Viktor Denysov* and Svitlana Kovtun
General Energy Institute of NAS of Ukraine, Ukraine
*Corresponding author:Viktor Denysov, General Energy Institute of NAS of Ukraine, 172, Antonovycha St., Kyiv, 03150, Ukraine
Submission:November 15, 2024;Published: December 13, 2024
ISSN:2770-6648Volume5 Issue2
Paper discusses the optimization of generation and storage technologies within power systems, focusing on minimizing electricity costs while ensuring reliable load coverage-an ongoing challenge for global power grids. Through test calculations, the study provides numerical estimates, maps the optimal distribution of generating and storage capacities, and evaluates the required hourly costs for electricity supply across different load schedules. The research explores the integration of various energy sources, including traditional generation and energy storage systems, to minimize overall electricity costs while meeting demand. The importance of calculating the weighted average cost of electricity, considering various discount rates and the relative costs of generation technologies, is emphasized. Additionally, the study highlights the strategic use of storage systems for both charging and discharging based on demand conditions, further reducing costs. A detailed analysis of the optimal distribution of generating and storage capacities is presented, underlining the role of storage systems in balancing load variations. The dual role of storage-acting as both a consumer and a supplier of electricity-enables more efficient use of available capacity, especially in combination with other generation technologies like nuclear and thermal power plants. The findings offer practical approaches for energy system operators and policymakers to design more economically efficient and sustainable power generation systems. Given the growing importance of renewable energy integration and energy storage, this research lays the foundation for future advancements in optimizing the energy balance and addressing challenges related to fluctuating energy demand.
Keywords:Generation and storage technologies; Integration of various energy sources; Analysis of the optimal distribution of generating and storage capacities
Abbreviations:CHP: Combined Heat and Power; HPP: Hydropower Plant; IPS: Integrated Power System; NPP: Nuclear Power Plant; PSPP: Pumped Storage Power Plant; RES: Renewable Energy Sources; SS: Battery Electric Storage System; TPP: Thermal Power Plant
The study of the development and improvement of energy systems is an urgent scientific problem, which is given considerable attention [1-13]. In case of a disruption in the continuous balance of supply and demand for electricity through operational and planned coverage of the load schedule by means of an appropriate amount of electricity generation and guaranteed delivery to consumption nodes, the network frequency and voltage levels in the power system change. This, in turn, may lead to mass consumer outages or damage to generating, transmission, and distribution equipment, as well as consumer electrical installations. All this underscores the relevance of solving the problem of calculating optimal operating modes for the generating and storage capacities within the power system, which ensure the minimization of the weighted average cost of generated electricity while covering the specified load. A comparative analysis of the weighted average cost of generated electricity, when the power system components operate in modes different from the base load mode, can serve as a justification for selecting the best option to solve this problem.
The weighted average cost depends on:
A. The amount of capital investments, including the cost of any
loans required to finance construction, which may prove to be
one of the main components of the final cost of electricity.
B. Operating costs throughout the entire life cycle.
C. Fuel costs.
Typically, the weighted average cost is determined using one of the versions of a widely used formula (1) [14], which depends on technological, regional, and economic parameters.
Where f is a mode from the list of allowable operating modes for the power unit. For each of the considered modes f, the capacity factor of the installed capacity of the k-th technology, CFk(f), takes one of the following values: Nom, 0.7* Nom; 0.5* Nom; 0.3* Nom. The value CFk(Nom) is the value in the base load mode.
Ekf – the amount of annual generation of the power unit when used in f mode.
i – discount (%).
Ckcap – investment.
Ckfix – fixed operating costs.
Ckvar(f) – variable operating costs, which according to
manufacturers include the cost of fuel and depend on the mode f.
T – power unit life cycle duration.
The aim of this work is research of optimal operating modes for the generating and storage capacities within the power system, which ensure the minimization of the weighted average cost of generated electricity while covering the specified load.
In the first of the two stages of modeling and determining the set of optimal modes for the use of generating and storage capacities on a subset of available technological solutions, a matrix Ckf− was calculated. The elements of this matrix represent the weighted average cost of electricity generated for each technology and for each of the f allowable operating modes of the power unit. Four generating technologies and one energy storage technology were selected for test calculations. Specifically, the following were considered.
1. Nuclear power unit NPP NuScale-in base load mode and
several maneuvering modes to cover the specified load using the
Turbine bypass technology.
2. Nuclear power unit NPP Holtec SMR-160-in base load
mode and several maneuvering modes to cover the specified load
using the Load Following technology.
3. Installation of the combined cycle.
4. Installation of the coal cycle.
5. Accumulator (SS-Storage System), with an installed
storage capacity of 30MW.
Modeling, calculation, and comparative assessment of the weighted average cost for each of the listed generating and storage technologies and installations were performed for each of the permissible maneuvering modes used in covering the model load schedule. The weighted average cost was calculated for the following discount values: 3%; 3.5% (which is a control value according to the manufacturer’s data); 5%; 7%; 7.5% (which is a control value according to the manufacturer’s data); and 10%. A comparison of the weighted average cost for all these technologies was carried out for discount values of 3.5% and 10% per year. The basis for selecting these discount values for comparing the weighted average cost is the availability of control values provided by the manufacturer for certain installations. The input data for calculating the weighted average cost of electricity for traditional technologies in base load modes and several maneuvering modes for covering the given load were obtained from [15-17]. The calculations of the weighted average cost values Ckf − for the listed generating and storage technologies and the results obtained are presented below. A comparison of the results of the modeling with the control values provided by the equipment manufacturers allowed confirming the adequacy of the model. In the second stage of modeling, using the obtained values of the weighted average cost Ckf − for the listed generating and storage technologies, a model was developed and tested to solve the problem of selecting optimal modes for utilizing the generating and storage capacities of the energy system. These modes are designed to minimize the cost of generated electricity at each time segment in the mode of covering the given load. The following steps were taken to implement the model. Using statistical information on the hourly power balance of the IPS of Ukraine for one of the critical days [18-19], Table 1 was created. Based on Table 1, Table 2 was calculated, showing the hourly absolute and relative power changes of the generating technologies NPP and TPP, as well as the absolute and relative changes in consumption power. Based on Tables 1 & 2, a model hourly schedule of the specified load was calculated for test calculations, and an assessment of the relative distribution of the installed capacity balance in the IPS of Ukraine was performed. This ratio was used in forming the set of generating and storage technologies for a separate model power supply node (Table 3).
Table 1:Hourly power balance (MW) of the IPS of Ukraine for a critical day, used for test calculations.
Table 2:Hourly absolute and relative power changes of the generating technologies NPP and TPP, as well as the absolute and relative changes in consumption power.
Table 3:Set of generating and storage technologies for a separate model power supply node.
The maximum available power is calculated according to the formula (2):
where k– technology number of a separate model power supply node.
PkMAX – the maximum available power of the k-th technology.
PkINST – the installed power of the k-th technology.
CFk(Nom) – capacity factor of the k-th technology in base load
mode.
The ratio of installed powers, considering the data from Table 2, is specified by expert assessment. The values of CFk(Nom) for each technology were obtained based on reference data from manufacturers [15-17, 19-22] and are provided in Table 3. Based on the parameters of Table 3, the following matrices were constructed.
1. The matrix EkAnnual(f) of the maximum available annual generation volumes for each technology in each of the f modes, according to formula (3), is presented in Table 4.
where – mode from the list of possible modes of technology use.
CFk(f) – capacity factor of the k-th technology in mode f, which
takes the values Nom, 0.7*Nom; 0.5*Nom; 0.3*Nom;
YH – number of hours per year – 8 760.
Table 4:Maximum available annual generation volumes for each technology in each of the f modes.
2. The matrix PkAvailable(f) of available loads, calculated using formula (4), is presented in Table 5.
Table 5:The matrix of available loads.
3. The matrix of electricity supply cost values per hour in mode f, calculated using formula (5), is presented in Table 6.
Table 6:Matrix of electricity supply cost values per hour in mode f.
Using the obtained results, the problem of calculating the binary matrix Bkf of optimal sets of generating and storage technology modes for each possible load coverage mode was formulated and solved, with the aim of minimizing the total cost of the generated electricity.
when applying the constraints (7), (8), (9):
As follows from Table 2, takes values from 0.7 to 0.95, with an average value of PmeanLoad = 0.86. Constraint (9) ensures the charging mode of the accumulator when PLoad < PLoadmean , meaning the accumulator is a consumer of electricity, and the discharging mode of the accumulator when PLoad > PmeanLoad , meaning the accumulator is an additional power source. Table 7 presents the results of the test optimization calculations and the resulting optimal distribution map of generating and storage capacities, along with the specific hourly electricity supply costs for each of the possible values (from 0.7 to 0.95) of the model load schedule.
Table 7:Map of generating and storage capacities, along with the specific hourly electricity supply costs for each of the possible values (from 0.7 to 0.95) of the model load schedule.
The paper discusses the optimization of generation and storage technologies in the power system. This optimization is crucial to reduce the cost of electricity while ensuring reliable load coverage, which is a constant challenge for power systems worldwide. The results obtained during the test calculations allowed us to obtain numerical estimates, a map of the optimal distribution of generating and storage capacities, and the required weather costs of supplying electricity for each of the possible values of the load schedule. The influence of integrating various energy sources, including traditional generation and energy storage systems, is considered. Models to simulate different operating modes are developed, addressing the problem of minimizing the total cost of electricity while meeting the required load schedule. It emphasizes how the combination of generating and storage capacities can help ensure a more costeffective energy supply. An important aspect of the research is the calculation of the weighted average cost of electricity, taking into account various discount rates and the relative costs of different electricity generation technologies. The article not only emphasizes the importance of optimizing generation costs but also highlights how storage systems can be strategically used for charging and discharging based on demand and supply conditions, leading to further cost reductions.
A detailed analysis of the optimal distribution of generating and storage capacities is presented, which is crucial for minimizing the weighted average cost of electricity. The concept of using energy storage systems for both charging and discharging, depending on load conditions, is a key part of the optimization. For example, when the load is below the average demand, storage systems act as consumers, absorbing excess energy, while when the load exceeds the average demand, these systems discharge energy, supporting the grid and reducing the need for expensive peaking power plants. The dual role of storage systems-acting both as a consumer and as a supplier of electricity-allows for more efficient use of available capacity. The ability to optimize the use of storage in combination with other generation technologies, such as nuclear and thermal power plants, can lead to a significant reduction in electricity costs. Presented research makes a significant contribution to the understanding of how generation and storage technologies can be jointly utilized to minimize the cost of electricity while maintaining reliable supply. The application of optimization models, along with the evaluation of cost factors, provides a practical approach for energy system operators and policymakers to design more economically efficient and sustainable power generation systems. Given the growing importance of integrating renewable energy sources and energy storage, this research lays the foundation for future advancements in optimizing the energy balance and addressing the challenges associated with the fluctuating nature of energy demand.
© 2024 Viktor Denysov. This is an open access article distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use, distribution, and build upon your work non-commercially.