Improving Efficiency of Electric Energy System and Grid Operating Modes: Review of Optimization Techniques

: Continuously growing tariff rates for energy carriers required to generate electrical and thermal energy bring about the need to search for alternatives. Such alternatives are intended for the reduction in the electricity and heat net costs as well as the expenses for the operation and maintenance of system elements and damage from power outages or deteriorated power quality. A way to reduce electricity and heat costs is the introduction of distributed energy resources capable of operating on both conventional (natural gas) and alternative (solar and wind energy, biomass, etc.) fuels. The problem of reducing electricity and, in some cases, heat costs are solved by applying mathematical optimization techniques adapted to a specific element or system of the industry in question. When it comes to power industry facilities, optimization, as a rule, includes reducing active power losses by controlling the system mode or specific power unit parameters; planning generating equipment operating modes; defining the optimal equipment composition; improving the regime and structural reliability of grids; scheduling preventive maintenance of equipment; searching for effective power unit operating modes. Many of the problems listed are solved using direct enumeration techniques; modern technical tools allow quickly solving such local problems with a large number of source data. However, in the case of integrated control over the power system or its individual elements, optimization techniques are used that allow considering a lot of operating limitations and the target function multicriteriality. This paper provides an analytical review of optimization techniques adapted to solving problems of improving the efficiency of the power facility operating modes. The article is made on the basis of the research conducted by the authors in the area of optimization of operating modes for electric energy systems and grids. The authors drew conclusions on the applicability of mathematical optimization methods in the power energy area. While conducting the research, the authors relied on their expertise in the development and introduction of the method to optimize the operation modes of energy supply systems with heterogeneous energy sources.


Introduction
Multiple ways are available to improve the efficiency of the power facility operating modes.Unfortunately, there is no universal way to solve all problems associated with energy systems and grids in an integral manner.Each occurring issue is settled in a unique way, adapted to the facility, its operating conditions, and limitations of the operation parameters of elements and/or systems depending on and/or affecting it.
These complex problems are solved by applying mathematical optimization techniques.
In the energy sector, the conventional optimization problems are: • Selecting the best configurations of power grids and systems; • 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 industry facilities, their number sharply reduces due to their limited application since multicriterial 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 demonstrate 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 mathematical 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' conclusions 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.

Conventional Approaches to Optimizing the Electric Energy System and Grid Operating Modes
As already mentioned above, the key challenge in solving energy optimization problems 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.
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): 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).To solve optimization problems, mathematical programming techniques are predominantly 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: 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.
where F is the target function; Вi is the heat consumption by the i-th unit, Рi is the unit load; γ is the incremental rate, Рс 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) 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) where F is the target function; хn is the criterion to be optimized; аn 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) ( ) 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

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 uncertainty [7], the complexity of electric energy generation, transmission, distribution, and consumption, 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, distribution, 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 thermal 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, extracting 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 between 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.Kh.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 costeffective 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 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.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 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 programming and sequential equivalenting technique.These issues were also studied in power supply systems that use renewable energy sources [34].Power system

ТG-turbogenerator
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 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 longand 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].
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 operating 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 shortterm 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 programming 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.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 optimization 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 uncertainty.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 programming 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][94][95] and considering the renewable source reliability are being developed [96].

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.
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.
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.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 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

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 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

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; • Feasible use of energy resources, in particular, defining the optimal fuel mix composition 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.

Figure 1 . 7 .
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.

Figure 3 .
Figure 3. Structural diagram of the power supply system with its own and external sources.

Table 2 .
Software products designed to calculate and optimize the electric energy system modes.