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energies
Article
Determination of Price Zones during Transition from Uniform
to Zonal Electricity Market: A Case Study for Turkey
Gokturk Poyrazoglu
Citation: Poyrazoglu, G.
Determination of Price Zones during
Transition from Uniform to Zonal
Electricity Market: A Case Study for
Turkey. Energies 2021,14, 1014.
https://doi.org/10.3390/en14041014
Academic Editor: Federico Silvestro
Received: 9 December 2020
Accepted: 8 February 2021
Published: 15 February 2021
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4.0/).
Electrical & Electronics Engineering, Ozyegin University, Istanbul 34794, Turkey;
gokturk.poyrazoglu@ozyegin.edu.tr; Tel.: +90-216-564-9278
Abstract:
In the electricity market, different pricing models can be applied to increase market
competitiveness. Different electricity systems use different market structures. Uniform marginal
pricing, zonal marginal pricing, and nodal marginal pricing methods are commonly used market
structures. For markets wishing to move from a uniform pricing structure to a more competitive
zonal pricing structure, the determination of price zones is critical for achieving a competitive market
that generates accurate price signals. Three different pricing zone detection algorithms are analyzed
in this paper including the k-means clustering and queen/rook spatially constraint clustering. Finally,
the results of a case study for the Turkish electricity system are shared to compare each method.
Keywords:
electricity market; zonal pricing; k-means clustering; spatially constrained clustering;
clustering quality
1. Introduction
Electricity is one of the forms of energy that cannot be used directly by the end-
user. It is used to transfer energy due to its speed and efficiency. However, it does not
occur spontaneously in nature and has to be available on demand. Based on the law of
conservation of energy [
1
], the amount of electricity fed into the grid must always be
equal to the amount of electricity consumed. Various production techniques are used to
generate electricity to meet demand. The generation cost of these techniques differs from
each other. There were vertically integrated electric generation-transmission-distribution
utilities before the market structures. Today, the main purpose of the electricity market is
to ensure this form of energy is generated in a way that will maximize social welfare while
keeping the supply and demand balance [2].
The uniform marginal pricing (UMP) method in day-ahead electricity markets is
designed to ignore physical transmission line capacities and the losses that occurred
during transmission. It also charges a single price for the market footprint. Therefore,
the only constraint is the supply and demand balance. Besides this balance, there are
physical constraints in the power network, such as transmission line capacities. In the
zonal marginal pricing (ZMP) method, the overall service area of the market is divided
into several zones based on the available transfer capacity among the pricing zones [
3
].
Theoretically, if there is no transmission congestion in the system, there is no difference
among zonal marginal prices. However, if transfer limits are active, then zonal marginal
prices begin to split [
4
]. Another pricing method is nodal marginal pricing or, in other
words, local marginal pricing where each location on the transmission grid, called a node,
is expected to have a location-based marginal price. Physical laws of power flow should be
included in the constraint set to find the locational marginal price (LMP) for each node.
Europe and America constructed electricity markets differently. They were shaped by
the discussions that started in the 1990s [
5
–
8
], and discussions are still ongoing for these two
continents [
9
–
11
]. Europe follows the ZMP system, but America follows the LMP system for
different reasons. Although, in theory, the LMP system accurately creates the price signal
accounting for the transmission constraints [
5
,
6
], Europe-wide cost-benefit analysis has not
Energies 2021,14, 1014. https://doi.org/10.3390/en14041014 https://www.mdpi.com/journal/energies
Energies 2021,14, 1014 2 of 13
yet been realized based on a study by the European Union [
12
]. One of the key findings
in the report is the requirement of defining and allocating new roles and responsibilities
to the institutes in Europe. In addition, the balancing markets being as close as possible
to real-time operations requires a change in view regarding the reference market. A very
detailed comparison of zonal and nodal markets is also studied in Reference [
9
], stating
that the zonal pricing model contains simplifications and requires additional mechanisms
to compensate the investments. However, the framework of transitioning from vertically
integrated utilities to the market structure follows a roadmap in several countries: UMP
first, then ZMP, and then LMP [13–15].
The contribution of this study is providing quantitative methods for identifying zones
during the transition from a UMP market to a ZMP market for developing countries
where competitive electricity markets are newly formed. A case study for the Turkish
electricity system has been completed to compare the methods. The Turkish day-ahead
electricity market has been operating since 2011. Until 2015, it was operated by the Turkish
transmission system operator (TEIAS) and, as of 2015, it has been operated by the market
operator, Exchange Istanbul (EXIST). The electricity market structure, especially the types
of bids and types of markets, is similar to the European counterpart, especially Nord Pool.
However, EXIST has been using UMP to clear the day-ahead market. There are local
discussions on whether zonal pricing should be implemented or not [
16
,
17
]. However,
there is no public announcement as of 2021.
This study proposes and applies three clustering methods on the pricing zone de-
tection of an electricity market. The detection of the zones problem is addressed by two
different methods: a machine learning approach in which the k-means clustering method
is applied and a spatial and temporal-based approach in which a spatially constrained
clustering method is applied. Both methods are applied to a case study of the Turkish elec-
tricity system. The quality of the clustering methods is quantified by Within-Cluster-Sum
of Squares and silhouette coefficient methods.
The rest of the paper is structured as follows. Section 2provides the mathematical model
of the optimum power flow in linear programming as well as the solution methodology
and the details of the Turkish electricity system. Section 3explains the cluster validation
techniques including the Silhouette score and elbow methods. Section 4describes the use of
k-means clustering in electricity-market zone-detection. Section 5describes the zone detection
by spatially constrained clustering. Section 6discusses the impact of three clustering methods
on the economy, social life, and politics. Lastly, Section 7concludes the study.
2. Nodal Market Model with Flow Limitations
The Optimum Power Flow (OPF) problem is first developed in France to identify the
economic management of the power fleet [
18
]. Later, the advanced models are discussed to
be used in day-ahead market design. The problem aims to find the dispatch of suppliers to
minimize the total fuel cost subject to a power balance and flow limits.
Although there are discussions on which OPF model should be used in a market
structure, we are going to explain the Direct Current Optimal Power Flow (DC-OPF) model
as given in Model 1. The objective function aims to minimize the total fuel cost of the
generators, as given in Equation (1). The fuel cost of generators can be considered as a
quadratic function: C
i
(G
i
) =
γi
+
βi
G
i
+
αi
G
i2
, yet the constant term (
γ
) is not included
for simplicity and non-necessity in Model 1. The real power balance equality, matching
generation to demand in each node, is given in Equation (2). The amount of power flow on
a transmission line between Node iand Node jis defined in Equation (3). All generator ’s
offered quantity is given by its limits in Equation (4). Finally, the line flow limit can be
modeled in Equation (5). This constraint is considered for the physical laws of power flow.
Energies 2021,14, 1014 3 of 13
MODEL 1. DC OPTIMAL POWER FLOW
Variables:
Gi:Dispatch of a generator at Node i
θi:Voltage angle at Node i
Pij:Line flow on the line connecting Node iand Node j
Parameters:
Di:Power demand at Node i
Bij:Susceptance of the line connecting Node iand Node j
Gimax:Maximum quantity offered to market from generator at Node i
Gimin:Minimum quantity offered to market from generator at Node i
Pijmax :
Maximum power flow allowed to transfer on the line connecting Node i
and Node j
α,β:Fuel cost coefficients for generators
minimize
G,P,θ∑
i∈Ω
aiG2
i+biGi(1)
Subject to
Gi−Di=∑
ie{i,∗}
Pij −∑
je{∗,i}
Pij ∀i∈N(2)
Pij =Bi jθi−θj∀i,j∈N(3)
Gmin
i≤Gi≤Gmax
i∀i∈Ω(4)
−Pmax
ij ≤Pij ≤Pmax
ij ∀i,j∈N(5)
One of the key results of Model 1 is the dispatch of generators (G
i
). However, another
key result is also coming from the dual-primal solution methodology of linear programming
(LP). It is the lambda variable, generally referred to as the Lagrange multiplier [
19
], assigned
to all equality constraints in the model by the Lagrange method to solve an LP. For any
given minimization problem with equality constraints, the problem can be solved using
the method of the Lagrange multiplier. The key idea is to modify a constrained problem to
be an easily solved unconstrained problem. For the general problem of Model 2 as given in
Equation (6), the Lagrangian function can be written as Equation (7).
Minimize f(x) subject to g(x) = 0 (6)
Minimize L(x,λ) = f(x) + λTg(x) (7)
A necessary condition for the minimum is the gradient of the Lagrange function, which
must be zero. Therefore,
∇
L
x
(x,
λ
) = 0 and
∇
L
λ
(x,
λ
) = 0. The created set of equations
from the gradient of the Lagrange function now can be solved by the lambda-iteration
algorithm and the inequalities given in Equations (4) and (5) are considered in the iteration
until the convergence condition is satisfied [
20
]. For the given problem of Model 1, the first
N entries of
λ
represent the marginal cost of supplying power to each bus. They are called
the locational marginal price (LMP). The LMP is the shadow price of Model 1. It is the dual
variable of the power balance equation given in Equation (2). The LMP is a nodal variable
so that it shows the price of electrical energy at each node [21].
The LMP can be used to monitor transmission congestion as well [
22
]. If there is
congestion on a line, then the price is higher at one of its connecting nodes, and lower at
the other node. A rise in hourly demand at a node can cause congestion. Thus, the price at
one side of the congested line can increase/decrease.
The physical properties of the power network (topology) are included as constraints in
the nodal market model. The electricity follows Kirchhoff’s current law (KCL) and voltage
law (KVL) so that the current flow does not follow the shortest path to reach the demand.
That is the main difference between the electricity market and the other commodity markets
that requires transportation. The power network is connected in the sense that any change
at any location has an impact on all other locations. Therefore, a phenomenon called “line
congestion” is likely to appear on the transmission lines that affect the available transfer
Energies 2021,14, 1014 4 of 13
capability between two nodes in the network. If the maximum flow limit constraint of a
transmission line is active at the solution, then the line is called congested.
Monitoring line congestion is one of the important steps in power system operations.
However, from the market perspective, any line congestion may cause LMP differentiation
within the market area [
4
,
23
]. If there is no congestion, the result of the nodal market model
is the same as the uniform market model.
A case study for the Turkish power systems includes 81 pricing nodes, 153 trans-
mission lines, and 318 generators. Eighty-one pricing nodes are selected from 81 cities
in Turkey. The transmission network as used in the case study is illustrated in Figure 1.
Transmission lines of 154 kV and 380 kV are considered in this study and their electricity
carrying capacity is altered according to their size.
Energies 2021, 14, x FOR PEER REVIEW 4 of 14
The physical properties of the power network (topology) are included as constraints
in the nodal market model. The electricity follows Kirchhoff’s current law (KCL) and volt-
age law (KVL) so that the current flow does not follow the shortest path to reach the de-
mand. That is the main difference between the electricity market and the other commodity
markets that requires transportation. The power network is connected in the sense that
any change at any location has an impact on all other locations. Therefore, a phenomenon
called “line congestion” is likely to appear on the transmission lines that affect the availa-
ble transfer capability between two nodes in the network. If the maximum flow limit con-
straint of a transmission line is active at the solution, then the line is called congested.
Monitoring line congestion is one of the important steps in power system operations.
However, from the market perspective, any line congestion may cause LMP differentia-
tion within the market area [4,23]. If there is no congestion, the result of the nodal market
model is the same as the uniform market model.
A case study for the Turkish power systems includes 81 pricing nodes, 153 transmis-
sion lines, and 318 generators. Eighty-one pricing nodes are selected from 81 cities in Tur-
key. The transmission network as used in the case study is illustrated in Figure 1. Trans-
mission lines of 154 kV and 380 kV are considered in this study and their electricity carry-
ing capacity is altered according to their size.
Figure 1. The high voltage transmission system in Turkey as adopted in the case study.
The generator dataset aggregates the individual power plants in a city into a single
power plant by fuel type. Fifteen fuel types are considered in the study: asphaltite, biogas,
coal, fuel oil, geothermal, hydro, import coal, lignite, LPG, naphtha, natural gas, solar
plant, thermal plant, waste heat, and wind. A power plant by fuel type is assigned to each
city if there is a power plant in the city’s footprint. A fuel cost is assigned to all fuel types.
The intermittency of renewable energy, such as wind, solar, and hydro, are assumed to
have a scheduled profile for the day. Therefore, no renewable curtailment or dispatchable
capacity is assumed. The geographical locations of the generators as adopted in the case
study are illustrated by fuel type in Figure 2.
Figure 1. The high voltage transmission system in Turkey as adopted in the case study.
The generator dataset aggregates the individual power plants in a city into a single
power plant by fuel type. Fifteen fuel types are considered in the study: asphaltite, biogas,
coal, fuel oil, geothermal, hydro, import coal, lignite, LPG, naphtha, natural gas, solar plant,
thermal plant, waste heat, and wind. A power plant by fuel type is assigned to each city if
there is a power plant in the city’s footprint. A fuel cost is assigned to all fuel types. The
intermittency of renewable energy, such as wind, solar, and hydro, are assumed to have a
scheduled profile for the day. Therefore, no renewable curtailment or dispatchable capacity
is assumed. The geographical locations of the generators as adopted in the case study are
illustrated by fuel type in Figure 2.
The historical demand of Turkey in 2019 is extracted from the Turkish Market Operator,
Exchange Istanbul (EXIST), transparency platform and used to calculate the nodal demand.
Nodal demand data is created by considering the population of the cities. The share of the
population is used as the share of electricity consumption. A sample day from 2019 is used
in the case study. The optimization problem of Model 1 is written by YALMIP [
24
] and
solved by CPLEX in MATLAB.
Energies 2021,14, 1014 5 of 13
Energies 2021, 14, x FOR PEER REVIEW 5 of 14
Figure 2. The generation facilities in Turkey by fuel type as adopted in the case study.
The historical demand of Turkey in 2019 is extracted from the Turkish Market Oper-
ator, Exchange Istanbul (EXIST), transparency platform and used to calculate the nodal
demand. Nodal demand data is created by considering the population of the cities. The
share of the population is used as the share of electricity consumption. A sample day from
2019 is used in the case study. The optimization problem of Model 1 is written by YALMIP
[24] and solved by CPLEX in MATLAB.
3. Cluster Validation
Cluster validation seeks to measure the quality of the clustering. The validity
measures are divided into three: external, internal, and relative validations [25].
The external validation is used when the class labels of the dataset are already
known. Some examples of external clustering validation measures are purity, maximum
matching, and F-measure [26]. These measures evaluate all points in the dataset by com-
paring their pre-label and post-labels. The contingency table induced for each cluster is
constructed and all three external measures can be calculated accordingly. However, the
clustering of LMPs for an electricity market is an unsupervised learning problem. Hence,
there exist no class labels at the beginning of the problem. Therefore, the external valida-
tion measures do not apply to such clustering.
The internal validation measures consist of calculations related to the data itself such
as intra-cluster and inter-cluster distances [27]. The Silhouette score concept is an internal
valuation of the clustering [26]. The silhouette coefficient (SC) of the clustering is defined
by Equation (8).
SC = (∑s
i
)/n (8)
where n is the number of points in the dataset and s
i
is the silhouette score of each point
in the dataset, as given in Equation (9).
𝑠=𝜇
𝑥−𝜇𝑥
𝑚𝑎𝑥𝜇
𝑥,𝜇𝑥
(9)
where 𝑥 is any point in the dataset, 𝜇
𝑥 is the mean distances between 𝑥 and
points in the closest cluster, and 𝜇𝑥 is the mean distance between 𝑥 and points in
its own cluster. The silhouette score and silhouette coefficient lie in the interval [–1, 1]. For
Equation (9) to be close to 1, 𝜇
𝑥 should be greater than 𝜇𝑥, as 𝜇𝑥 is a
measure of how dissimilar 𝑥 is to its own cluster and 𝜇𝑥 is a measure of how dis-
similar 𝑥 to other clusters. For Equation (9) to be close to -1, however, we require 𝜇𝑥
to be greater than 𝜇
𝑥, which implies a high dissimilarity within the cluster. There-
fore, if the coefficient is close to 1, we can conclude that the resultant clusters are dense
Figure 2. The generation facilities in Turkey by fuel type as adopted in the case study.
3. Cluster Validation
Cluster validation seeks to measure the quality of the clustering. The validity measures
are divided into three: external, internal, and relative validations [25].
The external validation is used when the class labels of the dataset are already known.
Some examples of external clustering validation measures are purity, maximum matching,
and F-measure [
26
]. These measures evaluate all points in the dataset by comparing their
pre-label and post-labels. The contingency table induced for each cluster is constructed
and all three external measures can be calculated accordingly. However, the clustering of
LMPs for an electricity market is an unsupervised learning problem. Hence, there exist no
class labels at the beginning of the problem. Therefore, the external validation measures do
not apply to such clustering.
The internal validation measures consist of calculations related to the data itself such
as intra-cluster and inter-cluster distances [
27
]. The Silhouette score concept is an internal
valuation of the clustering [
26
]. The silhouette coefficient (SC) of the clustering is defined
by Equation (8).
SC = (∑si)/n (8)
where n is the number of points in the dataset and s
i
is the silhouette score of each point in
the dataset, as given in Equation (9).
si=µmin
out (xi)−µin (xi)
maxµmin
out (xi),µin (xi)(9)
where
xi
is any point in the dataset,
µmin
out (xi)
is the mean distances between
xi
and points
in the closest cluster, and
µin (xi)
is the mean distance between
xi
and points in its own
cluster. The silhouette score and silhouette coefficient lie in the interval [
−
1, 1]. For
Equation (9) to be close to 1,
µmin
out (xi)
should be greater than
µin (xi)
, as
µin (xi)
is a measure
of how dissimilar
xi
is to its own cluster and
µin (xi)
is a measure of how dissimilar
xi
to other clusters. For Equation (9) to be close to
−
1, however, we require
µin (xi)
to be
greater than
µmin
out (xi)
, which implies a high dissimilarity within the cluster. Therefore, if
the coefficient is close to 1, we can conclude that the resultant clusters are dense and well
separated. However, if the coefficient is close to
−
1, the points are mis-clustered in which
the similarity of xiwith other clusters is greater than the similarity with its own cluster.
The relative validation requires varying parameter values, such as the number of
clusters to evaluate the quality of the clustering. The elbow method uses a varying number
of clusters versus the Within-Cluster-Sum of Squares (WCSS) to calculate the quality of
the cluster. The krepresents the number of clusters that the user expects to see in this
unlabeled data. Therefore, it is a parameter to choose by experience or by some other
Energies 2021,14, 1014 6 of 13
methods, such as the elbow method. The very first application of the elbow method can
be traced back to an article in Psychometrika [
28
], and it has been used as one of the
methods for determining the number of clusters in a data set in different domains, such as
electrical engineering [
29
,
30
], computer science [
31
], education [
32
], statistics [
33
,
34
], and
communications [35,36].
To find the optimal kvalue in the k-means clustering algorithm, the elbow method
shall be applied to the data. Since the elbow method runs k-means clustering on the dataset
for a range of values of k, then, for each kvalue, it computes the WCSS for all clusters.
The WCSS is the sum of the squared distance between each member of the cluster and its
centroid is given in Equation (10).
WCSS = ∑(xi,j −cj)2(10)
where x
i,j
is the ith observation assumed to be in Cluster jin the dataset and c
j
is the
centroid of the Cluster j. For a multi-dimensional space, the centroid is the mean position
of all the points in all the coordinate directions. The calculation of WCSS even for a given
number of clusters khas a Non-deterministic Polynomial-time (NP) hard complexity [
37
],
but existing heuristic algorithms may converge to a local optimum.
Once the WCSS and the number of clusters are illustrated in a two-dimensional graph,
it is likely to have WCSS beginning to level off at a certain number of clusters. The shape of
the curve looks like an elbow, where the method takes its name of the elbow method. The
elbow method suggests the optimal k-value where the change in WCSS begins to level off.
4. Zone Detection by k-Means Clustering
One of the methods that can be used to determine a pricing zone in the electricity
market is the method of the k-means clustering by using the similarity of locational marginal
prices. k-means clustering is a highly used, unsupervised clustering algorithm that takes
unlabeled data and returns the cluster label of entries out of a knumber of clusters. It
is originally developed to grouping nobservations into kclusters based on the distance
of the observation and the center or centroid of the cluster that the observation belongs
to [
38
]. Although there are variations on algorithms applied to different types of datasets,
the method has been used in several studies in power systems [39–42].
In the market, the zone is used as a terminology, as an area formed by price points
where electricity prices are similar or the same. For this reason, using the k-means clustering
algorithm on the LMPs calculated by Model 1 may open the way for the nodes with similar
prices to be placed in the same cluster and to use the nodes in this cluster as a zone. In this
study, the k-means clustering algorithm is applied to the LMP results from Model 1 for
a 24-h horizon and, thus, group the price points into clusters, including the hourly price
changes during the day.
In addition, 24-h LMPs of all nodes are used in the k-means algorithm to detect the
pricing zones with similar LMPs. The elbow method is applied to the dataset to find the
optimal kvalue. Figure 3represents the within-cluster-sum-of-squares (WCSS) versus the
number of clusters. The elbow is seen when the number of clusters is three. Since the elbow
method is only a decision support mechanism, four clusters are also studied.
A further internal valuation analysis by a silhouette score method to verify the findings
of the relative valuation by the elbow method is studied and silhouette scores of each point
and clusters (in different colors), as well as the cluster silhouette coefficient (red dashed
line), are illustrated in Figure 4for the k-means algorithm. The silhouette score of three
clusters is closer to 1 than the four clusters, indicating a more dense and well-separated
clustering.
Energies 2021,14, 1014 7 of 13
Energies 2021, 14, x FOR PEER REVIEW 7 of 14
Figure 3. Elbow method results of 24-h locational prices.
A further internal valuation analysis by a silhouette score method to verify the find-
ings of the relative valuation by the elbow method is studied and silhouette scores of each
point and clusters (in different colors), as well as the cluster silhouette coefficient (red
dashed line), are illustrated in Figure 4 for the k-means algorithm. The silhouette score of
three clusters is closer to 1 than the four clusters, indicating a more dense and well-sepa-
rated clustering.
(a)
(b)
Figure 4. Silhouette scores of K-means algorithm (a) three clusters, (b) four clusters.
Figure 5a illustrates the three-means clustering results of the 24-h Locational Mar-
ginal Prices (LMP). Four-means clustering results are also illustrated in Figure 5b.
Figure 3. Elbow method results of 24-h locational prices.
Energies 2021, 14, x FOR PEER REVIEW 7 of 14
Figure 3. Elbow method results of 24-h locational prices.
A further internal valuation analysis by a silhouette score method to verify the find-
ings of the relative valuation by the elbow method is studied and silhouette scores of each
point and clusters (in different colors), as well as the cluster silhouette coefficient (red
dashed line), are illustrated in Figure 4 for the k-means algorithm. The silhouette score of
three clusters is closer to 1 than the four clusters, indicating a more dense and well-sepa-
rated clustering.
(a)
(b)
Figure 4. Silhouette scores of K-means algorithm (a) three clusters, (b) four clusters.
Figure 5a illustrates the three-means clustering results of the 24-h Locational Mar-
ginal Prices (LMP). Four-means clustering results are also illustrated in Figure 5b.
Figure 4. Silhouette scores of K-means algorithm (a) three clusters, (b) four clusters.
Figure 5a illustrates the three-means clustering results of the 24-h Locational Marginal
Prices (LMP). Four-means clustering results are also illustrated in Figure 5b.
Energies 2021, 14, x FOR PEER REVIEW 8 of 14
(a)
(b)
Figure 5. (a) Three-means clustering of 24-h locational prices. (b) Four-means clustering of 24-h
locational prices.
The statistical measures to understand the differences between clusters are given in
Table 1 for 24-h k-mean clustering results. The mean values of LMPs within the clusters
are changing from $16.47/MWh to $40.80/MWh when four clusters are generated from a
daily dataset.
Table 1. Statistical measures of k-means clustering.
Method 24-h k-Means Clustering
Number of Clusters 3 4
Cluster Label 0 1 2 0 1 2 3
Min $/MWh 10.48 37.58 23.34 18.63 25.12 37.58 10.48
25% percentile $/MWh 16.47 40.29 26.17 19.38 26.59 40.29 16.39
Mean $/MWh 17.76 40.79 27.74 20.28 28.24 40.8 16.47
Median $/MWh 17.45 41.57 27.23 20.06 27.93 41.57 16.51
75% percentile $/MWh 19.45 42.04 29.47 20.66 29.89 42.04 16.94
Max $/MWh 21.9 42.5 34.14 23.57 34.14 42.5 18.53
Std. Dev. $/MWh 2.13 1.77 2.59 1.3 2.26 1.77 1.49
Variance $/MWh 4.57 3.13 6.75 1.69 5.13 3.13 2.23
5. Zone Detection by Spatially Constrained Clustering
Since the k-means clustering method in Section 4 only uses hourly electricity prices
as input, the geographical features of these price points are not used when separating the
zones. For this reason, while determining zones, the neighborhood status of the cities is
not evaluated. In electricity markets where zonal pricing is applied, power transmission
flow restrictions between two zones are generally imposed, implying that the zones are
geographically as well as electrically separated from each other. When using these power
transmission flow constraints, the cities that make up a zone are expected to be neighbors
to each other. Therefore, a temporal and spatial clustering method including geographical
neighborhood information is required. This method is called spatially constrained clus-
tering. The early applications of spatially constrained clustering are applied to landscape
Figure 5.
(
a
) Three-means clustering of 24-h locational prices. (
b
) Four-means clustering of 24-h
locational prices.
Energies 2021,14, 1014 8 of 13
The statistical measures to understand the differences between clusters are given in
Table 1for 24-h k-mean clustering results. The mean values of LMPs within the clusters
are changing from $16.47/MWh to $40.80/MWh when four clusters are generated from a
daily dataset.
Table 1. Statistical measures of k-means clustering.
Method 24-h k-Means Clustering
Number of Clusters 3 4
Cluster Label 0 1 2 0 1 2 3
Min
$/MWh
10.48 37.58 23.34 18.63 25.12 37.58 10.48
25% percentile
$/MWh
16.47 40.29 26.17 19.38 26.59 40.29 16.39
Mean
$/MWh
17.76 40.79 27.74 20.28 28.24 40.8 16.47
Median
$/MWh
17.45 41.57 27.23 20.06 27.93 41.57 16.51
75% percentile
$/MWh
19.45 42.04 29.47 20.66 29.89 42.04 16.94
Max
$/MWh
21.9 42.5 34.14 23.57 34.14 42.5 18.53
Std. Dev.
$/MWh
2.13 1.77 2.59 1.3 2.26 1.77 1.49
Variance
$/MWh
4.57 3.13 6.75 1.69 5.13 3.13 2.23
5. Zone Detection by Spatially Constrained Clustering
Since the k-means clustering method in Section 4only uses hourly electricity prices
as input, the geographical features of these price points are not used when separating the
zones. For this reason, while determining zones, the neighborhood status of the cities
is not evaluated. In electricity markets where zonal pricing is applied, power transmis-
sion flow restrictions between two zones are generally imposed, implying that the zones
are geographically as well as electrically separated from each other. When using these
power transmission flow constraints, the cities that make up a zone are expected to be
neighbors to each other. Therefore, a temporal and spatial clustering method including
geographical neighborhood information is required. This method is called spatially con-
strained clustering. The early applications of spatially constrained clustering are applied to
landscape and vegetation [
43
–
45
]. However, it is now used in various disciplines such as
geoinformatics [46], energy modeling [47], and pattern recognition [48].
Generally, in such studies, an assumption must be made of which geographical region
the price point represents. A price point can refer to a district, a city, or a region that
includes several of them. On behalf of emulating the example in the previous section, this
section will also accept every price point as an expression of a city in Turkey. In this case,
81 price points for 81 cities in Turkey and the geographical proximity of the city on the map
have been identified. These data are usually kept in GeoJson files.
A similar but slightly different approach than the k-means algorithm is required to
satisfy the spatial contiguity condition. The new clustering problem called the max-p-
regions problem can be modeled as Mixed-Integer Programming (MIP) and it can be solved
by a heuristic approach [
49
]. There are two different algorithms to which the spatially
constrained clustering method can be applied. These are the neighborhood detection
algorithms named Queen and Rook, which are referred to as their equivalents in the chess
game. If you consider the movement characteristics of the rook in the game of chess, it
is necessary to have the border of two cities in the north, south, east, or west in order to
understand whether the two cities are neighbors. Similarly, like the full free movement
features of the Queen in chess, even if two cities have a border at only one point, this point
neighborhood is valued during zone selection. It should not be forgotten that, if a study is
conducted over smaller settlements rather than cities, as in our example, the two methods
may yield completely different results. Nevertheless, in our example here, some cities have
a point neighborhood, and, therefore, the zone detection has been completed with both
Queen and Rook algorithms.
In the Queen and Rook algorithms, where evaluated within the clustering method in
geographical neighborhoods, a threshold value is determined depending on the value of
Energies 2021,14, 1014 9 of 13
the parameter to be clustered (it is the hourly price for the electricity market). This value
is one of the inputs of the algorithms. Depending on this threshold value, the algorithms
utilize a heuristic method to minimize the number of clusters while placing neighboring
points within the threshold into the same cluster [
50
]. While creating these zones, cluster
numbers were not given to the algorithms as in Section 4, but the desired number of zones
was obtained by changing the threshold value. In Figure 6a,c, pricing zones created with
Queen neighborhood features are shown with a threshold value of 0.2 and 0.15, respectively.
Similarly, the electrical pricing zones determined by Rook neighborhood features are shown
in Figure 6b,d with a threshold value of 0.2 and 0.14, respectively.
Energies 2021, 14, x FOR PEER REVIEW 9 of 14
and vegetation [43–45]. However, it is now used in various disciplines such as geoinfor-
matics [46], energy modeling [47], and pattern recognition [48].
Generally, in such studies, an assumption must be made of which geographical re-
gion the price point represents. A price point can refer to a district, a city, or a region that
includes several of them. On behalf of emulating the example in the previous section, this
section will also accept every price point as an expression of a city in Turkey. In this case,
81 price points for 81 cities in Turkey and the geographical proximity of the city on the
map have been identified. These data are usually kept in GeoJson files.
A similar but slightly different approach than the k-means algorithm is required to
satisfy the spatial contiguity condition. The new clustering problem called the max-p-re-
gions problem can be modeled as Mixed-Integer Programming (MIP) and it can be solved
by a heuristic approach [49]. There are two different algorithms to which the spatially
constrained clustering method can be applied. These are the neighborhood detection al-
gorithms named Queen and Rook, which are referred to as their equivalents in the chess
game. If you consider the movement characteristics of the rook in the game of chess, it is
necessary to have the border of two cities in the north, south, east, or west in order to
understand whether the two cities are neighbors. Similarly, like the full free movement
features of the Queen in chess, even if two cities have a border at only one point, this point
neighborhood is valued during zone selection. It should not be forgotten that, if a study
is conducted over smaller settlements rather than cities, as in our example, the two meth-
ods may yield completely different results. Nevertheless, in our example here, some cities
have a point neighborhood, and, therefore, the zone detection has been completed with
both Queen and Rook algorithms.
In the Queen and Rook algorithms, where evaluated within the clustering method in
geographical neighborhoods, a threshold value is determined depending on the value of
the parameter to be clustered (it is the hourly price for the electricity market). This value
is one of the inputs of the algorithms. Depending on this threshold value, the algorithms
utilize a heuristic method to minimize the number of clusters while placing neighboring
points within the threshold into the same cluster [50]. While creating these zones, cluster
numbers were not given to the algorithms as in Section 4, but the desired number of zones
was obtained by changing the threshold value. In Figure 6a and Figure 6c, pricing zones
created with Queen neighborhood features are shown with a threshold value of 0.2 and
0.15, respectively. Similarly, the electrical pricing zones determined by Rook neighbor-
hood features are shown in Figure 6b and Figure 6d with a threshold value of 0.2 and 0.14,
respectively.
(a)
(b)
(c)
(d)
Figure 6.
Spatially constrained clustering results, (
a
) Queen neighboring-3 clusters, (
b
) Rook neighboring-3 clusters,
(c) Queen neighboring-4 clusters, and (d) Rook neighboring-4 clusters.
For a quantitative comparison of queen and rook algorithms within the framework
of spatially constrained clustering (SCC), the statistical measures are given in Table 2for
queen-based SCC and Table 3for rook-based SCC.
Table 2. Statistical measures of queen-based spatially constrained clustering.
Method Queen-Based Spatially Constrained Clustering
Number of Clusters 3 4
Cluster Label 0 1 2 0 1 2 3
Min
$/MWh
12.35 10.49 18.08 10.49 12.35 16.42 16.29
25% percentile
$/MWh
16.52 16.47 21.16 16.48 16.47 18.64 18.64
Mean
$/MWh
19.58 19.85 25.36 21.41 19.38 21.47 25.38
Median
$/MWh
17.82 16.84 25.85 19.29 16.76 20.30 25.70
75% percentile
$/MWh
19.38 19.30 27.76 22.88 19.50 25.13 28.92
Max
$/MWh
42.04 42.50 41.58 40.29 42.50 27.93 42.04
Std. Dev.
$/MWh
6.11 7.58 4.88 7.18 6.43 3.68 8.00
Variance
$/MWh
37.35 57.47 23.84 51.55 41.38 13.57 63.94
Energies 2021,14, 1014 10 of 13
Table 3. Statistical measures of rook-based spatially constrained clustering.
Method Rook-Based Spatially Constrained Clustering
Number of Clusters 3 4
Cluster Label 0 1 2 0 1 2 3
Min
$/MWh
10.49 13.98 18.08 10.49 12.35 18.08 16.29
25% percentile
$/MWh
16.47 16.49 21.91 16.48 16.46 22.92 16.64
Mean
$/MWh
20.36 19.16 26.65 19.62 20.63 26.14 21.05
Median
$/MWh
19.12 16.92 26.59 18.15 16.97 26.48 19.01
75% percentile
$/MWh
20.39 19.01 28.79 20.31 19.64 27.41 21.24
Max
$/MWh
40.29 42.50 42.04 40.29 42.50 41.58 42.04
Std. Dev.
$/MWh
6.48 5.81 6.06 5.73 8.02 5.29 6.28
Variance
$/MWh
42.01 33.77 36.72 32.86 64.37 27.97 39.46
For comparison of different clustering methods used to determine pricing zones in
this study, the silhouette coefficients are given in Table 4. The k-clustering method using
three zones resulted in the most dense and well-separated clusters, while the Queen-based
SCC with four zones had the least.
Table 4. Silhouette coefficients of clustering methods.
Method Number of Clusters Silhouette Coefficient
k-means clustering 3 0.730
k-means clustering 4 0.576
Queen-based SCC 3 −0.019
Queen-based SCC 4 −0.101
Rook-based SCC 3 0.015
Rook-based SCC 4 −0.084
6. Discussion
6.1. Economic Impact
While electrical energy is bought and sold as a commodity under market conditions,
the price formed as an output of this market must be formed correctly. Commodity prices
are an argument used as a signal in investor decisions. Thanks to this signal, investors can
make the right decisions from choice of location to capacity selection in their buy or sell
investments.
The method that can be used in the transition to zonal pricing in the national markets,
where a single price is used in the electricity market, is explained in this study. In the later
stages of the study, we plan to examine the differences that may occur according to the use
of the created zones within a market structure and the single price market structure. At the
same time, we want to analyze the impact of zonal pricing on the intraday market with
combined modeling as day-ahead and intraday markets in the market design phase.
Uniform marginal price application, which is used as pricing of electrical energy
regardless of location, eliminates the feature of location choice in investment decisions
and signals that the investment can be made anywhere in the country. However, regional
pricing can create an accurate signal for investors in their decisions due to the energy losses
that occur between the places where electrical energy is produced and consumed and the
congestion that may occur during electricity transmission. Changing zonal prices may
reveal that there is no balance between supply and demand within a zone. Therefore, it
is necessary to purchase electricity from another zone or to transmit electricity to another
zone. It is understood that demand is higher than supply in zones where electricity prices
are higher, and this price signal encourages investors to put generation plants in this region.
Similarly, in zones with lower prices, it is understood that supply is higher than demand
and investors increase the demand in that region by increasing their industrial investments
in regions where cheaper electricity can be purchased. Considering the regional pricing
practice only as a method in which prices differ is a deficiency at this point. In fact, zonal
Energies 2021,14, 1014 11 of 13
pricing is an application that affects investment decisions and serves as a signal for the
formation of the supply-demand balance.
6.2. Social and Political Impact
The price of electricity is a social measure that has a big impact not only in the
energy sector but anywhere electricity is consumed. The price might also be used as
a political instrument by policymakers. The pricing system of electricity is not only
related to engineering and mathematical modeling disciplines. It is a very important
commodity of society that should be discussed in a multi-disciplinary platform. From
an engineering perspective, the proposed methodology of electricity pricing based on
an optimization problem to minimize the total production cost of electricity (Model 1) is
intended to maximize social welfare. Further explanations on the zonal markets and also
the discussions around how to find the best pricing zones in this study may not capture
and assess the political background of the energy sector entirely. However, the intentions of
mathematical modeling with the support of various simulations are always the beginning
of multi-disciplinary studies to quantify the necessity of a bigger change in society. The
planned future work of this study is further discussed in Section 6.3.
6.3. Future Work
The method that can be used in the transition to zonal pricing in the national markets,
where a single price is used in the electricity market, is explained in this study. In future
work, we plan to examine the differences that may occur in the bidding structure of the
power market, according to the use of the proposed zones. At the same time, we want to
analyze the impact of zonal pricing on the intraday market with combined modeling as
day-ahead and intraday markets as well as the balancing mechanism prices in the market
design phase.
7. Conclusions
Day-ahead electricity markets are an auction-based market where supply and demand
are brought together. Considering the physical properties of electrical energy, it can be
modeled as an optimization problem to maximize social welfare. While designing a
national electricity market, which is generally built on creating a single national price in
the first place, deepen with the transition to zonal or locational pricing methods and create
a more competitive structure.
This paper describes three clustering methods that might be used in zone detection
for a power market in the transition from a uniform price to a zonal price mechanism in the
day-ahead electricity market. For a case study of Turkey, three algorithms are tested, and
the final clusters’ geographical representations are illustrated on a map. These methods
can be used by policy-makers as a decision support mechanism. By optimal power flow
model as given in Model 1, locational marginal prices can be calculated for each price
point. Then zones can be determined by combining points with similar price ranges. One
of the methods described in this article is the spatial constraint clustering method, which
works to include the geographical proximity of price points, instead of single clustering by
LMPs. In this method, different zone preferences can be made by determining neighborly
relations as queen and rook, and different zone preferences can be formed by changing the
geographical regions expressed by point prices.
Funding: This research received no external funding.
Acknowledgments:
The author would like to thank Kerem Can Arayici, Dogukan Keser, and Ozan
Yurtsever for their efforts during their internship period. Several anonymous reviewers provided
thoughtful and detailed comments that greatly improved the final version of this article.
Conflicts of Interest: The authors declare no conflict of interest.
Energies 2021,14, 1014 12 of 13
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