Context, problem statement and research objectives
The history of power systems began in September 1882 when Thomas Edison established the first complete DC power system, providing electricity to 59 households However, the development of the transformer and AC transmission by L Gaulard and J.D Gibbs in Paris led to the dominance of AC systems over DC systems, marking a significant shift in electrical engineering.
The AC electrical network was introduced in 1893 as a basic system with limited generators and loads within a confined area As economies and populations expanded, global electricity production surged, with figures indicating that by the end of 2017, electricity generation had tripled compared to 1980.
Figure 1.1 – (a) Global electricity production, and (b) Carbon dioxide emissions by sectors
To meet the growing demand for energy, many countries have established large, centralized power generation facilities with capacities reaching tens of gigawatts However, high electricity consumption often leads to increased greenhouse gas emissions, as these power plants typically rely on polluting fossil fuels, with the exception of nuclear and hydroelectric sources Research indicates that electricity and heat production contribute significantly to global emissions, accounting for nearly half of the total greenhouse gases released.
Many countries are focusing on climate change mitigation, highlighted by the Kyoto Protocol of 1998, which was the first international agreement aimed at reducing greenhouse gas emissions Subsequent negotiations, such as COP25 in Paris in 2015, have intensified the pressure on governments to implement new energy policies that reduce reliance on fossil fuels like coal for power generation Various solutions have been proposed, with the development of renewable energy sources identified as a top priority in the ongoing efforts to combat climate change.
The article discusses various types of energy, including low-impact hydropower, wind power, solar power, and minor sources like biofuels and geothermal energy, which are categorized as Distributed Energy Resources (DER) DER refers to electricity production occurring close to customer locations to meet energy demands, with capacities ranging from a few kilowatts to tens of megawatts These technologies can utilize fossil fuels, renewable sources, or waste heat.
The installation of Distributed Energy Resources (DERs) presents numerous benefits, including the reduction of carbon emissions and the achievement of sustainability goals for long-term socio-economic development In resource-limited countries, DERs can decrease reliance on imported fuels by harnessing renewable energy sources Additionally, they enable local utilities to diversify their energy supply, alleviate congestion on high-load transmission lines during peak times, and offer essential ancillary services like frequency and voltage control, thereby minimizing transmission and distribution losses Furthermore, DER-based generating units can serve as a backup for critical loads during outages, and their ability to perform peak shaving during high tariff periods is a significant advantage.
Inverter-interfaced photovoltaic (PV) systems and wind energy technologies have seen significant advancements and cost reductions, positioning solar and wind energy as the future leaders in global electricity generation By 2040, it is anticipated that these renewable sources, along with low-impact hydro-power, will contribute 40% of global electricity, nearly doubling the 21% share from 2017 The growth in cumulative capacities for both PV systems and wind turbines has been remarkable, with global wind turbine capacity reaching 656 GW in 2019—14 times higher than in 2004—while cumulative PV capacity surged 174 times, from 3.7 GW in 2004 to approximately 647 GW in 2019 Notably, although wind energy has historically outpaced solar energy, projections for 2020 indicate that cumulative PV capacity will surpass that of wind turbines, with expected totals of 789 GW and 782 GW, respectively.
Unlike wind turbines, which primarily connect to High Voltage (HV) transmission grids, most photovoltaic (PV) systems are linked to Medium Voltage (MV) and Low Voltage (LV) distribution grids By the end of 2015, approximately 94% of Germany's cumulative installed PV capacity was associated with LV and MV grids Distribution System Operators (DSOs) have traditionally managed their networks with less investment in advanced technologies than Transmission System Operators (TSOs), making it more challenging for them to integrate Distributed Energy Resources (DERs), particularly PV systems, and maintain service quality This study focuses specifically on solar energy technologies, namely inverter-based PV systems, while also acknowledging wind energy systems connected to distribution networks through power electronic inverters.
Figure 1.2 – (a) Global cumulative capacity of wind turbines and solar PV systems, and (b) Distri- bution of PV capacity across voltage levels in Germany by 2015
Over the past decade, various standards have indicated that photovoltaic (PV) inverters should refrain from actively regulating voltage at their Points of Common Coupling (PCC) Additionally, grid codes mandate that connected PV systems maintain a power factor greater than 0.9, controlled by the Maximum Power Point Tracking (MPPT) system, to optimize energy extraction from PV panels Consequently, these systems have predominantly functioned as active power sources, lacking reactive power capabilities Furthermore, PV systems are required to disconnect from the grid upon detecting faults, a necessity that was relevant when the penetration level of PV systems was low.
Nevertheless, due to the rapid reduction in the price of photovoltaic cells and ad- vances in power electronics technology, the penetration of photovoltaic systems into the
MVandLVgrids can reach such a level that it can lead to a violation of grid integration
One significant issue is the risk of overload or overvoltage in both medium voltage (MV) and low voltage (LV) feeders, particularly when a substantial portion of photovoltaic (PV) systems is implemented This challenge arises from intermittent solar radiation, leading to an imbalance in the system.
Photovoltaic (PV) generation and load consumption are critical factors in energy management While some suggest limiting the maximum power extracted from PV systems, this approach conflicts with global policies aimed at reducing greenhouse gas emissions Consequently, numerous countries have developed specific grid codes to facilitate the integration of renewable energy sources.
Photovoltaic (PV) systems can enhance steady-state voltage regulation by managing reactive power These systems are designed to either inject or absorb reactive power, enabling local voltage control This functionality, known as static voltage support or voltage var control, has been highlighted in several recent studies.
1.1 Context, problem statement and research objectives 5
The disconnection of numerous photovoltaic (PV) systems due to anti-islanding protection can lead to severe consequences, including large-scale power outages Standards like IEEE 1547, UL 1741, and VDE-AR-N 4105 mandate that all PV systems in low-voltage (LV) networks disconnect within 0.2 seconds if the voltage at their Points of Common Coupling (PCC) drops below 0.8 p.u This rapid disconnection can exacerbate voltage drops caused by transmission faults, further destabilizing the active power balance in the grid To mitigate these risks, PV systems should implement Fault Ride Through (FRT) capabilities, allowing them to remain connected during grid violations and support voltage stability by injecting reactive power Additionally, new grid codes require PV systems to incorporate advanced functionalities such as frequency control, power quality management, remote demand response, and communication with smart inverters, enhancing their role in grid stability.
The dynamic voltage support capability of photovoltaic (PV) systems has made their fault contributions significant, altering their fault behaviors due to reactive power injection during faults Numerous issues stemming from high PV integration have been documented, particularly affecting radial distribution networks, with the severity of these problems varying based on the penetration and size of the PV systems.
Photovoltaic (PV) systems installed in distribution networks along medium voltage (MV) and low voltage (LV) feeders create bidirectional fault currents due to contributions from both external grids and downstream PV systems This can lead to issues for distribution protection devices, such as false or sympathetic tripping, and complicates coordination between reclosers and fuses, as PV systems may continue to supply power during a fault even when the feeder circuit breaker is open Consequently, the existing Fault Location and Isolation Systems (FLIS), which rely on non-directional fault indicators, need to be updated to address the challenges posed by bidirectional fault currents Failure to implement appropriate measures could significantly degrade system reliability metrics, including the System Average Interruption Duration Index (SAIDI) and Customer Average Interruption Duration Index (CAIDI).
Grid codes applicable to PV systems
Static voltage support requirement
Static voltage support, also known as voltage var control, involves managing voltage levels in the medium voltage (MV) grid during normal operations, ensuring that slow voltage fluctuations remain within permissible limits Notably, photovoltaic (PV) systems are required to assist in maintaining static voltage levels in the MV grid, especially when requested by the system operator The effectiveness of integrating static voltage support capabilities into PV systems connected to the MV grid has been well established over time.
In many countries, static voltage support requirements for photovoltaic (PV) systems connected to low-voltage (LV) grids are not commonly enforced, with Italy and Austria being notable exceptions due to higher associated costs Despite this, the significance of PV systems in LV grids continues to grow Consequently, newly installed PV systems will need to assume responsibility for managing grid voltage in the future The German Network Technology Forum has updated the code of practice for power plants connected to the low-voltage grid (VDE-AR-N).
To ensure steady-state voltage support, photovoltaic (PV) systems must possess reactive power control capabilities, allowing for either reactive power injection or absorption based on the power factor (cosϕ) at the point of common coupling (PCC) The power factor values can range from 0.95 underexcited to 0.95 overexcited, representing the second and third quadrants The operational level of reactive power can be adjusted accordingly.
2 variable set-point defined bycosϕ(P)-characteristic;
3 fixed value inM V ar, i.e constantQ;
4 controlled value defined byQ(V)characteristic.
The implementation of PV static voltage support varies significantly across different countries and even among Distribution System Operators (DSOs) within a single country For instance, Figure 1.3 illustrates the diverse Q(V) and cosϕ(P) characteristics mandated by various German DSOs.
Figure 1.3 – PV static voltage support
Dynamic grid support requirement
In terms of the dynamic grid support capability, the PV systems should be capable of:
1 staying connected in the event of faults in external grids (FRTrequirement);
2 feeding a reactive current to the network to support the grid voltage;
3 controlling the postfault reactive power consumption to not exceed the pre- fault value.
1.2 Grid codes applicable to PV systems 9
Fault Ride Through (FRT) requirements differ globally; for instance, the French grid code mandates that generating units exceeding 5 MV must stay connected during external faults, while Italian grid operators require that units linked to the Low Voltage (LV) grid with a rated power above 6 kVA must withstand external grid faults.
German grid legislation mandates grid connection obligations for low-voltage (LV) photovoltaic (PV) systems, similar to requirements in Japan that propose fault ride-through (FRT) standards for PV systems in LV distribution networks Recent studies highlight the importance of FRT characteristics during faults in PV systems across different countries.
Figure 1.4 – FRT requirements in various countries
Reactive current injection during grid faults serves two main purposes: it prevents inverter tripping due to over-current protection and aids in grid voltage recovery This reactive current control is activated when the grid voltage drops by more than 10% of the nominal voltage (below 0.9 p.u.) The required reactive current injection should be a minimum of 2% of the PV inverter's rated current for each percentage of voltage drop.
In the scenario where the ratio of instantaneous grid voltage during a fault (V) to the nominal voltage (Vn) is less than 0.5, the relationship can be expressed as V/Vn < 0.5 Here, V0 represents the grid voltage before the fault occurs, Iq denotes the reactive current, In signifies the nominal current, and Iq0 indicates the reactive current prior to the fault inception.
In the case of an unbalanced fault, it is crucial to limit the reactive current injection to ensure that the voltage on the healthy phases does not exceed 1.1 times the nominal voltage (Vn) at the Points of Common Coupling (PCC).
Dynamic voltage support is essential for photovoltaic (PV) systems during faults, requiring them to deliver reactive current at least equal to the inverter's rated current Unlike static voltage support, which applies to both medium voltage (MV) and low voltage (LV) systems, dynamic voltage support is specifically mandated for MV systems.
PV systems in most countries However, in the study, it is assumed that the PV systems connected to bothMVandLVgrids can offer dynamic voltage support during faults.
Frequency control via active power regulation
The intermittent nature of solar energy leads to uncertainty in the active power output of photovoltaic (PV) systems, which is influenced by external environmental conditions A high number of connected PV systems can result in significant fluctuations in power output, potentially causing frequency deviations and grid instability Additionally, the disconnection of numerous PV systems due to interface protection measures can exacerbate these issues In response, various authorities worldwide have revised their grid codes to include frequency control requirements through active power regulation For example, Germany mandates that connected PV systems must reduce their power production during instances of over-frequency.
In detail, when the system frequency exceeds 50.2 Hz, each PV system should re- duce its active power output with a gradient of 40%/Hz of the generated power [24].
PV systems must disconnect from the grid if the system frequency exceeds 51.5 Hz or falls below 47.5 Hz, as mandated by their interface protection Figure 1.6 illustrates the requirement for active power reduction during over-frequency conditions, which the PV inverter controller must regulate.
PV shall be disconnected from the grid iff ≤47.5 or f ≥51.5
(1.2) wherePmis the instantaneous available power delivered by the PV systems, andf is the system frequency inHz.
Thesis contributions
Figure 1.6 – Active power control at over-frequency
Table1.1represents several selected grid codes from European countries for PV sys- tems connected to distribution networks.
Table 1.1 – Grid code requirement for PV systems in different countries
Static voltage support Dynamic voltage support Active power reduction
Country MV LV MV LV MV LV
Germany Yes Yes Yes No Yes Yes
Austria Yes optional Yes No Yes Yes
Italy Yes >6 kV A Yes >6 kV A Yes Yes
France Yes No >5 M W No No No
Taking into account all the above, the contribution of the thesis can be summarized as follows:
This article presents a comprehensive overview of a PV inverter control strategy designed to comply with dynamic voltage support requirements set by new grid codes for PV systems connected to Medium Voltage (MV) and Low Voltage (LV) distribution networks It introduces the concept of injecting Negative Sequence (NS) currents during unbalanced faults to reduce active power oscillations and enhance fault detection Additionally, a fault model for PV systems is developed based on this control algorithm, culminating in the derivation of an equation that defines the magnitudes and angles of PV fault sequence impedances, with their potential values evaluated through analytical analysis.
The thesis introduces a directional algorithm specifically designed for distribution networks with high penetration of photovoltaic (PV) systems A key feature of this approach is its ability to handle the unique characteristics of PV fault currents and voltage waveforms Additionally, it remains unaffected by the high integration of inverter-based PV systems and various factors such as load imbalances, external grid short circuit power, nearby faults, fault types, and impedances This directional method is subsequently utilized to create effective protection schemes and Fault Location and Isolation Systems (FLIS).
Three strategies for coordinating protection schemes between medium voltage (MV) and low voltage (LV) distribution networks are essential for selective and coordinated operation These schemes enable redundancy, allowing one element to back up others while distinguishing between forward and reverse faults Proper coordination between MV and LV protections facilitates successful islanding for connected LV microgrids during external faults and ensures that the Fault Ride Through (FRT) requirements for connected photovoltaic (PV) systems are met.
The thesis presents two Fault Location Identification Systems (FLISs) designed for medium voltage (MV) distribution networks with significant photovoltaic (PV) integration The first system utilizes an Artificial Neural Network (ANN) method, achieving high accuracy in locating faulty line sections with rapid computation The second system is based on a Multiagent System (MAS), where local agents make decisions regarding fault location by exchanging information about fault direction By implementing the proposed FLIS, Distribution System Operators (DSOs) can minimize the duration of the power restoration process, thereby enhancing the System Average Interruption Duration Index (SAIDI) and Customer Average Interruption Duration Index (CAIDI).
The thesis presents a co-simulation system that integrates DIgSILENT|PowerFactory, Python, and an OPC-DA server In this setup, the network is simulated using PowerFactory, while the agents are developed in Python These Python-hosted agents receive real-time measurement signals from PowerFactory through the OPC-DA server, process the data, and send the results back to PowerFactory.
As a result, the obtained system allows to evaluate the proposedMAS-based FLISwithin the pure software environments.
The thesis introduces a Controller Hardware-in-the-Loop (CHIL) platform for testing the Multi-Agent System (MAS)-based Fault Location Identification System (FLIS) It ensures interoperability among the equipment by incorporating IEC 61850 communication alongside real controllers, such as Raspberry PIs, and digital relays.
Thesis structure
The thesis has been organized in 5 chapters, and 9 appendixes as follows:
In the first chapter, the thesis statement and objectives are mentioned We also sum- marize the thesis contributions in this chapter.
Chapter 2 outlines the models for essential system components, including overhead lines, underground cables, transformers, external grids, and loads, which are crucial for transient studies The loads are modeled to reflect both static and dynamic types, closely mimicking real-life transient behaviors This chapter also emphasizes the importance of new grid codes, conducting a comprehensive analysis of their applicability to photovoltaic (PV) systems across various countries The goal is to integrate these grid code requirements into PV models to achieve accurate transient behaviors for subsequent studies Additionally, a control strategy is developed and validated through simulations to ensure PV systems meet voltage dynamic support requirements.
Chapter 3 introduces an innovative directional algorithm designed for distribution networks featuring a high integration of photovoltaic (PV) systems The algorithm's effectiveness is assessed through an analytical approach that utilizes fault equivalent circuits based on the PV models established in the previous chapter.
The proposed directional method is evaluated through simulations in the DIgSILENT|PowerFactory software environment, where various fault scenarios are tested to assess its performance.
Chapter 4 introduces various protection schemes for medium voltage (MV) and low voltage (LV) networks The MV protection scheme ensures accurate fault operation within the protected MV network while facilitating selective operation with connected LV microgrids This selectivity allows for successful islanding of LV microgrids during faults in external high voltage (HV) or MV networks Additionally, the LV microgrid protection schemes feature adaptable setting groups for different operational modes, ensuring compliance with the fault ride-through (FRT) requirements of connected photovoltaic (PV) systems.
Chapter 5 introduces two Fault Line Identification Systems (FLIS) The first system utilizes a state-of-the-art Artificial Neural Network (ANN), specifically a Multi-layer Perceptron (MLP), for classifying faulty line sections This ANN is initially trained on a partial dataset and subsequently tested on the remaining data The second approach employs a Multi-Agent System (MAS) designed according to IEC 61850 standards The MAS-based FLIS is evaluated through a co-simulation system followed by testing on a Hardware-in-the-Loop (HIL) platform.
Appendices fromAtoIare included at the end of the thesis.
Modeling of distribution networks with PV systems
2.1 Introduction 17 2.2 Overview of distribution systems 17 2.2.1 LV distribution networks 18 2.2.2 MV distribution networks 19
2.3 Overview of distribution protection 21 2.3.1 LV distribution protection 21 2.3.2 MV distribution protection 22
2.4 Studied distribution networks 26 2.4.1 Description of Grid-1 26 2.4.2 Description of Grid-2 27 2.4.3 Description of Grid-3 30
2.5 DIgSILENT|PowerFactory 30 2.6 System impedance valuemodeling 31 2.6.1 HV external grid 31 2.6.2 Substation transformer 31 2.6.3 Overhead lines and underground cables 32 2.6.4 Load 32
2.7 PV systems 332.7.1 Structural configuration of a PV system 332.7.2 PV module equivalent circuit 342.7.3 PV array and MPPT algorithm 352.7.4 PV model for steady-state studies 362.7.5 PV model for transient studies 37
2.8 Battery energy storage system 47 2.8.1 Battery model 47 2.8.2 Frequency controller 48 2.8.3 Active/Reactive power controller 48 2.8.4 Battery charge control 49
2.9 Overview of IEC 61850 standard 492.10 Conclusion 50
Introduction
This thesis research focuses on validating algorithms for distribution protection schemes and the Fault Location and Isolation System (FLIS) using three real distribution networks provided by local utility companies, along with several Low Voltage (LV) microgrids containing detailed load and component data The chapter presents models of all components in these networks for electro-mechanical and electro-magnetic simulations using DIgSILENT|PowerFactory and Matlab/Simulink The simulations aim to achieve two objectives: first, to generate fault data that mimic real distribution network currents and voltages for validating the directional algorithm and ANN-based FLIS; second, to create fault operation scenarios for assessing the protection schemes and MAS-based FLIS Additionally, the modeled networks will be validated using the developed CHIL platform.
Overview of distribution systems
LV distribution networks
2.2.1.1 Overhead lines and underground cables
LV networks are the final stage in power systems and are typically operated manually The distribution transformer windings predominantly utilize the DYn-11 connection group In urban settings, LV networks primarily use underground cables, while rural areas favor overhead lines LV feeders often include numerous laterals and sub-laterals The structure of LV networks can be classified into three levels based on the reliability requirements of the connected loads.
The first level of a distribution transformer features an MV side connected to an incoming MV feeder, while the LV conductors are configured radially In the second level, the layout remains similar, but the outgoing LV feeders can either be open-ring or doubled, each linked to a single transformer LV network loads may vary between three-phase, two-phase, or single-phase, with the inclusion of two-phase and single-phase customers resulting in unbalanced characteristics within the LV networks Common cross-sectional areas for LV feeders include twisted overheads of 70 and 150 mm² aluminum with neutral sizes of 54.6 or 70 mm², as well as underground cables of 150 and 240 mm² aluminum with neutrals of 50, 70, or 95 mm².
MV/LV transformers have standard ratings of 50, 100, and 160 kV A for the pole- mounted type, and 160, 250, 400, 630, and 1,000kV Afor the pad-mounted type.
The IEC 60364-5-54 standard categorizes earthing systems for low voltage (LV) networks into three main types: IT, TT, and TN systems Each category is denoted by a two-letter designation, with the first letter indicating the earthing mode.
2.2 Overview of distribution systems 19 of the transformer neutral, "I" is the acronym of the French word "isolé" meaning isolated from earth, and "T" stands for "terre" meaning directly connected to the earth For the second letter, which is defined by the earthing method of the exposed conductive parts of installations, T indicates that the conductive parts of equipment frames are directly earthed, whereas N (neutre) implies that conductive parts of the equipment frame are directly connected to the neutral conductor The third earthing method, i.e TN, may further be divided into three sub-categories The first subgroup is named TN-C if the network-neutral and protective earth conductors of customer installations are the same. The second subgroup is called TN-S if these two conductors are independent The last one is abbreviated as TN-C-S if the TN-C method is applied between the neutral point of network transformer and the TN-C system.
Figure 2.2 – LV earthing systems with (a) IT, (b) TT, (c) TN-C, and (d) TN-S
MV distribution networks
MV networks typically operate in a radial configuration but can quickly form loops using normally opened switches, allowing for one feeder to serve multiple adjacent lines There are two main types of MV networks in use: urban and rural Urban networks, primarily consisting of underground cables, are designed for densely populated areas and utilize three-phase cables with synthetic or paper insulation to enhance power supply quality and minimize visual and weather-related impacts In contrast, rural networks predominantly feature overhead lines and cater to regions with low load density, such as rural areas, small towns, and villages.
Urban feeders typically range from 3 to 10 km in length, with cross-sectional areas of 150 or 240 mm², while rural feeders are longer, averaging 10 to 35 km and featuring cross-sectional areas of 240 mm² at the substation outlet and 148 mm² and 54 mm² for the main and lateral feeders, respectively The maximum allowable power for outgoing MV feeders is 5 MVA for rural networks and 6 MVA for urban networks, constrained by a 400 A limit from the HV/MV substation The positive sequence reactance per unit length of overhead lines is generally 0.3 to 0.35 Ω/km, while the zero sequence capacitance is approximately 5 pF/m for overhead lines, significantly higher for underground cables at around 0.155 µF/km for a 50 mm² section.
HV/MV substations vary in capacity, with ratings from 5MVA for small rural installations to over 280MVA for those in urban settings Typically, rural HV/MV distribution substations are equipped with a maximum of two transformers, while urban substations can accommodate up to three transformers.
The method of earthing, whether neutral or otherwise, is essential for defining the characteristics of earth faults, which can represent up to 80% of total faults and lead to increased ground voltages on healthy phases Currently, utility companies globally employ five primary earthing approaches for neutral earthing in medium voltage (MV) networks No single method is universally adopted; some are specific to certain countries, while multiple systems may coexist within a single nation.
Table 2.1 – MV earthing systems in several typical countries
The neutral system plays a crucial role in network planning, ensuring the safety of personnel and property while enhancing power supply quality The dielectric strength of networks and their components is significantly influenced by ground voltage rise during faults in HV, MV, or LV networks The response of these networks to ground faults varies, making the selection of a neutral earthing system vital, as it determines ground fault current levels and voltage surges, which often conflict Consequently, choosing the appropriate earthing system typically involves balancing technical requirements with operational costs.
Overview of distribution protection
LV distribution protection
LV network protection schemes vary significantly based on the practices and traditions of Distribution System Operators (DSOs) This article outlines the primary protection schemes employed by ENEDIS, the leading DSO in France.
An underground typeLVnetwork that is used in urban areas has the following pro- tections in series, from the customer location to the HV side of the MV/LV transformer.
A protection scheme of a typicalLVurban network is illustrated in Figure2.3.
Figure 2.3 – A protection scheme of a typical French LV underground-cable network
A circuit breaker labeled "d" is essential for disconnecting the low-voltage (LV) system from customer facilities during faults or overloads Standard rated currents for these breakers include 30, 45, 60, and 90 A, indicating their maximum setting limits Additionally, a fuse marked as AD is positioned at the entrance service to handle fault currents that surpass the breaking capacity of the customer circuit breaker In France, the standard ratings for this fuse are 45, 60, and 90 A.
A fuse labeled as FC is utilized in a building's distribution board to eliminate faults and prevent unnecessary disconnections of low-voltage outgoing feeders In France, the standard ratings for the FC fuse are restricted to 125 and 200 amperes.
The LV outgoing feeder features a fuse labeled FD at its start, which is responsible for clearing faults occurring between the fuse and the building's distribution board In France, the standard ratings for the FD fuse are limited to 200, 250, and 400 A.
The FMT fuse is essential for safeguarding MV/LV transformers from potential damage in distribution systems and offers backup protection for low-voltage feeders It is designed for networks operating at voltages ranging from 12 kV to 24 kV, with ratings available at 3, 6, and 16.
43, and 63 A There are also disconnecting switches for low voltage (IBT) and medium voltage (IMT) on both sides of the transformer.
An overhead line network, which is mainly used in rural areas, is equipped with the following protections, as shown in Figure2.4.
2 Customer’s circuit breaker d and a fuse AD accompanying this circuit breaker;
3 FD of the LV outgoing feeders, if applicable;
In pole-mounted substations, a circuit breaker D is utilized, while cabin-type substations may employ switch I or circuit breaker D This network configuration does not currently include fuses or circuit breakers for the MV/LV secondary distribution transformer, although their installation is under consideration.
5 A surge arrester for protecting transformers against atmospheric disturbances.
Figure 2.4 – A protection scheme of a typical French LV overhead-line network
MV distribution protection
MV protection schemes are designed to detect and eliminate various types of faults, including phase and ground faults The French MV protection scheme is organized into three levels, as illustrated in Figure 2.5.
1 Level 1: Protection of the outgoing feeder;
The Level 2 protection of the MV busbar is designed to safeguard the busbar and serve as a backup for potential failures in the outgoing feeder circuit breakers This protection mechanism is intended to trip the Circuit Breaker (CB) on the medium voltage side of the transformer.
3 Level 3: Protection of HV/MV transformer and associated equipment whose role is to protect the auxiliary equipment connected to the transformer on the
MVside This protection is to trip the CB on the HV side of the transformer.
Figure 2.5 – A French typical MV radial network and its different protection levels
Each level of protection features two types: phase protection and ground protection Phase protection, which operates independently of the network's grounding system, addresses phase faults and is primarily made up of phase overcurrent relays, whether definite or inverse time In contrast, ground protection must align with the network's earthing system to effectively manage ground faults, utilizing various protection types based on the grounding system and the specified protection levels.
The principles for calculating phase fault currents remain consistent across any radial network The primary goal of fault calculation is to identify the minimum fault current, which serves as the basis for establishing the current setting threshold This threshold is influenced by the current of a two-phase fault, which is typically lower than that of a three-phase fault As illustrated in Figure 2.5, the two-phase fault current can be defined by specific parameters.
(2.1) whereI F (2) is the two-phase fault current andVnis the grid nominal voltage;
Level 1: The setting current should be lower than0.8I F (2) , but it must be higher than the maximum load current of the protected feeder It also should be higher than the inrush current in the event of load recovery connected to the feeder.
Level 2: The busbar protection should not trip before the feeder protection if the fault is located on the feeder The most straightforward setting is to refer to the rated current of the HV/MV transformer or MV busbar fed from the feeder, i.e., 1.6 times the rated current of the transformer or 1.3 times the rated current of the busbar The lower value is selected after verifying that this setting is higher than 1.2 times the highest setting current of the outgoing feeders.
Level 3: The setting depends on that chosen forMVbusbar It is either twice the rated current of the transformer (in the case of a setting equal to 1.6 times the rated current of the transformer) or 1.6 times the rated current of the busbar (in the case of a setting equal to 1.3 times the rated current of the busbar).
The earthing system in FrenchMVdistribution networks is primarily low-resistance grounded In rural distribution networks, the ground-fault current is limited to 150-300
In urban networks with elevated capacitive currents, a resistor is utilized to limit ground fault current to a maximum of 1000A, effectively reducing the risk of excessive strain on equipment.
Level 1: The ground overcurrent function is set to 1.2 times the capacitive current of the feeder A margin of 20% is selected to prevent the protection from false tripping.
Level 2: The current threshold is set to be equal to 1.2 times the maximum current among the setting currents ofLevel 1.
Level 3: HV/MV transformers are mainly protected from non-electrical quantities that do not distinguish between multi-phase and single-phase faults This kind of protec- tion typically includes a Buchholz relay.
The principles of time selectivity settings described in this paragraph are only valid for networks equipped with definite time overcurrent protection, as is the case in Europe.
To ensure effective protection levels, it is essential to maintain a minimum interval of 0.3 seconds between them, which can be reduced to 0.25 seconds when utilizing digital or numerical relays Additionally, the time delay for protection on the customer side is set at 0.2 seconds, as per the NF C13-100 standard, and this value must be considered when calculating the time delay for outgoing feeder protection.
Level 1: ENEDIS uses only one time-delay of 0.5 s This value helps to ensure the minimum time interval between the user delay of 0.2sand network protections Delay of 0.5 salso can help to avoid the impacts of the inrush current caused by the load re- connection during the operation of reclosing function.
Level 2: The time delay of the protection level is set at 0.8sthat ensures the selectivity
2.3 Overview of distribution protection 25 interval of 0.3swith the protection of outgoing feeder This value is quite long, which may cause severe impacts on the busbar system Hence, an alternative method is using a direct transfer trip that will be presented in more detail in the subsequent section.
Level 3: Based onLevel 2time delay, the time delay of this level is fixed at 1.1s.
Apart from the above protections, there are other protection functions as follows, [57]:
1 Protection of the link between HV/MV transformer andMVbusbar;
A resistive earth detector monitors the current in the transformer neutral, specifically the ground current on the medium voltage (MV) side It serves as a supplementary safety measure for outgoing feeder ground protection and activates the incoming circuit breaker after a predetermined time delay.
3 Internal protection of the transformer acting on the CB on the HV side;
4 Tank earth protection of the transformer acting on the CB on the HV side.
Utilities commonly install reclosers at the start of medium voltage (MV) overhead feeders to quickly clear temporary faults, minimizing power interruptions for customers When a fault is detected by a feeder relay, it sends a trip signal to open the feeder circuit breaker (CB) For feeders with reclosers, the relay's time delay is reduced to 0.15 seconds, compared to the standard 0.5 seconds If the initial trip occurs, the relay switches to delayed trips for any subsequent faults, typically setting the time delay for the second and third trips to 0.5 seconds.
Figure 2.6 – Recloser cycles for (a) a transient fault, and (b) a permanent fault
After a predefined time delay, the recloser automatically commands the CB to reclose.
In the case of a transient fault, it is typically cleared, allowing the supply to be restored to customers connected to the affected feeder However, if the fault persists, the feeder relay will trip the circuit breaker again The recloser operation process for both transient and permanent faults is illustrated in Figure 2.6.
1 Fast cycle: recloses the CB within about 0.3 to 1safter the feeder CB opening;
2 Slow cycle: If the fault still exists, the feeder relay trips the CB again Then, the recloser is delayed for about 15 to 30sbefore reclosing the CB.
3 The CB is finally reopened if the fault still exists after 0.5sby the feeder relay.
Studied distribution networks
Description of Grid-1
The single-line diagram of Grid-1, depicted in Figure 2.7, illustrates a network powered by External Grid A or B through 63/20 kV transformers It features four feeders, with two modeled in detail, including inputs for line sections and low voltage (LV) loads All feeders consist of underground cables, with cross-sectional areas decreasing as they extend from the high voltage/medium voltage (HV/MV) substation Additionally, several laterals branch off from the feeder backbones to supply local LV loads via medium voltage/low voltage (MV/LV) transformers The LV loads, which include both three-phase and single-phase types, create an unbalanced network, with a total load capacity of 7 MVA and an assumed power factor of 0.9 Daily load consumption, illustrated in Figure A.1, fluctuates over a 24-hour period, peaking at 19:00 and reaching its lowest point at 04:00.
Three LV microgrids that contain various PV systems are included at nodes "06",
The grids "10" and "16" can operate in both grid-connected and islanded modes, although the latter is currently restricted In grid-connected mode, frequency is dictated by the external grid, while isolated mode necessitates the installation of a Battery Energy Storage System (BESS) for frequency and voltage regulation The focus of this study is LV microgrid 1, which comprises multiple PV systems and a BESS unit, as illustrated in Figure 2.8 The control algorithms for these generating units, developed in Chapter 2, comply with the latest grid code requirements, and the microgrid also includes a diesel generator.
The Grid-1 system, as illustrated in Figure 2.7, is designed to provide a reserve supply during prolonged islanding scenarios In this configuration, the Battery Energy Storage System (BESS) continues to manage essential grid services, including frequency control The study highlights that the low-voltage microgrid primarily operates in a grid-connected mode, transitioning to isolated operation only in response to faults in the external grid or the host medium-voltage feeder.
LVgrid earthing utilizes the TN type system, which is deemed the most suitable for LV microgrids due to its ability to maintain lower fault voltages compared to TT and IT systems Additionally, the TN system ensures that an earthed fault generates enough current to effectively activate an overcurrent protection device.
Description of Grid-2
Gird-2 is an isolated medium voltage (MV) network operating at voltages of 22 kV and 0.4 kV Initially, the network comprised seven transformer-diesel generator units Recent proposals include the installation of solar and wind energy-based distributed energy resources (DERs) along with a battery energy storage system (BESS), aligning with national investment initiatives.
Figure 2.8 – Single-line diagram of LV microgrid 1 electricity corporation and some local private companies The total installed capacity of
PV systems and wind turbine are intended to reach 6.8M W and 3M W, respectively.
Grid-2 features a structure akin to Grid-1, consisting of three radial feeders that derive power from the 22kV busbar systems at the generation center, serving a range of single-phase and three-phase low voltage (LV) loads Additionally, feeders 1 and 2 are interconnected at multiple locations through normally-open switches The earthing system implemented for Grid-2 employs a solidly and undistributed earthing method.
Figure 2.9 – Single-line diagram of Grid-2
Description of Grid-3
Grid-3 is a rural MV distribution network in France, connected to a 63kV external grid through a 63/20kV transformer It consists of six MV feeders, each represented by multiple line sections using the PI model Feeder 1 is highlighted, with total active and reactive powers of 4401 kW and 829 kV ar, respectively The loads are strategically distributed along the feeder, which is segmented into four zones by three switches (S1 to S3) Additionally, four photovoltaic (PV) systems, each with a capacity of 440 kW, are integrated across these zones.
Figure 2.10 – Single-line diagram of Grid-3
DIgSILENT|PowerFactory
DIgSILENT|PowerFactory is a leading power system analysis computer-aided tool for many applications in generation, transmission, distribution and industrial analysis.
The software offers extensive calculation capabilities for complex problems, utilizing advanced algorithms and real-time simulation features Its component library includes a vast selection of pre-defined and validated power system models.
DIgSILENT|PowerFactory offers a user-friendly graphic interface tailored to various study purposes, requiring different component inputs Its highly flexible and effective data management system allows users to model and simulate extensive networks with thousands of components Notably, the software employs a multi-variable database concept for classifying and storing data, simplifying the processes of data entry, filtering, sorting, and importing/exporting.
The Digsilent Programming Language offers a powerful tool for developing automated and integrated solutions, allowing users to create custom calculation functions tailored to their specific needs It is particularly useful in transient studies, facilitating the generation of control blocks for various system components, including synchronous generators, photovoltaic (PV) systems, wind systems, and protection and control systems.
System impedance valuemodeling
HV external grid
The thesis emphasizes the distribution network by modeling the high-voltage external grid as a voltage source with internal impedance This approach assumes that all synchronous generating units are located far from the studied distribution networks, allowing for the neglect of their transient responses However, the transient behavior of synchronous machine-based distributed generators, such as diesel generators within the distribution networks, remains significant.
Substation transformer
In this study, we utilize a three-phase two-winding transformer model to accurately represent both primary and secondary distribution transformers Given the unbalanced nature of the networks under investigation and the need for unbalanced fault analysis, it is essential to model the transformer in detail for each symmetrical sequence circuit The equivalent circuits for the Positive Sequence (PS), Negative Sequence (NS), and Zero Sequence (ZS) of the simulated transformer are depicted in Figure 2.11.
Figure 2.11 – (a) PS/NS and (b) ZS equivalent circuits of a transformer
The leakage reactances and winding resistances on both the primary and secondary sides, along with the magnetizing branch that accounts for core losses, are crucial in transformer analysis The transformer rating is determined by the maximum load capacity of connected feeders, typically ranging from 50% to 60% of its total rating Key factors for this study include the transformer rating, nominal voltages, and short-circuit voltage, while core losses and saturation are not considered Additionally, the transformer load tap changer on the high voltage side is manually adjusted for varying load scenarios to maintain voltage levels within ±10% at all customer connection points on the low voltage side.
Overhead lines and underground cables
Distribution feeders are typically short and consist of various sections with different cross-sectional areas, unlike transmission lines This study focuses on symmetrical, transposed medium voltage (MV) lines configured in a three-phase, three-wire layout, while low voltage (LV) lines, which may be single-phase, are excluded The analysis emphasizes fundamental frequency components, disregarding high-frequency elements Consequently, the well-established equivalent PI-circuit is deemed most appropriate for modeling distribution line sections, with line impedance sequence components calculated using specified equations.
(2.3) where Z s , Z m , Y s , and Y m are the sefl- and mutual impedances and admittances.
Figure 2.12 – Equivalent circuit of three-phase line
Load
Distribution networks serve a variety of electrical loads that meet daily life and production demands, including incandescent lamps, heaters, air conditioners, refrigerators in homes, and arc furnaces and motors in small to medium-sized factories These diverse electrical devices can be categorized into two main types: static loads and dynamic loads.
PV systems
Structural configuration of a PV system
Photovoltaic (PV) systems connect to the AC network through power electronic Voltage Source Inverters (VSIs) There are two primary configurations for PV systems: the two-stage system, which includes a boost DC/DC converter to prevent AC output power ripples from affecting PV voltage, and the single-stage system The latter configuration becomes feasible once a sufficient DC voltage level is achieved by connecting a proper number of PV modules in series, allowing for the removal of the boost converter The single-stage topology is favored for its higher efficiency, lower cost, and simpler implementation, making it the focus of this study.
Figure 2.14 – Single-line structural diagram of (a) single-state and (b) two-stage structures for grid-connected PV systems
The single-stage photovoltaic (PV) system, illustrated in Figure 2.14a, comprises a PV array, a DC-link capacitor, and a three-phase DC/AC inverter This setup connects to the grid through a filter and a step-up transformer Additionally, a Maximum Power Point Tracking (MPPT) controller is implemented to optimize power extraction from the system.
Photovoltaic (PV) panels operate at a Maximum Power Point Tracking (MPPT) that varies with atmospheric conditions like temperature and solar irradiation In the PV system configuration, the DC/AC inverter is responsible for controlling the DC-link voltage and fulfilling grid code requirements, which include static and dynamic grid support and power quality commitments This section explores the modeling and simulation of PV systems that adhere to the grid requirements outlined in Subsection 1.2.
PV module equivalent circuit
Solar cells are the building element of PV modules; their equivalent circuit is depicted in Figure2.15 The relationship between output current and voltage of a PV module, i.e.
I P V andV P V , can be expressed by the following equations [62]:
I sat = I sc,ST C +α i (T−T ST C ) exp q
The equation (2.8) defines key parameters for photovoltaic (PV) modules, where N cell represents the number of cells in the module It incorporates fundamental constants such as the electron charge (q = 1.6e −19) and the Boltzmann constant (K b = 1.38e −23) The diode factor (n) and temperature correction factors for current (α i) and voltage (α v) are also included, measured in 1/K Additionally, T denotes the temperature in Kelvin, while T STC refers to the temperature at Standard Test Conditions Lastly, E signifies the solar irradiation measured in watts per square meter (W/m²).
The cell saturation current (I_sat) is measured in amperes (A), while the photo-current at Standard Test Conditions (I_Ph) is also expressed in amperes (A) Series resistance (R_S) and shunt resistance (R_P) are indicated in ohms (Ω) Additionally, the short circuit current (Isc,STC) and open-circuit voltage (Voc,STC) are quantified in amperes (A) and volts (V) at Standard Test Conditions, respectively.
Figure 2.15 – Equivalent circuit of a PV cell
The parameters necessary for modeling the photovoltaic (PV) module, as outlined in Equations 2.6, 2.7, and 2.8, are detailed in Table A.1 These values are provided by manufacturers under standard test conditions (STC), which include an irradiation of 1000 W/m² and a temperature of 25°C Utilizing these parameters and the associated mathematical equations, the current-voltage (I-V) and power-voltage (P-V) characteristic curves of the PV module can be generated for various solar irradiation levels, as illustrated in Figure 2.16.
Figure 2.16 – PV characteristic curves at different solar irradiation
PV array and MPPT algorithm
The PV array model is created by connecting a specific number of PV modules, with our study utilizing 20 modules in series and 140 parallel strings As illustrated in Figure 2.16, the maximum output active power of the PV array is influenced by solar irradiation and cell temperature To optimize power extraction, a Maximum Power Point Tracking (MPPT) system is employed, utilizing algorithms such as the Perturb and Observe method and the Incremental Conductance method This MPPT system continuously adjusts the operating voltage of the PV array to maximize active power output, ensuring the system operates at peak efficiency The study further simplifies the MPPT system's operating mechanism by adjusting the maximum power point voltage (V mpp) and current (I mpp) based on temperature and irradiation correction factors for each simulation hour throughout the day.
V mpp =Vmpp,P V,ST Cã lnE lnEST C ãα v (2.9)
EST C ãα i (2.10) whereVmpp,P V,ST C andImpp,P V,ST C are the voltage and current at the maximum power point at the STC, respectively.
Then, the maximum output active power of the PV array corresponding to the oper- ating point with MPPT control would be:
The preliminary theoretical results of the modeled PV array with solar irradiation of
1000W/m 2 and the ambient temperature of 33° are shown in TableA.2.
PV model for steady-state studies
Time-domain transient simulations necessitate that initial parameters of the network are established through accurate power flow calculations These parameters reflect the steady-state operating conditions at the start of the transient simulation, ensuring that the derivatives of all state variables, including loads, generators, and controllers, are zero Consequently, prior to creating transient models for generating units such as photovoltaic (PV) systems and battery energy storage systems (BESS), it is essential to first develop their steady-state representations For effective power flow simulations, the active power output from the installed PV systems must be specified.
PV systems for each simulation scenario is calculated in advance according the equations given in Subsections2.7.2and2.7.3under normal condition with the MPPT control.
To meet the reactive power capacity requirements for PV systems connected to low and medium voltage distribution networks, it is essential to implement a local controller for each system that adheres to local regulations These controllers can operate in various modes, with the thesis focusing on the Q(V) characteristic, specifically the voltage Q-droop control mode This control algorithm adjusts the reactive power injection based on the deviation of grid voltage from a set-point value, while ensuring that the output does not exceed the maximum inverter capacity to prevent thermal damage The control unit's block diagram and characteristics are illustrated in Figure 2.17.
Based on the control characteristic illustrated in Figure 2.17, the additional reactive power that should be delivered by the PV systems for local voltage regulation can be determined by:
(2.12) where:V is the actual voltage,V;V ref is the voltage reference dictated by local operator,
V;Qis the actual output reactive power of the PV systems,V ar;Qsetpointis the specified dispatch reactive power of the PV system, V ar; S n is the PV nominal apparent power,
V A; Q droop is the reactive power increment for 1% voltage deviation, %; ddroopis the droop value needs to be assigned in the PV model, %.
Figure 2.17 – PV voltage Q-droop control
The study establishes a droop value of 2%, as advised by various national grid codes, leading to a 50% increase in reactive power relative to the nominal apparent power of the PV system during a 0.1 p.u voltage drop However, the amount of reactive power that the PV system can provide is contingent on its nominal inverter rating current Notably, the maximum reactive power that the inverter can deliver during standard operation using the Maximum Power Point Tracking (MPPT) method is limited.
S n 2 −P mpp 2 (2.13) wherePmppis the PV active power at the maximum-power operating point regulated by the MPPT controller;S n in the inverter rating apparent power.
PV model for transient studies
2.7.5.1 Selection of the control scheme
The transient response of Voltage Source Inverter (VSI)-based PV systems during grid faults is significantly influenced by their control algorithms, making accurate inverter control models crucial for transient studies Various control algorithms tailored for PV inverter operation under fault conditions have been explored, with a focus on meeting dynamic support requirements Among these, the double Synchronous Reference Frame (SFR) control algorithm has emerged as the most prevalent in recent research This method features two control sub-systems: one that manages positive-sequence current and another that regulates negative-sequence current, facilitating the estimation of reference current for the decoupling of active and reactive powers Notably, during symmetrical faults, the reference for negative-sequence current is set to zero.
Figure 2.18 – Schematic diagram of the PV system
The control frame utilized in [65] enhances the quality of active power output; however, it inadvertently causes oscillations in reactive power output and introduces NS current Conversely, the control algorithm presented in [66] effectively addresses these issues.
NScurrent leads to oscillations in both active and reactive output powers, which can be suppressed, as shown in [67], although this may introduce current distortion Alternative methods, discussed in [68] and [69], can meet Fault Ride Through (FRT) requirements by producing the necessary inverter currents However, these control schemes may pose a risk of excessively high inverter output currents during unbalanced voltage drops Therefore, selecting control algorithms involves balancing power oscillation with current quality.
To meet the dynamic grid support requirements outlined in Section 1.2, this study employs a control algorithm for PV inverters that consists of two loops: the inner current control loop and the outer voltage control loop The outer loop is responsible for regulating the inverter's DC current and maintaining the DC-bus voltage, providing a reference current to the inner loop The inner loop then adjusts the current to match this reference, optimizing the output active current while also managing the injection of PV reactive current to support grid voltage during faults A structural diagram of the three-phase VSI-based PV system is illustrated in Figure 2.18, followed by a detailed presentation of the PV systems' control scheme.
Based on the schematic diagram of the considered PV in Figure2.18, the relationship between the grid voltage and the VSI AC-side current is described by:
The equation Vdq = Edq + LdIdq/dt + RIdq (2.14) describes the relationship between grid voltage (Vdq), terminal voltage of the voltage source inverter (VSI) (Edq), and the AC-side current (Idq) in the dq-frame In this equation, L represents the inductance and R denotes the resistance of the filter, highlighting their critical roles in the dynamics of the VSI system.
By applying EquationB.1for Equation2.14, we obtain the expressions of the gridPS andNSvoltages in Synchronous Reference Frame (SFR) frame as:
E dq + =LdI dq + dt +RI dq + +jωLI dq + +V dq + (2.15)
E dq − =LdI dq − dt +RI dq − −jωLI dq − +V dq − (2.16)
Then, applying EquationsB.3andB.4to these above equations and rewriting them in separate d- and q-components, we can obtain the formulae describing the dynamics of
PSandNScomponents in the dq-frame as, [64]:
LdI q − dt =ωLI d − −RI q − +E q − −V q − (2.20) where I d + , I q + , I d − andI q − are the control outputs; E d + , E q + , E d − andE q − are the control inputs; andV d + ,V q + ,V d − andV q − are the disturbances.
In a VSI-based PV system, effective regulation of the DC-link voltage is essential for maximizing active power extraction To achieve this, it is necessary to derive the formulas that govern the DC-link voltage According to the power balance principle and as illustrated in Figure 2.14, the dynamics of the DC-bus in PV systems can be accurately determined.
The equation PDC = (2.21) indicates that the DC-side power of the PV inverter (PDC) is influenced by the capacity of the DC link (C) and the DC link voltage (VDC), while also factoring in the power generated by the PV array (PPV array).
In Equation 2.21, the photovoltaic (PV) array output fluctuates based on atmospheric conditions, making it uncontrollable by the system's control mechanisms Consequently, the control objective should focus on the Power Distribution Control (PDC) Assuming no losses during switching processes, the power on the DC side of the inverter can be equated to its AC side terminal power, represented as P_V SI This leads to the derivation of the equation that characterizes the dynamics of the DC bus from Equation 2.21.
C 2 dV DC 2 dt =P P V array −P V SI (2.22) whereP V SI is the AC-side power of the PV inverter.
In the given equation, VDC represents the state variable and control output, while PV SI serves as the control input, and PPV array signifies the disturbance The objective of this study is to manage the power output from the photovoltaic (PV) system, specifically the active power (PS) and reactive power (QS) Therefore, the AC-side terminal power of the PV inverter, PV SI, must be articulated in relation to these two power metrics.
QS dQ S dt (2.23) whereVSis the voltage at the PV coupling point.
Substituting for P V SI from Equation 2.23in Equation 2.22, we obtain the equation expressing the dynamic of the DC-bus voltage as: dV DC 2 dt = 2
2LQ S0 3V S 2 dQ S dt (2.24) whereP S0 andQ S0 are active and reactive power under a steady-state condition of the
From Equation2.24, we can deduce thatV DC is the output, P S is the control input, andPP V arrayandQSare the disturbance inputs.
The inverter apparent power under unbalanced grid faults is defined by, [64]:
By utilizing Equations B.3 and B.4 for V dq +, V dq −, I dq +, and I dq − in Equation 2.25, we can derive the expressions for active and reactive power in the analyzed PV systems during unbalanced fault conditions.
Equation 2.26 shows that, in addition to the fundamental components P0 and Q0, the active and reactive powers produced by VSI-based PV systems during unbalanced fault conditions include second-order harmonic coefficients, specifically Pc2.
P s2 ,Q c2 , andQ s2 These harmonic components are caused by the voltage unbalance As presented in [64], these coefficientsPc2,Ps2,Qc2, andQs2can be computed by:
In Equation 2.27, six components must be controlled, but there are only four current quantities available for control The primary goal of this study is to ensure that the photovoltaic (PV) active power output remains free of ripples, necessitating that the coefficients Pc2 and Ps2 are set to zero Consequently, we can eliminate the last two rows of the coefficient matrix in Equation 2.27, which results in the reactive power ripples of PV systems being left uncontrolled By assigning the values P and Q to P ref and Q ref, respectively, we can derive the reference quantities effectively.
(2.28) where I dref + andI qref + , I dref − andI qref − are reference currents inPS andNS SFR, respec- tively;D= V d + 2
. The determination ofP ref andQ ref is detailed in the following.
The value of Pref is derived from the output of the MPPT system, whereas that of
The Q reference is derived from the dynamic voltage support requirements, as shown in Figure 1.5, with a variable value of 2 selected in Equation 1.1b Unlike the static voltage support discussed in subsection 2.7.4 and Equation 2.13, connected PV systems must prioritize reactive power injection during faults to aid in grid voltage recovery During a fault, the PV maximum reactive current can reach the nominal inverter current when voltage drops below 0.5 p.u Consequently, PV systems can only operate at maximum power point if sufficient capacity is available The power reference determination flowchart is presented in Figure 2.19, with subscript n indicating nominal values in all equations.
Equation 2.12 no Equation 1.1c yes Equation 1.1b yes no
Figure 2.19 – Flowchart of the power reference generation process
Figure 2.20 illustrates the regulation of DC-link voltage, where the outer voltage control loop effectively maintains the DC-link voltage at the designated reference level during practical operation.
In this study, the maximum power point reference voltage (V mpp,ref) is assumed to remain constant during transient fault scenarios, despite the dynamic adjustments typically made by the MPPT system in response to changing weather conditions This assumption is valid due to the very short duration of the faults considered Consequently, the MPPT algorithm operates as outlined in Subsection 2.7.3, while Laplace transformation is applied to the relevant equations.
Figure 2.20 – Control block diagram of the modeled PV system in dual dq-frame
2.24, and consider PP V array andQS as disturbance inputs, one can deduce the transfer function of DC-link dynamics [71], as follows: sV DC 2 =−2