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06/10/2022
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Security Constrained Unit
Commitment and Economic
Dispatch by AC Sensitivity Factors
1
9881
Agenda
●I. Introduccion
●II. Proposed Method
●A. 1st stage: ZDAM model
●B. 2nd stage: SCUCED method
●III. MERIT-ORDER CRITERIUM ZDAM
RESULTS
●IV. SCUCED RESULTS ANALYSES
●V. Conclusions
●References
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Introduction (1/2)
●One of the most critical problems of power system
operation is the secure and economic scheduling
of the power production of the generation units over
time.
●This problem is typically referred to as the unit
commitment (UC) problem.
●The current UC are mixed-integer programming
problems, and they minimise the cost to supply
the forecasted electrical load considering the
power plants' technical constraints (e.g.,
minimum and maximum power, minimum up-/down-
time, etc.).
●The concept of security-constrained UC
(SCUC) has been introduced in [1] to obtain
a feasible solution from the network
perspective, including the network
constraints in the problem formulation.
●Despite the difficulty of the mathematical
problem, due to the complexity of the
objective function, the number of decision
variables, the length of the time horizon, the
number of system constraints and
operational requirements, it must be solved
in a small-time [2].
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Introduction (2/2)
●This paper proposes a bi-stage optimisation
problem to develop a SCUC with economic
dispatch (SCUCED) optimisation.
●Initially, a zonal day-ahead market (ZDAM)
optimisation problem is solved during the first stage.
●Then, it considers the interzonal flow bounds and
generators' rated power, aiming at minimising the
generation production costs.
●The dispatched power of the generators is exploited
in the second stage to solve the SCUCED
optimisation problem, in which the goal is to
minimise the re-dispatching, operating, and start-up
costs considering generators and network
constraints.
●In particular, in this stage, an AC load flow
is carried out to evaluate the overall
operating condition of the system.
●The network constraints are included in
the optimisation problem utilising linearised
sensitivity factors to consider both active
and reactive power balance, as well as the
network losses.
●The approach is applied to a modified
version of the IEEE 39-bus test system [8]-
[9].
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II. Proposed Method
II. Proposed Method
●Fig. 1 shows the framework of the proposed bi-
stage optimisation model.
●In the first stage, the ZDAM is solved by providing
the generation bids, the required load and the
interzonal flow bounds.
●It is a merit-order criterium market in which the
UC constraints are neglected, and only the unit's
rated power is considered.
●This formulation is based on the Pan European
Single DAM, which the cross-border constraints
must fulfil [10].
●In the second stage, the dispatched power obtained
from the ZDAM is used to develop a SCUCED
optimisation problem in order to fulfil generators and
network constraints.
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Fig. 1. Flow diagram showing the proposed
SCUCED method.
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II. Proposed Method
●The main advantage in subdividing the
methodology into two stages is represented by the
UC and ED re-dispatch involving the AC network
constraints in order to define generation scheduling
fulfilling the network requirements.
●In the European framework, these operations are
usually developed in the Intraday-Market keeping a
zonal detail of the transmission network [11].
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Fig. 1. Flow diagram showing the proposed
SCUCED method.
A. 1st stage: ZDAM model
●The ZDAM optimisation problem is the same as
proposed in [8], and in the following, it is briefly
explained below.
●Consider an electrical power system made up of NZ
market zones with NGgenerators installed among
them and NL interzonal connections.
●The ZDAM optimisation problem seeks to minimise
the generation costs (CT) at a single time period (tk)
over a time window composed of NTtime steps:
●where the vector of the total active power
dispatched (PG) at the moment tkis:
●and the total cost of generation (CT) at the
moment tk is:
●where Pgs(tk) is the accepted active power
of the s-th step (considering a set of NS
stepwise bids) of the g-th generator, and
Cgs is the marginal cost of the s-th bid step
of the g-th generator.
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( )
( )
min ,
kTk
tCt
GG
PP
( ) ( ) ( ) ( )
12
=
NG
T
k G k G k G k
t P t P t P t
G
P
( ) ( )
11
,==
=
GS
NN ss
T k g g k
gs
C t C P t
G
P
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A. 1st stage: ZDAM model
●The objective function is subject to the following
constraints:
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( ) ( ) ( )
1 1 1
= = =
−=
GS L
NN N
z s z tie d
g g k l l k z k
g s l
P t P t P t
( ) ( ) ( )
1 1 1 1= = = =
−=
GS LZ
NN NN
s tie d
g k l k z k
g s l z
P t P t P t
,
0 ( )
s s max
g k g
P t P
sNS, gNG
( )
max
1
0
=
S
Ns
g k g
s
P t P
( )
lb tie ub
l l k l
P P t P
gNG
lNL
B. 2nd stage: SCUCED method
●The objective function of the SCUCED goal is to
minimise thermal generator re-dispatching,
operating, and start-up costs and the cost of the
RES curtailment.
●The optimisation problem embeds, therefore:
○(i) minimum up- (MUT) and downtime (MDT),
○(ii) generators' active and reactive power limits,
○(iii) maximum branch power flow, and
○(iv) bus voltage constraints.
●The thermal unit operating costs are the unit
marginal ones to perform in a perfect competition
market. In contrast, a penalty fee is imposed on RES
to avoid their curtailment (downward re-dispatch).
●Generators' limits involve the compliance of
the minimum and the maximum power of
both active and reactive power and the MUT
and MDT.
●Moreover, these generators' parameters, as
well as the marginal costs, depend on the
power plant's technology and fuel.
●The ED is based on stepwise bids in order
to define a merit order criterium as well as in
ZDAM. The problem is solved considering
the generator's active power dispatch and
the RES curtailment as control variables.
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III. MERIT-ORDER CRITERIUM ZDAM RESULTS
III. MERIT-ORDER CRITERIUM ZDAM RESULTS
●In this stage, the authors formulated and solved the
problem as presented in [8]-[9].
●The modified IEEE 39-bus test system has an
installed capacity of 52% of RES and several
thermal generation units (TGU), both installed in
three market zones: Z1, Z2 and Z3.
●The TGUs have a piecewise marginal price
varying according to the technology and the fuel.
●The system's RES comprises 14 solar
power plants (SPPs) and ten wind power
plants (WPP) of different sizes, with a total
installed capacity of 3,600 MVA.
●The TGU technologies are combined cycle
(CC), combustion turbines (CT) and steam
turbines (ST), supplied by Natural Gas
(NG), Coal or Oil with a total capacity of
3,300 MVA among ten units.
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III. MERIT-ORDER CRITERIUM ZDAM RESULTS
●Table 1 shows the active power limits (PMIN and
PMAX), the start-up costs (CSU), and the MUT and
MDT of the TGUs. All the parameters, except the
maximum power, have been obtained considering
the available data of [12]-[13].
●In particular, they are evaluated concerning each
power plant's technology, fuel, and rated power.
●Therefore, the Exchange is the only generator
devoid of proper technical parameters and start-up
costs as it represents an equivalent interconnection
exchange.
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III. MERIT-ORDER CRITERIUM ZDAM RESULTS
●The ZDAM simulations are carried out during the
yearly peak load day, and its hourly profile is shown
in Fig. 2.
●The daily required energy is 72.85 GWh.
The resulting dispatched generation is
shown in Fig. 3.
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III. MERIT-ORDER CRITERIUM ZDAM RESULTS
●Fig. 4 shows the RES penetration percentage of the
required load. The RES covers a daily mean of 37%
of the total load, above the 32% of the European
2030 target [14].
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IV. SCUCED RESULTS ANALYSES
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IV. SCUCED RESULTS ANALYSES
●Fig. 5 shows the net re-dispatched power after the
SCUCED solving.
●Compared with the results of Fig. 3, it can be seen
during 3:00-5:00 that the Coal generator is kept
active at minimum power for the MUT constraint.
●During those hours, being a lack of production,
only the reference machine downward re-
dispatching and wind curtailment can allow the
power balance. In the market splitting hours,
the Exchange is the most exploited generator
for upward movement re-dispatching.
●It is the second cheaper unit, and due to the N-
1 security criterium of the ZDAM boundaries, its
dispatching was limited in the previous stage.
●Therefore, the total branch limits included in the
SCUCED allow the increase in Exchange
production, reducing the NG dispatched power,
which is more expensive during those hours.
●At 18:00 and 19:00, the CT and ST NG units
are dispatched in the ZDAM, but downstream
the SCUCED solution both are shut down. The
ST NG units have a MUT of 8:00, but both the
technologies have a marginal price higher than
the Exchange
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IV. SCUCED RESULTS ANALYSES
●Regarding the total re-dispatched costs reported in
Fig. 6, the RES curtailment cost equals 36.08 k$ for
the three hours.
●Fig. 7 and Fig. 8 show, respectively, the
maximum, mean and minimum values of the
branch loadings and nodal voltages after the
SCUCED solution.
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IV. SCUCED RESULTS ANALYSES
●Fig. 7 and Fig. 8 show, respectively, the maximum,
mean and minimum values of the branch loadings
and nodal voltages after the SCUCED solution.
●Finally, a comparison of the system losses
is presented in Fig. 11.
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V. CONCLUSIONS
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V. CONCLUSIONS
●In this paper, a bi-stage SCUED is proposed.
●The main advantage of this approach is the
simulation of SCUCED problems considering
linearised sensitivity matrices deriving from AC load
flow equations in the optimisation problem.
●Therefore, power flow and voltage, as well as the
UC, constraints are embedded in the proposed
method.
●The method has been applied to a modified version
of the IEEE 39-bus test system with 37% of RES
penetration during the yearly peak hour day.
●The results show that the generation is re-
dispatched, accomplishing generation and
network constraints set in the optimisation
problem.
●The RES has been curtailed only in the
hours with a low load required, in which only
wind power plants are dispatched in order to
satisfy the MUT constraint of the ST Coal
TUG.
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VI. REFERENCES
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VI. REFERENCES
[1] H. Ma and M. Shahidehpour, "Transmission constrained unit
commitment based on benders decomposition," Electr. Power Energy Syst., vol. 20, no.
4, pp. 287–294, April 1998.
[2] W. van Ackooij, I. Danti Lopez, A. Frangioni, F. Lacalandra, and M.
Tahanan, "Large-scale unit commitment under uncertainty: an updated literature
survey," Ann. Oper. Res., vol. 271, no. 1, pp. 11–85, 2018, doi: 10.1007/s10479-018-
3003-z.
[3] C. Yonghong, P. Feng, Q. Feng, X. Alinson, Z. Tongxin, et al. "Security-
Constrained Unit Commitment for Electricity Market: Modeling, Solution Methods, and
Future Challenges", TechRxiv, Preprint, 2022, doi: 10.36227/techrxiv.19500710.v1.
[4] D. Villanueva, A. E. Feijóo, and J. L. Pazos, "An analytical method to
solve the probabilistic load flow considering load demand correlation using the DC load
flow," Electr. Power Syst. Res., vol. 110, pp. 1–8, 2014, doi:
10.1016/j.epsr.2014.01.003.
[5] Q. Ploussard, L. Olmos, and A. Ramos, "A Search Space Reduction
Method for Transmission Expansion Planning Using an Iterative Refinement of the DC
Load Flow Model," IEEE Trans. Power Syst., vol. 35, no. 1, pp. 152–162, 2020, doi:
10.1109/TPWRS.2019.2930719.
[6] J. WANG, H. ZHONG, Q. XIA, and C. KANG, "Transmission network
expansion planning with embedded constraints of short circuit currents and N-1
security," J. Mod. Power Syst. Clean Energy, vol. 3, no. 3, pp. 312–320, 2015, doi:
10.1007/s40565-015-0137-8.
[7] K. Purchala, L. Meeus, D. Van Dommelen, and R. Belmans, "Usefulness
of DC power flow for active power flow analysis," 2005 IEEE Power Eng. Soc. Gen.
Meet., vol. 1, pp. 454–459, 2005, doi: 10.1109/pes.2005.1489581.
[8] G. Tricarico, R. Wagle, M. Dicorato, G. Forte, F. Gonzalez-Longatt, J. L.
Rueda, "Zonal Day-Ahead Energy Market: A Modified Version of the IEEE 39-bus Test
System", submitted to IEEE ISGT Asia 2022.
[9] G. Tricarico, R. Wagle, M. Dicorato, G. Forte, F.
Gonzalez-Longatt, J. L. Rueda, "A Modified Version of the IEEE 39-
bus Test System for the Day-Ahead Market", submitted to IEEE
ISGT Europe 2022.
[10] ENTSO-E, "Single Day-Ahead Coupling (SDAC) ".
Available online:
https://www.entsoe.eu/network_codes/cacm/implementation/sdac/#:
~:text=SDAC%20is%20an%20initiative%20between,power%20for%
20the%20following%20day (accessed on May 15, 2022).
[11] ENTSO-E, "Single Intraday Coupling (SIDC)".
Availabe online:
https://www.entsoe.eu/network_codes/cacm/implementation/sidc/
(accessed on May 15, 2022).
[12] An Extended IEEE 118-Bus Test System With High
Renewable Penetration. Available online:
https://item.bettergrids.org/handle/1001/120 (accessed on May 15,
2022).
[13] I. Peña, C. B. Martinez-Anidoand B. Hodge, "An
Extended IEEE 118-Bus Test System With High Renewable
Penetration," in IEEE Transactions on Power Systems, vol. 33, no.
1, pp. 281-289, Jan. 2018.
[14] Renewable Energy, Moving Towards a Low Carbon
Economy, Eur. Commission, Brussels, Belgium, 2018.
[15] Anantha Pai, Energy Function Analysis for Power
System Stability. Springer, 19.
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Security Constrained Unit
Commitment and Economic
Dispatch by AC Sensitivity Factors
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9881
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