2. Energies 2022, 15, 7177 2 of 16
• Distributing loads between power sources of both existing and designed power
supply systems;
• Improving the efficiency of using energy resources;
• Defining the optimal strategy for the energy system development—the construction
or reconstruction of an entire system or its individual facilities (choosing the location,
capacity, and term for commissioning new power plants, substations, ETLs);
• Choosing optimal routes for power facility inspection;
• Choosing the optimal composition of generating equipment;
• Choosing the best goods transportation routes, including fuel transportation;
• Improving the performance and structural reliability of power supply systems;
• Reducing damages from power outages and deteriorated power quality.
Despite a lot of mathematical optimization techniques, when it comes to power in-
dustry facilities, their number sharply reduces due to their limited application since multi-
criterial target function is to be set, and there are limitations in the form of equalities and
inequalities, depending on the rated or operating parameters of not only equipment and
lines but also grids, such as permissible node voltages and continuous maximum currents
and powers.
Another feature of applying optimization techniques to electric energy facilities is,
as a rule, the decomposition principle. The complex problem is split into parts, and each
subproblem is solved using one or another optimization technique.
The article provides the existing approaches to the practical improvement of the
efficiency of the operation modes in electric energy systems and grids by means of the
application of mathematical optimization methods. The authors’ intention was to demon-
strate a wide range of problems in the area to familiarize the reader with the optimization
method application and algorithmization and present the options for their adaptation to
the electric power facilities.
The paper consists of the following sections:
- Conventional approaches to optimizing the electric energy system and grid operating
modes—this section provides key optimization methods applied for the solution of
optimization problems in the energy area and observes their applications, advantages,
flaws as well as their practical relevance;
- Optimizing electric energy systems and grid operating modes using original mathe-
matical models—this section provides applied solutions developed by the scientists in
terms of mode optimization in the power energy facilities and their points of view. It
also describes the unique nature of such solutions and comprises the authors’ conclu-
sions concerning the feasibility of the application of the cases provided for solving the
problems at real facilities;
- IT solutions for optimization problems in the electric power industry—this section
considers the existing software introduced at the real electric power facilities to
solve optimization problems. Such products allow forecasting and correcting the
operation modes.
- Conclusions.
2. Conventional Approaches to Optimizing the Electric Energy System and Grid
Operating Modes
As already mentioned above, the key challenge in solving energy optimization prob-
lems is numerous limitations imposed on both independent (not affected by the system
operating mode, e.g., the energy characteristics of turbogenerators) and dependent (affected
by the system operating mode, e.g., the line power, defined when the grid is reconfigured
while solving the optimization problem) parameters. Many of them are non-linear and very
complex. This fact does not allow applying numerous optimization techniques described
in the mathematical literature.
3. Energies 2022, 15, 7177 3 of 16
As a rule, the steady-state modes of power systems, power plants, and grids are
subject to optimization. Depending on the facility considered, various optimality criteria
are applied.
Intra-plant optimization problems most frequently use technical optimality criteria,
except for the cases when several fuels are simultaneously exploited at the power plant.
These criteria include:
• Minimum energy resource (fuel, water, steam) consumption;
• Maximum efficiency (minimum energy loss);
• Minimum cost of energy carriers required to generate electrical or electrical and
thermal energy.
This is acceptable since semi-fixed costs do not depend on the electrical and thermal load.
When optimizing the grid operating mode, the following criteria can be used:
• Minimum energy loss in the grid;
• Minimum cost of the energy loss;
• Minimum damage from power outages or deteriorated power quality.
When considering the power supply systems of specific consumers, then the key
criteria will be:
• Minimum power consumption;
• Minimum energy loss in the grid.
Under the conditions of electric energy systems, the most proper optimality criterion
is minimum total costs; however, in many cases, it is replaced by minimum fuel costs.
The tasks of short-term planning are set as follows (Figure 1):
Energies 2022, 15, x FOR PEER REVIEW 3 of 17
As a rule, the steady-state modes of power systems, power plants, and grids are sub-
ject to optimization. Depending on the facility considered, various optimality criteria are
applied.
Intra-plant optimization problems most frequently use technical optimality criteria,
except for the cases when several fuels are simultaneously exploited at the power plant.
These criteria include:
• Minimum energy resource (fuel, water, steam) consumption;
• Maximum efficiency (minimum energy loss);
• Minimum cost of energy carriers required to generate electrical or electrical and ther-
mal energy.
This is acceptable since semi-fixed costs do not depend on the electrical and thermal
load.
When optimizing the grid operating mode, the following criteria can be used:
• Minimum energy loss in the grid;
• Minimum cost of the energy loss;
• Minimum damage from power outages or deteriorated power quality.
When considering the power supply systems of specific consumers, then the key cri-
teria will be:
• Minimum power consumption;
• Minimum energy loss in the grid.
Under the conditions of electric energy systems, the most proper optimality criterion
is minimum total costs; however, in many cases, it is replaced by minimum fuel costs.
The tasks of short-term planning are set as follows (Figure 1):
Figure 1. Optimized condition parameters in electric power systems and networks.
1. Choice of the optimal composition of operating units—F(P;n);
2. Optimal distribution of active and reactive power between sources—F(Pi;Qi);
3. Reduction in active power losses in electrical networks—↓ΔР;
4. Development of optimal energy balances and coverage schedules—F(Sload);
5. Determination of the value and placement of the operational power reserve—
F(P;n;X;Y);
6. Frequency regulation— f;
7. Voltage regulation— U.
Consider the basic optimization techniques used to solve energy facility problems
[1].
When calculating the optimal energy system operating modes, the following groups
of optimization techniques are applied [2,3] (Figure 2).
Figure 1. Optimized condition parameters in electric power systems and networks.
1. Choice of the optimal composition of operating units—F(P;n);
2. Optimal distribution of active and reactive power between sources—F(Pi;Qi);
3. Reduction in active power losses in electrical networks—↓∆P;
4. Development of optimal energy balances and coverage schedules—F(Sload);
5. Determination of the value and placement of the operational power reserve—F(P;n;X;Y);
6. Frequency regulation—
Energies 2022, 15, x FOR PEER REVIEW 3 of 17
As a rule, the steady-state modes of power systems, power plants, and grids are sub-
ject to optimization. Depending on the facility considered, various optimality criteria are
applied.
Intra-plant optimization problems most frequently use technical optimality criteria,
except for the cases when several fuels are simultaneously exploited at the power plant.
These criteria include:
• Minimum energy resource (fuel, water, steam) consumption;
• Maximum efficiency (minimum energy loss);
• Minimum cost of energy carriers required to generate electrical or electrical and ther-
mal energy.
This is acceptable since semi-fixed costs do not depend on the electrical and thermal
load.
When optimizing the grid operating mode, the following criteria can be used:
• Minimum energy loss in the grid;
• Minimum cost of the energy loss;
• Minimum damage from power outages or deteriorated power quality.
When considering the power supply systems of specific consumers, then the key cri-
teria will be:
• Minimum power consumption;
• Minimum energy loss in the grid.
Under the conditions of electric energy systems, the most proper optimality criterion
is minimum total costs; however, in many cases, it is replaced by minimum fuel costs.
The tasks of short-term planning are set as follows (Figure 1):
Figure 1. Optimized condition parameters in electric power systems and networks.
1. Choice of the optimal composition of operating units—F(P;n);
2. Optimal distribution of active and reactive power between sources—F(Pi;Qi);
3. Reduction in active power losses in electrical networks—↓ΔР;
4. Development of optimal energy balances and coverage schedules—F(Sload);
5. Determination of the value and placement of the operational power reserve—
F(P;n;X;Y);
6. Frequency regulation— f;
7. Voltage regulation— U.
Consider the basic optimization techniques used to solve energy facility problems
[1].
When calculating the optimal energy system operating modes, the following groups
of optimization techniques are applied [2,3] (Figure 2).
f;
7. Voltage regulation—
Energies 2022, 15, x FOR PEER REVIEW 3 of 17
As a rule, the steady-state modes of power systems, power plants, and grids are sub-
ject to optimization. Depending on the facility considered, various optimality criteria are
applied.
Intra-plant optimization problems most frequently use technical optimality criteria,
except for the cases when several fuels are simultaneously exploited at the power plant.
These criteria include:
• Minimum energy resource (fuel, water, steam) consumption;
• Maximum efficiency (minimum energy loss);
• Minimum cost of energy carriers required to generate electrical or electrical and ther-
mal energy.
This is acceptable since semi-fixed costs do not depend on the electrical and thermal
load.
When optimizing the grid operating mode, the following criteria can be used:
• Minimum energy loss in the grid;
• Minimum cost of the energy loss;
• Minimum damage from power outages or deteriorated power quality.
When considering the power supply systems of specific consumers, then the key cri-
teria will be:
• Minimum power consumption;
• Minimum energy loss in the grid.
Under the conditions of electric energy systems, the most proper optimality criterion
is minimum total costs; however, in many cases, it is replaced by minimum fuel costs.
The tasks of short-term planning are set as follows (Figure 1):
Figure 1. Optimized condition parameters in electric power systems and networks.
1. Choice of the optimal composition of operating units—F(P;n);
2. Optimal distribution of active and reactive power between sources—F(Pi;Qi);
3. Reduction in active power losses in electrical networks—↓ΔР;
4. Development of optimal energy balances and coverage schedules—F(Sload);
5. Determination of the value and placement of the operational power reserve—
F(P;n;X;Y);
6. Frequency regulation— f;
7. Voltage regulation— U.
Consider the basic optimization techniques used to solve energy facility problems
[1].
When calculating the optimal energy system operating modes, the following groups
of optimization techniques are applied [2,3] (Figure 2).
U.
Consider the basic optimization techniques used to solve energy facility problems [1].
When calculating the optimal energy system operating modes, the following groups
of optimization techniques are applied [2,3] (Figure 2).
4. Energies 2022, 15, 7177 4 of 16
Energies 2022, 15, x FOR PEER REVIEW 4 of 17
Figure 2. Energy optimization methods.
To solve optimization problems, mathematical programming techniques are pre-
dominantly used. They are focused on obtaining target functions within the set limits, e.g.,
the turbogenerator power within its energy characteristic (from the minimum allowable
to the maximum allowable active power with the steam consumption required for gener-
ation). In fact, mathematical programming techniques apply a direct enumeration of all
possible options within the set limits until the desired target function value is found.
Given the multivariance of the search values, these techniques perform enumeration
even for the knowingly false value ranges; however, modern technologies allow solving
such problems very quickly. The target function of the optimization model can be linear
or non-linear. Respectively, linear and non-linear programming techniques are used. In
some cases, variables can be discrete or integer. Thus, discrete and integer programming
techniques are used. If the data are probabilistic or non-deterministic, appropriately, sto-
chastic programming techniques and the game theory mathematical tools are used [1].
As already noted, under the conditions of electric power facilities, optimization can
be conducted according to several criteria. In this case, multicriteria optimization tech-
niques are used to search for optimal solutions. The essence of these techniques is to find
a compromise solution for all given optimization criteria. In order to distribute the power
plant load between thermal power plants operating in multiple, the incremental rate
method is used based on the priority loading of the most energy-efficient units, which is
determined by the minimum increment rate of their consumption. In other words, the
load is distributed in the sequence of increasing consumption increment rates of units op-
erating in multiple [3]. In this case, the unit’s idle consumption effect is not considered
since when operating in multiple, these values remain constant for any load distribution
option and, therefore, do not affect the option energy efficiency. The operating mode op-
timality condition also stipulates the minimum total fuel costs in the energy system.
An important optimization problem is to improve the energy system efficiency at
large industrial companies. Solving the operating mode optimization problem for an en-
ergy system of an industrial company with internal power plants and a significant amount
of secondary energy resources has the following specific points:
Figure 2. Energy optimization methods.
To solve optimization problems, mathematical programming techniques are predomi-
nantly used. They are focused on obtaining target functions within the set limits, e.g., the
turbogenerator power within its energy characteristic (from the minimum allowable to the
maximum allowable active power with the steam consumption required for generation).
In fact, mathematical programming techniques apply a direct enumeration of all possible
options within the set limits until the desired target function value is found.
Given the multivariance of the search values, these techniques perform enumeration
even for the knowingly false value ranges; however, modern technologies allow solving
such problems very quickly. The target function of the optimization model can be linear
or non-linear. Respectively, linear and non-linear programming techniques are used. In
some cases, variables can be discrete or integer. Thus, discrete and integer programming
techniques are used. If the data are probabilistic or non-deterministic, appropriately,
stochastic programming techniques and the game theory mathematical tools are used [1].
As already noted, under the conditions of electric power facilities, optimization can be
conducted according to several criteria. In this case, multicriteria optimization techniques
are used to search for optimal solutions. The essence of these techniques is to find a
compromise solution for all given optimization criteria. In order to distribute the power
plant load between thermal power plants operating in multiple, the incremental rate
method is used based on the priority loading of the most energy-efficient units, which is
determined by the minimum increment rate of their consumption. In other words, the load
is distributed in the sequence of increasing consumption increment rates of units operating
in multiple [3]. In this case, the unit’s idle consumption effect is not considered since
when operating in multiple, these values remain constant for any load distribution option
and, therefore, do not affect the option energy efficiency. The operating mode optimality
condition also stipulates the minimum total fuel costs in the energy system.
An important optimization problem is to improve the energy system efficiency at large
industrial companies. Solving the operating mode optimization problem for an energy
system of an industrial company with internal power plants and a significant amount of
secondary energy resources has the following specific points:
5. Energies 2022, 15, 7177 5 of 16
1. Along with the fuel and power transmission costs, the target cost function includes
the expenses associated with the purchase of electricity in the retail market (in some
cases, in the wholesale market);
2. The technical and economic features of station units will have breakpoints since power
plants frequently use fuel mixes; the composition of the latter depends on the station
power output;
3. Limitations are added as inequalities imposed on the power supplied by the energy
retail company for each point (group of points) of supply.
When solving the optimization problem for a relatively small number of units, the
most convenient way to consider constraint equation discontinuity is by applying the
dynamic programming technique in a discrete formulation [4].
Table 1 shows the target function type and the application area and key drawbacks for
some of the most common optimization techniques.
Table 1. Optimization Techniques.
Technique Description
Incremental rate technique
Target function
(example)
F = ∑Bi(Pi) + γ(∑Pi − Pc), [1]
where F is the target function; Bi is the heat consumption by the i-th
unit, Pi is the unit load; γ is the incremental rate, Pc is the station
service power
Application area
Calculating the optimal power distribution between any number of
stations or units within a station
Drawbacks
The method does not take into account:
- The possibility of using different fuels with different costs at
the station;
- Fuel costs associated with the transition from one state to
another;
- The impact of changes in the number of harmful emissions on
the energy cost.
Lagrange multiplier technique
Target function
(general form)
L(X,λ) = F(X) + ∑λiϕi(x) [1]
where F is the target function; X is the criterion to be optimized; λ is
the indefinite Lagrange multiplier
Application area
Defining favorable operating modes of power units, obtaining the
optimal load distribution between several units
Drawbacks Introducing additional variables to be eliminated with additional
equations
Linear programming technique
Target function
(general form)
F(x) = a1x1 + a2x2 + . . . +anxn, [1]
where F is the target function; xn is the criterion to be optimized; an
is the coefficients
Application area
Solving problems associated with the distribution of resources,
production planning, and arrangement of the transport work
Drawbacks Applying independent limitations
Dynamic programming technique
Target function
(example)
Cn =
n
∑
j=1
m
∑
k=1
Ck,j(yj) + Cst k, j(yj)
→ min,
where yj is the optimal control at the j-th step; Ck,j(yj) is the
consumption cost of a primary energy carrier to produce the steam
required to generate electricity at a full load of sources; Cst k,j(yj) is
the cost of steam consumption through the extraction points; n is
the number of power plant boilers connected to a single steam
pipeline; m is the total number of different primary energy carriers
used at the power plant
Application area
Solving the following: trajectory selection; consequential
decision-making; the use of manpower; inventory management
Drawbacks Duration of the calculations for systems with a large number of data
6. Energies 2022, 15, 7177 6 of 16
3. Optimizing Electric Energy System and Grid Operating Modes Using Original
Mathematical Models
Existing mathematical optimization techniques solve problems in various power
industry areas [5,6]. The key difficulties in solving such problems are the source data uncer-
tainty [7], the complexity of electric energy generation, transmission, distribution, and con-
sumption, and the power supply reliability [8]. No universal optimization technique exists,
and completely different methods are used to achieve specific goals. Classical optimization
techniques are modified and/or combined with others to achieve the target results.
In this industry, energy saving and efficiency are among the important problems to be
solved. These issues were of interest to researchers as far back as the last millennium when
thermal power plants were actively commissioned [9,10].
For energy-intensive companies, these problems arose almost immediately after the
increase in power consumption and the complexity of production, transmission, distribu-
tion, and consumption of energy resources and power. G.V. Nikiforov [11], I. Shkoda [12],
J. Bausa [13], and P. Hilber [14] considered ways to save heat and electricity and improve
power plant efficiency through the optimal operation of boiler-turbine equipment of ther-
mal power plants. Ref. [15] describes techniques for improving the efficiency of operating
modes of industrial power plant boilers and turbogenerators through the well-planned
distribution of thermal and electric power. The approach is based on applying dynamic
programming techniques. A.U. Lipets [16] described ways to improve the efficiency of
power units using gas as the main fuel by increasing the superheat temperature, extract-
ing heat from boilers, heating fuel gas, and using the heat of flue gases and secondary
superheated steam. N.M. Zinger described the choice of power plant’s optimal heat supply
modes depending on the heat load and the environmental temperature pattern [17,18].
Particular attention is paid to the issues of optimal reactive power generation by power
plants. Thus, the authors considered an optimization model based on the fuzzy adaptive
genetic algorithm; however, the application of this method is limited to rural grids only [19].
The article applies the dynamic programming technique to solve this problem [20].
V.A. Stennikov in [21], using the Lagrange method, distributed thermal energy be-
tween its sources in a reasonable way according to the criterion of minimum costs per total
load, with and without considering the thermal power limitations. The proposed technique
allows determining the sequence of sources to reach their maximum load.
Some scientific papers also focus a lot on the impact of the energy fuel parameters
on the power plant’s technical and economic performance. R.E. Aleshinsky analyzed
the fuel quality impact on the thermal power plant’s boiler efficiency [22]. In 2004, E.K.
Verbovetsky [23] developed a software package to estimate the impact of fuel resources
on the technical and economic performance of power equipment of plants operating on
coal dust. The authors described the optimal approach to “ . . . supplying dust with high
concentrations during coal combustion . . . ” in a boiler based on setting and defining the
cost-effective boiler parameters and coal grade [24].
The reasonable use of energy resources is among the key ways to improve the energy
efficiency of electric energy and power supply systems for industrial companies. Ref. [25]
considered ways of feasible use of energy resources by distributing the consumption of the
fuel required to generate electricity and heat at TPPs to increase their competitiveness in
the heat and electricity markets.
The environmental factor affects solving optimization problems for power supply
systems with industrial TPPs. Paper [26] considered the optimization of the operating
modes of power systems with TPPs by the minimum cost of the power plant energy
resources, considering the limitation of harmful emissions into the atmosphere. The issues
of using secondary energy resources (coke and blast-furnace gases) as the TPP fuel are
being solved for the industrial power supply system of large metallurgical enterprises.
The authors of [27] described an approach that allows the most effective use of secondary
energy resources by determining the optimal fuel mix composition for a power plant using
the direct enumeration method. In article [28], the issues of optimal coal supply and storage
7. Energies 2022, 15, 7177 7 of 16
were solved. The authors of [29] considered the issue of optimal air supply to the burner
for boiler efficiency improvement. Paper [30] considered the issues of the environmental
friendliness of power plants. The optimal level of the boiler’s NOx emissions is defined
using a genetic algorithm. The authoring team of [31] considered the issues of improving
the efficiency of mills at coal-fired power plants.
In addition, for power supply systems fed from an energy system, one of the key
optimization issues is also defining the feasible external source power, considering the
power purchased and electricity tariffs specified in the supply agreement. The block
diagram of such a network is shown in Figure 3.
of using secondary energy resources (coke and blast-furnace gases) as the TPP fuel are
being solved for the industrial power supply system of large metallurgical enterprises.
The authors of [27] described an approach that allows the most effective use of secondary
energy resources by determining the optimal fuel mix composition for a power plant us-
ing the direct enumeration method. In article [28], the issues of optimal coal supply and
storage were solved. The authors of [29] considered the issue of optimal air supply to the
burner for boiler efficiency improvement. Paper [30] considered the issues of the environ-
mental friendliness of power plants. The optimal level of the boiler’s NOx emissions is
defined using a genetic algorithm. The authoring team of [31] considered the issues of
improving the efficiency of mills at coal-fired power plants.
In addition, for power supply systems fed from an energy system, one of the key
optimization issues is also defining the feasible external source power, considering the
power purchased and electricity tariffs specified in the supply agreement. The block dia-
gram of such a network is shown in Figure 3.
Figure 3. Structural diagram of the power supply system with its own and external sources.
These issues were studied as far back as the last century [32], but this problem re-
mains relevant even now [33]. The authors of [33] described an approach that allows de-
fining the maximum power purchased from the energy system, considering the aforemen-
tioned factors. Paper [33] provided an optimization algorithm to define the feasible power
purchased from the energy system, considering internal generation and active power
losses in the power supply system. The algorithm is based on a modified dynamic pro-
gramming and sequential equivalenting technique. These issues were also studied in
power supply systems that use renewable energy sources [34].
Figure 3. Structural diagram of the power supply system with its own and external sources.
These issues were studied as far back as the last century [32], but this problem remains
relevant even now [33]. The authors of [33] described an approach that allows defining
the maximum power purchased from the energy system, considering the aforementioned
factors. Paper [33] provided an optimization algorithm to define the feasible power pur-
chased from the energy system, considering internal generation and active power losses in
the power supply system. The algorithm is based on a modified dynamic programming
and sequential equivalenting technique. These issues were also studied in power supply
systems that use renewable energy sources [34].
In some energy system sections, a shortage of active power occurs, leading to an
increase in the electricity net cost and tariff rates. The choice of ways to control the power
supply system in operating modes is most affected by the issues of providing its greatest
economic feasibility subject to the required conditions for communication with the energy
system. As a rule, two control methods were used: selecting an advantageous composition
of elements and mode parameters. When choosing an efficient operating mode, these two
problems have to be solved jointly in most cases. A.V. Pazderin [35], M.L. Korolev [36], V.S.
Khachatryan [37], N.I. Serebryannikov [38], K.A. Smirnov [39], and V.M. Letun [40] studied
8. Energies 2022, 15, 7177 8 of 16
these issues. This optimization problem was solved by applying the Newton, incremental
rates, and Lagrange methods.
A well-planned development strategy for the electric energy and power supply system
is also a priority optimization problem. A.S. Berdin [41] studied the development and
implementation of a methodology that allows analyzing and determining the power supply
system development strategy based on the fuzzy-set theory provisions, considering “... the
uncertainty of a part of the source data”. A.I. Fedotov [42] studied the issues of energy-
efficient industrial enterprise operation by optimizing the costs of power consumed from
the grid, considering the process specifics. Paper [43] described a method for developing
the optimal power consumption by an industrial enterprise, and in [44], this problem was
considered for the telecommunications sector.
Thus, the primary optimization problems should be set and solved for the joint
operation of energy and power supply systems. T.M. Alyabyshev [45] and V.A. Kozlov [46]
formulated generalized problems of optimal control over electric energy systems.
The research team of V.I. Poroshin, A.P. Romanenko, B.I. Ayuev, and S.I. Demidov
offer an applied approach to the intrahour optimization of the energy system operating
mode using the ERGEN—CORRECTOR software package in the Interregional Dispatching
Office (IDO) of the Urals [47]. The considered software package allows the IDO dispatcher
to determine the optimal active power settings of control objects for 20–60 min according
to the criterion of minimum fuel costs for energy sources.
In order to obtain feasible configurations of electrical systems and grids, research
teams considered the issues of simulating electric energy and power supply systems and
power grids to optimize their operating modes. P.S. Abakshin [48] studied this area.
The scope of Numerous studies includes defining the optimal load of the electrical and
thermal energy sources. N.N. Galashov [49] and V.A. Stennikov [21] proposed optimizing
the TPP turbogenerator and boiler loads to improve their performance.
Just in the middle of the last century, scientists began to develop software to optimize
the PP power equipment operation to solve the set problem. A.T. Kurnosov analyzed the
opportunities of the TPP technical and economic parameter calculation software, integrated
into the plant’s process, which allows for defining the heat load distribution between
boiler equipment and computing the cost of electric and heat energy [50]. This problem is
currently solved by using quite a number of software products (this issue is considered in
more detail in Section 4).
A team of authors developed a model to optimize steady-state operating modes by
active power based on a combination of linear programming and resource decomposition
techniques using the PRES and PRES-SUTKI software packages that allow planning long-
and short-term electric energy system operating modes [48].
In 1997, N.N. Galashov and V.V. Bespalov [49] developed a software package that
allows simulating the basic elements and calculating the power plant (thermal and nuclear)
thermal circuits by the given values of electric power, flow, parameters, and steam supply.
At the beginning of the 1990s, V.B. Borisoglebsky [51] proposed the use of computers for
technical and economic calculations at TPPs.
In particular, [52] considered a system that allows monitoring and forecasting of the
reactive power of photovoltaic power plants operating within the power system, which in
general allows controlling the voltage. Article [53] provides a model of a photovoltaic power
plant, which allows forecasting the impact of a power unit on the power supply system and
power quality and defining the optimal reactive power determining the effective voltage.
The authors of paper [54] solved this problem using a particle swarm, which sped up finding
the optimal solution for choosing the voltage. New approaches are being developed to
estimate the performance of systems with renewable energy sources. Studying the Gray
Wolf Optimization approach, which provides fast convergence of solving optimization
problems for systems with solar power plants, will allow the development of an automated
system for real-time calculation and forecasting of such system parameters in the future [55].
9. Energies 2022, 15, 7177 9 of 16
The issues of mathematical simulation of power systems with hydroelectric power
plants are also being solved, facilitating the forecast of the parameters for all possible oper-
ating modes [56]. In such systems, solving voltage control problems is also important [57].
D.A. Arzamastsev, A.V. Lipes, and A.L. Myzin [58] gave special attention to the issues
of the energy system’s grid optimal development strategy. They set the basic energy
system optimal development problems, provide “ . . . techniques for forecasting the electric
energy system loads and power consumption”, and describe in detail the key optimization
techniques to solve these problems.
At the end of the 20th century, options were considered [59] for the reconstruction of
boiler houses into small TPPs by installing gas turbine units there to improve the efficiency
of using energy fuel “ . . . in decentralized heat supply systems”. The paper provides
calculations confirming the feasible operation of such TPPs according to the heat and not
the electric schedule. Article [60] also discusses the prospects for commissioning combined
cycle and gas turbine plants when revamping TPPs, which have some advantages compared
to steam turbine plants, such as saving energy resources and reducing the electric and heat
energy costs.
Defining the optimal generating equipment composition is among the most important
optimization problems in the electric power industry. T.Sh. Gayibov [61] proposed defining
the feasible composition of generator equipment operating in the energy system by the
criterion of minimum costs.
In most cases, the electric energy system’s steady-state operating modes are optimized.
Many scientific teams are engaged in the calculation of steady-state modes; some studies
are given as an example. N.V. Goncharyuk [62] provided a technique for calculating
equivalent circuits with “ . . . accurately considered transformation ratios in the original
control system”, which allows solving the problems of short-term planning of the operating
modes (including optimal ones) of the considered grids.
The primary optimization problem of electric energy systems, as aforementioned, is
defining the feasible active power distribution between generators. S.K. Gursky proposed
using an adaptive algorithm for “ . . . solving the problem of defining the incremental
rates of active power losses in the grid” to determine the optimal PP load [63] since
this approach allows setting the source data as the nodal substation and PP loads for a
certain period. Later, the author of [64] proposed applying the guaranteed relative level
method based on the dynamic programming technique and considering the limitations
on the minimum consumption for both the entire energy system and individual PPs for
the short-term optimization of the PP units’ operation. Paper [65] described a software
package that allows for the optimal thermal and electric energy distribution between two
turbogenerators; however, the package does not consider the grid operating mode. Ref. [66]
also studied this field.
In order to solve optimization problems for electric energy systems, non-linear pro-
gramming techniques are used. In articles [67,68], O.T. Geraskin used the simplex technique.
According to [69], the curvature of the given target function surface and limitations can be
considered, respectively, by the second-order Newton and search vector projection methods.
V.A. Igumenshchev [70] and A.V. Malafeev [71] used the dynamic programming technique,
which allows defining the internal electric energy source generator loads according to the
criterion of minimum fresh steam costs to optimize the operation mode of the industrial
power supply system. A.A. Gerasimenko [72] proposed optimizing the electrical system
operating modes by reactive power (according to the criterion of minimum losses in the
grid) through the reduced gradient method, which allows defining the feasible parameters
in a single calculation step by the average load.
D.A. Arzamastsev [73,74] provided an algorithm to define the optimal reactive power
distribution for industrial power supply systems based on the sequential equivalenting
and indefinite Lagrange multiplier techniques, provided that the power balance and the
acceptable voltage level are maintained in the node. As the target function, the total
reactive power generation and distribution costs are taken, reduced to active power losses.
10. Energies 2022, 15, 7177 10 of 16
Later, V.A. Igumenshchev [75] proposed a dynamic model for optimizing reactive power in
nodes with sharply variable loads according to the criterion of minimum losses in the grid,
considering the limitations on the permissible parameters of excitation systems and the
synchronous machine rotor swinging angles and voltage fluctuations in industrial power
supply systems. As an optimization technique, a combination of successive intervals and
successive equivalenting techniques is used.
Despite the wide application of these techniques in the last century, they remain
relevant today. Section 4 considers software products developed on the basis of these opti-
mization techniques. A.I. Afanasiev [76] provided a technique for optimizing instantaneous
modes of open-loop lines by voltage, transformation ratio, and reactive power according to
the criterion of minimum power losses, based on the reduced gradient method, considering
penalty functions; violation of voltage limitations was introduced as a penalty criterion. A
technique for calculating seasonal operating modes was obtained based on the developed
methodology, the criterion of which is the minimum damage from losses and deteriorated
quality of electric energy (by voltage deviation).
E.V. Tsvetkov [77] considered a technique for defining the optimal electric energy
system operating modes by active power, considering the balance of power and the grid
factor using the Lagrange method. V.Z. Manusov considered the use of a genetic algorithm
to optimize electric energy systems by active power [78]. A.P. Chmutov [79] considers the
issues of optimizing the voltage regime of urban and rural grids based on the theory of
linear inequalities. T.B. Leshchinskaya [80,81] provided an algorithm for the multicriteria
problem of optimizing urban power supply systems, considering the source data uncer-
tainty. The basic criteria are the minimum total capital investment in the grid elements,
minimum power losses, and minimum total 10 (20) kV line length based on the Bayesian
information criterion.
Along with the aforementioned techniques, separable and approximating program-
ming is widely used; it approximates the target function using curved segments and
thereby reduces the optimization problem solution to linear programming [82,83]. T.Sh.
Gayibov [61] proposes the branch-and-bound algorithm to optimize the PP’s operating
equipment composition, where the optimality criterion is minimum total energy system
costs for the considered period. Along with the aforementioned optimization problems, B.I.
Ayuev [84,85] provides marginal state optimization models for given weighting directions
using the Lagrange method to analyze, plan, and control electric energy system modes.
Many current studies are devoted to optimizing the operating modes of power supply
systems with distributed generation sources: solar [86,87] and wind [88] power plants. It is
also important to study the behavior of promising electric energy systems, distinguished
by a large number of pumped storage, wind, and solar power plants; therefore, large
thermal and hydroelectric power plants should continue their operation [89]. Automated
simulation models of such systems will also allow estimating their parameters.
SmartGrids system simulation is becoming an urgent problem, and power plants are
simulated [90] to predict their optimal operating modes. Ref. [91] considered an approach
that allows for improving the Microgrid operation efficiency using the directed graph
theory. Optimizing power consumption is also important for these systems. Ref. [92]
solved this problem by applying the odd optimization method. Optimization models that
allow defining the optimal storage volume [93–95] and considering the renewable source
reliability are being developed [96].
4. IT Solutions for Optimization Problems in The Electric Power Industry
Automation of decision-making in the design and operation of facilities in various
industries is now taking on a massive scale. This is determined by the need to quickly
process a large amount of data, analyze them, and give recommendations for improvement
(for example). Energy is one of the leaders in implementing digital technologies. The use
of modern software products that allow automating the design, forecasting, monitoring,
control, and management of energy facilities has become a part of everyday work.
11. Energies 2022, 15, 7177 11 of 16
Currently, the software market is represented by a wide range of software systems,
modules, and simulators capable of calculating and analyzing optimal operating conditions
of electric energy systems.
Widespread software products are RastrWin, COSMOS, SDO-6, PSS®E, AREM, DIgSI-
LENT PowerFactory, Lincor, ANARES-2000, and MUSTANG.
The ANARES-2000, SDO-6, RastrWin, Lincor, and Siemens PTI software products
allow for reducing the active power loss in the grid by optimizing its modes. Some software
such as OPRES, AREM, ETAP Electrical Power System Software, and NEPLAN allow
defining the optimal unit locations, generated power, and the number of compensators.
TPP mode optimization programming and computing suite and OptiRamp® allow
defining the optimal loads for power equipment of industrial enterprises’ internal energy
sources; however, these packages can only perform intra-station optimization.
Table 2 shows the analyses of the software that allows calculating and optimizing the
electric energy facility modes.
Table 2. Software products designed to calculate and optimize the electric energy system modes.
Title Developer Key Functions
ANARES-2000
IDUES LLC, Novosibirsk, Russia,
and ISEM SB RAS, Irkutsk,
Russia [97]
Calculation, planning, design, and analysis of electric energy
system modes. The steady state is calculated based on the
modified Newton method in Cartesian coordinates with the exact
choice of the optimal step for multi-component circuits of any
configuration. The grid is optimized based on the gradient
descent method and allows reducing active power losses,
considering limitations on active and reactive power and voltage
by:
- Voltage and transformation ratio control;
- Defining the optimal circuit breaking point
SDO-6
Artemiev V.E., Voitov O.N.,
Mantrov V.A.,
Nasvitsevich B.G., Semenova L.V.
ISEM SB RAS, Irkutsk, Russia [98]
Calculating symmetrical steady-state modes using the
Newton-Raphson method with a variable step. The steady-state
modes are optimized according to the following criteria:
- Minimum active and reactive power losses in the grid;
- Minimum generation costs (active and reactive load
components), considering fuel tariffs and active power
flows for controlled lines and sections
RTDS (Real Time Digital
Simulator)
RTDS Technologies Inc.,
Winnipeg, Canada [99]
Real-time simulation, calculation, and analysis of the energy
system steady-state modes
COSMOS Prikhno V.L. [100]
Real-time calculation of the energy system modes based on
telemetric data. The package calculates steady-state modes and
optimizes energy systems in terms of reactive power
AREM
Technoinfoservice LTD, Kyiv,
Ukraine [101]
Autonomously analyzing grids based on the power balance
method by directly entering the grid configuration parameters
and importing them. The module allows optimizing the grid
modes:
- Defining the optimal transformation ratios of transformers;
- choosing circuit breaking points;
- Defining reactive power for compensation;
- Choosing the optimal power of compensators
RastrWin
Yekaterinburg Public Fund named
after D.A. Arzamastsev,
Yekaterinburg, Russia [102]
The software package allows calculating the steady-state grid
modes considering the frequency deviation. The grids are
optimized in terms of power losses, reactive power flows, and
voltage
MUSTANG
ODU North-West, Riga,
Latvia [103]
The software package is designed to calculate the steady-state
grid modes using the Newton-Raphson method. The heavy mode
convergence has been improved using the Matveev method
12. Energies 2022, 15, 7177 12 of 16
Table 2. Cont.
Title Developer Key Functions
DIgSILENT
PowerFactory
DIgSILENT GmbH, Gomaringen,
Germany [104]
The software package allows calculating symmetrical and
asymmetric steady-state modes of arbitrary configuration DC and
AC grids. The package allows for linear and non-linear
optimization of energy system modes, considering power flows
across sections and active and reactive power control limits
PSS®E Siemens PTI
Siemens Corporation, Erlangen,
Germany [105]
PSS®E allows calculating the grid flow distribution using the
iterative Newton-Raphson method. The software package
optimally distributes power according to the criterion of
minimum operating costs to reduce active and reactive power
losses, fuel and active and reactive power generation costs, and
reduce or increase active power flows and reactive power
generation reserve
DAKAR
ELEKS Software Representation
for the CIS Countries—Lviv,
Ukraine [106]
The DAKAR software is designed to calculate and analyze the
electric energy system steady-state modes using the EMF
compensation techniques, with or without considering the
frequency change in normal, marginal, and post-emergency states
OptiRamp® Statistics and Control, Inc., West
Des Moines, USA [107]
The Enterprise Electric Power Optimization and Management
System (EEPOMS) is intended for planning, controlling,
monitoring, and optimizing power generation. It defines the
optimal thermal and electric energy distribution with the
minimum fuel consumption or minimum losses of the enterprise,
as well as for the maximum efficiency of the PP units. The
optimization criterion may vary depending on certain factors
Energy CS
CSoft Development, Moscow,
Russia [108]
The software package calculates the steady-state modes of
complex electric energy systems. It identifies the most advanced
modes, considering the growth of loads and the transformation of
circuits
NEPLAN
NEPLAN AG, Küsnacht,
Germany [109]
The software product is designed for industrial power supply
and energy system analysis, planning, optimization, and control.
NEPLAN allows defining optimal circuit breaking points, reactive
power source installation places, and grid reconstruction plan
ETAP Electrical Power
System Software
ETAP Automation Inc., Irvine,
USA [110]
The package allows calculating steady-state and optimal
steady-state modes. ETAP defines the optimal flow distribution
(active and reactive power) using the internal point method,
considering the barrier function according to the criterion of
minimum power losses in distribution grids. The package also
allows defining the optimal reactive power source installation
places, their rated parameters, number, and generated power
according to the criterion of minimum source installation and
maintenance costs
5. Conclusions
An analysis of existing optimization techniques in the electric power industry shows a
variety of approaches to solving problems of the optimal electric energy system and grid
control, sufficiently developed and implemented at operating facilities.
The considered optimization techniques solve the following issues:
• Defining the reasonable active power and heat load distribution between the PP units
and between the PPs of the power supply and energy systems;
• Defining the optimal electric and thermal energy and reactive power source location
places;
• Defining the optimal grid configuration at the design stage also allows for improving
the system efficiency;
13. Energies 2022, 15, 7177 13 of 16
• Feasible use of energy resources, in particular, defining the optimal fuel mix composi-
tion at PPs, etc.
However, developing the electric power industry poses new challenges for researchers
in the field of improving the efficiency of electric energy systems and grids.
The review will be valuable for the researchers and developers and will provide
them with a guide to both fundamental and contemporary achievements in the area of
optimizing the modes of energy systems and grids. It will also help them to assess the
feasibility of optimization methods’ application on the basis of the scientific experience, the
advantages and flaws of the methods outlined by other scientists, as well as the methods’
potential adaptability to a certain task. This review also allows evaluating the application of
optimization methods during the development of engineering analysis automated systems
mostly focused on forecasting, calculation, and optimization of complex electric energy
systems and grids.
Author Contributions: Conceptualization, A.A.R. and A.V.V.; methodology, V.R.K.; writing—original
draft preparation, A.V.V.; writing—review and editing, V.R.K.; visualization, V.R.K.; project adminis-
tration, A.A.R.; funding acquisition, A.V.V. All authors have read and agreed to the published version
of the manuscript.
Funding: This research received no external funding.
Data Availability Statement: Not applicable.
Conflicts of Interest: The authors declare no conflict of interest.
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