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Review

Review of Battery Storage and Power Electronic Systems in Flexible A-R-OPF Frameworks

by
Aouss Gabash
Department of Automation Engineering, Institute of Automation and Systems Engineering, Technical University of Ilmenau, 98693 Ilmenau, Germany
Electronics 2023, 12(14), 3127; https://doi.org/10.3390/electronics12143127
Submission received: 2 June 2023 / Revised: 7 July 2023 / Accepted: 17 July 2023 / Published: 19 July 2023
(This article belongs to the Special Issue Impact of Renewable Energy Technologies on the Grid, Electric Vehicles and Sustainable Development)
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Abstract

:
This paper provides an overview of power electronics and its applications in various fields, emphasizing power conditioning and minimizing losses for high energy efficiency. It discusses the distinction between unidirectional and bidirectional converters and their applications in power systems. The significance of unidirectional and bidirectional power flow in different scenarios is explored. The importance of battery storage systems (BSSs) for grid stabilization, frequency regulation, and renewable energy integration is highlighted. The paper focuses on flexible active-reactive optimal power flow (A-R-OPF) frameworks in battery storage and power electronic systems, reviewing existing research, identifying gaps, and offering new perspectives. It addresses the challenges and potential of grid-scale energy storage for reliable and cost-effective power systems with high renewable energy penetration. The need for energy curtailment, demand response, and smart grid implementation is discussed. The paper emphasizes comprehensive coordination, new power lines, European collaboration, and smart grid implementation to meet the dynamic needs of Europe’s power grids.

Graphical Abstract

1. Introduction

Power electronics is a field of electrical engineering that employs electronic circuits to convert and regulate electrical energy between different forms such as alternating current (AC) to direct current (DC) (rectifier), DC to AC (inverter), DC to DC (dc-converter), or AC to AC (ac-converter) [1,2,3,4]. It has numerous applications, including hybrid renewable energies [5,6,7], small-scale/large-scale storage systems [8,9,10,11,12,13,14], electric vehicles [15,16], and industrial automation [17]. A block diagram of a power electronic system is shown in Figure 1. Here, the power processor unit [18] is a crucial component of any power electronic system, and it plays a central role in achieving high energy efficiency [19]. It is essential to minimize power losses in this unit due to the associated costs of wasted energy and the challenges in effectively managing the heat [20] generated as a result of energy dissipation [21,22]. This emphasizes the importance of modeling power conditioning systems and accounting for their losses in the power industry [23].
Traditional power systems rely on centralized generation plants and long-distance transmission lines to supply power to large consumption centers. The development of dispersed generation units, including renewables, is changing the traditional power system. Renewable sources offer advantages such as emission reduction, but they face higher costs and uncontrollable availability as shown in [3]. Integrating renewables into the grid requires power electronic technology [3], where the characteristics of dispersed generation units such as wind power [24,25] and photovoltaic (PV) generators [26,27] have been explored.
In addition, power converters are crucial for battery storage systems (BSSs) as they enable bidirectional power flow, allowing energy storage when there is excess power and releasing stored energy when needed [28]. In power electronic systems, unidirectional and bidirectional converters are two types of systems that have different capabilities in terms of power flow [29,30,31]:
  • Unidirectional Converter: A unidirectional converter, as the name suggests, allows power flow in only one direction. It typically converts power from a single source to a load or an output, as shown in Figure 1, without any backflow of power. In other words, it can convert energy from the input source and deliver it to the output, but it cannot transfer power in the opposite direction. Examples of unidirectional converters include rectifiers or dc-converters, which step up or step down the voltage level of a DC source.
  • Bidirectional Converter: A bidirectional converter, on the other hand, enables power flow in both directions. It can convert power from a source to a load and also allow power to flow back from the load to the source. This bidirectional capability is useful in applications where power needs to be exchanged or shared between different sources and loads. Bidirectional converters are commonly used in applications such as energy storage systems and electric vehicle charging stations. They enable functions such as charging/discharging batteries (active power (P)) or supplying/absorbing reactive power (Q) to power grids [32].
Figure 2 shows, for example, a power electronic system for connecting a utility-scale battery storage system (BSS) [13] to a medium-voltage (MV) power line.
In power system metering [33], unidirectional and bidirectional power flows refer to the direction in which electrical power is transferred [34]. The difference between the two power flows is as follows:
  • Unidirectional Power Flow: Unidirectional power flow occurs when electrical power moves in a single direction, typically from a power source to a load or consumer. In this scenario, power flows from the source to the load, and there is no provision (no specific arrangement or rule) for power to flow in the opposite direction. Examples of unidirectional power flow can be found in traditional electricity distribution systems, where power generated at a centralized power plant is transmitted through transmission and distribution lines to reach homes, businesses, and other electrical loads. The power flows in one direction, from the power plant to the consumers.
  • Bidirectional Power Flow: Bidirectional power flow allows electrical power to flow in two directions. This means power can be transferred not only from a source to a load but also from a load back to the source. Bidirectional power flow is commonly seen in systems involving energy storage, renewable energy integration, and electric vehicle charging. For example, in a system with solar panels and a battery, power generated by the solar panels can be used to charge the battery, that is, unidirectional power flow from solar panels to the battery. However, during times of high demand or when the solar panels are not generating sufficient power, the energy stored in the battery can be discharged to power the load, that is bidirectional power flow from the battery to the load. The concept of bidirectional power flow is to be distinguished for active and reactive power, as shown in Figure 3 [23], where i ∈ N, that is, the total number of nodes in a power grid.
A brief history of the competition between AC and DC networks and the mathematical formulations of optimal power flow (OPF) and A-R-OPF over 70 years (1943 to 2013) can be found in [23]. The objective of this paper is to review battery storage and power electronic systems in flexible A-R-OPF frameworks in the last decade to:
  • Provide a summary of the existing research.
  • Highlight gaps in current knowledge.
  • Offer a new perspective on the topic.

2. Sustainable Energy Systems

The term sustainable means that something is able to continue over a period of time, while the term energy is to be distinguished from the term electricity as follows [35]:
  • Energy, in a broader sense, encompasses all sources of energy, including electricity as well as other forms such as fuels for vehicles, heating [20], etc.
  • Electricity is considered a subset of energy, that is, electricity is a specific form or type of energy.
This distinction is important when setting renewable electricity goals [35]. Therefore, in this overview, the focus will be on MV converters [19,36,37,38] for interfacing large-scale BSSs, especially for electricity storage [8]. It was shown in [8] that grid stabilization, frequency regulation, and smoothing of wind and solar energy are mainly supported by battery electricity storage systems, which are primarily used as ancillary services or for facilitating the integration of large-scale solar and wind power into the existing power system. Such future storage systems are needed, for example, in Europe, as shown in Figure 4 [39], because of the increasing share of electricity from renewable sources as shown in Figure 5 [40]. The role of gross electricity consumption is crucial in energy policy, aiming to increase the share of renewables in Germany’s gross electricity consumption to up to 45% by 2025, highlighting its significance over regular electricity consumption [41]. The difference between the term gross and the term net (final) electricity consumption is explained using an illustrative example in Appendix A. Note that, for instance, in 2014, Germany both imported electricity from Austria and other countries and exported electricity to other countries, particularly during periods of excess wind power generation along the coastal areas, ensuring efficient use of resources [41].
The need for storage and flexibility [42,43,44], that is, the ability to change easily according to the situation, is important for many power systems, for example, Korean [45], Chinese, and German power systems [46]. However, this requirement is a dynamic process that necessitates regular updates based on priorities. Therefore, plans are typically revised to account for evolving energy policies, technological advancements, renewable energy integration, market developments, and other factors. These updates provide valuable insights for decision-making and foster cooperation among stakeholders [39].
In [39], two types of flexibility can be distinguished, along with a qualitative analysis of the potential flexibility sources:
  • Short-Duration Flexibility: From milliseconds up to a few hours to ensure power system stability [4,47,48]
  • Long-Duration Flexibility: From days up to several weeks for long periods to compensate for prolonged periods with a shortage of wind and solar generation [28,48,49]
To achieve the aforementioned flexibility, the implementation of grid-scale energy storage systems is necessary [50], where the potential and challenges of grid-scale energy storage for a reliable and cost-effective power system with high renewable energy penetration are explored. Grid services are discussed, methods are evaluated, obstacles to adoption are identified, the conflict between technical benefits and economic compensation is addressed, regulatory changes are examined, and the importance of further research in this area is emphasized. It was concluded that the most effective resource combination to address the challenges of renewable energy integration is being determined through ongoing research, as acknowledged barriers cannot be fully overcome by energy storage alone.
In contrast, the need for energy curtailment and demand response is also very important in many countries [51,52]. Studies suggested that renewable energy use can be enhanced and grid stability improved by combining energy storage with measures such as curtailment or demand response [53,54]. Investigating the effect of network constraints on renewable energy generation and curtailment in energy system models at the transmission level was the primary focus [52]. However, energy curtailment is a complex process occurring at various voltage levels, as depicted in Figure 6 [23], where (TR) symbolizes, for simplicity, a lossless transformer as a lossless line and (Curt.) curtailment refers to the reduction or limitation of electricity generation from renewable energy sources, particularly wind and solar, due to various reasons such as grid stability, grid congestion, or mismatch between supply and demand [47,55,56]. It is important to note that different countries have varied network infrastructures.
The electricity grid in Germany, for example, is subdivided into transmission and distribution grids with maximum voltage or very high-voltage (VHV), high-voltage (HV), MV, and low-voltage (LV). Transmission grids transport electricity across Germany and beyond, minimizing loss and supplying power to high-demand areas. The German HV grid connects to the wider European grid, spanning 35,000 km [57], where AC transmits electricity at 220–380 kV, while future DC lines can reach 525 kV. Let UN be the nominal line voltage, then UN ∈ [110, 150, 220, 380, 500, and 700 kV] [58,59,60] for the maximum voltage. Note that service companies operate and maintain these grids, ensuring fair access for power resellers and minimizing fluctuations caused by supply-demand imbalances. The four main transmission system operators (TSOs) (with control area responsibility) in Germany are TenneT (23,900 km of HV lines and cables [61]), 50 Hertz Transmission (more than 10,000 km [59]), Amprion (10,000 km [62]), and TransnetBW (3101 km overhead lines and cables in 2022 [63]). TenneT covers Germany’s transmission system from north to south, 50 Hertz operates in the north and east, Amprion in the west and southwest, and TransnetBW in Baden–Württemberg, as shown in Figure 7 [64].
In contrast, the number of power distribution system operators (DSOs) is quite extensive due to the decentralization of the power grid. There are numerous DSOs responsible for operating and maintaining the power distribution networks at the local level. These DSOs are responsible for delivering electricity to end-users, such as households and businesses, where UN ∈ [0.4, 3, 6, 10, 15, 20, 30, 60, and 110 kV] [58,59]. The exact number of DSOs in Germany can vary over time due to mergers, acquisitions, and restructurings within the power industry. Table 1 [65] gives the number of network operators in the last decade. TSOs collaborate with DSOs and other stakeholders to ensure efficient and secure operation of the power grid, with TSOs focusing on higher-voltage transmission, while DSOs manage lower-voltage distribution grids delivering electricity to end-users.
In summary, Europe’s grids face three key challenges: (1) increasing reliance on fluctuating energy sources, (2) integration of numerous power generation installations, and (3) the growing trend of electricity trading in the EU, particularly for Germany as a transit country between western and eastern markets. It highlights the importance of comprehensive coordination, the construction of new power lines, European collaboration, and the implementation of smart grids to efficiently link power generation, grids, and demand.

3. Dynamic Needs

Dynamic needs imply flexibility to effectively meet evolving requirements. For example, the curtailed energy in Germany, as shown in Figure 8 [66], is dynamic, that is continuously changing. In 2021, for instance, around 5.8 terawatt hours (TWh), equivalent to 5.8 billion kilowatt hours (kWh) or 5.8 million megawatt hours (MWh) of energy, were curtailed due to feed-in management measures for network stability. With an on-peak active energy price of 117 $/MWh [28], this led to a loss of 678.6 million dollars (M$/year). Using a hypothetical exchange rate of 1 USD = 0.93 EUR, this equates to a loss of over 500 million EUR in 2021. For comparison purposes, the gross power consumption in Germany from 2010 to 2021 is given in Table 2 [40].
It is worth noting that the implementation of the new Renewable Energy Sources Act (Erneuerbare–Energien–Gesetz; EEG) [67] is expected to drive a significant increase in the installation of renewable energy systems in Germany. This surge will primarily be seen in the annual growth of wind and solar power technologies, as depicted in Figure 9. The expansion target for 2030 is raised to at least 80% of Germany’s gross electricity consumption, that is, almost doubling the share within less than a decade. Active power provisions are planned in the new electricity network development plan (2021–2035). Additionally, the key aspects concerning reactive power management, as outlined in [67], can be summarized as follows:
  • The plan emphasizes efficient reactive power management and decentralized approaches.
  • It assumes that DSOs will handle their own requirements using their connected equipment and resources.
  • This decentralization reduces the need for compensation in the transmission grid and increases it in the distribution grid.
In summary, the new plan prioritizes efficient reactive power management and decentralized approaches, with DSOs responsible for meeting their own needs. Hence, there is a need for further investigation into the existing flexible A-R-OPF frameworks which are designed to handle dynamic power flows, varying energy sources, and changing grid conditions in an optimal manner. It incorporates mechanisms, algorithms, or models to optimize power flow and effectively manage reactive power on distribution levels based on system requirements and operational conditions. Moving forward, the next phase involves incorporating new states and degrees of flexibility, determined by the decision variables outlined in [24], to address the interconnection of power systems. This step aims to enhance the adaptability and responsiveness of the systems in the future.

4. Control Techniques

Power electronics control techniques play a crucial role in regulating and managing power electronic systems, thereby enabling precise control over electrical power conversion and conditioning [68]. These techniques ensure desired performance, efficiency, and reliability, making power electronics an efficient interface in distributed power generation and battery systems [69,70]. Recent advancements in control theory, computational intelligence, and signal processing have greatly influenced the development of new solutions for controlling power electronics [71]. A comprehensive review of, for example, current control techniques in three-phase voltage-source pulse width modulated converters, categorizing them into linear (proportional integral controllers and state feedback controllers) and nonlinear (bang-bang known as hysteresis and predictive controllers) groups is given in [72]. In [72], it also discusses briefly emerging trends such as the use of fuzzy and neural networks controllers as types of advanced control systems. Another recent work [73] provides an overview of artificial intelligence (AI) applications in power electronic systems, covering design, control, and maintenance phases, discussing optimization, classification, regression, and data structure exploration tasks. Below is a brief overview of commonly used power electronics control techniques, based on the above reviews:
  • Pulse Width Modulation (PWM) Control [74]: It is a widely used technique in power electronics. It involves varying the width of pulses within a fixed period to regulate the average voltage or current delivered to the load. Unlike pulse density modulation and pulse frequency modulation, which, respectively, modulate the density or frequency of pulses, PWM focuses on modulating the width or duration of pulses. It is extensively used in applications such as motor drives, uninterruptible power supplies, and PWM-battery [75].
  • Hysteresis/Bang-Bang Control [55]: It is a robust and simple control technique employed in power systems [56] and power electronics systems [71]. It operates by comparing the system’s output with predefined upper and lower hysteresis bands. If the output exceeds the upper band, the control action changes, and if it falls below the lower band, the control action reverts. Hysteresis control provides fast response making it suitable for applications such as converters, voltage regulators, and battery chargers.
  • Sliding Mode Control [76]: It is, in general, a nonlinear control technique that ensures robust performance even in the presence of uncertainties or disturbances [77]. It involves creating a sliding surface to drive the system states toward a desired trajectory. Sliding mode control offers excellent disturbance rejection, insensitivity to parameter variations, and fast transient response [78]. It finds applications in power factor control [79].
  • Model Predictive Control [80]: It is an advanced control technique that uses a dynamic model of a power electronics system to predict future behavior [71]. Based on this model, an optimization algorithm generates control actions that optimize a cost function while satisfying system constraints. MPC allows for predictive control of multiple system variables simultaneously, enabling superior performance and robustness. It is employed in applications such as grid-connected converters, renewable energy systems, and electric vehicle charging stations.
  • Artificial Intelligence-based Control [81]: There are several examples of AI-based control techniques. Some of the commonly used ones include [82]: (1) Fuzzy Logic: A rule-based control technique that uses fuzzy logic and set theory to handle imprecise or uncertain information [83,84]. It allows for the representation of linguistic variables and the definition of rules describing system behavior. Fuzzy logic control offers intuitive and flexible control, making it suitable for systems with nonlinearities or complex dynamics. It finds applications in power dc-converters and voltage regulation [85,86]. (2) Neural Networks: These techniques employ artificial neural networks to learn and approximate system behavior based on training data [87]. They offer adaptive control capabilities and can handle complex and nonlinear systems. It has been successfully applied in power electronics for applications such as BSSs [88]. Note that explainable AI is a concern in power electronics as many AI algorithms lack transparency, often referred to as the “black-box” feature [73]. (3) Genetic Algorithms: GA can be considered a type of power electronics control technique [89]. They are a computational optimization technique inspired by the principles of natural evolution and genetics. GA involves using a population of potential solutions and applying genetic operators such as selection, crossover, and mutation. Through iterative evolution, GA aims to find an optimal or near-optimal solution to a given problem [28,89]. In the context of power electronics, GA can be used to optimize parameters, control strategies, or system configurations, thereby enhancing the performance, efficiency, and reliability of power electronic systems [90,91].
The mentioned control techniques represent a subset of the wide range of strategies employed in power electronics applications. The selection of the optimal controller in power electronics or systems engineering depends on factors such as the application, system requirements, dynamics, performance objectives, complexity, robustness, and constraints, considering that different controllers have distinct strengths and weaknesses. In power electronics, the choice of controller also depends on operating conditions. Hybrid controllers, combining multiple strategies, can be used to leverage the advantages of different control approaches.

5. Role and Benefits of BSSs

In flexible A-R-OPF, for example on MV grids [92], BSSs provide enhanced flexibility and support for optimizing active and reactive power flow in power grids, offering various functions such as:
  • Frequency and Voltage Regulation: In interconnected grids, BSSs respond rapidly to frequency deviations [93], adjusting active power and regulating voltage levels through efficient management of reactive power. This enhances system stability, improves power quality, and strengthens grid performance. Similarly, in isolated grids, BSSs play a crucial role in monitoring and responding to frequency deviations. They inject power during high-demand periods to raise the frequency and absorb power during low-demand periods to lower it, maintaining a stable frequency range. BSSs also manage reactive power flow, regulating voltage levels for a consistent and reliable power supply in isolated grids [94].
  • Load Balancing and Peak Shaving: BSSs can help balance the active and reactive power demand by supplying electricity during peak periods and storing excess power during low-demand periods. In addition, BSSs can reduce peak power demand, alleviate grid strain by supplying extra active power in high-demand periods, and enhance grid stability and efficiency by providing reactive power support to regulate voltage levels and improve power quality.
  • Renewable Energy Integration and Grid Resiliency: Grid resiliency refers to the ability of an electric power system to withstand and recover from disruptions caused by natural disasters through understanding the causes of blackouts, preparing and hardening the grid, and leveraging new technologies for situational awareness and faster restoration. Grid resiliency means a power grid can handle and recover from problems such as natural disasters, equipment failures, cyber-attacks, or extreme weather events. BSSs facilitate the efficient integration of renewable energy sources by storing excess generation to minimize curtailments, and releasing it during periods of low renewable output, ensuring a continuous and stable power supply. Furthermore, BSSs can act as backup power sources during outages, providing uninterrupted electricity supply and enhancing grid resiliency.
  • Reverse Power Flow Optimization: BSSs play a crucial role in optimizing reverse power flow in interconnected grids [95]. When excess power is simultaneously injected into two neighboring grids, BSSs actively absorb and store the surplus energy, thereby preventing grid instability and voltage rise. By efficiently managing to reverse active power, BSSs help maintain system stability and ensure reliable operations in interconnected grids. In addition, BSSs regulate reactive power to control voltage levels, contributing to optimal power quality during reverse power flow conditions. Their flexibility and ability to provide such ancillary services enable effective reverse power optimization, enhancing the overall performance of interconnected grids. Furthermore, considering electricity prices [95], BSSs can take advantage of varying prices by charging during low-cost periods and discharging during high-cost periods, optimizing cost savings. The increasing volume of services procured by TSOs through distributed resources highlights the need for a more active role of DSOs in maintaining network integrity and facilitating services [96].
  • Transmission and Distribution Infrastructure Optimization: BSSs play a crucial role in power systems by providing active and reactive power support, ensuring stability, and promoting energy independence. Strategically located BSSs within the grid can alleviate congestion in transmission and distribution systems. They can store excess energy at one location and release it at another, reducing the need for infrastructure, for example, power lines, and upgrades.
In this context, achieving adequate coordination between TSOs and DSOs, taking into account the role of BSSs, becomes crucial. The integration of BSSs should be carefully considered, given their critical role in optimizing reverse power flow, absorbing surplus energy, and ensuring grid stability. To effectively address the technical constraints associated with distribution networks having multiple voltage levels, the adoption of comprehensive approaches becomes essential. Both single-phase and three-phase A-R-OPF frameworks hold significance, depending on the modeling objective. Simple and complex frameworks are recommended based on the specific application requirements. By incorporating BSSs and considering their role in conjunction with TSO-DSO coordination models, power systems can effectively leverage distributed energy resources, enhance grid stability, and optimize the utilization of sustainable resources. This, in turn, contributes to the development of more sustainable and reliable energy infrastructures. Finally, evaluating the cost-effectiveness of various approaches, such as reverse power allowance, renewable source curtailment, energy storage deployment, price modeling, and infrastructure upgrades, can provide valuable insights for future research.

6. Conclusions

An overview of power electronics and their applications is provided in this paper, with an emphasis on power conditioning and minimizing losses. The different power flow capabilities of unidirectional and bidirectional converters are discussed, highlighting their significance in renewable energy integration, energy storage, and electric vehicle charging. The research focuses on battery storage and power electronic systems in flexible A-R-OPF frameworks, with the aim of summarizing existing research, identifying knowledge gaps, and offering a new perspective.
The importance of achieving flexibility in power systems through grid-scale energy storage is emphasized. Energy curtailment, demand response, and their challenges are addressed, along with various network infrastructures, particularly in Germany. The challenges faced by Europe’s grids, the necessity of comprehensive coordination, the construction of new power lines, European collaboration, and the implementation of smart grids are highlighted. The paper underscores the importance of flexibility, providing examples such as curtailed energy in Germany and the anticipated increase in renewable energy installations. Efficient reactive power management and decentralized approaches are given emphasis. Overall, further research is needed on flexible A-R-OPF frameworks, incorporating mechanisms, algorithms, or hybrid models to optimize power flow and efficiently manage reactive power, while considering new states and degrees of flexibility.

Funding

This invited paper received no external funding.

Data Availability Statement

Not applicable.

Conflicts of Interest

The author declares no conflict of interest.

Appendix A

The terms gross and net electricity consumption can be understood through a simple numerical example. Let x and y be, respectively, the gross and net electricity consumption. In Energyland, a hypothetical country (or area), the total electricity generated within its boundaries is 1000 MWh/year. Additionally, Energyland imports 200 MWh of electricity from neighboring countries. Then, x can be calculated as in Equation (A1):
x = 1000 MWh/year + 200 MWh/year = 1200 MWh/year
This value represents the total amount of electricity used within Energyland, including all electricity consumed by end-users for various purposes. To calculate y, we must take into account losses that occur during the transmission/distribution process and self-supply. Here, self-supply refers to the consumption of electricity by the entity (or plant) that generates or produces it. Assuming that, in Energyland, there are transmission/distribution losses of 50 MWh/year and self-supply by power plants of 100 MWh/year, then y can be calculated as in Equation (A2):
y = x − 50 MWh/year − 100 MWh/year = 1050 MWh/year

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Figure 1. Block diagram of a power electronic system [2], with the abbreviation DEM (demand) representing an electrical load.
Figure 1. Block diagram of a power electronic system [2], with the abbreviation DEM (demand) representing an electrical load.
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Figure 2. A power electronic system to connect a utility-scale BSS to a MV power line.
Figure 2. A power electronic system to connect a utility-scale BSS to a MV power line.
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Figure 3. Power and energy balance at node i: (a) active power (b) reactive power, with the abbreviations CGE (conventional generator), and RGE (renewable energy generator).
Figure 3. Power and energy balance at node i: (a) active power (b) reactive power, with the abbreviations CGE (conventional generator), and RGE (renewable energy generator).
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Figure 4. Storage needs in MW in 2040.
Figure 4. Storage needs in MW in 2040.
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Figure 5. Share of electricity from renewable sources in gross electricity consumption in European countries in 2020.
Figure 5. Share of electricity from renewable sources in gross electricity consumption in European countries in 2020.
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Figure 6. Interconnected power networks.
Figure 6. Interconnected power networks.
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Figure 7. TSOs in Germany.
Figure 7. TSOs in Germany.
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Figure 8. Curtailed energy in Germany from 2010 to 2021 in gigawatt hours (GWh).
Figure 8. Curtailed energy in Germany from 2010 to 2021 in gigawatt hours (GWh).
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Figure 9. Expansion targets of (a) onshore wind power capacity and (b) solar-radiation power capacity in MW up to June 2022.
Figure 9. Expansion targets of (a) onshore wind power capacity and (b) solar-radiation power capacity in MW up to June 2022.
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Table
Table 1. Number of network operators in Germany.
Table 1. Number of network operators in Germany.
20122013201420152016201720182019202020212022
TSOs4
DSOs883883884880875878890883874872865
Table
Table 2. Gross power consumption in Germany from 2010 to 2021 in TWh.
Table 2. Gross power consumption in Germany from 2010 to 2021 in TWh.
201020112012201320142015201620172018201920202021
613602601600587590591592587570549570
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Gabash, A. Review of Battery Storage and Power Electronic Systems in Flexible A-R-OPF Frameworks. Electronics 2023, 12, 3127. https://doi.org/10.3390/electronics12143127

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Gabash A. Review of Battery Storage and Power Electronic Systems in Flexible A-R-OPF Frameworks. Electronics. 2023; 12(14):3127. https://doi.org/10.3390/electronics12143127

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Gabash, Aouss. 2023. "Review of Battery Storage and Power Electronic Systems in Flexible A-R-OPF Frameworks" Electronics 12, no. 14: 3127. https://doi.org/10.3390/electronics12143127

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