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European Market Coupling Algorithm incorporating
clearing conditions of block and complex orders
Grigoris A. Dourbois* and Pandelis N. Biskas
Power Systems Laboratory, Department of Electrical and Computer Engineering
Aristotle University of Thessaloniki, Greece
*
Corresponding author: [email protected]
1
Abstract- In this paper an algorithm for the solution of the
European electricity market coupling is presented, considering
all block and complex orders available in the European Power
Exchanges. The model takes into account the clearing conditions
of profile and regular block orders, linked block orders,
exclusive group of block orders and flexible hourly orders, as
well as the clearing conditions of Minimum Income Condition
and Load Gradient orders, possibly under a scheduled stop
condition. The model considers also hourly flow ramping
constraints on single interconnections or group of
interconnections,
net
position
ramping
constraints,
interconnection losses and tariffs. The flow-based approach is
implemented, using the zonal PTDF matrix. The algorithm
eliminates possible paradoxically accepted block and MIC
orders within an iterative process. The proposed algorithm is
evaluated in a pan-European day-ahead electricity marketplace.
only the supply hourly offers subject to Load
Gradient condition Slg ⊆ S
d ∈ Da
po ∈ POa
eg ∈EG
fh ∈ FH a
Index Terms—European electricity market, block and
complex orders, iterative algorithm, mixed integer linear
programming.
I.
NOMENCLATURE
A. Indices and Sets
set of dispatch periods in the dispatch day
t ∈T
(typically, the dispatch period is one hour)
a∈ A
set of European bidding areas
set of bidding areas connected to bidding area a
a′ ∈ Aa
AaAC , AaDC set of bidding areas connected to bidding area a
with
an AC and DC line, respectively,
A ∪ AaDC = Aa
set of interconnections and inter-zonal corridors;
L = LAC ∪ LDC (for AC/DC interconnections
and inter-zonal corridors, respectively) connecting
area a to a’.
set of simple supply hourly offers submitted at
bidding area a, Sa ⊆ S ; the subset Slg includes
AC
a
l ∈L
s ∈ Sa
This work was supported in part by the State Scholarships
Foundation of Greece in the context of the “IKY Fellowships of
Excellence for Postgraduate studies in Greece – Siemens Program”
and in part by the General Secretariat of Research and Technology
(GSRT), Hellenic Ministry of Education and Religious Affairs,
Culture and Sports, in the context of the Action “ARISTEIA II”
(Project Code: 4596)
p ∈ Pa
set of simple demand hourly bids submitted at
bidding area a, Da ⊆ D
set of profile block orders submitted at bidding
area a, where po includes sp ∈ SPa for supply
profile block offers, dp ∈ DPa for demand profile
block bids, and slp ∈ SLPa for supply linked
profile block offers;
POa = SPa ∪ DPa ∪ SLPa , POa ⊆ PO
Set of exclusive groups of block orders
set of flexible hourly orders submitted at bidding
area a, where fh includes fho ∈ FHOa for flexible
hourly offers and fhb ∈ FHBa for flexible hourly
bids;
FH a = FHOa ∪ FHBa , FH a ⊆ FH
set of combinatorial products submitted at bidding
area a, where p includes sp ∈ SPa , dp ∈ DPa ,
slp ∈ SLPa fho ∈ FHOa and fhb ∈ FHBa ;
,
Pa = SPa ∪ DPa ∪ SLPa ∪ FHOa ∪ FHBa ∪ EGa
Pa ⊆ P
B. Parameters
price-quantity pair of the hourly priced energy
Pst , Qst
offer s in dispatch period t, in €/MWh and
MWh, respectively
price-quantity pair of the hourly priced demand
Pdt , Qdt
bid d in dispatch period t, in €/MWh and MWh,
respectively
price-quantity pair of profile block order po, in
Ppo , Q tpo
€/MWh and MWh, respectively; the quantity
Q tpo for a given profile order po may be
Pfho , Q fho
Pfhb , Q fhb
different in each dispatch period t
price-quantity pair of flexible hourly order
fho/fhb, in €/MWh and MWh, respectively; the
flexible hourly offers/bids constitute just one
quantity
Tpo (Tpo )
slp
IM sp
IM eg
po
LAa+,l , LAa−,l
max
R min
po , R po
LGsup,t , LGsdn,t
RU a , RDa
rd
FLru
l , FLl
FLl
starting (ending) dispatch period of profile block
order po
Incidence matrix relating the supply linked
profile block order slp to the supply profile
block order sp (when equal to 1);
Incidence matrix relating the profile block order
po to exclusive group eg (when equal to 1);
Incidence matrices relating the corridor l to area
a; denoting start of corridor l (the elements of
LAa+,l are equal to 1, else zero) and end of
corridor l, respectively (the elements of LAa+,l
are equal to -1, else zero);
Minimum and maximum acceptance ratio of
profile block order po in p.u., respectively;
maximum increment/decrement allowed in a
Load Gradient Order
ramp up and ramp down rate limit of the net
position of bidding area a from hour t-1 to hour
t, in MWh, respectively;
ramp up and ramp down rate flow limit from
bidding area a to bidding area a΄ from hour t-1
to hour t, in MW, respectively;
line flow limit in corridor l, in MW
Lossl
Power Transfer Distribution Factor on
interconnection (or inter-zonal corridor) l for an
energy transfer from area α to reference area ref,
in p.u.
loss factor of line l, in p.u.
Tariffl
flow tariff in line l,in €/MW
PTDFl a ,ref
C. Main variables
cleared quantity of supply entity s in dispatch
xst
period t, in MWh
t
cleared quantity of demand entity d in
xd
dispatch period t, in MWh
clearing status of flexible hourly offer/bid
u tfho , u tfhb
fho/fhb, respectively, in dispatch period t
u po
clearing status of profile order po
line flow in corridor l, in MW
flowt
l
flowl+,t ,
painj,t
flowl−,t two positive components (in different
directions) of line flow in corridor l, in MW
Net energy injection to bidding area a during
dispatch period t.
D. Functions
cost function of the supply offer s in dispatch
cst
period t, in €/h
t
utility function of the demand bid d in dispatch
cd
period t, in €/h
cost/utility function of product p in dispatch
c tp
period t, in €/h
t
function denoting cleared quantity of product p
vp
in dispatch period t, in MWh
II. INTRODUCTION
The integration of the European electricity markets has
initiated with the integration of the day-ahead markets, and it
is expected to continue within the next years with the
subsequent integration of the intra-day and balancing
markets. The PCR market coupling algorithm [1] is already
used for the solution of the day-ahead markets of the
Northern, Central and Western European Power Exchanges
(PXs), it has already incorporated the Italian PX in February
2015 and it is expected to incorporate also the CentralEastern PXs till December 2015.
The solver developed by the PCR members for the
European day-ahead market coupling is called “EUPHEMIA”
[1], and concerns a primal-dual iterative process, which
incorporates all orders/products tradable in the European
PXs, namely simple hourly, block (Nordpool, CWE),
complex (OMIE, Iberian market) and PUN (GME, Italy)
orders. The model description and the functionality of the
EUPHEMIA solver have been published in October 2013 [1].
Block orders are “fill-or-kill” (all-or-nothing) orders,
namely they are accepted or rejected in their entirety and they
are the main reason for not existing a market equilibrium with
uniform prices in the da-ahead market. These orders
introduce inter-temporal constraints and mimic some of the
unit technical (e.g. technical minimum) and operational
constraints (e.g. fuel availability, especially for hydro units)
and/or multi-period cost structures (start-up cost, shut-down
cost, no-load or minimum-load cost). Complex orders
constitute a set of simple step-wise supply hourly orders that
are subject to a Minimum Income Condition (MIC) and/or a
Load Gradient (LG) condition, with or without a “scheduled
stop” condition and are tradable in Spanish power Exchange
OMIE [2].
In the literature several papers have been published during
the last years presenting methods to facilitate the nonconvexities occurred in the day-ahead market by introducing
block orders (simulating the “COSMOS” solver, which was
used previously for the solution of CWE day-ahead market)
[3]-[10]. In [3] the “Centralized Market Coupling” method is
applied to a network consisting of several areas, through an
iterative procedure. The results are compared with the ones
achieved by a single pool, simulated by means of a market
splitting method. In [4], the prospect of integration of a fivemarket system using the “Trilateral Market Coupling”
algorithm is examined, while in [5], the need for price
coordination between power exchanges, so that prices can
correctly give locational signals for network development,
generation and consumption is thoroughly discussed. In view
of the forthcoming coupling, a centralized market splitting
algorithm is implemented in [6] respecting the standard
market regulatory framework of PXs and power pools
including the products and the operation and system
constraints that are used. In [7] a bi-level model is presented,
containing integer variables in the upper level and continuous
variables in the lower level, whereas in [8] a MPEC model is
presented and is used for the clearing of power exchanges
with block orders. The model is decomposable into a MIQP
and a linear pricing problem. It uses a branch-and-bound
algorithm, and cuts are added to the optimization problem. In
[9]-[10] a new MIP formulation for the European day-ahead
market clearing is presented avoiding complementarity
constraints to express market equilibrium conditions. In [9] a
second stage is used where an uplift price is computed, which
is imposed to each paradoxically accepted block order, in
order to ensure a nonnegative social welfare of all accepted
orders. In [10] the new MIP model has also a decomposable
structure and allows Benders-like cuts.
However, to the best of the authors’ knowledge, the
clearing of European day-ahead markets with simultaneously
block and complex orders, and incorporating the full
functionality of EUPHEMIA, has not been presented yet. In
this paper, the flow-based day-ahead market coupling
problem is mathematically formulated as a Mixed-Integer
Linear Programming (MILP). An iterative process is
employed for handling the Paradoxically Accepted Blocks
(PABs) and the MIC orders not satisfying their minimum
income clearing condition. The main goal of this paper is not
to present a model comparable to EUPHEMIA but to present
and evaluate a new, different model for the clearing of the
pan-European day-ahead market bearing and covering the full
functionality of EUPHEMIA, except for the modeling of
PUN orders, which require a different modeling approach for
their simulation. The proposed model is tested in terms of
solvability and computational efficiency using a test case of
similar size to the cases tested by EUPHEMIA [11].
III.
PROBLEM FORMULATION
As stated in the Introduction, the full set of simple, block
and complex orders, tradable in the European day-ahead
markets and simulated by EUPHEMIA, has been
incorporated in our model. The related optimization problem
is formulated as a Mixed Integer Linear Programming model,
due to the presence of binary variables for handling the fillor-kill conditions of block orders, considering also their
possible Minimum Acceptance Ratios. It is noted that the
MIC orders do not require a binary variable for their
handling; the hourly sub-orders of a MIC order are included
as simple hourly orders in the MILP model, and then a postprocess checks for the satisfaction of their price clearing
condition, as described in the following Section.
The day-ahead market clearing problem is formulated as
follows:
t
⎡ ∑ cst − ∑ cdt + ∑ csp
⎤
−
⎢ s∈Sa
⎥
d ∈Da
sp∈SPa
Min ∑ ∑ ⎢
⎥ +
t
t
t
a∈A t∈T ⎢ ∑ cdp +
∑ c fho − ∑ c fhb ⎥
(1)
fho∈FHOa
fhb∈FHBa
⎣⎢ dp∈DPa
⎦⎥
∑ Tariffl ⋅
flowlt
∑
∑
l∈L
∑
s∈Sa
xst
−
∑
fho∈FHOa
∑
l∈L
LAa+,l
d ∈Da
xdt +
vtfho −
⋅[
sp∈SPa
∑
fhb∈FHBa
flowl+,t
, ∀d ∈ D, t ∈ T
(4)
∑ u tfho ≤ 1
∀fho ∈ FHO, t ∈ T
(5)
∑ u tfhb ≤ 1
∀fhb ∈ FHB, t ∈ T
(6)
t∈T
t∈T
max
R min
po u po ≤ x po ≤ R po u po
xslp ≤
∑
po∈PO
∑
sp∈SP
slp
IM sp
xsp
∀sp ∈ SP
IM eg
po x po ≤ 1
painj,t −
∑
fho∈FHOa
−
xst +
s∈Sa
∑
painj,t
∀po ∈ PO
vtfho +
painj,t −1
∀eg ∈ EG
∑
xdt −
d ∈Da
∑
fhb∈FHBa
∑
sp∈SPa
vtsp +
vtsp −
∑
dp∈DPa
vtdp +
vtfhb −
− (1 − Lossl ) ⋅
(9)
∑
dp∈DPa
vtdp −
vtfhb = 0 , ∀a ∈ A , t ∈ T
(10)
≤ RU a
, ∀ a ∈ A, t ∈ T
(11)
painj,t −1 − painj,t ≤ RDa
, ∀ a ∈ A, t ∈ T
(12)
xst − xst −1 ≤ LGsup,t
, ∀s ∈ S lg , t ∈ T
(13)
xst −1 − xst ≤ LGsdn,t , ∀s ∈ S lg , t ∈ T
(14)
flowlt =
∑
a∈A
painj,t ⋅ PTDFl a , ref
∀ a ∈ A , l ∈ LAC , t ∈ T
flowlt = flowl+,t − flowl−,t
flowlt ≤ FLl
∀ a∈ A
, l ∈ L, t ∈ T
, ∀ l ∈ L, t ∈ T
(15)
(16)
(17)
flowlt − flowlt −1 ≤ FLru
l
, ∀ l ∈ L, t ∈ T
(18)
flowlt −1
, ∀ l ∈ L, t ∈ T
(19)
−
flowlt
≤
FLrd
l
where
cst = Pst ⋅ xst
cdt = Pdt ⋅ xdt
ctp = Pp ⋅ vtp
∀s ∈ S , t ∈ T
(20)
∀d ∈ D , t ∈ T
(21)
∀p ∈ P, t ∈ T
(22)
( (
)
(
t
vtsp = usp ⋅ Qsp
⋅ U t − Tsp − U t − Tsp
( (
))
∀sp ∈ SP, t ∈ T
)
(
t
vtdp = udp ⋅ Qdp
⋅ U t − Tdp − U t − Tdp
))
(23)
(24)
vtfho = u tfho ⋅ Q fho
∀fho ∈ FHO, t ∈ T
(25)
vtfhb = u tfhb ⋅ Q fhb
∀fhb ∈ FHB, t ∈ T
(26)
(2)
flowl−,t ] −
∑ LAa−,l ⋅ [ flowl+,t ⋅ (1 − Lossl ) − flowl−,t ] = 0
, ∀s ∈ S , t ∈ T
(7)
(8)
∀dp ∈ DP, t ∈ T
l∈L
xst ≤ Qst
xdt ≤ Qdt
, ∀a ∈ A , l ∈ L , t ∈ T
(3)
The objective function (1) comprises the total offer cost
minus the total load utility plus the cost incurred from the
flow tariffs. The objective function is subject to market order
and network constraints. The market order constraints express
the feasibility region of the problem solution concerning the
simple supply offers and demand bids, and the clearing
conditions of block orders (profile block orders, linked block
orders, exclusive groups of block orders and flexible hourly
orders) and complex orders. Especially, equation (2)
represents the power balance equation in each bidding area.
Constraints (3)-(4) express the feasibility region of the
problem solution concerning the simple supply offers and
demand bids. Constraints (5)-(6) express the clearing
conditions for flexible hourly offers/bids. Equation (7)
imposes that the clearing status of a profile block order
should always be zero or between its minimum and maximum
acceptance ratio (the latter is usually equal to 1). In case of a
max
regular block order ( R min
po = R po = 1 ) equation (7) is
converted into a “fill-or-kill” constraint. Constraint (8)
expresses the relationship between the linked block orders
and their “parent” orders. Constraint (9) forces the sum of the
accepted ratios of block orders belonging to exclusive group
eg to be less than 1. Equation (10) defines the net injection
(also called “net position”) of bidding area a. Equations (11)(12) denote the limitation on the variations of the net position
from period t-1 to period t. Constraints (13)-(14) indicate that
the amount of energy that is matched by the hourly suborders belonging to a Load Gradient order in dispatch period t
is limited by the amount of energy that was matched by the
hourly sub-orders in the dispatch period t-1.
Finally, a DC power flow model represents the inter-zonal
flow on AC lines; additionally, tariffs and variable losses are
included for the DC lines. Equations (15)-(16) define the
inter-zonal flow on AC lines and constraint (17) represents
the limit of the flow in both AC and DC lines. Equations
(18)-(19) express the hourly variations of the flow over an
interconnector. The ramping limit may be different for each
period. For the first period, the limitation of flow takes into
account the value of the flow of the last hour of the previous
day.
Equations (20)-(22) express the cost/utility functions of
hourly and profile orders that are included in the objective
function and are defined by the product of the corresponding
cleared quantity-price pairs. Equations (23)-(26) express the
cleared quantities of the hourly and profile block offers/bids.
IV.
SOLUTION ALGORITHM
The MILP model described above is solved within an
iterative process for handling the Paradoxically Accepted
Block orders and the orders not satisfying Minimum Income
Condition. The proposed process constitutes a simpler
process as compared to the iterative processes of
EUPHEMIA [1]; it employs the following steps:
a) The MILP problem described in Section II is solved, and
the market clearing prices (MCPs) for each trading
period (hour) of the trading day and for each bidding
area, along with the attained welfare of each block order,
are attained.
b) A post-process begins, in which the algorithm determines
the existence of paradoxically accepted block and
complex orders, as follows:
i) In case the welfare of an accepted block order is
negative, then the block order is designated as a
paradoxically accepted block (PAB) and it is
withdrawn from the Order Book.
ii) In case the Minimum Income Condition of a MIC
order is not satisfied even though some of its hourly
sub-orders have been cleared (which are not due to
the enforcement of a “scheduled stop” condition),
namely in case the required revenues of the MIC
order (incorporating both the variable and fixed
term) are greater than the acquired market revenues
from the market solution (sum for all hours of the
product of cleared hourly quantities multiplied by
the respective hourly MCPs), then two separate
cases are designated:
1) In case the required revenues are greater than the
acquired market revenues, but their difference is
less than a pre-defined threshold (X %) of the
required revenues, then the MIC order is
designated as paradoxically accepted, but it is
given another Y-1 chances to be normally
accepted in the following iterations of the
algorithm. Parameter Y is also pre-defined by the
respective PXs.
2) In case the required revenues are greater than the
acquired market revenues, but their difference is
greater than a pre-defined tolerance (X %) of the
required revenues, then it is considered that
there is no possibility that this MIC order shall be
ever normally accepted (satisfy its MIC
condition), and it is withdrawn from the Order
Book.
c) In case there is at least one designated paradoxically
accepted block or MIC order after step (b), the algorithm
continues with a new iteration in step (a). Otherwise, the
algorithm terminates.
It should be noted that MIC orders under a “scheduled
stop” condition (with non-zero cleared quantities for the first
three hours of the day) have a special treatment during the
iterative process, as denoted in step b)ii).
Parameters X and Y can be pre-defined by the respective
PX(s), considering the flexibility level that should be given
the paradoxically accepted MIC orders to have more chances
to satisfy their required revenues. Parameter Y (>1) has been
set due to the fact that in each iteration of the iterative process
a number of block orders are designated as PABs and are
withdrawn from the Order Book (see step b)i) above) leaving
“space” for other orders (block and/or MIC) to be normally
accepted. For example, a MIC order that is too close to satisfy
its MIC condition at one iteration, could take advantage of the
withdrawal of some PABs (corresponding to supply offers) at
the end of this iteration, and given that MCPs will be higher
at the next iteration, may succed in satisfying its MIC
condition at the next iteration of the process.
Profoundly, the selection of values for parameters X and
Y differentiates slightly the attained solution of the algorithm,
as further demonstrated in Section IV.B.
The overall solution algorithm is illustrated in Fig.1.
Solution of the Pan European centralized
market splitting problem
TABLE I.
For each bidding area
Iterations
For each hour
Calculation of MCPs
Binary variables
of Paradoxically
Accepted Blocks
are fixed to zero
and give another
Y chances or
remove the
appropriate
complex orders
Calculation of:
Welfare of block orders
Required market revenues of MIC orders
Acquired market revenues of MIC orders
MIC Orders
Are there
any paradoxically
accepted blocks?
NO
NO
Final Solution
Are
Required >Acquired
revenues?
YES
YES
Case A:
If
Required - Acquired
< X%
Required
Give Y-1 chances to be satisfied
Y=max(0,Y-1)
Case B:
If
Required - Acquired
> X%
Required
Remove from the order book
Figure 1. Overal solution algorithm
V.
the iterative process, due to the gradual withdrawal of PABs
from the Order Book (shown in the last column of Table I).
TEST RESULTS
A. Test Case
The algorithm is tested in the pan-European electricity
market, consisting of 25 existing and prospective power
exchanges, comprising a total of 42 bidding areas, since
Norway, Sweden, Denmark and Italy have 5, 4, 2 and 6
bidding zones respectively. A simplified version of the
European transmission grid is used in this paper, consisting of
59 AC and 12 DC transmission lines. The reactance of each
"equivalent" interconnector has been computed as the
reactance of all parallel AC lines between the bidding areas,
as depicted in a network model for the whole continental
Europe, provided by ENTSO-E under a non-disclosure
agreement (NDA).
It should be noted that the authors do not have the
submitted market orders in European PXs fed to EUPHEMIA
solver, since such information constitutes commercial data
that cannot be easily disclosed by the respective PXs. For
demonstration purposes, a set of 90,000 simple hourly priced
energy offers are randomly created for all bidding areas,
along with approximately 100 priced demand bids for each
bidding zone. Additionally, a set of 2,900 block orders
(profile block offers/bids, linked profile block offers/bids,
flexible hourly offers/bids, flexible block offers/bids) and 80
complex orders (subject to Minimum Income, Schedule Stop,
Load Gradient, or combining Minimum Income and Load
Gradient Condition) are randomly created. Table I presents
the problem size in each iteration, along with the number of
PABs. The number of binary variables is decreasing during
PROBLEM SIZE IN EACH ITERATION
Single
Equations
1
2
3
4
5
6
7
495,657
Single
Variables
Binary
Variables
Number
of PABs
501,138
10,376
9,917
9,876
9,830
9,828
9,824
9,823
459
41
46
2
4
1
0
B. Test results
For demonstration purposes, some indicative clearing
results are presented in this Section.
The clearing status (CS) of selected profile block offers is
presented on Table II, along with their offer prices, the
corresponding weighted average clearing prices (WACPs,
considering the start/end times of each profile offer) and their
Minimum Acceptance Ratios (MARs). The clearing status of
PBO286 is normally equal to 1, since the offer price is less
than the respective WACP. Profile block offers PBO1061 and
PBO34 bear MARs equal to 0.5 and 0.75, respectively.
PBO1061 is partially accepted and the weighted average
price is exactly equal to the offer price 31.39 €/MWh.
However, the PBO34 is also partially cleared even though the
offer price is lower than the weighted average clearing price.
This is attributed to the various constraints of the model (as
enumerated in Section II) that affect the clearing of an order.
Specifically, in this case an hourly net position ramping
constraint is binding (with a non-zero shadow price, equal to
the difference between the offer price and the WACP), and it
constrains the overall injection in the bidding area where
PBO34 has been submitted.
Table III presents the clearing process of a MIC order
with a schedule stop condition. In this run, X=20% and Y=3.
In the first three iterations, the MIC order is within the predefined tolerance (X) and it is given all three chances to be
satisfied. After the 3rd iteration, it is designated as a
paradoxically accepted MIC order (since it still has a nonzero cleared quantity), and it is withdrawn from the Order
Book, keeping only the hourly sub-orders of the first three
hours in the Order Book, due to the specified schedule stop
condition.
TABLE II.
Profile
offer
code
PBO286
PBO1061
PBO34
PROFILE BLOCK OFFERS CLEARING
Offer
price
[€/MWh]
40.57
31.39
49.66
WACP
[€/MWh]
MAR
[p.u.]
CS
[p.u.]
56.12
31.39
53.60
1.00
0.50
0.75
1.000
0.829
0.863
TABLE III.
Iter.
no
1
2
3
4
5
Cleared
Quantity
[MWh]
3,295.20
3,596.76
3,634.07
300.00
300.00
MIC ORDERS CLEARING PROCESS
Required revenues
per cleared MWh
[€/MWh]
60.46
60.00
59.95
115.00
115.00
Acquired market
revenues per cleared
MWh [€/MWh]
55.70
58.40
58.34
51.52
51.52
VI.
CS
[p.u.]
1
1
1
0
0
10
525.30
9
8
7
525.20
6
5
525.15
4
Welfare
525.10
Iterations
Welfare [106 €]
525.25
2
525.05
1
0
525.00
20%
25%
30%
35%
40%
45%
Value of parameter X
50%
60%
70%
Figure 2. Number of iterations and total welafare as a function of X
12
525.19
10
Welfare [106 €]
8
Welfare
525.19
Iterations
6
525.18
4
525.18
Iterations
525.19
525.19
2
525.18
0
525.18
2
3
4
5
In this paper a novel iterative algorithm for the clearing of
the pan-European day-ahead electricity market, eliminating
the paradoxically accepted blocks and MIC orders, is
presented. A MILP model is formulated integrating the full
set of block and complex orders which are tradable in
European PXs and fed to EUPHEMIA solver. The algorithm
is tested in a European zonal network using the flow-based
approach. The performed benchmarking verifies the
applicability of the proposed algorithm for the solution of
real-world day-ahead markets, since the computational
requirements are minimal. Further research shall be focused
in the incorporation of PUN orders and the transformation of
the zonal-based model into a nodal-based model for the better
handling of intra-zonal congestion in the European
transmission network.
REFERENCES
3
Iterations
CONCLUSIONS
6
Value of parameter Y
Figure 3. Number of iterations and total welafare as a function of Y
These hourly sub-orders are cleared by the market
solution, providing a total quantity of 300 MWh at the final
solution. Profoundly, the MIC condition is not valid for this
cleared quantity.
Finally, a sensitivity analysis is performed related to the
values of X and Y. Figures 1 and 2 illustrate the number of
iterations for attaining algorithm convergence and the total
welfare as a function of the values of X and Y, respectively.
The model has been implemented in GAMS [12] and
solved using CPLEX 12.5.1. , running in a desktop PC, with
Intel Quad Core i7 CPU processor at 3.4 GHz, 16 GB RAM.
The convergence tolerance was set to 1e-06. The total
execution time for the convergence of the solution algorithm
is less than 3 minutes in all cases studied.
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