Integration of Distributed Energy Resources and provision of Ancillary Services: control strategies for Microgrids and Electric System management

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(1)POLYTECHNIC SCHOOL Department of Electrical, Electronics, Telecommunications Engineering and Naval Architecture. PHD IN SCIENCE AND TECHNOLOGIES FOR ELECTRICAL ENGINEERING, NAVAL ENGINEERING AND COMPLEX SYSTEMS FOR MOBILITY CURRICULUM: ELECTRICAL ENGINEERING SSD ING-IND/33. Integration of Distributed Energy Resources and provision of Ancillary Services: control strategies for Microgrids and Electric System management Monica Crosa di Vergagni. Supervisor: Prof. Ing. Stefano Massucco December, 2019.

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(3) Abstract. Nowadays, the expansion of the electric power systems is globally heading towards a more sustainable and reliable development. The increasing interest for an environmentally conscious and sound use of the available assets is fostering the penetration of the renewable energy sources (RES), bringing significant benefits to economy and society, as: the reduction of the greenhouse gases emissions; public health improvement; more stable energy prices; the diversification of the energy supply; and more efficient and resilient electric grids. The transmission and distribution grids, once dominated by conventional fossil fuel-fired power plants, are now experiencing important transformations. Renewable resources, especially wind and solar, are displacing the traditional thermal generation, leading to considerable changes in the power systems dynamic behavior. The growing number of inverter-based devices connected to the grid, that have a great impact on the stability of the electric networks, as well as the variability, unpredictability and intermittency which characterize the RES, are posing new challenges to the system operators. As opposed to synchronous generators, which inherently provide inertia to the system, renewable power plants are usually decoupled from the grid through power electronic converters, causing critical stability issues in terms of voltage control, load balancing and frequency regulation. The recent developments in the information and communication technologies, as well as the wide spread of intelligent measurement devices, are contributing to improve the performance of the power system operation and leverage the opportunities coming from the exploitation of the new assets and the great amount of available data. Moreover, notable changes are also occurring on the demand side, as advanced digital technologies and control strategies are fostering their active participation to the system management and to a more inclusive and competitive electric market. The present thesis addresses the issue of the energy transition and the consequent significant transformation that the power systems are currently undergoing, focusing on the possible solutions that can be implemented in order to face the increasing challenges and take full advantage of the electric grid available resources. The aim of this study is providing both a general overview of the recent technological developments that have characterized the global evolution of the electric power systems. 2.

(4) in the last decades, as well as a more detailed description of the advanced control algorithms, regulation logics and innovative strategies that can be implemented for their optimal management. In particular, the focus will be on the efficient exploitation of renewable energy sources, electric storage devices and controllable loads. The thesis is structured considering the different trends and innovations that have taken place in the transmission systems, and the advanced management techniques and technological developments that have had a significant impact on the distribution systems. After a thorough introduction of the present electric networks and energy markets design and operation given in Chapter 1, Chapter 2 and Chapter 3 focus on the integration and exploitation of the new assets available at the transmission level, while Chapter 4 and Chapter 5 investigate the modern control methods and operation management strategies implemented at the distribution level. In particular, the chapters are organized as follows: in Chapter 2, different load control strategies for the provision of frequency regulation services are illustrated, tested and discussed; Chapter 3 deals with the integration of wind power plants and their potential contribution to the system reliability; Chapter 4 presents the design, implementation and operation of an optimization platform for distribution networks management; Chapter 5 describes an Energy Resources Management technique applied to the controllable assets of a Microgrid; the overall conclusions and final remarks are reported in Chapter 6. The present work is the outcome of the scientific research that I developed during the three years long Ph.D. program, in collaboration with and funded by ABB S.p.A.. 3.

(5) Acknowledgments I would like to start by saying thank you to all my PhD colleagues, as each one of them taught me many valuable lessons. I wish to thank: Matteo Saviozzi, the most helpful, for his precious insights and continuous support; Fabio D’Agostino, for sharing his technical knowledge and for always being a model of professional behavior in the work environment; Andrea Vinci, for his tireless efforts to assist me with IT issues, in hopes of teaching me to get through them by myself; Andrea Bagnasco, for showing me a complete different perspective of how an engineer can be in the workplace; Giacomo Schiapparelli, for his positivity and his cheerful and kind support; Francesco Conte, who deserves a special thanks, for guiding me since I was an undergraduate student, helping me the most in growing my technical skills; and Paola Pongiglione, who shared with me the long journey from the first day of BSc until the last day of this PhD, for her availability and sincere willingness to help but, most importantly, for the time we spent together enjoying the sun outside, relaxing and, sometimes, just chatting, setting the engineering aside for the very length of those short breaks. I wish to express my deepest gratitude to my major Professor Stefano Massucco, for leading me with constant dedication and the most admirable willingness to help me achieve my goals, grow in knowledge and ambition, improving as an engineer and as a person, that I could have ever wished for. He provided me with very valuable and constructive suggestions that I will always remember. I wish to show my appreciation to Professor Federico Silvestro, for sharing his outstanding scientific and technical knowledge, representing a reliable source of answers, solutions and advice, helping me gain the fundamental engineering skills I will need the most. I would like to acknowledge the great support of Professor Enrico Ragaini and the truly appreciated contribution of ABB SACE, without whose guidance and funding my research project could not have reached its goal. I am particularly grateful for the generous support given by Professor Carlo Alberto Nucci and Mr. John McDonald, as they assisted me during this academic program and agreed to review my final thesis. I am sincerely thankful for their mentorship and advice.. 4.

(6) Thanks to all my friends for their ability to make me forget about the academic career I was pursuing in all those times when I was eagerly seeking distraction and, at the same time, for showing me their true admiration and pride for my hard work and achievements. I wish to address my biggest and most sincere thanks to all my family members, for their continuous support, patience, understanding and trust, for encouraging me to follow my aspirations, develop my talents, make my own decisions, test myself and learn to aim high, while always being there when their help and participation was most needed.. 5.

(7) Contents Abstract .............................................................................................. 2 Acknowledgments............................................................................... 4 Contents ............................................................................................. 6 1.. Introduction .............................................................................. 10 1.1 1.2 1.3. 2.. Energy Markets and Ancillary Services .........................................11 Demand Response ......................................................................13 Microgrids Design and Operation ................................................15. Load Contribution to Frequency Regulation Services .................. 18 2.1 Control Strategies .......................................................................20 2.1.1 Synthetic Inertia Definition ........................................... 20 2.1.2 Synthetic Inertia Control Logic...................................... 22 2.1.3 Fast Primary Frequency Regulation Control Logic ........ 26 2.1.4 Combined SI/FPFR Control Logic .................................. 28 2.2 Load Models ...............................................................................29 2.2.1 Refrigeration System Model ......................................... 29 2.2.2 Water Heating Systems Model ..................................... 31 2.2.3 Load Aggregate Model.................................................. 32 2.2.4 Loads Parameters ......................................................... 32 2.2.5 Mathematical Model Implementation in MATLAB/Simulink™ 34 2.3 Network Model ...........................................................................36 2.3.1 Electric system characterization ................................... 36 2.3.2 Electric Grid Model Implementation in MATLAB/Simulink™ 39 2.3.3 Generating Units Model ............................................... 40 2.3.4 Frequency Regulations Model ...................................... 40 2.3.5 Load Model ................................................................... 41 2.3.6 Interconnections Model ............................................... 41 2.4 Simulations .................................................................................42 2.4.1 Simulation Scenarios..................................................... 42 2.4.2 Simulations types and parameters ............................... 51. 6.

(8) 2.4.3 Evaluation Metrics ........................................................ 53 2.5 Results ....................................................................................... 55 2.5.1 Over-frequency event .................................................. 55 2.5.2 Under-frequency event ................................................ 60 2.5.3 Numerical results.......................................................... 65 2.5.4 Sensitivity analysis ........................................................ 71 2.6 Conclusions ................................................................................ 73. 3.. Wind Power Integration and Control .......................................... 76 3.1 Network and Wind Farm Model .................................................. 77 3.1.1 Aerogenerator Model ................................................... 78 3.1.2 Network and Wind Farm Model ................................... 80 3.2 The Control Strategy ................................................................... 82 3.2.1 The Adaptive Kinetic Energy Control ............................ 82 3.3 Simulations and Results .............................................................. 87 3.3.1 Simulation Scenarios .................................................... 87 3.3.2 Results .......................................................................... 88 3.4 Conclusions ................................................................................ 93. 4.. An Optimization Platform for Distribution Grids ......................... 94 4.1 Data Management System .......................................................... 96 4.2 DMS Design and Functionalities .................................................. 98 4.2.1 The Architecture of the Optimization Platform ........... 98 4.2.2 Advanced Control Functionalities .............................. 101 4.3 Test Site ................................................................................... 103 4.3.1 Medium Voltage Network .......................................... 103 4.3.2 Installation Campaign ................................................. 104 4.4 Example of an Application: Volt/VAr Control ............................. 107 4.4.1 The Volt/VAr algorithm .............................................. 108 4.4.2 Simulations and results .............................................. 109 4.5 Example of an Application: Optimal Power Flow ....................... 110 4.5.1 The OPF algorithm ...................................................... 111 4.5.2 Test Site: a Low Voltage Grid ...................................... 111 4.5.3 Simulation Scenarios .................................................. 115 4.5.4 Results ........................................................................ 116 4.6 Conclusions .............................................................................. 120. 5.. Energy Resources Management Techniques for Microgrids....... 122 5.1. Algorithm Structure .................................................................. 123. 7.

(9) 5.1.1 Acquisition .................................................................. 126 5.1.2 Average ....................................................................... 127 5.1.3 Forecast ...................................................................... 129 5.1.4 Displacement Estimation ............................................ 129 5.1.5 Curves calculation ....................................................... 132 5.1.6 Priority identification .................................................. 136 5.1.7 Switching ..................................................................... 140 5.2 Test Case Scenario .................................................................... 140 5.2.1 Test Case Microgrid .................................................... 140 5.3 Simulations and Results ............................................................ 144 5.3.1 Simulation Scenarios................................................... 144 5.3.2 Communication Architecture ..................................... 150 5.3.3 Key Performance Indicators........................................ 151 5.3.4 Simulation Results ...................................................... 152 5.4 Conclusions............................................................................... 159. 6.. Conclusions ............................................................................. 160. Appendix A. The Optimal Power Flow.............................................. 164 A.1 Overview of the Optimal Power Flow .............................................. 164 A.2 Power Flow Equations ..................................................................... 165 A.3 Inequality constraints ...................................................................... 166 A.4 Mathematical Formulation .............................................................. 167 A.5 OPF Algorithm Implementation ....................................................... 170 A.5.1 Sets ................................................................................. 171 A.5.2 Variables ......................................................................... 172 A.5.3 Parameters ..................................................................... 173. Bibliography.................................................................................... 176 Publications originated during the Ph.D ........................................... 188 Projects developed during the Ph.D ................................................. 190 International experiences and courses attended during the Ph.D ..... 192. 8.

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(11) Chapter 1. 1. Introduction The total renewable energy generation capacity installed worldwide reached 2350 GW at the end of 2018, making up about a third of total installed capacity. The decade-long trend of strong growth in renewable generation can be registered in every region of the world and for all different technologies. In particular, wind and solar accounted for 84% of the renewable energy capacity global annual increase of 7.9% in 2018. A focus on the growth of each technology in 2018 can be summarized as follows [1]: Solar Energy: the solar energy capacity leads the global growth rate with an increase of 24%, which corresponds to 94 GW. Asia accounts for the majority of it: about 70% of the global increase, corresponding to 64 GW; Wind Energy: the greatest expansion of the wind energy capacity has been registered in China and the USA, making up for about 41% and 14% of the 49 GW total global increase, respectively; Hydropower: the growth in hydropower plants installation is estimated to have increased by over 3% globally, with the 8.5 GW of new installed capacity in China accounting for the majority of the growth; Bioenergy: modern bioenergy is considered to have untapped potential when considering its exploitation in the transport and industry sectors. China, India and the UK together contributed to the total bioenergy capacity expansion with 3.6 GW; Geothermal Energy: the 539 MW of total global growth in geothermal capacity has mostly been registered in Turkey and Indonesia, accounting for about the 41% and 25%, respectively. The European Climate-Energy Package approved by the European Union aims at reducing the Green House Gas (GHG) emission by 40% in 2030, compared to the levels registered in 1990. Moreover, the European guidelines intend to reach the target of 30% of renewable energy share in the end uses and 27% of energy efficiency improvement.. 10.

(12) 1. Introduction. 11. In order to strike the 2030 European target in terms of energy consumptions saving, GHGs emissions reduction and increase in the share of renewable sources, it is necessary to define a clear path oriented toward fostering low-carbon technologies, production systems and solutions. The fight against climate change and the consequent decarbonization of the economic sector will be possible only with the implementation of political changes and strategic decisions. Ambitious investments need to be planned for a radical reorganization of entire sectors, such as the industrial, the transport and the civil sectors, which play a major role in the GHGs emission. The energy sector is undertaking significant changes as well: the way the energy is generated, transported and supplied is evolving and the integration and efficient operation of the advanced technologies are bringing about new challenges and opportunities that need to be faced and leveraged. The energy transition, which is currently taking place all over the world, is affecting the way electric power systems are controlled and managed, involving considerable structural developments. The leading factors that are driving the modernization of the electric systems are [2]: • the increasing penetration of Renewable Energy Sources (RESs) which, overall, is expected to grow by 1200 GW in the next five years. According to the International Energy Agency (IEA) the share of renewable generation in the world’s electricity production is expected to reach 30% in 2024 [1]; • the significant reduction in the conventional fossil fuel-fired power plants, which rely on coal, natural gas or petroleum products. This shift in the energy share is causing critical stability and reliability issues; • the “electrification” of the consumptions, which involves switching the heating and cooling systems, or other appliances, to be electrically powered. This strategic electrification is also concerning the transportation sector. Considering this fast-changing scenario, the electric system operators are asked to integrate and fully exploit the new available technologies, implementing structural and regulatory upgrades, leading the way toward a more sustainable and reliable power system.. 1.1. Energy Markets and Ancillary Services. In order to achieve the targets declared in the Sustainable Development Goals (SDGs) set by the United Nations General Assembly in 2015 [3] and, at the same time, meet the full potential of the renewable energy sources, the right policies and rigorous sustainability regulations will be essential. In this context, the energy markets are undertaking significant efforts to improve their performance and facilitate the integration of the new. University of Genova. Monica Crosa di Vergagni.

(13) 1.1. Energy Markets and Ancillary Services. 12. available resources. Both wholesale and retail markets are critical to enable the Distributed Energy Resources (DERs) to be monetized and fully exploited [4]. During the last twenty years, the electricity systems have restructured from the traditional vertically integrated model to competitive wholesale markets, but the recent shift towards a sustainable economy and the employment of environmentally sound technologies is bringing about the need for a new modernization. In the wholesale market, the energy resources are usually dispatched according to their cost of operation, taking the technical requirements and constraints into account. The costs of transmitting, distributing and delivering the electricity to the end users is then reflected in the retail market. The economic dispatch and congestion management techniques that are used to be applied to the transmission systems, which are generally based on Optimal Power Flow (OPF) algorithms able to take both operational costs and electrical constraints into account, need now to be adapted and employed at lower voltage levels, as the RESs are commonly connected to the distribution grid. The innovative OPF methods should be designed in order to address the criticalities related to the different network topologies, the potential power flow inversions and phase imbalances. Even though the electricity markets design and framework vary among different countries, they share the common goal of allowing open access to transmission and distribution systems and to the provision of all services under their control, ensuring long-term reliability of grid operation, security of supply, economic competitiveness and environmental sustainability for current and future consumers. The system operators are aware that the regulatory barriers and the lack of economic incentives are the main obstacles to the increasing penetration of renewable sources. The challenges caused by the volatility and intermittency of the renewable generation and the unpredictability of the demand make it necessary to search for new market paradigms and flexibility options. In this context, a significant revolution in the electricity market structure has been represented by the inclusion of both renewable sources and flexible demand in the provision of ancillary services to the grid. The ancillary services, which aim at keeping the frequency and voltage within their desired limits, balancing generation and load demand and granting the security of supply at the least cost of operation, can be categorized based on the timescale of the response to a request. These services typically include: voltage control; frequency regulation; spinning, non-spinning and replacement reserve provision; and black start capability. As an example, the Volt/Var Optimization technique, which will be thoroughly described in the present thesis, can be applied to the available resources in order to increase system flexibility by providing local reactive power support to the grid as an ancillary service. The procurement of ancillary services can occur in the day-ahead as well as in the realtime market, depending on the market structure.. Monica Crosa di Vergagni. PhD in Electrical Engineering.

(14) 1. Introduction. 13. The variability and uncertainty of the Distributed Generation (DG) and the load consumption increase the ancillary services requirements, affecting both scheduling and pricing. Moreover, the impacts vary depending on the system conditions, which makes it even more difficult to predict and allocate the necessary power reserves. As the number of traditional power plants connected to the grid keeps decreasing, in favor of renewable energy sources, the reserve margin available for the provision of ancillary services shrinks as well. Similarly, the system inertia, which is automatically provided by conventional generators as part of their grid connection, is decreasing, as power electronics-based power plants lack inherent inertial response. The high share of inverter-based generation units, which are decoupled from the grid and do not provide rotational inertia, implies faster frequency dynamics, leading to a more challenging frequency control and load balancing. The electric systems worldwide have already experienced critical situations in terms of frequency and voltage stability, due to unexpected contingencies, generation and demand forecast errors, temporary lack of dispatched conventional generators and low rotational inertia [5]. In this context, as the need of new entities able to support the regulation activities is becoming more urgent and compelling, RESs and active loads participation to the provision of ancillary services can represent a valuable option as well as an adequate solution, leading also to the emergence of new market players and the implementation of new market products. The peculiarities of loads and renewables sources, which are characterized by different technologies, electrical constraints and power profiles, need to be considered in the definition of innovative ancillary services, able to enhance the flexibility options that the new assets can offer. Therefore, the key enabling factors for their inclusion in the provision of regulation services are: the definition of performance-based products; the separation of capacity and energy products; and the separation of upwards and downwards products. The distributed resources can be included in the voltage and frequency control services through the Demand Response (DR) programs, that foster the customers active participation to the electricity markets by making short-term variations in their consumption.. 1.2. Demand Response. Over the last decade, the distribution networks have experienced the most significant changes, as the installation of medium and small-scale renewable power plants, the deployment of smart meters and advanced metering infrastructures (AMI) and the spread of digital technologies have mostly interested the grid-edge. The increased amount of data made available by the growing number of intelligent devices, sensors and controllers distributed throughout the grid and at the customer University of Genova. Monica Crosa di Vergagni.

(15) 1.2. Demand Response. 14. interface, enhanced the interest for device interoperability and data analysis. The shift to an open energy market framework and the developments in the Information and Communication Technology (ICT) which made real-time communication easier and more cost-effective, fostered the customer transition toward an active role in the electric grid management. The ability of the end user to respond to reliability or price signals coming from the system operator, or from a service provider, by varying its power demand is usually referred to as Demand Response. The Federal Energy Regulatory Commission (FERC) defined the DR as a variation in the load demand, with respect to the expected demand, according to price signals or specific incentives meant to decrease the electricity consumption [6]. The DR programs represent an effective resource toward an efficient and sustainable development of the electric grid, which would help coping with the uncertainty and variability of the renewable generation. The DR includes all the actions taken by the user in response of external signals, which can involve planned demand variations, load shifting or shaving and the direct control of customer’s devices, such as heating and cooling systems. The load profile of the user can be partially or fully controlled, according to the electric system requirements. The implementation of DR programs involves the exploitation of the intelligent devices ability to regulate the load demand in order to provide ancillary services to the grid, leveraging the great amount of data made available by the distributed smart meters. The grid automation, monitoring and control are therefore paramount for the development of such procedures. Different system operators offer a wide selection of DR schemes and tariffs in order to foster a more efficient use of the available energy and encourage the electric market competition. The DR promotes the end users’ interaction and awareness, leading to economic benefits for both customers and grid operators. Recently, DR programs evolved in order to include not only the dispatchable load but the distributed generation and the electric storage devices as well. The demand-side response to electricity needs at the retail and wholesale levels can be aggregated, managed and provided as comparable services that reduce the need for competitive energy and capacity sources [4]. The dispatchable loads and distributed resources are able to provide high-quality regulation services and, in many occasions, represent a more efficient resource than the traditional assets. Compared to the performance of the conventional generating units in the provision of regulation services, the DR results to be faster, more flexible and even more cost-effective when it comes to short-term reliability services. The concept of Smart Grid (SG) is strictly related to the implementation of DR schemes. Most of the benefits coming from the investments in SG applications, as those related to. Monica Crosa di Vergagni. PhD in Electrical Engineering.

(16) 1. Introduction. 15. a more efficient control of the demand or to the installation of advanced ICT technologies, positively affect and foster the developments of DR programs. The inclusion of distributed generation and dispatchable loads in DR programs has gained remarkable attention, especially for the control and management of Microgrids, where the reliability and stability issues related to load demand forecasting errors and the uncertainty in renewable energies production are particularly challenging [7].. 1.3. Microgrids Design and Operation. The installation of renewable power plants at the distribution voltage level for generating power locally or closer to the end users has been one of the major trends of electric grids evolution over the last decades, driven by the gradual depletion of fossil fuel resources, poor energy efficiency and increasing environmental awareness. The development and integration of DG systems, which are usually installed at the distribution level and whose size is normally smaller than 50 MW, is driven by significant technical, economic and environmental benefits but need, at the same time, a reorganization and considerable structural changes of the traditional electric networks. In this context, small-scale active distribution networks able to operate either connected to the grid or in islanded mode, known as Microgrids, are fast-growing and promising resources. A Microgrid can be defined as an integrated energy system including interconnected loads and DERs, designed to supply electrical and heat loads, with the objective of ensuring security of supply as well as efficiency and reliability of operation. Usually connected to the low or medium voltage level, it represents a flexible controllable entity able to provide system services and support grid operation. The physical components making up a Microgrid vary depending on its size, location and implemented functionalities, but they typically include, but are not limited to: sensors and smart meters; energy storage devices; inverter-based energy resources; controllable loads; protection equipment; and an advanced communication infrastructure. The Microgrids development shows several advantages and benefits: • They are characterized by a significant penetration of renewable resources, representing an environmental benefit in terms of GHG emission reduction; • they promote grid reliability and security, since the islanded capability allows to improve grid resiliency in case of blackouts, outages or other difficulties occurring in the main grid [4]; • they are suitable for supplying power to remote areas where supply from the national grid is either difficult or not secure, representing a low-cost solution for rural electrification and a cheaper alternative to infrastructure modernization; • they can foster the integration of DERs, as the power generated at the distribution level can be directly fed to the distribution networks;. University of Genova. Monica Crosa di Vergagni.

(17) 1.3. Microgrids Design and Operation. 16. • they are characterized by localized energy resources which are usually installed close to the customers’ premises, leading to a reduction in the electrical losses from long distance transmission; • they can meet local electrical/heat requirements, supplying uninterruptible power, improving local reliability and providing voltage support at the consumer level [8]; • they can be controlled and managed as a single entity by the system operator, who can rely on its availability for the provision of regulation services. The Microgrid is therefore a strongly interconnected system able to ensure a particularly reliable operation, fully exploiting the available resources while complying with the regulatory constraints of the system operator. The implemented regulation logics of the Microgrid need to ensure the correct management of the power flow exchanged with the main grid, an efficient communication and a secure delivery of information and control signals. A Microgrid can usually rely on advanced technological devices, communication architectures and control strategies, which grant a seamless transition from the gridconnected to the islanded mode and enable to optimize the asset utilization in both states of operation. Therefore, the resources necessary for reliably and efficiently managing the Microgrids are already accessible to the system operators, that only need to identify their potentials and take full advantage of the available opportunities.. Monica Crosa di Vergagni. PhD in Electrical Engineering.

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(19) Chapter 2. 2. Load Contribution to Frequency Regulation Services The progressive installation of renewable power plants has profoundly modified the Italian and European electrical power systems. As opposed to traditional generating units, renewable generators are widely distributed throughout the electrical network, they are hardly predictable and not dispatchable and their inclusion in the provision of ancillary services to the grid is still an on-going process. As an example, the Italian electric grid is already characterized by reduced reserve margins for the frequency regulation services, which depend on the number of synchronous generators on service [1]. In this context, the possibility of having new entities other than the traditional generating units enabled to provide frequency regulation services is becoming more urgent, if not compulsory, even during normal operating conditions [9],[10]. The possibility of including the electric load in grid regulation and management activities is gaining attraction, as the load is already widely distributed and easily controllable. The controlled loads would need to vary their power demand to support the frequency recovery, without compromising the final customer comfort. One of the most promising solutions is the active participation of thermostatically controlled loads (TCLs), as refrigerators and water heaters (boilers), to frequency regulation activities [11]-[13]. The scientific community has been very interested and active in this research topic, making a wide and diversified selection of recent literature available. A control strategy applied to an aggregate of domestic refrigerators and intended to linearly vary their temperature set point according to the frequency value, has been proposed and tested in the British electrical grid [13]. The authors in [14]-[19], consider an aggregate of thermostatic loads controlled in order to follow an arbitrary power profile. The above-mentioned approaches are based on completely or partially centralized control strategies, which therefore assume the availability of real time telecommunication infrastructures.. 18.

(20) 2. Load Contribution to Frequency Regulation Services. 19. In order to control domestic devices, which are widely distributed and usually not connected to an efficient communication platform, a decentralized control strategy is more advantageous and it provides faster and more convenient applicability and implementation. The European Network of Transmission System Operators for Electricity (ENTSO-E) proposes a decentralized approach [10], defining the guidelines for future grid codes and suggesting simple rules for the frequency sensitivity of thermostatically controlled devices that could become mandatory in the near future. In particular, the ENTSO-E defines the guidelines for the control activation and deactivation, with respect to a specific frequency dead-band and it proposes a control strategy based on the variation of the temperature set-point of the thermostat proportional to the frequency deviation from its nominal value. The IEES Laboratory of the University of Genova, within a collaboration with RSE S.p.A. (Ricerca Sistema Energetico), conducted a study where the ENTSO-E procedure has been evaluated and tested using an accurate model of the Sardinian electric system for the year 2020 [20]-[22]. Thermo-dynamic models of fridges and boilers have been developed and stochastic external signals that have an influence on their operation, such as the external air temperature and the hot water utilization profile, have been defined. In the above-mentioned studies, the control strategy proposed by ENTSO-E has proved to enable thermostatic loads to provide an effective support to the primary frequency regulation, compensating for the decrease of the total regulating energy of the grid caused by the high level of renewable resources penetration. The control parameters of the proposed strategy have been optimized in [22], to obtain an efficient and robust contribution to the primary regulation, without severe repercussions on the secondary regulation. The potential degradation of the secondary regulation performance, which can be caused by the energy payback of the active loads that follows the power variation defined by the control strategy, it is a crucial point which can determine the effective applicability of the proposed control logics. Specifically, a great variation of the load power demand, followed by a comparable recovery, can lead the frequency to overcome the control activation dead band twice. The solution to this problem, as shown in [22], consists in limiting the frequency controller gain value, known as frequency sensitivity coefficient (FSC). However, a great number of participating controlled devices could lead to a similar problem, even if the FSC was limited. Therefore, three alternative control logics, other than the one proposed by the ENTSOE, have been designed and evaluated in [23] and [24]. The latter are not based on the variation of the thermostat temperature set points but on the forced activation or deactivation of the controllable devices driven by the definition of a specific set of thresholds, generated with a proper stochastic distribution. The simulations performed in [24], which considered a single scenario of the Sardinian network for the year 2020, showed the efficiency and reliability of the proposed solution. Henceforth, the three alternative strategies defined in [23] that are able to grant the same successful contribution to primary frequency regulation as the ENTSO-E control logic but without compromising the secondary regulation performance and which have University of Genova. Monica Crosa di Vergagni.

(21) 2.1. Control Strategies. 20. been improved and tested considering a great number of different scenarios, will be discussed. In order to test the above-mentioned strategies, the model of the Sardinian network for the year 2030, characterized by a high penetration of renewable energy sources and the absence of coal and oil generation units has been implemented. The present chapter outlines the results of an analysis conducted with the scope of identifying the flexibility degree and the propensity of electric loads to supply ancillary services to the grid as well as evaluating the potential fast active power support that domestic thermal loads aggregates, as refrigerators and water heaters, can supply for grid frequency stability. Moreover, the minimum technical requirements needed to grant an effective contribution to the frequency regulation are identified. As previously stated, the impact of a load flexible management on the frequency regulation has been evaluated in a regional/national grid, making use of a forecasted grid model of Sardinia for the year 2030, considering the occurrence of both over- and underfrequency events.. 2.1. Control Strategies. The proposed control strategies, which will be described in the following, are meant to manage the active load support to frequency regulation services by varying its power demand as a function of local measurements of the grid frequency. In particular, the regulation activities which have been considered are: 1. the provision of synthetic inertia (SI), where the controllable loads aggregate would vary its active power demand proportionally to the Rate of Change of Frequency (RoCoF); 2. the Fast Primary Frequency Regulation (FPFR), where the controllable loads aggregate would vary its active power demand proportionally to the frequency deviation from its nominal value; 3. a combination of the above-mentioned services of SI and FPFR, where the controllable loads aggregate would start by varying its active power demand proportionally to the RoCoF and then perform a transition towards a variation proportional to the frequency deviation.. 2.1.1 Synthetic Inertia Definition In order for an aggregate of loads to emulate the inertia provision, its total active power demand should vary proportionally to the value of the RoCoF. To do so, the TCLs would need to change their thermostat status 𝑞 according to the implemented control logic. Let us consider the following relation between the frequency and the power: 𝑃𝑚 − 𝑃𝑒 = 𝑀. Monica Crosa di Vergagni. 𝑑𝑓 , 𝑑𝑡. (2.1). PhD in Electrical Engineering.

(22) 2. Load Contribution to Frequency Regulation Services. 21. where 𝑃𝑚 is the mechanical power [W], 𝑃𝑒 is the electric power [W], 𝑀 is the inertia coefficient [W ⋅ s 2 ] and 𝑓 is the grid frequency [𝐻𝑧]. The value of 𝑀 can be expressed as a function of the start-up time 𝑇𝑎 [𝑠]: 𝑀=. 𝑁 𝑃nom 𝑇𝑎 , 𝑓nom. (2.2). 𝑁 where 𝑓𝑛𝑜𝑚 is the grid nominal frequency [𝐻𝑧] and 𝑃nom is the grid nominal power [W]. Following a power variation on the grid 𝛥𝑃𝑒𝑥𝑡 , the Rate of Change of Frequency [Hz/s] can be defined by the following equation:. 𝐷𝑓 =. 𝑑Δ𝑓 𝑑𝑓 𝛥𝑃𝑒𝑥𝑡 = =− , 𝑑𝑡 𝑑𝑡 𝑀. (2.3). where Δ𝑓 = 𝑓 − 𝑓nom . The introduction of a power variation proportional to the RoCoF: Δ𝑃𝐼𝑆 = 𝑀𝑆𝐼 ⋅ 𝐷𝑓. (2.4). would lead to the following equation: 𝑀 ⋅ 𝐷𝑓 = −Δ𝑃𝑒𝑥𝑡 − 𝑀𝑆𝐼 ⋅ 𝐷𝑓.. (2.5). Therefore, the resulting RoCoF can be expressed as: 𝑓=−. 1 Δ𝑃 . 𝑀 + 𝑀𝑆𝐼 𝑒𝑥𝑡. (2.6). 𝑀𝑆𝐼 [W ⋅ s] represents the load contribution to the resulting system inertia. Its value is equal to the power variation driven by a RoCoF value of 1 𝐻𝑧/𝑠. The equivalent inertia would be: 𝑀𝑒 = 𝑀 + 𝑀𝑆𝐼 ,. (2.7). which, in terms of start-up time can be expressed as: 𝑇𝑎,𝑒 =. 𝑀𝑒 𝑓nom 𝑀𝑓nom 𝑀𝑆𝐼 𝑓nom = 𝑁 + = 𝑇𝑎 + 𝑇𝑎,𝑆𝐼 , 𝑁 𝑁 𝑃nom 𝑃nom 𝑃nom. (2.8). where 𝑇𝑎,𝑒 is the equivalent start-up time and 𝑇𝑎,𝑆𝐼 is the virtual start-up time, equal to: 𝑇𝑎,𝑆𝐼 =. University of Genova. 𝑀𝑆𝐼 𝑓nom . 𝑁 𝑃nom. (2.9). Monica Crosa di Vergagni.

(23) 2.1. Control Strategies. 22. 2.1.2 Synthetic Inertia Control Logic The thermostat, which defines the status of the refrigerators and water heaters controllable devices, is a two-point controller. When, for a certain controlled temperature 𝑇1 , a desired temperature set-point 𝑇1𝑑 is specified (which would be the water temperature for boilers and the inside air temperature for refrigerators), the thermostat logic which defines the activation or deactivation status 𝑞 will be: for boilers: 𝑔𝑜𝑒𝑠 𝑓𝑟𝑜𝑚 1 𝑡𝑜 0 𝑔𝑜𝑒𝑠 𝑓𝑟𝑜𝑚 0 𝑡𝑜 1 𝑚𝑎𝑖𝑛𝑡𝑎𝑖𝑛 𝑡ℎ𝑒 𝑠𝑡𝑎𝑡𝑢𝑠. 𝑖𝑓 𝑇1 > 𝑇1𝑑 + Δ 𝑖𝑓 𝑇1 < 𝑇1𝑑 − Δ 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒. for refrigerators: 𝑔𝑜𝑒𝑠 𝑓𝑟𝑜𝑚 0 𝑡𝑜 1 𝑔𝑜𝑒𝑠 𝑓𝑟𝑜𝑚 1 𝑡𝑜 0 𝑚𝑎𝑖𝑛𝑡𝑎𝑖𝑛 𝑡ℎ𝑒 𝑠𝑡𝑎𝑡𝑢𝑠. 𝑖𝑓 𝑇1 > 𝑇1𝑑 + Δ 𝑖𝑓 𝑇1 < 𝑇1𝑑 − Δ 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒. The quantity 2Δ is the thermostat dead-band. The standard thermostat control logic can be represented as shown in Figure 2.1:. Figure 2.1. Standard thermostat logic. In order to emulate the synthetic inertia, it is necessary to force the status of the thermostat as a function of the RoCoF. The proposed control logic defines the thermostat status of each device 𝑞 by the following equation: 𝑞 = 𝑞𝑇 + 𝑞𝑆𝐼 ,. Monica Crosa di Vergagni. (2.10). PhD in Electrical Engineering.

(24) 2. Load Contribution to Frequency Regulation Services. 23. where 𝑞𝑇 is the status given by the standard thermostat logic and 𝑞𝑆𝐼 is the one defined by the synthetic inertia algorithm. The latter can be equal to either 0, 1 or -1. The proposed control algorithm can be represented by the diagram in Figure 2.2, where the subscript 𝑖 refers to the 𝑖 𝑡ℎ controllable device:. Figure 2.2. Control scheme for the algorithm of the Synthetic Inertia (SI) provision. The algorithm is meant to generate a 𝑞𝑆𝐼 either equal to 0 or 1 when 𝑞𝑇 is equal to 0 and a 𝑞𝑆𝐼 either equal to 0 or -1 when 𝑞𝑇 is equal to 1. From the above diagram in Figure 2.2, it is noted that if 𝑞𝑇 = 0 (and, therefore, 1 − 𝑞𝑇 = 1) only the lower branch is active, which can determine values of 𝑞𝑆𝐼 either equal to 0 or 1, while if 𝑞𝑇 = 1 only the upper branch, which can determine values of 𝑞𝑆𝐼 either equal to 0 or -1, is active. In both cases, when 𝑞𝑆𝐼 = 0 the thermostat status is defined solely by the standard logic. Otherwise, the proposed control logic forces the activation (lower branch) or the deactivation (upper branch) of the controllable device. In the activation branch (i.e., the lower branch), the measured RoCoF 𝐷𝑓 𝑚 is compared with the threshold value ̅̅̅̅ 𝐷𝑓 . When 𝐷𝑓 𝑚 ≥ ̅̅̅̅ 𝐷𝑓 the additional thermostat status 𝑞𝐼𝑆 = 1 forces the activation of the device. In the deactivation branch (i.e., the upper branch) ̅̅̅̅. When 𝐷𝑓 𝑚 ≤ −𝐷𝑓 ̅̅̅̅ the additional 𝐷𝑓 𝑚 is compared with the threshold value −𝐷𝑓 thermostat status 𝑞𝑆𝐼 = −1 forces the deactivation of the device. In both cases, when ̅̅̅̅ , the thermostat status returns to be defined 𝐷𝑓 𝑚 goes back inside the dead band ±𝐷𝑓 by the standard logic. The upper-most block in Figure 2.2 stops the operation of the synthetic inertia algorithm when the controlled temperature 𝑇1 goes outside a certain security range [𝑇 𝑚𝑖𝑛 , 𝑇 𝑚𝑎𝑥 ]. Let us consider an aggregate of 𝑁 thermal devices with a nominal power of 𝑃nom [𝑊]. Each 𝑖 𝑡ℎ device has a threshold equal to ̅̅̅̅ 𝐷𝑓𝑖 , determined by a uniform distribution between 0 and a maximum value ̅̅̅̅ 𝐷𝑓max [𝐻𝑧/𝑠], fixed for all controlled devices, which means that ̅̅̅̅ 𝐷𝑓𝑖 ∼ 𝑈(0, ̅̅̅̅ 𝐷𝑓max ). Given a certain working point, there would be 𝑁 𝑎 ondevices and 𝑁 𝑑 off-devices. It follows that 𝑁 = 𝑁 𝑎 + 𝑁 𝑑 . Let us suppose that 𝑁, 𝑁 𝑎 and 𝑁 𝑑 are very large numbers. Under these assumptions, the thresholds of the on- and offdevices are still uniformly distributed. Figure 2.3 gives a graphic representation of the synthetic inertia algorithm logic of operation. In order to simplify the representation, and. University of Genova. Monica Crosa di Vergagni.

(25) 2.1. Control Strategies. 24. without loss of generality, the devices are ordered with the first 𝑁 𝑑 off-devices and the remaining 𝑁 𝑎 on-devices.. Figure 2.3. Thresholds distribution in the synthetic inertia emulation algorithm. Given a measured RoCoF value 𝐷𝑓 𝑚 > 0, the 𝑖 𝑡ℎ off-device would turn on if 𝐷𝑓 𝑚 ≥ ̅̅̅̅ 𝐷𝑓𝑖 . Therefore, as shown in Figure 2.3, all the off-devices with a threshold value lower than 𝐷𝑓 𝑚 would change their status. Being the thresholds uniform random variables, the quantities 𝑞𝑆𝐼,𝑖 are Bernoulli binary random variables ℬ(𝑟), independent and identically distributed. The probability of having 𝑞𝑆𝐼,𝑖 = 1, referred to as 𝑟, is equal to the probability of having ̅̅̅̅ 𝐷𝑓𝑖 ≤ 𝐷𝑓 𝑚 . Therefore, being ̅̅̅̅ 𝐷𝑓𝑖 ∼ 𝑈(0, ̅̅̅̅ 𝐷𝑓max ), it follows that: 𝑟(𝐷𝑓 𝑚 ) = 𝑃(𝑞𝑆𝐼,𝑖 = 1|𝐷𝑓 𝑚 ) = 𝐷𝑓 𝑚 ̅̅̅̅𝑖 ≤ 𝐷𝑓 𝑚 ) = 𝑃(𝐷𝑓 . ̅̅̅̅ 𝐷𝑓 max. (2.11). The number of devices that would turn on is equal to: 𝑁𝑑 𝑎 𝑛𝐼𝑆. = ∑ 𝑞𝑆𝐼,𝑖 .. (2.12). 𝑖=1. It is well known that the sum of 𝑛 Bernoulli variables 𝑥 ∼ ℬ(𝑟) is a binomial random 2. variable with mean value 𝜇 = 𝐸(𝑥) = 𝑛𝑟 and standard deviation 𝜎 = √𝐸(𝑥 − 𝐸(𝑥)) = √𝑛𝑟(1 − 𝑟). Therefore, the variation coefficient would be:. Monica Crosa di Vergagni. PhD in Electrical Engineering.

(26) 2. Load Contribution to Frequency Regulation Services. 𝜎∗ =. 25. 𝜎 √𝑛𝑟(1 − 𝑟) = |𝜇| 𝑛𝑟. (2.13). which goes to zero if 𝑛 goes to infinity. Sufficiently high values of 𝑛 lead to 𝑥 ≈ 𝜇 = 𝑛𝑟. 𝑎 In the specific case of 𝑛𝐼𝑆 : 𝑎 𝑛𝑆𝐼 ≈ 𝑁 𝑑 ⋅ 𝑟(𝐷𝑓 𝑚 ) =. 𝑁𝑑 𝐷𝑓 𝑚 . ̅̅̅̅ 𝐷𝑓 max. (2.14). The resulting variation of the load power demand would be: 𝑎 𝑎 Δ𝑃𝑆𝐼 = 𝑃nom 𝑛𝑆𝐼 ≈. 𝑁 𝑑 𝑃nom 𝑎 𝐷𝑓 𝑚 = 𝑀𝑆𝐼 𝐷𝑓 𝑚 , ̅̅̅̅ 𝐷𝑓 max. (2.15). proportional to the RoCoF value, as desired. The equivalent gain is: 𝑎 𝑀𝑆𝐼 =. 𝑁 𝑑 𝑃nom , ̅̅̅̅ 𝐷𝑓 max. (2.16). which depends on the working point (given by the number of off-devices) and inversely proportional to the control parameter ̅̅̅̅ 𝐷𝑓 max . Considering the aggregate nominal power nom nom 𝑃𝑡𝑜𝑡 = 𝑁𝑃 ,the equivalent gain can be expressed in p.u. as: 𝑎 ̅𝑆𝐼 𝑀 =. 𝑁 𝑑 𝑃nom 𝑁𝑑 1 = ⋅ . nom max ̅̅̅̅ ̅̅̅̅ 𝑁 𝑁𝑃 𝐷𝑓 𝐷𝑓 max. (2.17). In a similar fashion, the variation of the load power demand when 𝐷𝑓 𝑚 < 0, can be expressed by the following equation: 𝑑 𝑎 Δ𝑃𝑆𝐼 = 𝑃nom 𝑛𝑆𝐼 ≈. 𝑁 𝑎 𝑃nom 𝑑 𝐷𝑓 𝑚 = 𝑀𝑆𝐼 𝐷𝑓 𝑚 , ̅̅̅̅ 𝐷𝑓 max. (2.18). with: 𝑁 𝑎 𝑃nom ̅̅̅̅ 𝐷𝑓 max. (2.19). 𝑁𝑎 1 ⋅ . 𝑁 ̅̅̅̅ 𝐷𝑓 max. (2.20). 𝑑 𝑀𝑆𝐼 =. and: 𝑑 ̅𝑆𝐼 𝑀 =. University of Genova. Monica Crosa di Vergagni.

(27) 2.1. Control Strategies. 26. In summary, the load power demand variation requested by the control action would be: 𝑎 𝑀𝐼𝑆 𝐷𝑓 𝑚 𝑖𝑓 𝐷𝑓 𝑚 ≥ 0 Δ𝑃𝐼𝑆 = { 𝑑 . 𝑀𝐼𝑆 𝐷𝑓 𝑚 𝑖𝑓 𝐷𝑓 𝑚 < 0. (2.21). 2.1.3 Fast Primary Frequency Regulation Control Logic In order to support the Primary Frequency Regulation, the load aggregate would need to vary its power demand proportionally to the value of the frequency deviation. The control strategy proposed for the FPFR it is realized similarly to the SI control logic previously described, with the difference that the input signal is now the frequency deviation from its nominal value (instead of the RoCoF value used for the SI). The control ̅̅̅̅ scheme is depicted in Figure 2.4: in this case, the on-device is deactivated if Δ𝑓 ≤ −Δ𝑓 and the off-device is activated if Δ𝑓 ≥ ̅̅̅̅ Δ𝑓 .. Figure 2.4. Control scheme for the Fast Primary Frequency Regulation algorithm. Considering an aggregate of 𝑁 components, each device has a frequency threshold ̅̅̅̅ Δ𝑓𝑖 , 𝑖 = 1,2, … , 𝑁. The thresholds are uniformly distributed between 0 and the control parameter ̅̅̅̅ Δ𝑓 max , therefore ̅̅̅̅ Δ𝑓𝑖 ∼ 𝑈(0, 𝑓 ̅max ). As for the previous case, the control is inhibited if the temperature 𝑇1 exceeds the security range [𝑇 𝑚𝑖𝑛 , 𝑇 𝑚𝑎𝑥 ]. Going through the same mathematical steps described in Section 2.1.2, the requested load power variation results to be: 𝑎 𝑘𝐹𝑃𝐹𝑅 Δ𝑓 𝑖𝑓 Δ𝑓 ≥ 0 Δ𝑃𝐹𝑃𝐹𝑅 = { 𝑑 , 𝑘𝐹𝑃𝐹𝑅 Δ𝑓 𝑖𝑓 Δ𝑓 < 0. (2.22). where: 𝑎 𝑘𝐹𝑃𝐹𝑅 =. 𝑁 𝑑 𝑃nom , ̅̅̅̅ Δ𝑓 max. Monica Crosa di Vergagni. 𝑑 𝑘𝐹𝑃𝐹𝑅 =. 𝑁 𝑎 𝑃nom ̅̅̅̅ Δ𝑓 max. (2.23). PhD in Electrical Engineering.

(28) 2. Load Contribution to Frequency Regulation Services. 27. are the equivalent control gains, which in p.u. become: 𝑎 𝑘̅𝐹𝑃𝐹𝑅 =. 𝑁𝑑 1 ⋅ max , 𝑁 ̅̅̅̅ Δ𝑓. 𝑑 𝑘̅𝐹𝑃𝐹𝑅 =. 𝑁𝑎 1 ⋅ max . 𝑁 ̅̅̅̅ Δ𝑓. (2.24). The resulting load power variation would then be proportional to the frequency deviation. The equivalent control gains expressed in (2.24) depend on the working point (since 𝑁 𝑑 and 𝑁 𝑎 are the off- and the on-devices, respectively) and on the control parameter ̅̅̅̅ Δ𝑓 max . The value of ̅̅̅̅ Δ𝑓 max can be set in order to obtain a behavior similar to that of the traditional generators, even though the reaction of the load would be faster. The control gain 𝑘𝑔 of a traditional generation unit with a nominal power of 𝑃𝑔nom can be defined in order to get a specific value for the statism 𝑏𝑝 : 𝑘𝑔 =. 𝑃𝑔nom . 𝑓nom 𝑏𝑝. (2.25). Therefore, by comparing equation (2.25) with the expressions of the control gains in (2.23), the maximum frequency deviation allowed can be set according to the following equation: ̅̅̅̅ Δ𝑓 max = 𝑓nom 𝑏𝑝 .. (2.26). The resulting 𝑏𝑝 that characterizes the behavior of the load results to be different for positive and negative frequency variations, since it would depend on 𝑁 𝑑 when Δ𝑓 ≥ 0 and on 𝑁 𝑎 when Δ𝑓 < 0. In order to have a uniform value, the working point would have to be known, and the maximum frequency deviation allowed would have to be set accordingly as follows: ̅̅̅̅ Δ𝑓𝑎max =. 𝑓nom 𝑏𝑝 𝑁 𝑑 , 𝑁. ̅̅̅̅ Δ𝑓𝑑max =. 𝑓nom 𝑏𝑝 𝑁 𝑎 , 𝑁. (2.27). which would lead to the following uniform control gains: 𝑎 𝑑 𝑘̅𝐹𝑃𝐹𝑅 = 𝑘̅𝐹𝑃𝐹𝑅 =. 𝑁𝑃nom . 𝑓nom 𝑏𝑝. (2.28). However, in order to fulfill the requirements of this approach each device would need to know the working point of the entire aggregate, which is absolutely unrealistic. Figure 2.5 shows the frequency/temperature characteristics of the devices controlled by the FPFR algorithm.. University of Genova. Monica Crosa di Vergagni.

(29) 2.1. Control Strategies. 28. Figure 2.5. Frequency/temperature characteristics for the FPFR control strategy.. 2.1.4 Combined SI/FPFR Control Logic The two control strategies previously described can be combined in order to obtain both contributions from the thermal loads aggregate. The input signal of the proposed hybrid control logic is defined as: 𝛼∆𝑓 𝑚 + (1 − 𝛼)𝐷𝑓 𝑚 .. (2.29). The initial value of 𝛼 is equal to zero. As soon as a power imbalance causes a frequency variation, the controller starts operating having 𝐷𝑓 𝑚 as input signal, therefore implementing the SI control logic. After a certain pre-set amount of time, equal to 𝑡𝑠𝑤𝑖𝑡𝑐ℎ , the parameter 𝛼 starts increasing and reaches the value of 1 after a transition interval of time 𝑡𝑟𝑎𝑚𝑝 . When 𝛼 = 1, the controller receives ∆𝑓 𝑚 as input signal, therefore implementing solely the FPFR control strategy. The combined control strategy is designed over three phases: the SI algorithm operates first, followed by a transition period with a duration equal to 𝑡𝑟𝑎𝑚𝑝 , during which both control strategies operate simultaneously, which terminates with the FPFR control. The parameter 𝛼 leads the transition of the input signal as well as the transition of the thresholds in a similar fashion, which can be expressed for each 𝑖 𝑡ℎ device by the following equation:. ̅̅̅̅𝑖 + (1 − 𝛼(𝑡))𝐷𝑓 ̅̅̅̅𝑖 . 𝛼(𝑡)Δ𝑓. Monica Crosa di Vergagni. (2.30). PhD in Electrical Engineering.

(30) 2. Load Contribution to Frequency Regulation Services. 29. The profile of the parameter 𝛼 over time is shown in Figure 2.6.. Figure 2.6. The evolution of the parameter 𝜶 over time. It is necessary to define and detect the significant event that triggers the action of the controller. Therefore, two activation thresholds have been defined, one for the RoCoF and one for the frequency deviation, respectively equal to ±𝐷𝑓𝑎𝑐𝑡 [Hz/s] and ±Δ𝑓𝑎𝑐𝑡 [Hz]. As soon as the threshold 𝐷𝑓𝑎𝑐𝑡 is exceeded, the SI control is activated. Then, if also Δ𝑓𝑎𝑐𝑡 is exceeded, the transition process starts after 𝑡𝑠𝑤𝑖𝑡𝑐ℎ . The last phase of the combined control strategy, where the FPFR control operates, remains active for an interval of time 𝑇𝐹𝑃𝐹𝑅 which lasts for at least 20 minutes, waiting for the secondary frequency regulation activities to be completed.. 2.2. Load Models. In order to accurately analyze the dynamics of the load aggregate, the developed and implemented models of the residential refrigeration systems and the sanitary hot water heaters will be thoroughly described.. 2.2.1 Refrigeration System Model A common refrigeration system is made of a cooling compartment, a freezer compartment, and their respective contents. The thermal energy exchange is shown in Figure 2.7.. University of Genova. Monica Crosa di Vergagni.

(31) 2.2. Load Models. 30. Figure 2.7. Thermal energy exchange in a refrigeration system. The model is made of four controlled components (whose controlled temperature is denoted by 𝑇1 , 𝑇2 , 𝑇3 and 𝑇4 ), the external temperature and the heat pump. The latter extracts the heat from both fridge and freezer compartments. There exist refrigeration systems with two independent heat pumps, but the ones with single heat pump are the most common. In order to represent the thermal heat exchange performed by the heat pumps, two positive variables with unitary sum 𝜂1 and 𝜂4 are introduced, which denote the separate share of heat absorbed by the fridge compartment and by the freezer compartment, respectively. Consequently, two equivalent performance coefficient (COP) can be defined as 𝛾1,𝐺 = 𝜂1 𝛾 and 𝛾4,𝐺 = 𝜂4 𝛾, where 𝛾 is the effective COP of the heat pump. The dynamics of the temperature 𝑇𝑖 [°𝐶] can be described by the following equations: 𝑈1,2 𝐴1,2 𝑈1,4 𝐴1,4 𝑈1,𝑒 𝐴1,𝑒 (𝑇1 − 𝑇2 ) − (𝑇1 − 𝑇4 ) − (𝑇1 − 𝑇𝑒 ) 𝑚1 𝑆1 𝑚1 𝑆1 𝑚1 𝑆1 1 − 𝛾 𝑞𝑃nom 𝑚1 𝑆1 1,𝐺. (2.31). 𝑇̇2 = −. 𝑈1,2 𝐴1,2 (𝑇2 − 𝑇1 ) 𝑚1 𝑆1. (2.32). 𝑇̇3 = −. 𝑈3,4 𝐴3,4 (𝑇3 − 𝑇4 ) 𝑚3 𝑆3. (2.33). 𝑇1̇ = −. 𝑇4̇ = −. 𝑈1,4 𝐴1,4 𝑈3,4 𝐴3,4 1 Δ𝑇4,1 − Δ𝑇4,3 − 𝛾 𝑞𝑃nom 𝑚4 𝑆4 𝑚4 𝑆4 𝑚4 𝑆4 4,𝐺. Monica Crosa di Vergagni. (2.34). PhD in Electrical Engineering.

(32) 2. Load Contribution to Frequency Regulation Services. 31. where: 𝑚𝑖 is the mass of the 𝑖 𝑡ℎ component [𝑘𝑔]; 𝑆𝑖 is the specific thermal capacity [𝐽 𝑘𝑔−1 °𝐶 −1 ] ; 𝑈𝑖,𝑗 and 𝐴𝑖,𝑗 are the U-value [𝑊 °𝐶 𝑚−2 ] and the area [𝑚2 ] of the heat exchange between the 𝑖 𝑡ℎ and the 𝑗𝑡ℎ thermal components (the external ambient is considered to have infinite mass); 𝑃nom is the heat pump nominal electric power [𝑊]; 𝑞 is the thermostat status.. 2.2.2 Water Heating Systems Model A water heating system, which will be referred to as boiler, is made of a storage space where the water is heated up by an electrical resistance exploiting the Joule effect, under the control of a thermostat. The heat exchange can be represented as shown in Figure 2.8.. Figure 2.8. Thermal heat exchange in a water heating system. Let us suppose that there is a unique internal controlled water temperature 𝑇1 inside the boiler. When the hot water is requested by the user, an equivalent cold water flow (denoted by 𝑤(𝑡) [𝑚3 𝑠 −1 ]) enters the heating space. If the cold water temperature is equal to 𝑇𝑜 [°𝐶], the thermal heat exchanged can be described by the following equation:. 𝑇1̇ = −. 1 𝑤(𝑡) 1 (𝑇1 − 𝑇𝑒 ) − (𝑇1 − 𝑇𝑜 ) + 𝜂𝑞𝑃nom , 𝑅1,𝑒 𝑆𝑤 𝑉𝜌 𝑉 𝑆𝑤 𝑉𝜌. (2.35). where: 𝑇𝑒 is the external room temperature; 𝑅1,𝑒 is the thermal resistance with respect to the thermal exchange with the outside [°𝐶 𝑊 −1 ]; 𝑇𝑜 is the cold water temperature; 𝑉 is the volume of the boiler [𝑚3 ]; 𝑆𝑤 is the water specific thermal capacity [𝐽 𝑘𝑔−1 °𝐶 −1 ]; 𝜌 is the water density [𝑘𝑔 𝑚−3 ]; 𝜂 and 𝑃nom are the nominal efficiency and the nominal power, respectively [𝑊]; 𝑞 is the thermostat status.. University of Genova. Monica Crosa di Vergagni.

(33) 2.2. Load Models. 32. 2.2.3 Load Aggregate Model The goal of the study presented in this Chapter is the evaluation of the impact of a flexible management of the thermal loads contribution to frequency regulation activities, considering a regional or national electric network. The huge number of such loads makes it impossible to simulate the behavior of each single load, making it necessary to consider an aggregate model. In the following, two types of thermal loads will be considered: 𝐶𝐿𝑓 (refrigerators) and 𝐶𝐿𝑤 (boilers), each component of the same class will be characterized by similar parameters and nominal powers 𝑃𝑟nom and 𝑃𝑏nom [𝑊], equal to the power of the loads of the same type installed in the considered grid. For each class, a number 𝑁 of sets of parameters with mean value equal to that associated to the reference class and a standard deviation 𝜎𝑀𝐴 ranging between 10-20% is generated. Each set identifies a load belonging to the considered class and it represents the behavior of an aggregate of loads whose nominal power is equal to 𝑃xnom /𝑁, with 𝑥 = 𝑟, 𝑏. The number 𝑁 needs to be sufficiently low in order to allow the numerical simulation of all the loads aggregates and sufficiently high to represent the variability of the considered systems and the corresponding working conditions with adequate accuracy. The output of the numerical simulation of the set of aggregates is the thermostats status 𝑞x , with 𝑥 = 𝑟, 𝑏. The total power absorbed by the set of loads of the class 𝐶𝐿x is equal to: 𝑁. 𝑃x =. 𝑃xnom. ∑ 𝑗=1. 𝑞x𝑖 . 𝑁. (2.36). 2.2.4 Loads Parameters In the present Section, the parameters of the refrigerators and boilers reference devices will be presented. 2.2.4.1. Refrigerators. The refrigerator/freezer considered as benchmark is the Whirlpool WTE 31132 TS with a capacity of 232/88 fridge/freezer. The parameters which have been used in the simulations have been chosen according to the technical data described in [25] and after a tuning performed through a series of simulations with the goal of reproducing specific temperature profiles similar to the experimental data reported in [26] and [27]. The resulting parameters are described in Table 2.1 and Table 2.2.. Monica Crosa di Vergagni. PhD in Electrical Engineering.

(34) 2. Load Contribution to Frequency Regulation Services. 33. Table 2.1. Benchmark refrigeration devices: thermal components characteristics Component. Mass (𝒎𝒊 [𝒌𝒈]). Refrigerator Air (𝑻1 ). 10. 2200. 10. 4000. 4. 4000. 5. 1000. Refrigerator Content (𝑻𝟐 ) Freezer Content (𝑻𝟑 ) Freezer Space (𝑻𝟒 ). Specific Heat (𝑺𝒊 [𝑱/(𝒌𝒈 °𝑪)]). Table 2.2. Benchmark refrigeration devices: thermal conductivity coefficients Connection. Component 1. Component 2. Area [𝒎𝟐 ]. U-value [𝑾/ ( 𝒎𝟐 𝑲)]. 𝐿1,𝑒 𝐿1,2. Fridge Air Fridge Air. Outside Fridge Content. 2 1. 0.5 12.5. 𝐿1,4. Fridge Air. Freezer Space. 0.26. 2.5. 𝐿3,4. Freezer Content. Freezer Space. 0.4. 12.5. 𝐿4,𝑒. Freezer Space. Outside. 0.97. 0.15. The values reported in the previous tables are the mean values that characterize the class of loads taken into consideration. The following Table 2.3 describes the electrical parameters of the reference model. Table 2.3. Electrical parameters of the refrigerator/freezer load. Parameter. Measurement Unit. Value. Heat pump/fridge COP. Symbol 𝛾1,𝐺. -. 0.4560. Heat pump/freezer COP. 𝛾4,𝐺. Heat pump nominal power Thermostat dead band. -. 0.7440. nom. W. 100. 2Δ. °C. 1. 𝑃. The values of the two equivalent COP 𝛾1,𝐺 and 𝛾4,𝐺 , which refer to the thermal energy absorption capacity of the heat pump from the fridge and from the freezer, respectively, have been obtained considering an actual COP 𝛾 = 1.2 and considering the share absorbed from the fridge 𝜂1 equal to the 38% of that absorbed from the freezer. 2.2.4.2. Boilers. The water heater considered as benchmark is the Ariston TI-PLUS 100 V RTS/S, whose technical data is reported in Table 2.4.. University of Genova. Monica Crosa di Vergagni.

(35) 2.2. Load Models. 34. Table 2.4. Benchmark water heater devices: technical data Parameter Capacity. Measurement Unit 𝑙. Value 99. 𝑊. 1500. 𝑘𝑊ℎ/24ℎ. 1.39. Nominal power Thermal dispersion (Δ𝑡 = 45°𝐶). The remaining parameters useful for the model definition are listed in Table 2.5. Table 2.5. Benchmark water heater devices: thermal and control parameters Parameter Water thermal capacity. Symbol 𝐶1 = 𝑆𝑤 𝑉𝜌. Measurement Unit 𝐽/°𝐶. Value 414414. 𝑅1,𝑒. °𝐶/𝑊. 0.777. Thermal resistance of the 𝑳𝟏,𝒆 connection Heat pump efficiency. 𝜂. -. 1. Thermostat dead band. 2Δ. °𝐶. 10. It is worth noticing that the thermostat dead band is, in this case, 10 ℃, significantly larger than that defined for the refrigerators’ temperature control.. 2.2.5 Mathematical Model Implementation in MATLAB/Simulink™ The thermal load aggregates models previously described have been implemented in the MATLAB/Simulink™ platform, as it will be described in detail in the following paragraphs. 2.2.5.1. Refrigerators aggregate. The block diagram of the refrigerators aggregate developed in Simulink™ is shown in Figure 2.9, where the principal components are highlighted: the thermal model of the refrigerators aggregate (green box), the external temperature and thermal noise generation (pink box) and the proposed load control logic (blue box). The thermal model is implemented according to equations (2.31)-(2.34), for a certain number 𝑁 of refrigerators. The parameters of the 𝑁 models are generating by randomly varying, with a standard deviation 𝜎𝑀𝐴 , those listed in Section 2.2.1. The refrigerators thermal models receive the external temperatures 𝑇𝑒 and the thermal disturbances Δ𝑃 generated according to the models reported in [28]. In particular, the external temperature 𝑇𝑒 is generated by following an external temperature profile and then elaborated according to the presence (or absence) of heating and/or cooling systems. The Simulink model takes the percentages of houses equipped with heating and cooling systems into account. The operation of the refrigerators is then driven by the status of the respective thermostats, which can either follow the standard thermostat logic or the proposed control strategy, as described in Section 2.1. The output of the model is the aggregate power demand.. Monica Crosa di Vergagni. PhD in Electrical Engineering.

(36) 2. Load Contribution to Frequency Regulation Services. 35. Fridge thermal model. External temperature and thermal noise generation. Load control logic. Figure 2.9. Refrigerators aggregate block diagram developed in Simulink™. 2.2.5.2. Water heaters aggregate. The block diagram of the water heaters aggregate model developed in Simulink™ is shown in Figure 2.10. The principal components of the implemented model, highlighted in Figure 2.10, are: the water heaters aggregate thermal model (green box), the external air temperature, cold water temperature and consumption profiles generation (pink box) and the proposed thermostat control logic (blue box). The thermal model is implemented according to equations (2.35), for a certain number 𝑁 of boilers. The parameters of the 𝑁 models are generating by randomly varying those listed in Section 2.2.2, with a standard deviation 𝜎𝑀𝐴 . The boilers thermal models receive the external temperature 𝑇𝑒 , the water temperature 𝑇𝑜 and the water consumption profiles generated according to the models reported in [28]. Similarly to refrigerators, the external temperatures 𝑇𝑒 are generated by following an external temperature profile and then elaborated according to the presence (or absence) of heating and/or cooling systems. The operation of the boilers is then driven by the status of the respective thermostats, which can either follow the standard thermostat logic or the proposed control strategy, as described in Section 2.1. The output of the model is the aggregate power demand.. University of Genova. Monica Crosa di Vergagni.

(37) 2.3. Network Model. 36 Boilers thermal model. External air temperature, cold water temperature and consumption profiles generation.. Load control logic. Figure 2.10. Boilers aggregate block diagram developed in Simulink™.. 2.3. Network Model. The test site chosen for verifying the efficiency and reliability of the proposed methodology is the Sardinian electric network, considering the 2030 scenario. Data is made available by RSE.. 2.3.1. Electric system characterization. The following Table 2.6 describes the technical characteristics of the Sardinian and Corse system components, which are grouped as: • Sardinian generation units; • Corse generation units; • HVDC links. The Sardinian generation units are classified in 5 different groups: G1) hydropower plants; G2) coal power plant; G3) combustible oil power plant; G4) gas turbine; G5) biomass, solar thermal and equivalent plants. G2 and G3 groups are not displayed in Table 2.6 as coal and combustible oil power plants are not expected in the 2030 Sardinian electric network scenario. The other generation units are two synchronous compensators of 250 MW, the wind power plants and the PVs, with the expected nominal power for the year 2030. The generation system in Corse is represented by three equivalent groups (hydropower, diesel and gas turbine), which are considered to be connected to the Sardinian electric grid through the synchronous interconnection SARCO. In the above-mentioned table, the three HVDC links are also listed: two links with the Italian peninsula (SAPEI) and one link with both the Italian peninsula and Corse (SACOI).. Monica Crosa di Vergagni. PhD in Electrical Engineering.

(38) 2. Load Contribution to Frequency Regulation Services. 37. Table 2.6 features, for each component, the following parameters: • Active nominal power 𝑷𝒏𝒐𝒎,𝒊 [MW]: the maximum generated power of the generation units or the maximum imported power of the HVDC links. • Minimum operating power 𝑷𝒎𝒊𝒏,𝒊 [MW]: the minimum generated power of the generating units or the maximum exported power of the HVDC links. The pumped hydropower plants represent an exception as they can absorb power from the grid, therefore they minimum power is negative. • Start-up Time 𝑻𝒔,𝒊 [s]: it is a measure of the synchronous machines dynamic inertia, it is defined as the time required to the generating unit to reach the nominal speed Ωnom , starting from the stationary position with a nominal torque of 𝑃𝑛𝑜𝑚 /Ω𝑛𝑜𝑚 [29]. It is not defined for renewable sources nor HVDC links. Table 2.6. Technical characteristics of the Sardinian and Corse electric grid. Unit. Type. 𝑷𝐧𝐨𝐦,𝒊 [MW]. 𝑷𝒎𝒊𝒏,𝒊 [MW]. 𝑻𝒔,𝒊 [s]. Generation Units in Sardinia Idro Bacino (G1) Pumped Hydro (G1) Unit 2 (G4) Unit 1 (G5) BioDisp (G5) Thermal Unit (G5) SARLUX (G5) Synchronous Compensator 1 Synchronous Compensator 2 Photovoltaic Wind Bio Energetic Run-of-river Hydro. Idro Idro Gas Turbine CC-Gas Turbine Biomass Thermal - Other Equivalent Compensator. 155 207 100 80 5 127 550 250. 0 -207 25 24 2 51 165 0. 7.5 7.5 15.3 9.4 15.3 14.9 9.4 3.5. Compensator. 250. 0. 3.5. Photovoltaic Wind Bio Energetic Run-of-river Hydro. 2230 3250 50 17. 0 0 0 0. -. Equivalent Generation Units in Corse Diesel Gas Turbine Hydro SAPEI SACOI. Equivalent Diesel 167.98 Equivalent GT 107.3 Equivalent Hydro 125.8 HVDC Links HVDC 1000 HVDC 300. 100 50 0. 13.5 17.6 8.1. -1000 -300. -. As shown in Table 2.7, the SAPEI link contributes to the primary frequency regulation.. University of Genova. Monica Crosa di Vergagni.

(39) 2.3. Network Model. 38. Table 2.7 describes, for each component, the primary and secondary frequency regulation characteristics: • Statism 𝑏𝑝,𝑖 [%]: percentage value of the permanent statism for the generating units that contribute to the primary frequency regulation. “No” indicates that the corresponding units do not participate to the regulation activities. The assigned values are compliant with the prescriptions published by TERNA [30]. • (HAlf) Dead Band 𝛥𝑓𝑖𝑡ℎ [mHz]: frequency range within which the primary regulation is disabled. “No” indicates that the corresponding units do not participate to the regulation activities. The assigned values are compliant with the prescriptions published by TERNA [30]. • Rate limiter 𝑅𝑖% [%/min]: maximum percentage power variation, with respect to the nominal power, performed by the generating units dispatched for the secondary frequency regulation over one minute. “No” indicates that the corresponding units do not participate to the regulation activities. The assigned values are compliant with the requirements published by TERNA [30]. Table 2.7. Frequency control characteristics of the Sardinian and Corse electric grid. Unit. Type. 𝑏𝑝,𝑖 [%]. Δ𝑓𝑖𝑡ℎ [mHz]. 𝑅𝑖% [%/min]. Generation Units in Sardinia Idro Bacino (G1) Pumped Hydro (G1) Unit 2 (G4) Unit 1 (G5) BioDisp (G5) Thermal Unit (G5) SARLUX (G5) Synchronous Compensator 1 Synchronous Compensator 2 Photovoltaic Wind Bio Energetic Run-of-river Hydro. Idro Idro Gas Turbine CC-Gas Turbine Biomass Thermal - Other Equivalent Compensator. 4% 4% 5% 5% 5% 5% 5% No. 20 No 10 10 10 10 10 No. 60% No 8% 8% 8% No 8% No. Compensator. No. No. No. Photovoltaic Wind Bio Energetic Run-of-river Hydro. No No No No. No No No No. No No No No. 5% 5% 5%. 10 10 10. 8% 8% 8%. 5% No. 0.02 No. No No. Equivalent Generation Units in Corse Diesel Gas Turbine Hydro SAPEI SACOI. Equivalent Diesel Equivalent GT Equivalent Hydro HVDC Links HVDC HVDC. Monica Crosa di Vergagni. PhD in Electrical Engineering.