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In this paper, self-adaptive controllers for renewable energy communities based on data-driven approach are proposed to mitigate the voltage rise and transformer congestion at the community level. In the proposed approach, the transformer loading percentage is estimated by the trained data-driven model, which uses the extreme gradient boosting regression algorithm based on a measurement set acquired from critical coupling points of the communities. To avoid voltage rise issues, the droop control parameters (i.e., voltage threshold for P − V , Q−V curves) are adaptively tuned based on the solar irradiance availability and estimated transformer loading. The proposed approach has been tested in the IEEE European LV distribution network. Results showed that the control approach could effectively reduce 22.2% of the total overloaded instances, while still keeping voltage magnitude in the operation range. This method can help DSOs manage voltage violation and congestion without further communication.

As smart grids come into reality, our grid is also accommodating more and more distributed and renewable generation. How more solar generation can be enabled in areas of high distributed generation penetration is the main focus of this research. An automated PV analysis tool is developed to identify critical cases to time efficiently assess medium voltage photovoltaic system maximum capacity. The tool incorporates a set of sub-processes and methods to identify critical cases with spatial, temporal and electrical features. Results show that more than 99% time reduction can be achieved with higher than 97% accuracy compared to running analysis for yearly datasets. Also potentially seven times more PV can be enabled with distribution network state estimation and the PV analysis tool.

Many countries have experienced a surge in the level of the penetration of solar PV systems in the last decade. A huge portion of the newly deployed PV systems are connected to low voltage Grid. High Penetration of PVs at this level could potentially disrupt the normal operation of distribution network. A major concern is the impact of these units on power quality indices. Namely, photovoltaic panels could increase the level of voltage and current unbalance, deteriorate harmonic distortion and cause the voltage rise. These concerns may prohibit higher pentation levels of PVs. Thus, proper assessment techniques are vital for network operators for the planning and decision-making process. On the other hand, many characteristics of PV system are inherently uncertain. These uncertainties should be properly modeled in assessment framework. The main effort of research communities is to propose new methodologies that could model the uncertainty of solar power generation and stochastic assessment methods that could accurately estimate the state of the operation of the network with different levels of penetration of solar photovoltaics. This paper provides a comprehensive review of recent publications and trend of research activities regarding methods of representing uncertain variables and stochastic assessment techniques for power system quality analysis.

The Swedish Energy Agency has a target to increase solar photovoltaics (PV) power production by up to 5-10% of the total electricity demand by the year 2040. The PV potential for the residential market is high and its contribution to the total installed PV capacity is expected to increase significantly. The technical requirements should be met to keep high reliability and good power quality at the customers, therefore, it is important for planning reasons to proactively find the maximum amount PV power that can be connected at each low-voltage network without violating the performance of the grid. This amount is known as the hosting capacity. A method for PV hosting capacity estimation by taking overvoltage and transformer overload as performance indices was developed in this thesis. The method does not require any knowledge about the topology of the network. The overload hosting capacity can be estimated for any combination of customers having PV power and for the overvoltage hosting, the minimum at each penetration level can be estimated. The method was implemented on four low-voltage networks located in a typical Vattenfall medium-voltage network and the comparison of the estimation results to a power flow simulation showed good correspondence. It was shown how the impact of PV power in adjacent secondary substations can be accounted for. Using SS-EN50160 voltage limits, the studied networks were able to handle 3-7 times the PV penetration level needed (8 kWp at 20% of the customers) to achieve the national goal in Sweden without grid investments.

The Swedish Energy Agency has a target to increase solar photovoltaics (PV) power production by up to 5-10% of the total electricity demand by the year 2040. The PV potential for the residential market is high and its contribution to the total installed PV capacity is expected to increase significantly. The technical requirements should be met to keep high reliability and good power quality at the customers, therefore, it is important for planning reasons to proactively find the maximum amount PV power that can be connected at each low-voltage network without violating the performance of the grid. This amount is known as the hosting capacity. A method for PV hosting capacity estimation by taking overvoltage and transformer overload as performance indices was developed in this thesis. The method does not require any knowledge about the topology of the network. The overload hosting capacity can be estimated for any combination of customers having PV power and for the overvoltage hosting, the minimum at each penetration level can be estimated. The method was implemented on four low-voltage networks located in a typical Vattenfall medium-voltage network and the comparison of the estimation results to a power flow simulation showed good correspondence. It was shown how the impact of PV power in adjacent secondary substations can be accounted for. Using SS-EN50160 voltage limits, the studied networks were able to handle 3-7 times the PV penetration level needed (8 kWp at 20% of the customers) to achieve the national goal in Sweden without grid investments.

© 2007-2012 IEEE. The intermittent photovoltaic (PV) units significantly affect the performance of distribution systems, and they often cause several operational problems, most importantly, voltage rise/drop. At high PV penetration, excessive tap movements of transformers and high curtailed PV power are expected to completely solve the voltage violation problem. In this paper, we propose an optimal voltage control method for distribution systems considering the number of tap movements of transformers and the active power curtailment of PV units. The objective function of the proposed method comprises: 1) voltage drop violation, 2) voltage rise violation, 3) tap movement rate (TMR) of transformers, and 4) curtailed power of PV (CPPV). A multiobjective grey wolf optimizer integrated with a Lévy mutation operator (GWO-Lévy) is formulated to accurately solve the voltage control problem. A 24-h simulation is performed on the 119-bus distribution system with PV and different types of loads. The performance of GWO-Lévy is compared with three other optimizers, finding that it achieves the best performance. The simulation results demonstrate the efficacy of the proposed method for solving the voltage violation problem with PV while simultaneously optimizing TMR and CPPV.

The increasing quantity of PV generation connected to distribution networks is creating challenges in maintaining and controlling voltages in those distribution networks. Determining the maximum hosting capacity for new PV installations based on the historical data is an essential task for distribution networks. Analyzing all historical data in large distribution networks is impractical. Therefore, this paper focuses on how to time efficiently identify the critical cases for evaluating the voltage impacts of the new large PV applications in medium voltage (MV) distribution networks. A systematic approach is proposed to cluster medium voltage nodes based on electrical adjacency and time blocks. MV nodes are clustered along with the voltage magnitudes and time blocks. Critical cases of each cluster can be used for further power flow study. This method is scalable and can time efficiently identify cases for evaluating PV investment on medium voltage networks.

The hosting capacity approach is presented as a planning, improving, and communication tool for electrical distribution systems operating under specific uncertainties, such as power quality issues, power stabilities, and reliability, among others. In other words, it is an important technique, when renewable sources are present, to answer the amount of power that is possible to supply to the system without trespassing power performance limits. However, the power flow in a distribution system, for instance, can change throughout time due to the penetration of distributed generation, as well as load consumption. Based on the dynamic nature existing in distribution grids nowadays, it is important to highlight that the hosting capacity should not be calculated in a specifically chosen time only, but must be analyzed throughout a period of time. Thus, this paper introduces an extended concept of hosting capacity in relation to an integrated impact of harmonic voltage distortion and voltage rise as a function of time for daily, weekly, monthly, or even yearly periods. This extended concept is named as Dynamic Hosting Capacity (DHC(t)). General aspects of DHC(t) are demonstrated via measured data on a photovoltaic system (PV) connected at a low-voltage (LV) side of a university building.

The hosting capacity approach is presented as a planning, improving, and communication tool for electrical distribution systems operating under specific uncertainties, such as power quality issues, power stabilities, and reliability, among others. In other words, it is an important technique, when renewable sources are present, to answer the amount of power that is possible to supply to the system without trespassing power performance limits. However, the power flow in a distribution system, for instance, can change throughout time due to the penetration of distributed generation, as well as load consumption. Based on the dynamic nature existing in distribution grids nowadays, it is important to highlight that the hosting capacity should not be calculated in a specifically chosen time only, but must be analyzed throughout a period of time. Thus, this paper introduces an extended concept of hosting capacity in relation to an integrated impact of harmonic voltage distortion and voltage rise as a function of time for daily, weekly, monthly, or even yearly periods. This extended concept is named as Dynamic Hosting Capacity (DHC(t)). General aspects of DHC(t) are demonstrated via measured data on a photovoltaic system (PV) connected at a low-voltage (LV) side of a university building.

Voltage drop and rise at network peak and off-peak periods are one of the major power quality problems in low voltage distribution networks. Additionally, the ever increasing demand for electricity along with the other requirements are driving modern day power systems towards more distributed generation (DG). Integration of large scale DG can be limited by these voltage variations. Therefore, it is of high interest to investigate the voltage support strategies that are able to successfully mitigate these problems. One of the solutions is to use energy storage systems (ESS). On the one hand limited amount of energy storage might not have the desired impact. On the other hand it is not possible to install large amount of energy storage as this would increase the costs substantially. Therefore it is required to optimally place and size energy storage. The purpose of this thesis is to investigate the optimal placement and sizing of battery energy storage with the integration of renewable energy sources (RES) in a low voltage distribution network. An optimization model has been developed in order to identify the potential battery size and location combinations that increase the RES hosting capacity of the distribution network. The optimization tool used for this problem is the Genetic Algorithm (GA). Among the most important features of this algorithm stands its robustness and ability to provide good results in optimization processes. The functionality and the performance of the developed model is assessed using an IEEE benchmark network that has shown to be adequate for both the dynamic and steady-state analysis. The results of this work show that the voltage problems caused by the integration of RES can be mitigated by optimal placement and sizing of battery energy storage. They also show that besides the the voltage profile improvement reduction of losses can be achieved., Electrical Engineering, Mathematics and Computer Science, Electrical Sustainable Energy, Erasmus Mundus, European Wind Energy Master (EWEM)

Voltage drop and rise at network peak and off-peak periods are one of the major power quality problems in low voltage distribution networks. Additionally, the ever increasing demand for electricity along with the other requirements are driving modern day power systems towards more distributed generation (DG). Integration of large scale DG can be limited by these voltage variations. Therefore, it is of high interest to investigate the voltage support strategies that are able to successfully mitigate these problems. One of the solutions is to use energy storage systems (ESS). On the one hand limited amount of energy storage might not have the desired impact. On the other hand it is not possible to install large amount of energy storage as this would increase the costs substantially. Therefore it is required to optimally place and size energy storage. The purpose of this thesis is to investigate the optimal placement and sizing of battery energy storage with the integration of renewable energy sources (RES) in a low voltage distribution network. An optimization model has been developed in order to identify the potential battery size and location combinations that increase the RES hosting capacity of the distribution network. The optimization tool used for this problem is the Genetic Algorithm (GA). Among the most important features of this algorithm stands its robustness and ability to provide good results in optimization processes. The functionality and the performance of the developed model is assessed using an IEEE benchmark network that has shown to be adequate for both the dynamic and steady-state analysis. The results of this work show that the voltage problems caused by the integration of RES can be mitigated by optimal placement and sizing of battery energy storage. They also show that besides the the voltage profile improvement reduction of losses can be achieved., Electrical Engineering, Mathematics and Computer Science, Electrical Sustainable Energy, Erasmus Mundus, European Wind Energy Master (EWEM)

Voltage rise (VR) is the resulting issue of reverse power flow from solar PVs, owing to their highpenetration in the distribution network (DN). The main purpose of this thesis is to mitigate VR in suchsituation. Mitigation methods found in literature are evaluated in chapter 1 from PV-inverter andDistribution Network Operator (DNO)-side.By accurate assessment of the impact of high PV penetration in distribution networks, a risk-free level ofPV penetration can be estimated for each customer, to prevent the VR. Accordingly, a comprehensiveIndex-Based Assessment (IBA) methodology to investigate the impact of high PV penetration in DNs isdeveloped in Chapter 2 which suggests such safe margin and compares it to the Basic Active PowerCurtailment (BAPC) method in a modified IEEE 13-bus network.According to the literature review, diverse criteria are considered by hypothetical decision makers, such ascost, required data infrastructure, control complexity and energy losses. A Priority-Based Decision-MakingMethodology (PBDMM) is developed to consider these criteria in evaluating state-of-the-art of VR mitigationmethods. PBDMM is based on an Analytical Hierarchy Process (AHP), utilizing pair-wise comparisonstechnique. Consequently, reactive power control (RPC) methods are more robust than other VR mitigatingmethods. Accordingly, in Chapter 4, major reactive power control methods are elaborated and the resultsare compared to a base case with no applied VR control strategy and PVs operate at unity power-factor.Finally in chapter 5 a novel index-based single-point-reactive-power-control (SPRPC) methodology isintroduced for VR mitigation by absorbing adequate reactive power in a central fashion. The proposedindex uses short circuit impedance analysis for best point assessment. SPRPC benefits from "Networkeffect" and is supported by DNOs, technically and financially, which makes it simple and efficient for VRmitigation. With SPRPC, existing PV inverters do not need to be upgraded a

Solar energy from photovoltaic (PV) is among the fastest developing renewable energy systems worldwide. Driven by governmental subsidies and technological development, Europe has seen a fast expansion of solar PV in the last few years. Among the installed PV plants, most of them are situated at the distribution systems and bring various operational challenges such as power quality and power flow management. The paper discusses the modelling requirements for PV system integration studies, as well as the possible techniques for voltage rise mitigation at low voltage (LV) grids for increasing PV penetration. Potential solutions are listed and preliminary results are presented.

The rapidly increasing penetration of rooftop PV systems in rural LV distribution networks calls for the attention of DNOs in order to secure end-user voltage range. In times of high photovoltaic generation and low load consumption, voltage at PCCs may exceed the specified upper limit and make PV inverters trip. This phenomenon hinders further PV integration in the network although MV/LV transformer and conductors are by far not used up to their full capacity yet. In this thesis, voltage rise problem is analysed through load flows and simulations on a suitably designed rural test network model implemented in PowerFactory software. The suggested local voltage support strategies by the German directive VDE-AR-N 4105 and the recent European standard EN 50438, namely PF(P) and Q(V), which require reactive power control capability of photovoltaic inverters, are implemented, tested and analysed in order to check their effectiveness and compare their behaviour. As active power curtailment capability is also already required by some DNOs, a dynamic active power curtailment control algorithm is designed and tested as well, taking into account the local load demand and the network’s feed-in limitations. Afterwards, local battery storage is also incorporated in every PV system model and all the three aforementioned strategies are tested and analysed again. All studied strategies manage to mitigate the voltage rise problem up to a PV-integration level of 10 kW/household. However, their effectiveness is compared in terms of a set of evaluation criteria for a range of PV-integration levels. Subsequently, the best candidate strategy, among the ones studied, emerges through the help of experts’ opinion and a suitably designed overall evaluation score number, for both the perspectives of a DNO and a PV system owner. It is revealed that the overall preference of a DNO is for a solution which involves active power curtailment and local storage, in contrast to the overall preference of, Electrical Sustainable Energy, Electrical Engineering, Mathematics and Computer Science

This project was an innovative approach in developing smart coordination of available energy resources to improve the integration level of PV in distribution network. Voltage and loading issues are considered as the main concerns for future electricity grid which need to be avoided using such resources. A distributed control structure was proposed for the resources in distribution network to avoid noted power quality issues.

This paper proposes the use of a common DC link in residential buildings to allow customers to inject their surplus power that otherwise would be limited due to AC power quality violation. The surplus power can easily be transferred to other phases and feeders through common DC link in order to maintain the balance between generated power and load. PSCAD-EMTDC platform is used to simulate and study the proposed approach. This paper suggests that this structure can be a pathway to the future DC power systems.

The rapidly increasing penetration of rooftop PV systems in rural LV distribution networks calls for the attention of DNOs in order to secure end-user voltage range. In times of high photovoltaic generation and low load consumption, voltage at PCCs may exceed the specified upper limit and make PV inverters trip. This phenomenon hinders further PV integration in the network although MV/LV transformer and conductors are by far not used up to their full capacity yet. In this thesis, voltage rise problem is analysed through load flows and simulations on a suitably designed rural test network model implemented in PowerFactory software. The suggested local voltage support strategies by the German directive VDE-AR-N 4105 and the recent European standard EN 50438, namely PF(P) and Q(V), which require reactive power control capability of photovoltaic inverters, are implemented, tested and analysed in order to check their effectiveness and compare their behaviour. As active power curtailment capability is also already required by some DNOs, a dynamic active power curtailment control algorithm is designed and tested as well, taking into account the local load demand and the network’s feed-in limitations. Afterwards, local battery storage is also incorporated in every PV system model and all the three aforementioned strategies are tested and analysed again. All studied strategies manage to mitigate the voltage rise problem up to a PV-integration level of 10 kW/household. However, their effectiveness is compared in terms of a set of evaluation criteria for a range of PV-integration levels. Subsequently, the best candidate strategy, among the ones studied, emerges through the help of experts’ opinion and a suitably designed overall evaluation score number, for both the perspectives of a DNO and a PV system owner. It is revealed that the overall preference of a DNO is for a solution which involves active power curtailment and local storage, in contrast to the overall preference of, Electrical Sustainable Energy, Electrical Engineering, Mathematics and Computer Science

There is already strong evidence that rooftop solar photovoltaic (PV) units at low voltage (LV) distribution networks are creating major impacts on the operation of the electricity networks, both at the low and medium voltage (MV) levels. With the proliferation of solar PV penetration, LV distribution grids are experiencing the issues of reverse power flow and voltage rise. As a result, the hosting capacities of many distribution feeders are already close to their maximum limit. This prompts many utilities to impose a barrier to the installation of new solar PV units at the LV distribution level and to reduce the PV size allocated for household. In addition, fluctuations in PV power output due to passing clouds can result in significant voltage fluctuation, especially in weak distribution grids. With an unbalanced allocation of single phase PV units, 4-wire LV distribution networks can experience an increase of neutral current and therefore the neutral potential (or neutral-to-ground voltage) can exceed the acceptable limit. In the context of the problems outlined above, an accurate assessment of the impact of solar PV on distribution networks is becoming necessary so that effective mitigation actions can be taken, and the PV penetration level can be increased. With such a background, this thesis aims at: developing a comprehensive and realistic assessment approach for the impact of solar PV on distribution networks, analysing the impact using the developed approach in real network environment with smart grid measurements, and proposing mitigation strategies for the particular problems identified above. First, this thesis has developed a comprehensive modelling and analysis approach for integrated medium voltage (MV) and multigrounded low voltage (LV) distribution networks for an accurate assessment of solar PV impact. Using this approach, PV integrated networks can be modelled by retaining their wiring configurations, such as 3- wire configurations for MV networks

There is already strong evidence that rooftop solar photovoltaic (PV) units at low voltage (LV) distribution networks are creating major impacts on the operation of the electricity networks, both at the low and medium voltage (MV) levels. With the proliferation of solar PV penetration, LV distribution grids are experiencing the issues of reverse power flow and voltage rise. As a result, the hosting capacities of many distribution feeders are already close to their maximum limit. This prompts many utilities to impose a barrier to the installation of new solar PV units at the LV distribution level and to reduce the PV size allocated for household. In addition, fluctuations in PV power output due to passing clouds can result in significant voltage fluctuation, especially in weak distribution grids. With an unbalanced allocation of single phase PV units, 4-wire LV distribution networks can experience an increase of neutral current and therefore the neutral potential (or neutral-to-ground voltage) can exceed the acceptable limit. In the context of the problems outlined above, an accurate assessment of the impact of solar PV on distribution networks is becoming necessary so that effective mitigation actions can be taken, and the PV penetration level can be increased. With such a background, this thesis aims at: developing a comprehensive and realistic assessment approach for the impact of solar PV on distribution networks, analysing the impact using the developed approach in real network environment with smart grid measurements, and proposing mitigation strategies for the particular problems identified above. First, this thesis has developed a comprehensive modelling and analysis approach for integrated medium voltage (MV) and multigrounded low voltage (LV) distribution networks for an accurate assessment of solar PV impact. Using this approach, PV integrated networks can be modelled by retaining their wiring configurations, such as 3- wire configurations for MV networks

There is already strong evidence that rooftop solar photovoltaic (PV) units at low voltage (LV) distribution networks are creating major impacts on the operation of the electricity networks, both at the low and medium voltage (MV) levels. With the proliferation of solar PV penetration, LV distribution grids are experiencing the issues of reverse power flow and voltage rise. As a result, the hosting capacities of many distribution feeders are already close to their maximum limit. This prompts many utilities to impose a barrier to the installation of new solar PV units at the LV distribution level and to reduce the PV size allocated for household. In addition, fluctuations in PV power output due to passing clouds can result in significant voltage fluctuation, especially in weak distribution grids. With an unbalanced allocation of single phase PV units, 4-wire LV distribution networks can experience an increase of neutral current and therefore the neutral potential (or neutral-to-ground voltage) can exceed the acceptable limit. In the context of the problems outlined above, an accurate assessment of the impact of solar PV on distribution networks is becoming necessary so that effective mitigation actions can be taken, and the PV penetration level can be increased. With such a background, this thesis aims at: developing a comprehensive and realistic assessment approach for the impact of solar PV on distribution networks, analysing the impact using the developed approach in real network environment with smart grid measurements, and proposing mitigation strategies for the particular problems identified above. First, this thesis has developed a comprehensive modelling and analysis approach for integrated medium voltage (MV) and multigrounded low voltage (LV) distribution networks for an accurate assessment of solar PV impact. Using this approach, PV integrated networks can be modelled by retaining their wiring configurations, such as 3- wire configurations for MV networks

This paper proposes the use of a common DC link in residential buildings to allow customers to inject their surplus power that otherwise would be limited due to AC power quality violation. The surplus power can easily be transferred to other phases and feeders through common DC link in order to maintain the balance between generated power and load. PSCAD-EMTDC platform is used to simulate and study the proposed approach. This paper suggests that this structure can be a pathway to the future DC power systems.

This paper addresses the voltage rise constraints that are initiated from increased renewable generation resources in low voltage distribution networks. In this paper, an approach which is able to mitigate these voltage rise constraints and allow for increased distributed generator penetration is presented. The proposed approach involves utilizing the distribution transformers static tap changer to reduce the distribution feeder voltage setpoint. The proposed approach is modeled on a generic low voltage distribution network using the PSS SINCAL© simulation software package and is also implemented in a real low voltage distribution network to verify its practicality. Results indicate that this approach can be implemented to mitigate the voltage rise constraint and increase small-scale embedded generator penetration in a high proportion of low voltage feeders while avoiding any substantial network costs.

Voltage rise and drop are the main power quality challenges in Low Voltage (LV) network with Renewable Energy (RE) generators. This paper proposes a new voltage support strategy based on coordination of multiple Distribution Static Synchronous Compensators (DSTATCOMs) using consensus algorithm. The study focuses on LV network with PV as the RE source for customers. The proposed approach applied to a typical residential LV network and its advantages are shown comparing with other voltage control strategies.

Often voltage rise along low voltage (LV) networks limits their capacity to accommodate more renewable energy (RE) sources. This paper proposes a robust and effective approach to coordinate customers' resources and control voltage rise in LV networks, where photovoltaics (PVs) are considered as the RE sources. The proposed coordination algorithm includes both localized and distributed control strategies. The localized strategy determines the value of PV inverter active and reactive power, while the distributed strategy coordinates customers' energy storage units (ESUs). To verify the effectiveness of proposed approach, a typical residential LV network is used and simulated in the PSCAD-EMTC platform.

Voltage rise is one of the main factors which limits the capacity of Low Voltage (LV) network to accommodate more Renewable Energy (RE) sources. This paper proposes a robust and effective approach to coordinate customers’ resources and manage voltage rise in residential LV networks. PV is considered as the customer RE source. The suggested coordination approach in this paper includes both localized control strategy, based on local measurement, and distributed control strategy based on consensus algorithm. This approach can completely avoid maximum permissible voltage limit violation. A typical residential LV network is used as the case study where the simulated results are shown to verify the effectiveness of the proposed approach.

In this paper surface discharge along the oil-pressboard interface was investigated. Surface discharges were measured both in time domain by means of an oscilloscope and as phase resolve patterns. The effect of temperature from 20°C to 90°C on surface discharge inception, extinction and surface flashover voltage were investigated. Trend of number and maximum magnitude of PD was compared for 20°C and 90°C over time. The effect of voltage rise and surface flashover on number and maximum magnitude of PD were investigated. The results show that PD inception voltage is lower for higher temperature but surface flashover voltage is higher for higher temperature. However for 90°C the final damage due to surface discharge is much severe compared to 20°C., QC 20121128

Admissible range of grid voltage is one of the strictest constraints for the penetration of distributed photovoltaic (PV) generators especially connection to low voltage (LV) public networks. Voltage limits are usually fulfilled either by network reinforcements or limiting of power injections from PVs. In order to increase PV penetration level further, new voltage support control functions for individual inverters are required. This paper investigates distributed reactive power regulation and active power curtailment strategies regarding the development of PV connection capacity by evaluation of reactive power efforts and requirement of minimum active power curtailment. Furthermore, a small scale experimental setup is built to reflect real grid interaction in the laboratory by achieving critical types of grid (weak and sufficiently stiff).