GENERATION UNIT COMMITMENT MIXED INTEGER LINEAR MODEL FOR SIMULTANEOUS HEAT AND ELECTRIC DAILY LOAD COVERING
The unit commitment problem nowadays is widely used in the electric power sector. The problem was first time formulated in the 1940-s and still developing both methodologically and by including an additional number of technologies each of which has a different unique mathematical treatment correspon...
Збережено в:
| Дата: | 2023 |
|---|---|
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
General Energy Institute of the National Academy of Sciences of Ukraine
2023
|
| Теми: | |
| Онлайн доступ: | https://systemre.org/index.php/journal/article/view/13 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | System Research in Energy |
| Завантажити файл: |  |
Репозитарії
System Research in Energy| _version_ | 1871103025986142208 |
|---|---|
| author | Sergii Shulzhenko |
| author_facet | Sergii Shulzhenko |
| author_institution_txt_mv | [
{
"author": "Sergii Shulzhenko",
"institution": null
}
] |
| author_sort | Sergii Shulzhenko |
| baseUrl_str | https://systemre.org/index.php/journal/oai |
| collection | OJS |
| datestamp_date | 2026-07-18T12:57:30Z |
| description | The unit commitment problem nowadays is widely used in the electric power sector. The problem was first time formulated in the 1940-s and still developing both methodologically and by including an additional number of technologies each of which has a different unique mathematical treatment corresponding to the specific technology's behavior. The common characteristic of the problem such as that is dedicated to the electricity production sector, hence the mathematical formulation is following pure electricity sector transformation but during the last years the Power-to-X technologies are implemented and their further development is expected in the future. This requires the advancement or at least modification of the problem formulation to meet possible exchange and usage between different types of energy within one integrated power system. The goal of the article is to further development of the existing versions of the unit commitment problem, which are dedicated to the operation of the generation in the power system by implementing additional equations allowing contemplation of the heat energy-producing technologies which are dedicated to cover a heat-energy load of the district heating systems. This should allow for conducting comprehensive studies of the simultaneous operation of electric- and heat-generating technologies to meet the energy demand of local energy systems, which is important for designing distributed generation mix, for example at a municipal level. The proposed mixed integer linear generation unit commitment model for simultaneous heat and electric daily load covering is described in the article. The proposed model in addition to the pure electric power balance also meets heat load using only-heat technologies (fuel boilers), combined heat and power units, and also industrial-scale electric boilers - which are converting electricity to heat energy. |
| doi_str_mv | 10.15407/srenergy2023.01.025 |
| first_indexed | 2026-03-24T02:00:42Z |
| format | Article |
| fulltext |
System Research in Energy. 2023. 1(72) 25
МОДЕЛЮВАННЯ, ОПТИМІЗАЦІЯ
ТА ПРОГНОЗУВАННЯ В ЕНЕРГЕТИЦІ
______________________________________________________________________
ISSN 2786-7102 (Online), ISSN 2786-7633 (Print)
https://doi.org/10.15407/srenergy2023.01.025
UDC 621.311.661.51
Sergii Shulzhenko, PhD (Engin.), Senior Researcher, https://orcid.org/0000-0002-7720-0110
General Energy Institute of NAS of Ukraine, 172, Antonovycha St., Kyiv, 03150, Ukraine;
e-mail: mail2ua@gmail.com
________________________________________________________________________________
GENERATION UNIT COMMITMENT MIXED INTEGER LINEAR MODEL
FOR SIMULTANEOUS HEAT AND ELECTRIC DAILY LOAD COVERING
Abstract. The unit commitment problem nowadays is widely used in the electric power sector. The
problem was first time formulated in the 1940-s and still developing both methodologically and by
including an additional number of technologies each of which has a different unique mathematical
treatment corresponding to the specific technology's behavior. The common characteristic of the problem
such as that is dedicated to the electricity production sector, hence the mathematical formulation is
following pure electricity sector transformation but during the last years the Power-to-X technologies are
implemented and their further development is expected in the future. This requires the advancement or at
least modification of the problem formulation to meet possible exchange and usage between different
types of energy within one integrated power system. The goal of the article is to further development of
the existing versions of the unit commitment problem, which are dedicated to the operation of the
generation in the power system by implementing additional equations allowing contemplation of the heat
energy-producing technologies which are dedicated to cover a heat-energy load of the district heating
systems. This should allow for conducting comprehensive studies of the simultaneous operation of
electric- and heat-generating technologies to meet the energy demand of local energy systems, which is
important for designing distributed generation mix, for example at a municipal level. The proposed mixed
integer linear generation unit commitment model for simultaneous heat and electric daily load covering
is described in the article. The proposed model in addition to the pure electric power balance also meets
heat load using only-heat technologies (fuel boilers), combined heat and power units, and also industrial-
scale electric boilers - which are converting electricity to heat energy.
Keywords: mixed integer linear model, unit commitment problem, integrated power system, electric
boilers, power-to-X technologies, conventional electricity generating technologies.
1. Introduction
The unit commitment problem nowadays is widely used in the electric power sector [1, 4, 5].
The problem was first time formulated in the 1940-s but the first algorithm developed to solve the unit
commitment problem was proposed in 1959 [1]. The first mixed integer linear problem (MILP) regarding the
unit commitment was formulated in 1962 [1, 3] after Bellman’s fundamental work on dynamic operation
research was published [2]. The mathematical formulation is still developing both methodologically and by
including an additional number of technologies each of which has a different unique mathematical treatment
corresponding to the specific technology's behavior. The common characteristic of the problem such as that
is dedicated to the electricity production sector, hence the mathematical formulation is following pure
electricity sector transformation but during the last years the Power-to-X technologies are implemented and
their further development is expected in the future. This requires the advancement or at least modification of
the problem formulation to meet possible exchange and usage between different types of energy within one
integrated power system. In general, the objective function of the unit commitment problem is formulated as
follows [1]:
Total production costs = (Fuel cost + Start-up cost + Shut-down cost+ Maintenance cost) —> min. (1)
This formulation was published in 2018, but in 2022 the general formulation became more
comprehensive [5]:
System Research in Energy. 2023. 1(72) 26
Min (Production cost + Start-up cost + Shut-down cost + Emission cost + Maintenance cost). (2)
Equation (2) includes “Production cost” instead of “Fuel cost” in (1), and this is more correct as during
the operation of the power unit not only fuel but also other resources are consumed, e.g., pure water,
chemicals etc. The “Emission cost” in (2) became more important in current times as a number of
governments are adopting the decision to reach climate neutrality and fast penetration of renewable
technologies, e.g., wind, solar photovoltaic, and biomass competing with conventional power units. But this
parameter could be included in the constraints section of the unit commitment problem formulation as rather
the limits for emissions are applied to the electric power generation, nor minimization of payment for
unrestricted emissions amount.
The unit commitment problem “behavior” is mainly described in the constraints section. The typical
constraints are [5, 6, 7]: Demand constraint – exact equilibrium between production (supply) and
consumption for each period; Power generation limits – each unit should not exceed nominal installed
capacity and should not be lower than technical generating limit; Power output ramping limits – period-to-
period increase/decrease of power output should be within the technical possibility of the unit; Operation/idle
time constraints – describes allowed operational modes behavior of each unit; Emission constraints –
imposed to not exceed allowed emission volumes, e.g., from coal-fired units; Fuel constraints – limits
available fuel on stock for each or for the group of fuel burning units for each time step. The list of the
constraints and their formulation could vary depending on the goal of the study/calculations.
The goal of the article is to further development of the existing versions of the unit commitment
problem, which are dedicated to the operation of the generation in the power system by implementing
additional equations allowing contemplation of the heat energy-producing technologies which are dedicated
to cover a heat-energy load of the district heating systems. This should allow for conducting comprehensive
studies of the simultaneous operation of electric- and heat-generating technologies to meet the energy
demand of local energy systems, which is important for designing distributed generation mix, for example at
a municipal level. The proposed mixed integer linear generation unit commitment model for simultaneous
heat and electric daily load covering is described in the article. The proposed model in addition to the pure
electric power balance also meets heat load using only-heat technologies (fuel boilers), combined heat and
power units, and also industrial-scale electric boilers, which are converting electricity to heat energy.
The MILP unit commitment problem for the Integrated power system of Ukraine was formulated in
several papers [8, 9] which are aimed at correctly describing specifics of power generation units used in
Ukraine and their typical operation modes. These mathematical models are corresponding only to the electric
power sector in the sense that only the electric power balance (equilibrium of production and consumption
for each time step) is taken into account, but while covering the demand for electric power the combined heat
and power (CHP) units simultaneously participate with all other exactly electric power units. To include
CHP in formulation only volumes of electric energy generated by them are taken into account and the
volume of heat power is neglected. As CHPs are operated according to the demand for heat consumption by
households, tertiary, and industry sectors this approach is artificial and far from real life. Of course, the
levels of electric power consumption also depend on the atmospheric temperature, but in Ukraine, exactly
heat generation technologies are widely used to meet heat energy demand. Hence, to more correctly include
CHPs in electric power balance also other heat energy production units, such as fuel boilers, should be
considered, due to CHPs and fuel boilers together covering heat energy demand in reality. This requires
taking into consideration within the mathematical model formulation not only the electric power balance but
also the heat energy balance, considering the possibility of each technology participating in supplying an
appropriate type of energy to meet the appropriate type of energy demand.
2. Mathematical model formulation
The MILP unit commitment problem proposed in this paper is formulated with the use of the below-
listed sets, parameters, and variables. T — set of periods, as the one day is considered then set consists
24 elements (a day with 1 hour time resolution); K — set of all power units of all power stations including
thermal power plants (TPP), nuclear power plants (NPP), combined heat and power stations (CHP),
autoproducers (APr), hydro units of hydroelectric power stations (HPS) and units of hydro pumping storages
stations (HPSS), and also wind (Wind) and photovoltaic (PV) power stations; PSK — set of hydro pumped
System Research in Energy. 2023. 1(72) 27
storages stations (namely – Kyiv, Dnister and Tashlyk HPSS), for each HPSS the set of hydro units is
determined — KPSU ; TPPK — set of thermal power plants, for each TPP the set of power units is
determined — TPPU ; CHPK — set of CHP plants, for each CHP the set of power units is determined —
CHPU ; RK — the set of renewable generators (Wind and PV); HBM — the set of fuel burning boilers
producing the heat energy (mostly natural gas burning boilers in Ukraine); EHBM — the set of industry scale
electric boilers producing the heat energy; W
tP — the variable corresponding to the curtailed electric power
production by Wind, constant MW during one-time step (MWh); PV
tP — the variable corresponding to the
curtailed electric power production by PV, constant MW during one-time step (MWh); G
ktP — electric
power produced by technologies included in the set \ ( )
PS TPP R CHP
K K K K K , constant MW during one-
time step (MWh); TPP
kutP — the variable corresponding to the electric power produced by TPP’s power unit,
constant MW during one-time step (MWh); _CHP E
kutP — the variable corresponding to the electric power
produced by CHP’s power unit, constant MW during one-time step (MWh); _CHP H
kutP — heat energy
produced by CHP’s power unit, constant MW during one-time step (MWh); _HB H
mtP — the variable
corresponding to the heat energy produced by fuel fired boiler, constant MW during one-time step (MWh);
_ _EHB H P
mtP — the variable corresponding to the heat energy produced by electric boiler, constant MW
during one-time step (MWh); G
kuty — binary variable, equal to 1 (one), if hydro unit is operating in
generation mode, otherwise is 0 (zero); G
kutP — the variable corresponding to the electric power produced
by HPSS in generation mode, constant MW during one-time step (MWh); P
kuty — binary variable, equal to
1 (one), if hydro unit is operating in pumping mode, otherwise is 0 (zero); P
kutP — electric power consumed
by hydro unit of HPSS in pumping mode, constant MW during one-time step (MWh); I
tz — the variable
corresponding to imported electric power, constant MW during one-time step (MWh); E
tz — the variable
corresponding to exported electric power, constant MW during one-time step (MWh); Wc — parameter
corresponding to the price of electricity produced by wind farms, USD/MWh; PVc — parameter
corresponding to the price of electricity produced by solar photovoltaic plants, USD/MWh; G
ktc —
parameter corresponding to the price of electricity produced by technologies from set
\ ( )
PS TPP R CHP
K K K K K , USD/MWh; TPP
kutc — parameter corresponding to the price of electricity
produced by each type of thermal power plant units, USD/MWh; _CHP E
kutc — parameter corresponding to
the price of electric energy produced by combined heat and power plant units, USD/MWh; PSG
kutc —
parameter corresponding to the price of electric energy produced by hydro pumping storages station units,
USD/MWh; _CHP H
kutc — parameter corresponding to the price of heat energy produced by combined heat
and power plant units, USD/MWh; _HB H
mtc — parameter corresponding to the price of the heat energy
produced by fuel burning boilers, USD/MWh; _EHB H
mtc — parameter corresponding to the price of the heat
energy produced by electric boilers, USD/MWh.
The proposed objective function is minimizing the production cost of both electricity and heat energy:
\( )
_ _
1 1 1 1 1 1
1 1 1
_ _
1
[ ]
[ ]
[
PS TPP R CHP TPP TPP CHP CHP
PS KPS
C
K K K K KT K U K U
W W PV PV G G TPP TPP CHP E CHP E
t t kt kt kut kut kut kut
t k k u k u
T K U
G G PSG I I E E
kut kut kut t t t t
t k u
U
CHP H CHP H
kut kut
u
P c P c P c P c P c
y P c z c z c
P c
= = = = = =
= = =
=
+ + + + +
+ + − +
+
∑ ∑ ∑ ∑ ∑ ∑
∑ ∑∑
_ _ _ _ _
1 1 1 1
] min.
CHP HP HB EHBT K M M
HB H HB H EHB H P EHB H
mt mt mt mt
t k m m
P c P c
= = = =
+ + →∑ ∑ ∑ ∑ ∑
(3)
System Research in Energy. 2023. 1(72) 28
There are two equilibrium equations (constraints) are needed to provide the electric and heat energy
production-consumption balance for each time step. The first equation is for electric energy (4), and the
second one is for heat energy (5).
( )
_\( )
_
1 1 1 1 1
_ _
1 1 1
; ;
PS TPP R CHP E TPP TPP CHP CHP
PS KPS EHB
K K K K K K U K U
W PV G TPP CHP E
t t kt kut kut
k k u k u
K U M
G G P P EHB E C I E E
kut kut kut kut mt t t t
k u m
P P P P P
y P y P P z z D t T
= = = = =
= = =
+ + + + +
+ − − + − = ∀ ∈
∑ ∑ ∑ ∑ ∑
∑∑ ∑
(4)
_ _ _
1 1 1 1
; ,
CHP CHP HB EHBK U M M
CHP H HB EHB H P H
kut mt mt t
k u m m
P P P D t T
= = = =
+ + = ∀ ∈∑ ∑ ∑ ∑ (5)
where E
tD — the parameter corresponding to the electric energy demand in the energy system, constant MW
during one-time step (MWh); H
tD — the parameter corresponding to the heat energy demand in the district
heating, constant MW during one-time step (MWh); _ _EHB E C
mtP — the variable corresponding to the electric
energy consumed by the electric boiler from the grid for the heating the carrier (water), constant MW during
one-time step (MWh).
The constraints regarding the operation of various electricity-generating technologies for the electric
load covering are described in detail in [8, 9], hence below is a mathematical formulation (behavior
description) of the operation of the heat-generating technologies. The mathematical models dedicated to the
optimization of the operation of heat-generating technologies themselves are described in many papers, e.g.
detailed description is represented in [10] published as a result of the European Union’s Horizon 2020
research and innovation programme. But the common practice is the use of separate mathematical models
and appropriate tools for the district heating and electric grids, which does not exactly correspond to the real
situation "on the ground". Actually, such separate development of district heating and electric grids often
results in inefficient operation of CHP as an electricity producer first-of-all in summer-time. And instead, the
usage of electricity for heating is often limited by the local electric grids, which are not corresponding to
maintaining the appropriate load for the transformation of electricity to heat. And that is why the
simultaneous modeling of the unit commitment for electric and heating load covering could be a promising
technique first of all for the local district heating and electric grid planning, but also could be used for the
whole power system state level as some generators' installed capacity is much bigger as required at the local
level.
The rapid implementation of solar photovoltaic generation at the local level is an important driver for
the use of electric boilers as the usual situation of the excess of electricity produced by solar technologies
exactly during the day-time. At the level of the energy system, the common practice is to temporarily curtail
the excess of solar generation, but another way is to use it for the heating or at least the hot water supply. Of
course, the usage of this excess electricity for heating should be in equilibrium with the heat energy demand
curve, which is required to be stored for some time in the heat storage, and as shown in the [11, 12] the
actual district heating grid storage capacity is enough both in winter-time and in summer to accumulate and
store about 3 GW of heat energy for several hours, that is the realistic base for implementation of electric
boilers into district heating grids.
The constraints that describe the use of electric boilers consist of two types of equations: the first one
sets the limits of power that could be consumed (electric power) or produced (heat energy) during
appropriate periods of a day (6); the second one requires fulfillment of one-day energy balance the sense of
which is all electricity that we consume for heating purposes should be outputted to the district heat for
storing and then wholly consumed by users for heating purposes (7).
_ _ _ ; ; ... ; ... ;EHB E C MAX C night night day day
mt m start end start endP P m M t t t t t T ≤ ∀ ∈ ∀ ∈ ⊂
System Research in Energy. 2023. 1(72) 29
_ _ _ ; ; ... ; ... ;EHB E C MIN C night night day day
mt m start end start endP P m M t t t t t T ≥ ∀ ∈ ∀ ∈ ⊂ (6)
_ _ _ ; ; 1... 1; 1... 1; 1... ;EHB H P MAX P night night day day LAST
mt m start end start endP P m M t t t t t t T ≤ ∀ ∈ ∀ ∈ − + − + ⊂
_ _ _ ; ; 1... 1; 1... 1; 1... ,EHB H P MIN P night night day day LAST
mt m start end start endP P m M t t t t t t T ≥ ∀ ∈ ∀ ∈ − + − + ⊂ (7)
where _MAX C
mP — the parameter corresponding to the maximum electric power limit that could be consumed
by an electric boiler for heating purposes from the electric grid, MW; _MIN C
mP — the parameter corresponding
to the minimum electric power limit that should be consumed by an electric boiler for heating purposes from
the electric grid (usually equal to 0 (zero), MW; _MAX P
mP — the parameter corresponding to the maximum
heat energy that could be consumed by a user from the heating district grid this heat was earlier produced by
the electric boiler, and hence stored in the district heating grid, MW; _MIN P
mP — the parameter corresponding
to the minimum heat energy that could be consumed by a user from the heating district grid (usually equal to
0 (zero) this heat was earlier produced by the electric boiler, and hence stored in the district heating grid,
MW; night
startt — the time-step during a night-time (index of set T) is a parameter corresponding to the allowed
starting time of electric boiler heating the heat carrier consuming the electricity from the grid; night
endt — the
time-step during a night-time (index of set T) is a parameter corresponding to the time when the electric
boiler should stop consuming the electricity from the grid and hence stop heating the heat carrier; day
startt — the
time-step during a day-time (index of set T) is a parameter corresponding to the allowed starting time of
electric boiler heating the heat carrier consuming the electricity from the grid; day
endt — the time-step during a
day-time (index of set T) is a parameter corresponding to the time when the electric boiler should stop
consuming the electricity from the grid and hence stop heating the heat carrier; LASTt — the last time-step
during a day-time (maximum index of set T).
The breakdown of the set T into two periods is explained by the usual modes of the power system –
during night-time, the power system has an excess of electric power, and during this period the additional
consumption of electric power is a factor that allows increasing electric grid stability; during the day-time
especially under large penetration of renewables which are producing peaking power (usually solar
generation) also there is an excess of electric power which should be consumed or curtailed. The
consumption of electric energy between these periods is forbidden for electric boilers, for the reason of
ensuring electric grid stability.
The last constraint requires the exact equilibrium between the energy volume that was consumed by
electric boilers for heating the heat carrier during the whole day and that one consumed by the users from the
district heating grid where it is stored (8).
_ _ _ _
1 1 1 1
.
EHB EHBT M T M
EHB E C EHB H P
mt mt
t m t m
P P
= = = =
=∑ ∑ ∑ ∑ (8)
According to (8) an exact equilibrium between the consumption of energy (i.e. electricity) and the
energy production (i.e. heat energy) is required, which assumes the absence of heat losses during its storage,
but if the heat energy stores for a long time the losses will be not equal to a zero, especially in winter. This
would be corrected by applying appropriate parameter corresponding to the specific heat losses according to
the air temperature at the right part of the constraint (8), but according to the equations (6, 7) it is assumed
that all stored heat energy is consumed over the next several hours, and in that case, this coefficient is close
to 1(one) and has been not presented in (8).
3. Results of calculation and discussion
The calculations were made for three scenarios. In the first scenario, the Hydro Pumped Storages
(HPS) are used to cover the electricity load, and electric boilers (ElB) are not used to cover the heat load –
System Research in Energy. 2023. 1(72) 30
ElBNo&HPSYes Scenario. In the second scenario, the HPS are not used to cover the electricity load, and
electric boilers are used to cover the heat load, and hence consume electricity from the electric grid –
ElBYes&HPSNo Scenario. In the third scenario, both HPS and electric boilers are used – ElBYes&HPSYes
scenario. To demonstrate the action of the proposed model the actual data regarding electric load covering
for the 14 of July 2018 was used. The heat load has been constructed according to the typical heat load for
the summer season based on [10]. The input data regarding hour-to-hour electricity and heat energy
consumption, and generation profiles of NPP, autoproducers, wind, and solar generation are presented in
Tab. 1.
Table 1. The input data for the calculations
Time step
(hour)
Heat energy
consumption,
MWh
Electric
energy
consumption,
GWh
NPP
generation,
GWh
Autoproducers
generation,
GWh
Wind
generation,
GWh
Solar PV
generation,
GWh
1 1363.2 9.27 3.92 0.06 0.19 0
2 1168.5 8.93 3.92 0.06 0.13 0
3 1168.5 8.72 3.92 0.06 0.10 0
4 1168.5 8.65 3.92 0.06 0.08 0
5 1168.5 8.52 3.92 0.06 0.08 0.03
6 779.0 8.74 3.92 0.06 0.07 0.10
7 779.0 9.04 3.92 0.06 0.07 0.35
8 779.0 9.21 3.92 0.06 0.03 0.87
9 1947.4 9.92 3.92 0.06 0.01 1.48
10 1947.4 10.36 3.92 0.06 0.04 2.21
11 2336.9 10.53 3.92 0.06 0.05 2.50
12 2336.9 10.73 3.92 0.06 0.12 2.63
13 1947.4 10.68 3.92 0.06 0.16 2.58
14 1947.4 10.70 3.92 0.06 0.21 2.16
15 1752.7 10.50 3.92 0.06 0.20 1.99
16 1752.7 10.48 3.92 0.06 0.15 1.78
17 1168.5 10.55 3.92 0.06 0.17 1.46
18 1168.5 10.58 3.92 0.06 0.19 1.03
19 2531.7 10.44 3.92 0.06 0.17 0.32
20 2531.7 10.21 3.92 0.06 0.08 0.09
21 2726.4 10.32 3.92 0.06 0.05 0
22 2726.4 10.65 3.92 0.06 0.09 0
23 2921.2 10.07 3.92 0.06 0.06 0
24 1947.4 9.49 3.92 0.06 0.08 0
Sum 42064.8 237.3 94.1 1.5 2.6 21.6
The MILP mathematical model is written in MathProg [13] language, a freeware version of AMPL.
As a solver, the GNU GLPK [14] program is used. The overall time for one calculation with standard table
PC is about 5 seconds. The result of calculations according to each scenario is the schedule of power output
for each technology used to cover electricity and heat load during the day. The Tab. 2 and 3 are representing
the results of calculations for the third scenario when electric boilers with a 500 MW total capacity are
implemented and simultaneously all existing in Ukraine Hydro Pumping Storage Stations are used. Similar
calculations were made for the first and second scenarios and the comparison of all scenarios is represented
in Tab. 4.
Table 2. The results of calculations for covering electric load according to the ElBYes&HPSYes scenario
Time step
(hour)
Combined
heat and
power, GWh
Thermal
Power Plant,
GWh
Hydro
generation,
GWh
Hydro Pumping
Stations
(pumping),
GWh
Hydro
Pumping
Stations
(generation),
GWh
Electric Boilers
(consumption),
GWh
1 1.4 4.0 0.2 - - 0.5
2 1.3 3.8 0.2 - - 0.5
3 1.3 3.6 0.2 0.4 - 0.2
4 1.4 3.4 0.7 0.4 - 0.5
System Research in Energy. 2023. 1(72) 31
Continuation of Table 2.
Time step
(hour)
Combined
heat and
power, GWh
Thermal
Power Plant,
GWh
Hydro
generation,
GWh
Hydro Pumping
Stations
(pumping),
GWh
Hydro
Pumping
Stations
(generation),
GWh
Electric Boilers
(consumption),
GWh
5 1.3 3.3 0.8 0.4 - 0.5
6 1.2 3.1 0.3 - 0.3 0.3
7 1.1 2.9 0.3 - 0.3 -
8 1.2 2.9 0.4 0.4 0.3 -
9 1.3 3.1 0.7 0.6 - -
10 1.2 3.2 0.3 0.6 - -
11 1.4 3.4 0.2 0.4 - 0.5
12 1.4 3.6 0.2 0.6 - 0.5
13 1.4 3.7 0.5 1.1 - 0.5
14 1.4 3.5 0.9 0.9 - 0.5
15 1.3 3.3 0.4 0.5 0.3 0.5
16 1.2 3.1 0.2 0.1 0.3 -
17 1.1 3.1 0.2 0.1 0.7 -
18 1.2 3.1 0.4 - 0.8 -
19 1.3 3.3 0.4 - 1.0 -
20 1.4 3.5 0.5 - 0.7 -
21 1.4 3.7 1.0 - 0.2 -
22 1.4 3.7 1.4 - - -
23 1.4 3.5 1.1 - - -
24 1.3 3.3 0.8 - - -
Sum 31.1 81.0 12.1 6.7 5.1 4.9
Table 3. The results of calculations for covering heat load according to the ElBYes&HPSYes scenario
Time step
(hour)
Combined heat and
power, MWh
Natural Gas
fired boilers,
MWh
Other boilers incl.
biomass, MWh
Electric Boilers (supply
already earlier generated and
stored heat energy), MWh
1 500 276 400 -
2 500 186 315 -
3 500 96 400 -
4 500 81 400 -
5 500 102 400 -
6 460 45 127 -
7 420 45 80 88
8 458 45 80 50
9 498 383 400 500
10 460 800 80 441
11 500 1250 400 -
12 500 1250 400 -
13 500 860 400 -
14 500 860 400 -
15 500 686 400 -
16 462 244 400 500
17 422 225 80 295
18 447 445 80 50
19 487 978 400 500
20 500 945 400 500
21 500 1139 400 500
22 500 1139 400 500
23 500 1335 400 500
24 500 445 336 500
Sum 11.6 13.9 7.6 4.9
According to the results (table 4) the most feasible third scenario (ElBYes&HPSYes scenario) as it
requires minimum usage of gas-fired boilers to cover heat energy load, hence minimum natural gas
consumption. At the same time, according to this scenario, the about minimum operation of gas-fired CHP is
needed causing additional minimization of natural gas consumption. The interesting result is that with the
absence of Hydro Pumping Station operations (ElBYes&HPSNo scenario) also possible to guarantee the
System Research in Energy. 2023. 1(72) 32
coverage of electric and heat energy load, but in that case, the usage of coal-fired Thermal Power Plants is
maximum causing additional emissions of greenhouse gases and hazardous air pollution. The last result is
showing that the implementation of electric boilers into the electric grid serves as a source of additional
power grid flexibility, causing its safer operation.
Table 4. The comparison of results of calculations according to the scenarios
Technology
Scenario
ElBNo & HPSYes ElBYes & HPSNo ElBYes & HPSYes
Electricity load covering, GWh per day
Combined heat
and power 32.1 27.1 31.1
Thermal power plants 75.0 82.6 81.0
Hydro 12.1 13.0 12.1
Electric Boilers
(consumption) 0 5.3 4.9
Heat energy load covering, GWh per day
Combined heat
and power 12.0 11.6 11.6
Natural Gas fired
boilers 17.9 16.6 13.9
Other boilers incl.
biomass 8.0 6.4 7.6
Electric Boilers
(supply already
earlier generated
and stored heat
energy)
0 5.3 4.9
4. Conclusions
The unit commitment problem nowadays is widely used in the electric power sector, and is still
developing both methodologically and by including an additional number of technologies each of which has
a different unique mathematical treatment corresponding to the specific technology's behavior. The
penetration of the Power-to-X technologies during last years requires the advancement or at least
modification of the problem formulation to meet possible exchange and usage between different types of
energy within one integrated power system. The proposed mixed integer linear generation unit commitment
model is a further development of the existing versions of the unit commitment problem, which are dedicated
to the operation of the generation in the power system by implementing additional equations allowing
contemplation of the heat energy-producing technologies which are dedicated to cover a heat-energy load of
the district heating systems. This allows for conducting comprehensive studies of the simultaneous operation
of electric- and heat-generating technologies to meet the energy demand of local energy systems, which is
important for designing distributed generation mix, for example at a municipal level. The proposed model in
addition to the pure electric power balance also meets heat load using only-heat technologies (fuel boilers),
combined heat and power units, and also industrial-scale electric boilers – which are converting electricity to
heat energy.
The proposed MILP generation unit commitment mathematical model is written in MathProg
language, a freeware version of AMPL. As a solver, the GNU GLPK program is used. The overall time for
one calculation with a standard table PC is about 5 seconds. The result of calculations according to each
scenario is the schedule of power output for each technology used to cover electricity and heat load during
the day.
According to the results of calculations the most feasible scenario is corresponding the simultaneous
use Electric Boilers and Hydro Pumping Storage Stations, and this scenario requires minimum usage of gas-
fired boilers to cover heat energy load, hence minimum natural gas consumption. At the same time,
according to this scenario, the about minimum operation of gas-fired CHP is needed causing additional
minimization of natural gas consumption. The interesting result is that with the absence of Hydro Pumping
System Research in Energy. 2023. 1(72) 33
Station operations (the use of Electric Boilers, but not use Hydro Pumping Storages scenario) also possible to
guarantee the coverage of electric and heat energy load, but in that case, the usage of coal-fired Thermal
Power Plants is maximum causing additional emissions of greenhouse gases and hazardous air pollution.
This result is showing that the implementation of electric boilers into the electric grid serves as a source of
additional electric grid flexibility, causing its safer operation.
Acknowledgments
I highly appreciate input from research fellows of General Energy Institute NAS of Ukraine, namely
Ph.D. Tetiana Nechaeva, Ph.D. Volodymyr Derii, Ph.D. Oleksandr Teslenko for consultancies regarding heat
load profile construction, estimation of the adequacy of the heat energy producing technologies modeling,
and for discussion of the results obtained.
References
1. Abdou, I., & Tkiouat, M. (2018). Unit Commitment Problem in Electrical Power System: A Literature Review.
International Journal of Electrical and Computer Engineering, 8(3), 1357–1372.
https://doi.org/10.11591/ijece.v8i3.pp1357-1372
2. Bellman, R. (1957). Dynamic Programming. Princeton University Press: Princeton, NJ, USA.
3. Garver, L.L. (1962). Power generation scheduling by integer programming-development of theory. Transactions
of the American Institute of Electrical Engineers. Part III: Power Apparatus and Systems, 81(3), 730–734.
4. Padhy, N.P. (2004). Unit commitment-a bibliographical survey. IEEE Transactions on Power Systems, 19(2),
1196–1205. https://doi.org/10.1109/TPWRS.2003.821611
5. Montero, L., Bello, A., & Reneses, J. (2022). A Review on the Unit Commitment Problem: Approaches,
Techniques, and Resolution Methods. Energies, 15(4), 1296. https://doi.org/10.3390/en15041296
6. Taibi, E., Nikolakakis, T., Gutierrez, L., Fernandez, C., Kiviluoma, J., Rissanen, S., & Lindroos, T.J. (2018).
Power system flexibility for the energy transition: Part 2, IRENA FlexTool methodology.
7. Troy, N., Flynn, D., Milligan, M., & O'Malley, M. (2012). Unit Commitment With Dynamic Cycling Costs. IEEE
Transactions on Power Systems, 27(4), 2196–2205. https://doi.org/10.1109/TPWRS.2012.2192141
8. Shulzhenko, S.V., Turutikov, O.I. & Tarasenko, P.V. (2019). Model of Mathematical programming with integer
variables for determining the optimal regime of loading of hydroelectric pumped storage power plants for
balancing daily profile of electric loads of the power system of Ukraine. The Problems of General Energy, 4(59),
13–23 [in Ukrainian]. https://doi.org/10.15407/pge2019.04.013
9. Shulzhenko, S., Turutikov, O., & Bilenko, M. (2020). Mixed integer linear programming dispatch model for
power system of Ukraine with large share of baseload nuclear and variable renewables. 2020 IEEE 7th
International Conference on Energy Smart Systems (ESS), Kyiv, Ukraine, 363–368.
https://doi.org/10.1109/ESS50319.2020.9160222
10. Pre-design support online tool. Fifth generation, low temperature, high exergy district heating and cooling
networks. URL: http://www.flexynets.eu/en/ (last accessed: 28.12.2022).
11. Derii, V.O., & Bilodid, V.D. (2019). Limiting possibilities of the accumulation of thermal energy in centralized
heat supply systems The Problems of General Energy, 2(57), 41–45 [in Ukrainian].
https://doi.org/10.15407/pge2019.02.041
12. Derii, V.O. (2019). Complexes of electric heat generators for the control of electric load of regional power systems
The Problems of General Energy, 3(58), 17–23 [in Ukrainian]. https://doi.org/10.15407/pge2019.03.017
13. Makhorin, A. (February 2016). Modeling Language GNU MathProg. Language Reference – for GLPK.
Version 4.58. URL: http://ftp.gnu.org/gnu/glpk/glpk-4.63.tar.gz (last accessed: 28.12.2022).
14. GLPK (GNU Linear Programming Kit). URL: https://www.gnu.org/software/glpk/ (last accessed: 28.12.2022).
МОДЕЛЬ ЦІЛОЧИСЛОВОГО МАТЕМАТИЧНОГО
ПРОГРАМУВАННЯ ЗАВАНТАЖЕННЯ ГЕНЕРУВАЛЬНИХ
ПОТУЖНОСТЕЙ ДЛЯ ОДНОЧАСНОГО ПОКРИТТЯ
ГРАФІКІВ ЕЛЕКТРИЧНОГО
ТА ТЕПЛОВОГО НАВАНТАЖЕННЯ
Сергій Шульженко, к.т.н., ст. наук. співр., https://orcid.org/0000-0002-7720-0110
Інститут загальної енергетики НАН України, вул. Антоновича, 172, м. Київ, 03150,
Україна;
e-mail: mail2ua@gmail.com
https://doi.org/10.3390/en15041296
https://doi.org/10.15407/pge2019.04.013
https://doi.org/10.15407/pge2019.02.041
https://doi.org/10.15407/pge2019.03.017
http://ftp.gnu.org/gnu/glpk/glpk-4.63.tar.gz
https://www.gnu.org/software/glpk/
System Research in Energy. 2023. 1(72) 34
Анотація. Моделі оптимального завантаження генерувальних потужностей для покриття
графіків навантаження наразі широко використовуються для досліджень електроенергетичних
систем. Математичне формулювання моделі вперше було здійснено у 1940-х роках, але і зараз ці
математичні моделі розвиваються як методологічно, так і за рахунок включення до їх складу
додаткових (нових) технологій, кожна з яких представлена специфічними (унікальними)
рівняннями, що відображають особливості функціонування технологій. Загальною
характеристикою моделі є те, що вона присвячена лише сектору електроенергетики, тобто
розвиток моделі відбувається по мірі розвитку саме технологій електроенергетики, але
протягом останніх років до складу електроенергетичних систем впроваджуються технології
Power-to-X, і очікується, що цей процес буде продовжений. Це вимагає вдосконалення або
принаймні модифікації математичного формулювання оптимізаційної задачі для врахування
можливого обміну та використання між різними видами енергії в одній інтегрованій
енергосистемі. Метою статті є подальший розвиток існуючих версій моделі оптимального
завантаження генерувальних потужностей для покриття графіків навантаження
електроенергетичної системи, за рахунок використання додаткових рівнянь, які дозволяють
розглядати технології виробництва теплової енергії, призначені для покриття графіків теплового
навантаження систем централізованого теплопостачання. Це повинно дозволити проводити
комплексні дослідження одночасної роботи технологій виробництва електро- та теплової енергії
для покриття попиту місцевих енергетичних систем, що є актуальним для формування
структури розподіленої генерації, наприклад, на рівні окремого населеного пункту або громади. У
статті запропонована модель цілочислового математичного програмування завантаження
генерувальних потужностей для одночасного покриття графіків електричного та теплового
навантаження. Запропонована модель крім суто електричного балансу забезпечує покриття
теплового навантаження із використанням технологій генерування теплової енергії (паливні
котли), теплових електроцентралей, а також промислових електричних котлів, які
перетворюють електроенергію в тепло.
Ключові слова: модель цілочислового математичного програмування, задача оптимального
завантаження генеруючих потужностей, об’єднана енергосистема, електрокотли, технології power-
to-X, традиційні технології генерації електроенергії.
Надійшла до редколегії: 27.01.2023
|
| id | systemreorg-article-13 |
| institution | System Research in Energy |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2026-07-19T01:01:39Z |
| publishDate | 2023 |
| publisher | General Energy Institute of the National Academy of Sciences of Ukraine |
| record_format | ojs |
| resource_txt_mv | systemreorg/72/8036f8d8483e8591a00cd03c3519c472.pdf |
| spelling | systemreorg-article-132026-07-18T12:57:30Z GENERATION UNIT COMMITMENT MIXED INTEGER LINEAR MODEL FOR SIMULTANEOUS HEAT AND ELECTRIC DAILY LOAD COVERING МОДЕЛЬ ЦІЛОЧИСЛОВОГО МАТЕМАТИЧНОГО ПРОГРАМУВАННЯ ЗАВАНТАЖЕННЯ ГЕНЕРУВАЛЬНИХ ПОТУЖНОСТЕЙ ДЛЯ ОДНОЧАСНОГО ПОКРИТТЯ ГРАФІКІВ ЕЛЕКТРИЧНОГО ТА ТЕПЛОВОГО НАВАНТАЖЕННЯ Sergii Shulzhenko mixed integer linear model, unit commitment problem, integrated power system, electric boilers, power-to-X technologies, conventional electricity generating technologies. модель цілочислового математичного програмування, задача оптимального завантаження генеруючих потужностей, об’єднана енергосистема, електрокотли, технології power-to-X, традиційні технології генерації електроенергії. The unit commitment problem nowadays is widely used in the electric power sector. The problem was first time formulated in the 1940-s and still developing both methodologically and by including an additional number of technologies each of which has a different unique mathematical treatment corresponding to the specific technology's behavior. The common characteristic of the problem such as that is dedicated to the electricity production sector, hence the mathematical formulation is following pure electricity sector transformation but during the last years the Power-to-X technologies are implemented and their further development is expected in the future. This requires the advancement or at least modification of the problem formulation to meet possible exchange and usage between different types of energy within one integrated power system. The goal of the article is to further development of the existing versions of the unit commitment problem, which are dedicated to the operation of the generation in the power system by implementing additional equations allowing contemplation of the heat energy-producing technologies which are dedicated to cover a heat-energy load of the district heating systems. This should allow for conducting comprehensive studies of the simultaneous operation of electric- and heat-generating technologies to meet the energy demand of local energy systems, which is important for designing distributed generation mix, for example at a municipal level. The proposed mixed integer linear generation unit commitment model for simultaneous heat and electric daily load covering is described in the article. The proposed model in addition to the pure electric power balance also meets heat load using only-heat technologies (fuel boilers), combined heat and power units, and also industrial-scale electric boilers - which are converting electricity to heat energy. Моделі оптимального завантаження генерувальних потужностей для покриття графіків навантаження наразі широко використовуються для досліджень електроенергетичних систем. Математичне формулювання моделі вперше було здійснено у 1940-х роках, але і зараз ці математичні моделі розвиваються як методологічно, так і за рахунок включення до їх складу додаткових (нових) технологій, кожна з яких представлена специфічними (унікальними) рівняннями, що відображають особливості функціонування технологій. Загальною характеристикою моделі є те, що вона присвячена лише сектору електроенергетики, тобто розвиток моделі відбувається по мірі розвитку саме технологій електроенергетики, але протягом останніх років до складу електроенергетичних систем впроваджуються технології Power-to-X, і очікується, що цей процес буде продовжений. Це вимагає вдосконалення або принаймні модифікації математичного формулювання оптимізаційної задачі для врахування можливого обміну та використання між різними видами енергії в одній інтегрованій енергосистемі. Метою статті є подальший розвиток існуючих версій моделі оптимального завантаження генерувальних потужностей для покриття графіків навантаження електроенергетичної системи, за рахунок використання додаткових рівнянь, які дозволяють розглядати технології виробництва теплової енергії, призначені для покриття графіків теплового навантаження систем централізованого теплопостачання. Це повинно дозволити проводити комплексні дослідження одночасної роботи технологій виробництва електро- та теплової енергії для покриття попиту місцевих енергетичних систем, що є актуальним для формування структури розподіленої генерації, наприклад, на рівні окремого населеного пункту або громади. У статті запропонована модель цілочислового математичного програмування завантаження генерувальних потужностей для одночасного покриття графіків електричного та теплового навантаження. Запропонована модель крім суто електричного балансу забезпечує покриття теплового навантаження із використанням технологій генерування теплової енергії (паливні котли), теплових електроцентралей, а також промислових електричних котлів, які перетворюють електроенергію в тепло. General Energy Institute of the National Academy of Sciences of Ukraine 2023-04-07 Article Article application/pdf https://systemre.org/index.php/journal/article/view/13 10.15407/srenergy2023.01.025 System Research in Energy; No. 1 (72) (2023): System Research in Energy; 25-34 Системні дослідження в енергетиці; № 1 (72) (2023): Системні дослідження в енергетиці; 25-34 2786-7102 2786-7633 en https://systemre.org/index.php/journal/article/view/13/11 Copyright (c) 2023 Sergii Shulzhenko https://creativecommons.org/publicdomain/zero/1.0 |
| spellingShingle | mixed integer linear model unit commitment problem integrated power system electric boilers power-to-X technologies conventional electricity generating technologies. Sergii Shulzhenko GENERATION UNIT COMMITMENT MIXED INTEGER LINEAR MODEL FOR SIMULTANEOUS HEAT AND ELECTRIC DAILY LOAD COVERING |
| title | GENERATION UNIT COMMITMENT MIXED INTEGER LINEAR MODEL FOR SIMULTANEOUS HEAT AND ELECTRIC DAILY LOAD COVERING |
| title_alt | МОДЕЛЬ ЦІЛОЧИСЛОВОГО МАТЕМАТИЧНОГО ПРОГРАМУВАННЯ ЗАВАНТАЖЕННЯ ГЕНЕРУВАЛЬНИХ ПОТУЖНОСТЕЙ ДЛЯ ОДНОЧАСНОГО ПОКРИТТЯ ГРАФІКІВ ЕЛЕКТРИЧНОГО ТА ТЕПЛОВОГО НАВАНТАЖЕННЯ |
| title_full | GENERATION UNIT COMMITMENT MIXED INTEGER LINEAR MODEL FOR SIMULTANEOUS HEAT AND ELECTRIC DAILY LOAD COVERING |
| title_fullStr | GENERATION UNIT COMMITMENT MIXED INTEGER LINEAR MODEL FOR SIMULTANEOUS HEAT AND ELECTRIC DAILY LOAD COVERING |
| title_full_unstemmed | GENERATION UNIT COMMITMENT MIXED INTEGER LINEAR MODEL FOR SIMULTANEOUS HEAT AND ELECTRIC DAILY LOAD COVERING |
| title_short | GENERATION UNIT COMMITMENT MIXED INTEGER LINEAR MODEL FOR SIMULTANEOUS HEAT AND ELECTRIC DAILY LOAD COVERING |
| title_sort | generation unit commitment mixed integer linear model for simultaneous heat and electric daily load covering |
| topic | mixed integer linear model unit commitment problem integrated power system electric boilers power-to-X technologies conventional electricity generating technologies. |
| topic_facet | mixed integer linear model unit commitment problem integrated power system electric boilers power-to-X technologies conventional electricity generating technologies. модель цілочислового математичного програмування задача оптимального завантаження генеруючих потужностей об’єднана енергосистема електрокотли технології power-to-X традиційні технології генерації електроенергії. |
| url | https://systemre.org/index.php/journal/article/view/13 |
| work_keys_str_mv | AT sergiishulzhenko generationunitcommitmentmixedintegerlinearmodelforsimultaneousheatandelectricdailyloadcovering AT sergiishulzhenko modelʹcíločislovogomatematičnogoprogramuvannâzavantažennâgeneruvalʹnihpotužnostejdlâodnočasnogopokrittâgrafíkívelektričnogotateplovogonavantažennâ |