6TH INTERNATIONAL CONFERENCE ON MODERN POWER SYSTEMS MPS2015, 18-21 MAY 2015, CLUJ-NAPOCA, ROMANIA
Market Clearing Price Forecasting in Deregulated
Electricity Markets Using a Fuzzy Approach
Gheorghe Grigoraș
Bogdan Constantin Neagu
Power Systems Department
„Gheorghe Asachi” Technical University
Iaşi, Romania
[email protected]
Power Systems Department
„Gheorghe Asachi” Technical University
Iaşi, Romania
[email protected]
schedules generation and price responsive demand hour-byhour for the operating day so as to respect all generator and
security (reliability) constraints and to minimize operating cost.
Abstract— In the paper, the ordinal optimization method for
Marginal Clearing Price (MCP) forecasting is proposed. The
basic idea is to use a competition based simulation model, in
order to analyze the influence of the bidding strategies on MCP,
and to establish the optimal bidding strategies of generators in
uncertainty conditions of the nodal loads. For nodal loads, the
fuzzy models were used. As a result, this proposed approach has
the advantages of a good accuracy of MCP estimation in a
deregulated market.
The main objective of the generators in an electricity
market is to establish optimal bidding strategies to maximize
profit [1]-[4]. Achieving this is influenced by a number of
factors affecting decision making [3], [4]: load forecasting
system, variable cost of generation (starting cost, the cost of
going to empty etc), bidding strategies of other participants,
marginal clearing price forecasting of the energy market,
various forms of bilateral contracts, and different constraints
(technical, security etc.).
Keywords— deregulated electricity matkets; market clearing
price; fuzzy techniques.
I.
INTRODUCTION
A review of the literature was indicated that different
techniques have been used to solve this problem: neural
networks [5], [6], neuro-fuzzy [7] or evolutionary calculus [8].
For questions relating to the bids, these are generally associated
with uncertainty and complexity of the electricity market.
Thus, for to remove the calculation difficulties, it is more
appropriate to inquire which solution is better, instead of
searching an optimum solution [9].
In deregulated power systems, a free market structure is
advocated for competition among participants as generators
and consumers. To ensure nondiscriminatory access to the
transmission networks by all participants, an Independent
System Operator (ISO) is created for each power system. There
are two distinct models for ISOs: the pool model and the
bilateral/multilateral model. In the pool model, all generators
and consumers transact with the pool, where the least
expensive is dispatched. Therefore, the responsibility of a
Power Exchange (PX) – determining generators outputs by
economic dispatch functions - is managed by the ISO. This
idea is based on the concept that a natural monopoly would
ensure a least cost dispatch of all generators in the system.
In the bilateral model all generators and consumers transact
witch each other, independently. This model is based on the
concept that the regulation of the commercial market should be
minimized, and the market efficiency is achieved by consumers
choosing their own suppliers [1].
In the paper, the ordinal optimization method for Marginal
Clearing Price (MCP) forecasting is proposed. The basic idea is
to use a competition simulation model, in order to analyze the
influence of the bidding strategies on MCP, and to establish the
optimal bidding strategies of generators in uncertainty
conditions of the nodal loads. For nodal loads, the fuzzy
models were used.
II.
FUZZY MODELING
Uncertainty in fuzzy modeling represents a measure of
nonspecifically characterized by possibility distributions. This
is, somewhat similar to the use of probability distributions,
which characterize uncertainty in probability theory. Linguistic
terms used in our daily conversation can be easily captured by
fuzzy sets for computer implementations. A fuzzy set contains
elements that have varying degrees of membership. Elements
of fuzzy set are mapped to a universe of a membership
function. Fuzzy sets and membership functions are often used
interchangeably. The selection of membership function is one
of the most important stages of working with fuzzy sets.
Subjective judgment, intuition and expert knowledge are
commonly used in constructing membership function. For a
correct choice, a Decision Maker (DM) can use his experience,
but also perform a statistical analysis [4], [10]. In this operation
The pool is an e-commerce market place. The ISO uses a
market-clearing tool, to clear the market, which is normally
based on a single round auction [2]. Although most electricity
is bought and sold under long-term bilateral contracts, perhaps
5 to 10% will be traded day-ahead and in real-time. These
short-term trades could be a consequence of changed
circumstances (e.g., a competitive retail provider signed up
more customers than it anticipated or a generator completed its
planned maintenance outage faster than it expected to), or they
could be part of a company risk management strategy. In this
case, ISO calls for suppliers and buyers to submit hourly bid by
10.00 a.m., on the day before the operating day. The ISO then
evaluates these bids using its security constrained unit
commitment optimization computer model. This model
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6TH INTERNATIONAL CONFERENCE ON MODERN POWER SYSTEMS MPS2015, 18-21 MAY 2015, CLUJ-NAPOCA, ROMANIA
establishing the membership function should be integrated
specialist expertise in the industry (operators and dispatchers in
the power system, for example). The membership values of
each function are normalized between 0 and 1.
The cost offered by generator i, Ci, for simplicity, is here
characterized by a quadratic function:
Ci ( Pgi ) = c0i + c1i Pgi + c2i Pgi
(1)
~
A ⇔ ( x1 , x2 , x3 , x4 ) = [ m,n,a ,b ]
(2)
µ(X)
1
b
a
0
x1
x2=m
x3
X
Fig. 1. Triangular membership function
µ(X)
IV.
1
a
0
x1 x2=m
b
x3=n x4X
BIDDING MODEL AND ASSUMPTIONS
In an electricity market, each generator submits an offer to
sell power. An independent system operator (ISO) is
responsible for scheduling the generators, and for dispatching
the power of those units that are scheduled on. A fundamental
assumption is that an electricity pool schedules generation by
minimizing the total offered cost [4], [11], [12]:
Ordinal optimization is based on the following two tenets:
N
CT = min
∑
Ci ( Pgi )
(3)
• It is much easier to determine “order” than “value”. To
determine whether A is better or worse than B is a simpler
task than to determine how much better is A than B (i.e. the
value of A-B) especially when uncertainties exist.
i =1
subject to
Pgimin ≤ Pgi ( t ) ≤ Pgimax i = 1 ,... , N
(4)
• Instead of asking the “best for sure”, we seek the “good
enough with high probability”. This goal softening makes
the optimization problem much easier.
N
∑P
gi
= Ps
ORDINAL OPTIMIZATION METHOD
The aggregated bid curve and the powers awards are made
in the ascending order of the bids, the goal of the ISO being the
maximization of the total social welfare of generators and
consumers [1]. From ISO point of view, its problem is
deterministic [11]. However, the bidding problems are
generally associated with the uncertainty and complexity of the
market and with the computational difficulties, so in these
situations it is desirable to ask which solution is better as
opposed to looking for an optimal solution. A systematic bid
selection method based on ordinal optimization is developed in
[9], to obtain “good enough bidding” strategies for generation
suppliers. Ordinal optimization provides a way to obtain
reasonable solution with much less effort. The ordinal
optimization method has been developed to solve complicated
optimization problems possibly with or without uncertainties.
Fig. 2. Trapezoidal membership function
III.
(6)
where c0i is generation’s fixed cost and c1i , c2i the cost
coefficients (c1i , c2i >0).
For generators, the bidding strategies are considered using
a fixed demand as in usual electricity pool. The generators
submit their bids in the same form as of their marginal cost, by
increasing or keeping constant their bid curve coefficients.
The bid consists of price offers and the amount of load to be
satisfied by the market for each hour. Thus, a generator with
an energy unit Gi having production cost Ci sets a bid price pi
for that unit. The winners will be determined by the ordered
price bid stack given the demand level.
All the bids of the generators are collected by ISO, who
decides Marginal Clearing Price (MCP) and hourly generation
levels of each power generator [11]. The MCP is set as the
lower price unit where the corresponding offered quantities
are equal to or exceed the demand. This principle, combined
with the constraints set by the power generator’s capacity
range and the fact that there is no demand side bidding, may
oblige the dispatching of a power generator at its technical
minimum even though this exceeds the demand.
It is important to re-emphasize that irrespective of whether
marginal pricing or pay-as-bid pricing is used, the market is
cleared by solving the same type of optimization problem
defined by (3) – (6).
Uncertainties in power systems related to the load levels
can be represented as fuzzy numbers, with membership
functions over the real domainℜ. A fuzzy number can have
different forms: linear, piecewise-linear, hyperbolic, triangular,
trapezoidal, or Gaussian. Most used forms are the triangular
~
and trapezoidal. A fuzzy number A is usually represented by
its breaking points, Fig. 1 and Fig. 2:
~
A ⇔ ( x1 , x2 , x3 ) = [ m , a ,b ]
2
(5)
i =1
where N represent the total number of generators from system,
To apply ordinal optimization framework to integrated
generation scheduling and bidding, major efforts are needed to
build power market simulation models and to devise a strategy
to construct a small but good enough select set. The basic idea
Pgimin and Pgimax are the minimum and maximum generation
limits.
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6TH INTERNATIONAL CONFERENCE ON MODERN POWER SYSTEMS MPS2015, 18-21 MAY 2015, CLUJ-NAPOCA, ROMANIA
obtained in the case of Strategy S3 (below 1.5 percent), when
the generators bid more power slices (in our case 10 slices).
is to use a rough model that describes the influence of bidding
strategies on market clearing price, MCP.
V. STUDY CASE
To illustrate the simulating action and MCP forecasting, a
simple electricity pool model with five generators is
considered. The generators are part of a power system with 11
nodes, Fig. 3. The test power system was modeled in
PowerWorld simulation software.
Table 2. Generator bid prices
Strategy
Slice
Size [MWh]
G1
G3
G5
G7
100 166,66 66,66 66,66
100 166,66 66,66 66,66
100 166,66 66,66 66,66
60
100
40
40
60
100
40
40
60
100
40
40
60
100
40
40
60
100
40
40
30
50
20
20
30
50
20
20
30
50
20
20
30
50
20
20
30
50
20
20
30
50
20
20
30
50
20
20
30
50
20
20
30
50
20
20
30
50
20
20
No.
S1- low
bid
(3 slices)
1
2
3
1
2
3
4
5
1
2
3
4
5
6
7
8
9
10
S2average
bid
(5 slices)
S3- high
bid
(10
slices)
Bid Prices [$/MWh]
G10
100
100
100
60
60
60
60
60
30
30
30
30
30
30
30
30
30
30
G1
9,97
11,51
13,05
9,66
10.59
11,51
12,43
13,36
9,43
9,89
10,35
10,82
11,28
1174
12,20
12,66
13,13
13,59
G3
10,57
13,34
16,11
10,02
11,68
13,34
15,00
16,66
9,61
10,44
11,27
12,10
12,93
13,76
14,59
15,41
16,25
17,08
G5
11,20
12,48
13,76
10,94
11,71
12,48
13,25
14,02
10,75
11,14
11,52
11,90
12,29
12,67
13,06
13,44
13,82
14,21
G7
10,97
12,22
13,47
10,72
11,47
12,22
12,97
13,72
10,53
10,90
11,28
11,68
12,03
12,41
12,78
13,16
13,54
13,91
1875
2100
G10
10,95
14,29
17,61
10,29
12,29
14,29
16,29
18,29
9,79
10,79
11,79
12,78
13,78
14,78
15,78
16,78
17,77
18,77
20.0
Price [$/MWh]
Strategy S1
Strategy S2
15.0
Fig. 3. The test power system
5.0
10.0
It assumed that each generator bids more slices in the
market corresponding to a portion of cost curve. This is
equivalent to assume that each generator owns more slices
(production units). For each generator were considered three
bidding strategies identified by linguistic categories "low bid"
(3 slices) – Strategy 1, "average bid" (5 slices) – Strategy 2 and
"high bid" (10 slices) – Strategy 3. Using the characteristics
presented in Table 1 and equation (6), the bid prices are
calculated, Table 2.
0
Fig. 4. The aggregated bid curves for strategies S1 and S2
B
[$/MW h]
7,66
7,53
9,60
9,40
72,9
c
[$/MW2 h]
0,0077
0,0083
0,0096
0,0094
0,0100
Pmin
[MW]
100
100
50
50
100
Pmax
[MW]
400
600
250
250
600
3.5
Strategia
Strategy 1
Strategia
Strategy 2
2
6
Strategia
Strategy 3
3
2.5
Eroare a [%]
G1
G3
G5
G7
G10
a
[$/h]
58,9
65,6
96,0
94,0
72,9
1250
Generator Bid [MW]
Table 1. Economic characteristics for the generators
Generator
625
The assumptions for MCP forecasting are the following:
•
ISO uses a market clearing tool based on a single
round of bidding;
•
the bids of load are ignored;
•
bilateral contracts are ignored.
Further, the effect of load uncertainty on MCP will be
assessed using the fuzzy models for nodal loads. Using the
fuzzy models and ordinal optimization method, MCP was
forecasted for each bidding strategy. The results are presented
in Fig. 5.
The comparison of obtained results indicated a high
influence of bidding strategies and load uncertainties on MCP
forecasting. Thus, the lowest forecasting errors of MCP were
2
1.5
1
0.5
0
1
3
4
5
7
8
9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
Tim p [h]
Fig. 5. Forecasting errors of MCP
CONCLUSIONS
In the paper, an approach for the hourly market clearing
price forecasting in a deregulated electricity market
environment using fuzzy models for nodal loads is proposed.
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6TH INTERNATIONAL CONFERENCE ON MODERN POWER SYSTEMS MPS2015, 18-21 MAY 2015, CLUJ-NAPOCA, ROMANIA
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The ordinal optimization method has been used to solve
optimization problem with load uncertainties using a market
model that describes the influence of bidding strategies on
market clearing price. It was assumed that each generator bids
more power slices in the market corresponding to a portion of
cost curve. This is equivalent to assuming that each generator
owns more slices (production units), with “low bid” (Strategy
S1), “medium bid” (Strategy S2), and “high bid” (Strategy S3).
As a result, this forecasting method of MCP has the
advantages of a good accuracy in a deregulated market.
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