlements according to G12 tariff
and the use of reduced prices in the off-peak zone in the non-heating season for the operation of
household appliances, mainly between 13:00 and 15:00. G11 consumers should have greater
consumption of electricity in the peak period of the non-heating season differing by the same amount
in relation to the consumption of G12 consumers during this period. To fulfill the above-mentioned
assumption, the difference between energy consumption in the peak period of G11 tariff (E
aG11p
) and
G12 tariff (E
aG12p
) should be equal to the difference between energy consumption in the off-peak
period of G12 (E
aG12o
) and G11 tariff (E
aG11o
), which may be described with a following Equation (2):
11 11 12 12 12 12 11 11
ee ee
ss ss
DD DD
aG G i aG G i aG G i aG G i
D p D p Do Do
EHEHEHEH−=−
(2)
where: D
s
, D
e
indicate the beginning and the end of the non-heating period, p means the peak
period, o indicates the off-peak period, H
Gxxi
means i
th
relative hourly energy consumption values for
the considered profiles of standard tariff groups Gxx in relation to total annual electricity
consumption E
aGxx
.
Figure 3.
The levels of daily electricity consumption broken down by tariffand peak/off-peak zone,
for the G12 tariffconsumer with an annual consumption of 2526 kWh (based on statistical data [
56
])
and for the G11 tariffconsumer with annual consumption of 2236 kWh (resulting from Equation
(3)), according to the standard load profiles of the Enea Operator distribution system operator (DSO)
from 2017.
An exemplary analysis of the electricity consumption trend line in the off-peak zone of G12
customers for 2017 profiles allows for setting the beginning of the non-heating season at D
s
=125
th
day
of the year, i.e., 5 May 2017. Analogical analysis for the consumption increase in G12 off-peak period
for heating in the autumn–winter period allows to determine the end of the non-heating season at
De=265th day of the year, i.e., 22 September 2017.
The annual energy consumption of the G11 tariffconsumer is assumed at E
aG11
level and the
consumption of the G12 tariffconsumer at E
aG12
level. Based on the analysis of standard load profiles
for these tariffgroups in the non-heating season, on the example of 2017 shown in Figure 3, using the
assumption (b) presented above, an equation can be formulated to determine the relation of annual E
aG12
consumption of a representative G12 tariffconsumer and annual E
aG11
consumption of a representative
G11 tariffconsumer. The shift in energy consumption of G12 customers in this period is due to their
transition from settlements according to G11 tariffto settlements according to G12 tariffand the use of
reduced prices in the off-peak zone in the non-heating season for the operation of household appliances,
mainly between 13:00 and 15:00. G11 consumers should have greater consumption of electricity in the
peak period of the non-heating season differing by the same amount in relation to the consumption of
G12 consumers during this period. To fulfill the above-mentioned assumption, the difference between
energy consumption in the peak period of G11 tariff(E
aG11p
) and G12 tariff(E
aG12p
) should be equal
Energies 2019,12, 4317 10 of 22
to the difference between energy consumption in the off-peak period of G12 (E
aG12o
) and G11 tariff
(EaG11o), which may be described with a following Equation (2):
EaG11
De
X
DsX
p
HG11i−EaG12
De
X
DsX
p
HG12i=EaG12
De
X
DsX
o
HG12i−EaG11
De
X
DsX
o
HG11i(2)
where: D
s
,D
e
indicate the beginning and the end of the non-heating period, pmeans the peak period,
oindicates the off-peak period, H
Gxxi
means i
th
relative hourly energy consumption values for the
considered profiles of standard tariffgroups Gxx in relation to total annual electricity consumption E
aGxx
.
Having performed the mathematical transformations of Equation (2) defined above, the annual
energy consumption of a representative G11 tariffconsumer before their transition to G12 tariffcan be
calculated as follows:
EaG11 =EaG12
(PDe
DsPoHG12i+PDe
DsPpHG12i)
(PDe
DsPoHG11i+PDe
DsPpHG11i)(3)
Equation (3) allows to determine the mutual relation between annual energy consumption of
a representative consumers of considered tariffsystems in the result of a decision to change the tariff
settlement from one-zone to double-zone tariff, taking into account the load profiles data published
by the DSOs. In particular, based on this relation, the annual equivalent energy consumption of
G11 consumers with a given level of annual consumption in the G12 tariffmay be determined,
which reflects changes in the manner and purposes of electricity use of those consumers settled
for electricity according to particular tariffs following the load consumptions patterns given by the
considered standard load profiles. This mutual relation is graphically shown in Figure 3where the
consumption level of G12 customer is assumed to be average annual electricity consumption for G12
consumers based on statistical data [
56
], the G11 annual consumption level reflects the consumption
of considered representative G12 customer before the change of energy use settlement to G12 tariff
calculated using Equation (3) while the shapes of electricity consumption profiles for both tariffs are
based on the standard load profiles.
The determined annual energy consumption of G11 tariffconsumer group E
aG11
corresponding to
its electricity consumption in the G12 tariffE
aG12
after changing its energy settlement from tariffG11 to
G12 allows to calculate the average price elasticity of demand significant for energy suppliers in terms
of increased consumption in the long term due to average price reduction for the G12 tarifftaking into
account the energy consumption shift from peak to off-peak periods influencing the final settlement
for energy use. The methodology for determining the above-mentioned price elasticity of demand is
presented below.
3.4. Average Price Elasticity of Demand Calculation for TOU Customers
The method of establishing the mutual relation of annual electricity consumption of the consumer
changing the settlement from G11 to G12 allows also to determine the average daily load shift
∆
E
dp→o
of
household appliances to the off-peak period by the TOU tariffconsumers. This value can be calculated
based on the difference in energy consumption in the non-heating season in tariffs G12 and G11 for
certain annual electricity consumption values E
aG11
and E
aG12
, taking into account the number of days
of the non-heating season, according to the equation:
∆Edp→o=EaG11PDe
DsPpHG11i−EaG12PDe
DsPpHG12i
De−Ds+1(4)
It is assumed that G12 tariffcustomers make such an average shift on each day of the year.
Multiplying the value obtained from the Equation (4) by the number of days in the year D
a
, a total load
shift from the peak zone to the off-peak zone of household appliances
∆
E
pdoo
, when using the G12
tariff, may be obtained according to the formula:
Energies 2019,12, 4317 11 of 22
∆Epdoo =∆Edp→o·Da(5)
In order to determine the additional energy consumed by G12 customers for heating purposes in
the off-peak period
∆
E
oheatG12
, the off-peak energy consumption in the corresponding period for the
single-zone tariffE
aG11o
should be subtracted from the energy consumption in the TOU tariffE
aG12o
according to the Equation (6). The value obtained from the subtraction of hourly profiles should be
reduced by the increased daily off-peak consumption summed for each day of this season, as a result
of shifting part of the household appliances consumption for each day of this season specified by
Equation (4). Equation (7) may be used to determine the off-peak annual consumption of G12 and G11
tariff, respectively, EaG12o and EaG11o :
∆EoheatG12 = (EaG12o−EaG11o)−(De+Da−Ds+1)·∆Edp→o(6)
EaGxxo =EaGxx ·(
Ds−1
X
1X
o
HGxxi +
Da
X
De+1X
o
HGxxi)(7)
Additionally, slight increase in energy consumption observed in peak periods of the heating
season in Figure 3for G12 tariffcustomers should be included in the analysis. Presumably, it results
from the use of available heating devices on particularly cold winter days. Thus, the additional energy
consumption will be determined as the difference in energy consumption in the peak period E
aG12p
and the energy consumption in the same period for the flat tariffE
aG11p
. The value obtained from the
subtraction of hourly profiles should be increased by the reduced daily peak consumption for the G12
tariffsummed for the heating season days due to the household appliances induced consumption shift
to off-peak zone determined by (4), which leads to the following relationships:
∆EpheatG12 = (EaG12p−EaG11p) + (Ds+Da−De+1)·∆Edp→o(8)
EaGxxp =EaGxx ·(
Ds−1
X
1X
p
HGxxi +
Da
X
De+1X
p
HGxxi)(9)
Equation (9) may be used to determine the peak annual consumption of G12 and G11 tariff
consumers EaG12p and EaG11p, respectively.
Calculated components of electricity usage that differentiate its consumption between consumers
settled in accordance with G12 and G11 tariffallow to determine the annual average price elasticity
of demand based on Equation (1). The initial values are energy consumption in G11 tariffequal to
E
aG11
and the price of electricity together with its distribution services P
G11
, including fixed fees as
well. This price may be calculated as follows:
PG11 =CEG11 +SvarG11 +Sq+OPG11
EaG11
, (10)
where: C
EG11
is the unit price of energy in flat tariff,S
varG11
is the variable rate of distribution fee for
flat tariff,S
q
is the variable quality rate, uniform for all tariffs, and O
PG11
stands for the sum of fixed
fees in the flat tariff. The first three components of the price P
G11
(10) form the variable part P
vG11
of
the energy price together with its distribution services.
In the case of a double-zone settlement, the total price depends on the average settlement price
P
avG12
for both zones resulting from the amount of energy consumed in particular zones in the
considered calculation period and electricity prices with distribution rates applicable in these zones:
PavG12 =(CEG12p+SvarG12p)·EaG12p+ (CEG12o+SvarG12o)·EaG12o
EaG12p+EaG12o
+Sq+OPG12
EaG12p+EaG12o
, (11)
Energies 2019,12, 4317 12 of 22
where: C
EG12p
,C
EG12o
are unit energy prices in the double-zone tariff: Peak and off-peak; S
varG12p
,
S
varG12o
are the variable rates of peak and off-peak distribution fees for a double-zone tariff;O
PG12
stands for the sum of fixed fees charged in the double-zone tariff;E
aG12p
,E
aG12o
are energy consumption
values during the peak and off-peak periods in the dual-zone tariff,E
aG12
=E
aG12p
+E
aG12o
. The first
two components of the G12 tariffprice (11) form the variable part P
vG12
of the energy price together
with its distribution services.
The changes in the average price P
avG12
are affected by changes in energy consumption value in
particular zones resulting in its increase in the TOU tariffand the energy consumption shift between
zones. The increase in energy consumption value after transferring the settlement to the G12 tariff
∆EG11→G12 can be determined on the basis of the following equation
∆EG11→G12 =∆EoheatG12 +∆EpheatG12 (12)
The shift of household appliances use from the G11 peak zone to the off-peak G12 will not affect
the total increase in energy consumption, because such consumption exists in both tariffs.
Finally, the annual price elasticity of demand of G12 tariffconsumers
εa av
can be determined
using the following relationship:
εa av =∆EG11→G12
EaG11
/PavG12 −PG11
PG11
(13)
All components of the Equation (13) may be determined by summing hourly energy consumption
determined according the standard load profiles for G12 and G11 tariffs, while maintaining the relation
of annual energy consumption between G12 and G11 determined in accordance with relationship (3).
Knowledge of the price elasticity of demand is very important due to the anticipated effects of the
introduction of zonal tariffs. The change in energy consumption
∆
Eas a result of the introduction
of the two-zone tariffcan be forecasted using the equation derived from the transformation of the
Equation (13) to the form:
∆EG11→G12 =εa av ·EaG11 ·PavG12 −PG11
PG11
(14)
Based on this relationship, an appropriate price change may be designed to stimulate desirable
changes in energy consumption.
4. Calculation Results—Case Study of Average Annual Price Elasticity of Demand for Sample
Distribution System Area in Poland
Based on the presented model, a case-study of price elasticity of demand calculation was performed
for the residential consumers located in the area of one of Polish DSOs. To determine the average
price elasticity of demand for individual years, the following data was used: Load profiles of one
of Polish DSOs (Enea Operator Sp. z o.o.) for tariffgroups G11 and G12 for the years 2016 [
57
] and
2017 [
58
], and tariffprices for one of Polish electricity suppliers (Enea S.A.) [
59
,
60
], as well as rates
for distribution services for Enea Operator [
61
,
62
]. Tariffprices for considered years are presented in
Table 2for the years 2016 and 2017. The values of the average annual price elasticity of demand were
determined based on the aforementioned data and Equations (2)–(13) presented in Section 4.
The average annual consumption of the G12 consumer for the considered DSO’s operation area is
assumed at a level presented in the first row of Table 3, for the years 2016 and 2017, and it equals 2687
and 2526 kWh/c/a, respectively, based on the data presented in [56].
For the considered consumption levels, the customer’s total annual payments for the use of
electricity depends on a variable rate in the range of 85% to 90% with the greater influence of fixed
rate in 2017 rather than in 2016. Higher fixed rate in G12 tariffcreates a threshold for the feasibility of
entering zonal settlements to be overcome by higher yearly consumptions.
Energies 2019,12, 4317 13 of 22
Table 2.
Fixed and variable components of costs incurred by customers related to the supply of
electricity by Enea S.A. and Enea Operator Sp. z o.o. in 2016 and 2017.
Year Tariff
Variable Rate Fixed Rate
PLN/kWh PLN/a
Peak Off-peak
2016 G11 0.4295 119.40
G12 0.5140 0.2208 145.92
2017 G11 0.4198 155.88
G12 0.5023 0.2166 182.40
Using the model for price elasticity of demand determination and specifically the Equations
(2)–(13), a case study of average annual elasticity values was carried out. The specific calculation
results are presented as subsequent calculation steps in Table 3.
Based on the calculation results, a load balance may be settled for the peak and off-peak TOU G12
tariffconsumption. These balances may be formulated as follows, for the peak and off-peak period:
EaG12p=EaG11p+∆EpheatG12 −∆Epdoo (15)
EaG12o=EaG11o+∆EoheatG12 +∆Epdoo (16)
It should be noted that the value of the average annual price elasticity of demand is determined for
a given shape of the energy consumption profiles in G11 and G12 tariffs. On the other hand, settlement
prices for electricity use in accordance with the aforementioned tariffs are unchanged as to the value of
variable components (independent of the amount of energy consumed) and change with the amount of
energy consumed as a result of settling the fixed component for different consumption values of annual
energy. Thus, unit prices are not constant for customers having different annual energy consumptions,
but slightly decrease with increasing energy consumed to a limit equal to the sum of variable rates
at very high energy consumption. The simple relationship (13), used to demonstrate the introduced
methodology of elasticity calculation, can be transformed into more complex one after substituting
cost of energy usage P
G11
and P
avG12
with their formulas containing fixed tariffrates O
PG11
and O
PG12
and variable tariffrates P
vG11
,P
vpG12
, and P
voG12
in (13) in order to illustrate their influence on elasticity.
The elasticity values thus change along with the change in the consumer’s annual energy consumption
according to the following equation:
ε= EaG12
EaG11
−1!/
β+OPG12
EaG12
PvG11 +OPG11
EaG11
−1
, (17)
where the ratio of E
aG12
/E
aG11
is possible to be determined from standard load profiles using the Equation
(3), whereas the
β
constant is introduced only to clarify the calculation process and entails multiplication
product of variable overall peak electricity price P
vpG12
and the sum of hourly consumption values
for peak period for all days of the year D
a
and multiplication product of variable overall off-peak
electricity price P
voG12
and the sum of hourly consumption values for off-peak period for the days D
a
:
β=PvpG12 ·
Da
X
1X
p
HG12i+PvoG12 ·
Da
X
1X
o
HG12i(18)
The decrease of unit electricity prices with the increase in energy annual consumption for the
adopted, constant in shape, standard load profiles results in the decrease of the average annual value
of the price elasticity of demand for the greater annual customer energy use as shown in Figure 4.
Energies 2019,12, 4317 14 of 22
Table 3.
Results of the particular calculation procedure steps and final results of the average annual
price elasticity of demand calculations for 2016 and 2017.
Year 2016 2017
1
EaG12—total consumption [kWh]—based on statistical data [56]
2687 2526
2
EaG11—total consumption [kWh]—based on Equation (3)
2389 2236
3
PG11—G11 tariffprice [PLN/kWh]—based on Equation (10) and Table 2
0.4795 0.4895
4
∆Epdoo—household appliances shift [kWh]—based on Equations (4) and (5)
peak off-peak peak off-peak
−90.894 90.894 −97.008 97.008
5
∆EoheatG12—off-peak heating [kWh]—based on Equation (6)
224.549 222.085
6
∆EpheatG12—peak heating [kWh]—based on Equation (8)
73.447 68.575
7
EaG12—total consumption [kWh]—based on Equations (15) and (16)
peak off-peak peak off-peak
1616.274 1074.619 1491.668 1034.412
8
PavG12—G12 average price [PLN/kWh]—based on Equation (11)
0.4510 0.4575
9
εa av
—G12 consumer’s average annual price elasticity [-]—based on Equation (13)
−2.103 −1.988
Energies 2019, 12, x FOR PEER REVIEW 15 of 24
into more complex one after substituting cost of energy usage P
G11
and P
avG12
with their formulas
containing fixed tariff rates O
PG11
and O
PG12
and variable tariff rates P
vG11
, P
vpG12
, and P
voG12
in (13) in
order to illustrate their influence on elasticity. The elasticity values thus change along with the change
in the consumer's annual energy consumption according to the following equation:
−
+
+
−= 1/1
11
11
11
12
12
11
12
aG
PG
vG
aG
PG
aG
aG
E
O
P
E
O
E
E
β
ε
,
(17)
where the ratio of E
aG12
/E
aG11
is possible to be determined from standard load profiles using the
Equation (3), whereas the β constant is introduced only to clarify the calculation process and entails
multiplication product of variable overall peak electricity price P
vpG12
and the sum of hourly
consumption values for peak period for all days of the year D
a
and multiplication product of variable
overall off-peak electricity price P
voG12
and the sum of hourly consumption values for off-peak period
for the days D
a
:
12 12 12 12
11
aa
DD
vpG G i voG G i
po
PHPH
β
=⋅ +⋅
(18)
The decrease of unit electricity prices with the increase in energy annual consumption for the
adopted, constant in shape, standard load profiles results in the decrease of the average annual value
of the price elasticity of demand for the greater annual customer energy use as shown in Figure 4.
Figure 4. Variability of the average price elasticity of the demand of the G12 time-of-use (TOU) tariff
customers depending on the annual energy consumed.
5. Results Concerning Residential Zonal Tariffs’ Efficiency
The main function of zonal tariff is the reduction of energy consumption during the peak zone
and the following increase in energy consumption during the off-peak zone. The desired effect can
be obtained by shifting energy consumption from the peak prices period to off-peak prices period
and by increasing energy use during the off-peak hours. Therefore, the energy efficiency of the zonal
tariffs’ operation can be assessed taking into account the desired effects in the form of increases or
Figure 4.
Variability of the average price elasticity of the demand of the G12 time-of-use (TOU) tariff
customers depending on the annual energy consumed.
5. Results Concerning Residential Zonal Tariffs’ Efficiency
The main function of zonal tariffis the reduction of energy consumption during the peak zone
and the following increase in energy consumption during the off-peak zone. The desired effect can be
obtained by shifting energy consumption from the peak prices period to off-peak prices period and by
increasing energy use during the off-peak hours. Therefore, the energy efficiency of the zonal tariffs’
Energies 2019,12, 4317 15 of 22
operation can be assessed taking into account the desired effects in the form of increases or limitations
of energy consumption during G12 tariffzones in relation to energy consumption in corresponding
periods in the flat tariff.
The assessment of the annual impact of the G12 tariffcomposed of two price zones is important
especially for energy suppliers and network operators in the aspect of shifting the load from peak
periods, when the network devices are overloaded and high energy prices occur in the market, to the
load valley, when lower prices and significantly lower loads are encountered. According to the
results of the calculations presented in Table 3, for each zone, the following efficiency coefficients can
be proposed:
•Energetic efficiency of the peak zone:
EFp%=100 ·
EaG12p−EaG11p
EaG11p
=100 ·
∆EpheatG12 −∆Epdoo
EaG11p
; (19)
•Energetic efficiency of the off-peak zone:
EFo%=100 ·EaG12o−EaG11o
EaG11o
=100 ·
∆EoheatG12 +∆Epdoo
EaG11o
. (20)
Using zonal efficiencies, the suppliers can determine possible savings in energy volumes to be
purchased in the peak zone and additional quantities necessary to be acquired in the off-peak zone to
cover energy consumption of consumer group settled according to the G12 tariffafter the change of
settlements from G11 tariff.
Zonal efficiencies defined above allow for the proposition of the annual average energy efficiency
calculation of the zonal tariff, using the following Equation (21):
EFenG12% =100 ·
∆Eo−∆Ep
EaG11 =EFo%EaG11o
EaG11
−EFp%
EaG11p
EaG11 =
=100 ·
∆EoheatG12+∆Epdoo +∆Epdoo −∆EpheatG12
EaG11
(21)
The definition of annual average energy efficiency proposed above, being a function of zonal
efficiencies, reflects the correct functionality of the zonal tariffand is the result of the total energy
savings made in the peak zone and the increase in consumption in the off-peak zone in relation to
energy consumptions in the same periods in G11 tariff.
Zonal efficiencies allow also to determine changes in tariffrevenues of energy suppliers and of
network operators, as well as in costs incurred by customers as a result of changing the tariffsettlement
from G11 to G12. Changes in these cash flows can be determined using the prices of energy with its
distribution service P
G11
for the G11 tariffgiven by the Equation (10) and zonal peak and off-peak
prices of energy with the distribution service P
G12p
and P
G12o
for the G12 tariff, which can be as well
determined using the Equation (10) by substituting in it the relevant variable charges for each zone
from Table 4and adding the fixed charges in G12 given in this table divided by E
aG12
. The determined
values of zonal tariffprices and zonal energy efficiencies allow to calculate the financial cash flow
increment of zonal tariffin result of increased customer payments using the following relationship:
EFc f %=100 ·
∆CFG12
CFG11
=EFo%·EaG11o·PG12o−EFp%·EaG11p·PG12p
EaG11 ·PG11
(22)
The increase in payments by consumers in G12 tariffin relation to the previously used G11,
given by the above equation, is usually positive because energy savings in the peak zone may not
balance larger energy purchases in the off-peak period, usually consumed for heating purposes.
Energies 2019,12, 4317 16 of 22
The best measure of G12 tariffefficiency for the customers may be the average unit cost of
using electricity, satisfying their energy need in relation to the equivalent unit cost under G11
tariff. Such indicator, describing electricity price reduction, can be determined using the following
relationship:
EFf cust%=100 ·PavG12
PG11
=(EFp%+100)·EaG11p·PG12p+ (EFo%+100)·EaG11o·PG12o
EaG12 ·PG11
(23)
The energy and financial efficiencies described above resulting from the changing the tarifffrom
G11 to G12 are calculated for the analyzed DSO area using values of the energy consumptions in G11
and G12 tariffgiven in Table 3, previously applied to determine the average price elasticity of the
demand of the G12 customers, and are presented as percentage values in Table 4.
Table 4. Efficiencies of G12 zonal tariffin 2016 and 2017 given by formulas (19) to (23) in [%].
Year EFp% [%] EFo% [%] EFenG12% [%] EFcf% [%] EFfcust% [%]
2016 −1.069 41.559 13.934 8.441 94.071
2017 −1.870 44.608 15.546 9.914 93.460
The results presented in Table 4indicate a much higher efficiency of the zonal tariffoperation in
the off-peak period compared to the peak period. Average annual energy efficiency, resulting from the
average of zonal efficiencies weighted by G11 tariffenergy consumptions in the peak and off-peak
periods of the G12 tariff, is around 15%.
Financial efficiency reveals the increase in revenues of energy suppliers and network operators
resulting from customers switching the tarifffrom G11 to G12 and its value does not exceed 10%.
The considered tariffswitching by customers allows them to reduce the electricity settlement price by
approximately 6%.
The Equations (21) and (22), which allow to state that the energy efficiencies values of the two-zone
tariff, depend only on the mutual relations of parameters of standard load profiles for tariffs G11 and
G12 taking into account that the relation between EaG11 and EaG12 is given by relationship (3).
The financial efficiencies, given by relationships (22) and (23), depend on the values of energy
prices together with its delivery service, which diminish with the increase of energy consumption as
a result of the influence of fixed charges. Therefore, the efficiency depends to a small extent on the
ratio of fixed charges and energy consumed under tariffs G12 and G11.
6. Discussion of the Results
The main contribution of the presented study is the new method of determining price elasticity
of electricity demand of customers of the dual-zone G12 tariffgroup. The standard load profiles
published by DSOs in Poland for the purpose of hourly settlement of energy suppliers in the wholesale
market were used to present the new methodology for determining price elasticity of demand. The key
to the analytical determination of price elasticity of the demand of customers using zonal tariffs is the
analysis of changes in their energy consumption in individual time zones in flat and TOU tariffs in
order to determine the quantitative responses to price signals. In the case of standard load profiles
applied to the tariffgroups used by households, it was possible to determine the shift of consumption
from the peak period to the off-peak period and the consumption changes in both peak and off-peak
periods. The quantitative analysis of such changes and their summation in analyzed zones forms the
basis for determining the average annual price elasticity of demand of customers using zonal tariffs.
The analyzed load profiles indicate that, in winter, contrary to the economic logic, the increases in
energy consumption in the peak zone occur as well, as the result of consumers’ behavior forced by the
current climatic conditions and easy access to electric heat sources.
Energies 2019,12, 4317 17 of 22
The results concerning the customers’ price elasticity of demand values are obtained for
representative customers using flat and two-zone tariffs. In the study, only the average consumption
and prices differentiation in tariffs’ zones were taken into account, but further studies could be
developed on this basis to analyze elasticity values for regional consumers (for instance country
or town inhabitants) but adequate data from smart metering systems are necessary to be obtained.
Such analysis could be widened on customer groups using specific appliances or heating systems,
provided the measurement data from smart metering systems, reflecting the influence of the specific
devices comparing to the customers not using them, is available. The average, rather low, level of
G12 tariffcustomer electricity consumption used in the case study, that is 2687 and 2526 kWh/c/a
for the years 2016 and 2017, respectively, indicate that they may be equipped with heating systems
fuelled by fossil fuels and may be using portable electricity heating devices occasionally during very
cold days. Simultaneously, they are trying to increase the savings in the zonal tariffby shifting the
appliances’ utilization to off-peak zone. Further differentiations concerning customer elasticity values
could be based on their average income, but in such cases additional dedicated customer survey results
should be available. It should also be noted that the price elasticity of demand values are not linear in
a wide range of price volatility [
10
], and the formula (13) is approximately accurate only for small price
changes comparing to prices used to determine the average elasticity using standard load profiles for
individual tariffs.
Average annual price elasticity of electricity demand values obtained within the study (
−
2.10 and
−
1.99 for the years 2016 and 2017, respectively) indicate a very high elasticity of residential customers
for price changes. Such high values of price elasticity of demand may only be found in a few other
studies [
19
,
20
,
35
], mostly in case of long-term price elasticity of demand. Most of the various, extensive
studies, presented in Table 1, present the price elasticity of electricity demand at a level between 0 and
−
1, indicating quite low flexibility of household consumers. However, it should be noted that values of
price elasticity of demand within the presented study are calculated for the group of customers deciding
voluntarily to change their profile of electricity utilization to reach some savings, and that group is
responsible for only about 20% of the electricity consumption generated by residential customers
in Poland.
In the presented study the influence of fixed distribution rates on price elasticity of demand
is also discussed but only in the context of their decreasing importance with the growth of annual
energy consumed. Higher fixed rates in G12 tariffcreate a threshold for the feasibility of entering
into zonal settlements to be overcome by higher yearly electricity consumptions. Some tariffs apply
significant values of fixed rates to limit their use by customers with lower electricity consumption.
The investigation of customers’ elasticities using zonal tariffwith various levels of fixed rates and similar
energy consumption supplied by different companies could result in fruitful outcomes concerning best
strategy of cost allocation into the fixed and variable rates.
Wider application of the proposed methodology can be expected in the future, when more accurate
load profiles are available for the presented analyses on the basis of data supplied from smart metering
systems, which are going to be more and more commonly used for customer billing.
The new indicators for assessing the efficiency of the tariff’s impact on the customer load profile
were also proposed in this paper. The energy indicators, determined for analyzed tariffzones, illustrate
the efficiency of the zonal tariffin fulfilling its two functions: The decrease of consumption in the
peak zone and energy shifting from peak zone to the off-peak zone, as well as the increase of energy
consumption in the off-peak zone. Zonal efficiencies of the G12 tariffare defined to indicate possible
profits from electricity consumption, shifting from the peak zone to the off-peak zone, even in the case
of zero increase in annual energy consumption, resulting in zero value of customer elasticity, and not
only from the simple balance of the increase of energy consumption in the off-peak zone and reduction
of energy consumption in the peak zone.
Energies 2019,12, 4317 18 of 22
7. Conclusions
Demand side management resources based on tariffsystems provide a stable and effective measure
to make use of a power system in a more efficient way. Tariffdemand management programs play
an important role in enabling the transformation of the load profile of electricity consumers as in
Poland about 60% of energy is supplied using zonal electricity settlements [
63
]. The real impact of tariff
programs depends on the universality of their use and on customers’ reactions to the change in the
settlement price that is the price for energy supply along with its distribution services. Determining the
price elasticity of the demand of customers using zonal tariffs is particularly important for developers
of demand management programs, whose aim is to improve the efficiency of the proposed price
differentiation within zonal tariffprograms. That is the main reason of numerous studies focused on
price elasticity determination reported within the literature review in this paper. Common methods of
demand price elasticity determination are based on historical data concerning price level development
together with their observed influence on electricity consumption level. To explore this influence,
some more or less sophisticated mathematical models are used. In the presented method for the given
tariffsystems, the customer’s decision on tariffsystem choice and the following changes in his/her
electricity utilization are explored. Customers’ load profiles comparison, reflecting the changes in
electricity consumption as a result of price offers presented by energy suppliers and DSOs, constitute
an interesting basis reflecting the current power supply conditions for determining the price elasticity
of the demand of customers responding to these offers.
The goals of this study were reached by presenting the alternative method for determination of
the price elasticity of electricity demand for residential customers using zonal tariffs, its application for
the selected distribution area in Poland, and evaluation of the efficiency of the zonal tariffinvestigated.
This creates a new tool for organizers of tariffbased demand side response programs. It is particularly
applicable to customers with rather low electricity consumption, which are usually settled using tariff
systems. The presented method allows to improve the tariffsystem for a group of customers in a steady
way, making use of the feedback based on aggregated profiles of their electricity consumption, and thus
enabling the corrections in real price elasticity evaluation of customer groups and easing the effect
of nonlinearity of its value with the electricity price change. It would be beneficial to develop such
a system in the future. As price elasticity of demand is considered nonlinear with changing prices,
the possibility to perform an ongoing determination of elasticity value of the customer group being
settled according to a considered tariff, resulting in the possibility to introduce some improvements in
its efficiency, is the new prospective for supply companies and network operators.
The proposed efficiency indicators can be used as well by regulatory authorities responsible for the
approval of electricity tariffs, considering the supply and distribution companies business’ feasibility and
customers’ possibilities to participate in power system efficient utilization with the prospective remuneration
for undertaking the effort to change their electricity consumption profile. Zonal tariffs’ financial efficiencies
reflect the win-win operation of the analyzed zonal tariff demand management program, resulting in the
increase in the program organizers’ revenues, i.e., increases in energy and distribution services sales, as well
as lowering the average price for satisfying the electricity needs of the customers.
The presented new approach towards elasticity determination should be analyzed in further
case studies verifying its usefulness in the proper design of electricity tariffs. The progress in
implementation of smart metering systems, being the source of real customer consumption profiles,
and their aggregates following the same electricity utilization pattern, create the base for the introduced
methodology exploration and more precise control of the effects of tariffdemand side response
programs implemented. Using the determined elasticity values of their customers settled according
to TOU tariffs based on the presented methodology, electricity suppliers, and distribution system
operators may easily, quantitatively, estimate the influence of TOU customers on the power system.
Supplementary Materials:
The following are available online at http://www.mdpi.com/1996-1073/12/22/4317/s1,
Table S1: Standard load profiles for 2016, Table S2: Standard load profiles for 2017.
Energies 2019,12, 4317 19 of 22
Author Contributions:
Conceptualization, J.A. and A.W.; methodology, J.A.; validation, J.L.; formal analysis, A.W.;
investigation, A.W.; writing—original draft preparation, A.W.; writing—review and editing, J.A.; supervision, J.L.;
project administration, J.A.; funding acquisition, J.L.
Funding:
This research was funded by the Institute of Electric Power Engineering of Poznan University of
Technology, grant number 04/41/DSPB/4337.
Conflicts of Interest: The authors declare no conflict of interest.
Appendix A
Table A1. List of symbols used for the proposed price elasticity of demand determination method.
Symbol Unit Explanation
o- Index related to the off-peak period
p- Index related to the peak period
βPLN/kWh Constant introduced to clarify the calculation process
CEG11 PLN/kWh Unit electric energy price in G11 tariff
CEG12p, CEG 12oPLN/kWh Unit electric energy price in peak and off-peak periods of G12 tariff
∆CFG12 PLN
Annual income growth for the supplier and the DSO due to customer tariffchange from G11 into G12
CFG11 PLN Annual income of the supplier and the DSO from customer using the G11 tariff
Da- Number of days in the year
Ds,De- Starting and ending day of the non-heating season
∆EkWh Change in annual electricity consumption
∆Edp→okWh Average daily load shift of household appliances to the off-peak period by the TOU tariffconsumers
∆Epdoo kWh
Total annual energy consumption shift from the peak zone to the off-peak zone of household appliances
when using the G12 tariff
∆EoheatG12 kWh Additional annual energy consumed by G12 customers for heating purposes in the off-peak period
∆EpheatG12 kWh Additional annual energy consumed by G12 customers for heating purposes in the peak period
∆EG11→G12 kWh Increase in annual energy consumption value after transferring the settlement from G11 to G12 tariff
E1kWh Initial annual electricity consumption
Ea(EaG11 ,EaG12 ,
EaGxx)
kWh Total annual electricity consumption (may relate to total annual electricity consumption in residential
customers’ tariffgroups in general or tariffs G11 and G12)
EaG11o,EaG 12o,
EaGxxo
kWh Annual off-peak electricity consumption in G11 and G12 tariffs or in residential consumers’ tariffs
in general
EaG11p,EaG 12p,
EaGxxp
kWh Annual peak electricity consumption in G11 and G12 tariffs or in residential consumers’ tariffs
in general
EFp%,EFo% % Energetic efficiency of the peak and off-peak zones
EFenG12%% Annual average energy efficiency of the zonal tariff
EFcf% % Financial cash flow increment of the zonal tariff
EFfcust% % G12 tariff’s efficiency for the customers
ε- Price elasticity of electricity demand
εa av - Annual price elasticity of demand of G12 tariffconsumers
Gxx - Residential customers’ tariffs, related to in general, including G11 and G12 tariffs
HGxxi,HG11i,
HG12i
- Relative electricity consumption in the ith hour of the year of a representative customer expressed in
relation to its annual consumption EaGxx
OPG11 ,OPG12
PLN/month
Sum of fixed fees in the G11 and G12 tariffs
∆PPLN/kWh Change of the settlement price for purchase and supply of electricity
P1PLN/kWh Initial settlement price for purchase and supply of electricity
PG11 PLN/kWh Price of electricity together with its distribution services in G11 tariff
PavG12 (PG12p,
PG12o)
PLN/kWh Average electricity settlement price for G12 tariff
PvG11 ,PvG12
(PvpG12 ,PvoG12 )
PLN/kWh Variable part of the energy price together with its distribution services in G11 and G12 tariffs (for G12
tariffmay be divided into variable part of the price in peak and off-peak periods)
SqPLN/kWh Variable quality rate, uniform for all electricity tariffs
SvarG11 PLN/kWh Variable rate of distribution fee for G11 tariff
SvarG12p,
SvarG12o
PLN/kWh Variable rates of peak and off-peak distribution fees for G12 tariff
Energies 2019,12, 4317 20 of 22
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