Data for Optimal Estimation of Under-Frequency Load Shedding Scheme Parameters by Considering Virtual Inertia Injection

: The data presented in this paper are related to the paper entitled “Optimal Estimation of Under-Frequency Load Shedding Scheme Parameters by Considering Virtual Inertia Injection”, available in the Energies journal. Here, data are included to show the results of an Under-Frequency Load Shedding (UFLS) scheme that considers the injection of virtual inertia by a VSC-HVDC link. The data obtained in six cases which were considered and analyzed are shown. In this paper, each case represents a different frequency response configuration in the event of generation loss, taking into account the presence or absence of a VSC-HVDC link, traditional and optimized UFLS schemes, as well as the injection of virtual inertia by the VSC-HVDC link. Data for each example contain the state of the relay, threshold, position in every delay, load shed, and relay configuration parameters. Data were obtained through Digsilent Power Factory and Python simulations. The purpose of this dataset is so that other researchers can reproduce the results reported in our paper.


Introduction
In electric power systems (EPSs), frequency serves as an indicator of the equilibrium between power generation and demand.Therefore, when generation exceeds demand, frequency tends to rise, signaling an abundance of available power; conversely, if demand surpasses generation, the frequency decreases, indicating strain on the system [1,2].Maintaining a stable frequency is essential for ensuring the reliability and efficiency of EPSs, as deviations from the standard frequency may lead to disruptions, equipment damage, or even blackouts [3,4].
Faults in EPSs represent critical disruptions that may severely compromise the balance between generation and demand, ultimately leading to unacceptable frequency deviations.When a fault occurs, it disrupts the normal flow of electricity within the system.As a consequence, the frequency of the system may deviate from its nominal value, reaching levels that are outside the acceptable range.A disruption may result in a sudden loss of generation; such is the case with faults that cause the frequency to reach the activation points of under-frequency relays in thermal generation units, compelling them to disconnect and exacerbating the imbalance to the extent of eventually triggering a blackout [3].
To prevent the frequency from reaching undesired values in the event of faults, Under-Frequency Load Shedding (UFLS) schemes that disconnect portions of loads when the frequency drops are used as a last-resort protection.Several researchers have focused their attention on UFLS schemes, specifically exploring the application of computational techniques for operational optimization.
For example, in [5], a multi-objective approach using Particle Swarm Optimization (PSO) is presented.This approach determines both the magnitude of load shedding and the delay for each load shedding stage.Alternatively, [6] presents an adaptive strategy that incorporates neural networks and examines the transient stability of the network.In [7], the authors employ a Genetic Algorithm (GA), with input neurons including total generation, total system load, hydro generation reserve, and RoCoF, to minimize load shedding.A UFLS scheme that minimizes load shedding by detecting frequency excursions is presented in [8].This is achieved using mixed-integer linear programming optimization and solved through several stochastic scenarios.In addition, [9] delves into the design of a fuzzy logic-based UFLS controller for a system operating in islanded mode with a single generator.The UFLS discussed in [10] operates on a neuro-fuzzy method, determining the amount of load to shed to avoid cascading outages.In [11], a UFLS scheme is presented to minimize load shedding using a grasshopper optimization algorithm, with a focus on low-frequency oscillations throughout all stages.
Several studies using mixed-integer linear programming for UFLS schemes are highlighted in [8,12,13], all of which are aimed at minimizing load shedding and guaranteeing system stability.Another proposal, described in [14], suggests a zoning mechanism based on static voltage stability using the Fisher-Jenks natural breaks algorithm.This zoning approach groups buses based on reactive power margin, and UFLS schemes are devised for each zone, taking into account their independent frequency response characteristics, in particular the rate of change of frequency (RoCoF).
Many of the aforementioned UFLS schemes simplify the problem configuration by setting the parameters of each UFR unit to be identical, without taking into account factors such as associated load and proximity to generation nodes, among others.This simplification results in inappropriate estimates of the load-shedding block, which could lead to incorrect frequency recoveries or, in some cases, over-frequencies.In contrast, the methodologies presented in [15,16] approach the optimization problem simplistically by ignoring several parameters of the UFLS scheme, focusing only on the amount of load shedding.This simplification limits the solution of the problem and may result in incorrect parameter estimates.Although [4] takes these parameters into account, the methodology does not provide an estimate of the UFR locations that could have the greatest impact on the behavior of the UFLS scheme.
The general inertia of EPSs has traditionally been linked to synchronous machines that release or store kinetic energy in their rolling masses in the event of unbalances.With the penetration of renewable energies and devices that use power electronics for their connection to the system, the general inertia decreases because these sources do not naturally store energy and therefore do not react to changes in operating conditions.However, it is possible to implement control schemes that modify the dynamics of the power electronics interfaces to react to changes in frequency.Thus, HVDC links can emulate the behavior of synchronous generators by reacting to power delivery based on different techniques such as RoCoF detection.However, these strategies modify the dynamic behavior of the power system, and it is necessary to develop UFLS schemes that consider inertia emulation by HVDC links.Thus, in [1], a study was presented in which a GA was used to determine each of the parameters of the UFLS scheme when considering the inertial response of the HVDC VSC links, but the configuration data and the results obtained were not included in detail.For the development of the simulations in which the data were used, the Digsilent Power Factory electrical systems simulation software version 2018 (Gomaringen, Germany) was used.The simulations consisted of load flows that served to determine the initial state of the system, and from this, dynamic simulations were performed to understand the behavior of the frequency in the event of an unbalance caused by the loss of a generator.
The proposed methodology was evaluated with the IEEE 39-bus system.For all the cases evaluated, the power unbalance is caused by the loss of generator 09 and the frequency behavior over time is determined.The set of case studies is made up as follows: Case 1 considers the 39-bus IEEE system without topological modifications.Case 2 considers the power injection by the HVDC VSC link; in this case, there is no control loop to emulate the inertia.Case 3 includes a non-optimized UFLS scheme, and the operation of the HVDC SVC link without inertia emulation is considered.Case 4 includes the non-optimized UFLS scheme and the HVDC VSC link with a control loop that allows it to emulate inertia.Case 5 considers an optimized UFLS scheme with an AG, and the operation of the HVDC VSC link without inertia emulation is considered.Finally, Case 6 considers the optimized UFLS scheme, the operation of the HVDC VSC link, and the activated inertia emulation control loop.The case studies are further developed and analyzed in depth in [1].Thus, the dataset published in this article includes the data used in the development of [1] and also includes the data corresponding to its results.
Electrical systems are sets of elements that by themselves have a variety of complexities in their sizing, modeling, control, and parameterization, so providing data in an open way for other researchers to access previous information helps research in this field of engineering to advance steadily.Thus, some researchers have chosen to publish data related to their research.Thus, in [17], a dataset containing measurements of electricity consumption in five houses located in the Lucerne region of Switzerland is described.In [18], a dataset and a procedure for the optimization of the charging configuration of electric vehicles in low-voltage grids are presented.The main purpose of [19] is the collection and structuring of spatio-temporal data from electrical networks for further processing and analysis.In [20], a dataset, a measurement platform for RGB images, and electrical data of a photovoltaic panel with different irradiation and shading conditions are presented.In [21], a study of distributed generator hosting capacity in an electric power distribution system on the campus of the University of São Paulo in Brazil is presented.Detailed information on the distribution system is provided, including the parameters of the cables and transformers used.A dataset including active and reactive power measurements under different load conditions is also presented.
This paper presents the configuration data of the IEEE 39-bus test system that was used for the evaluation of the frequency behavior under the loss of a generating unit.The case studies include a base case in which the operation of the power system with the HVDC VSC link and the UFLS scheme out of operation is considered.The other case studies evaluate the frequency response to different combinations of these elements.A GA was employed to determine the optimal configuration of the UFLS scheme, and these data are included as input to this work.Finally, both the configurations of the UFLS schemes evaluated in [1], and the frequency and time values with which the result curves were constructed are included.With the data provided, it is possible to make comparisons and replicate the work carried out in [1]; furthermore, other systems can be adapted to test the interaction of the proposed methodology.

Data Description
This section includes the data description developed in [1].The results are carefully organized for a better understanding of the document.Furthermore, the data are available in a public repository at https://zenodo.org/records/11371325(accessed on 5 June 2024).Please, take Table 1 as the basis for the data description.The dataset consists of four Excel files whose names and contents are described below: • File Grid_information.xlsx:This file contains the main parameters of the IEEE 39-bus network.In Sheet1, the value of each load is specified according to the connected bus.Sheet2 presents the parameters of the transmission lines, specifying the start and end bus, impedance values, and length.Sheet3 describes the main parameters of the transformers in the system, including nominal power value, voltage ratio, and shortcircuit impedance.Sheet4 displays the type of bus associated with the generator, the nominal apparent power value, and the dispatched active and reactive powers.• File Parameters_UFLS.xlsx:This file contains the parameters of each Under-Frequency Relay (UFR) that makes up the Under-Frequency Load Shedding (UFLS) scheme used in each of the study cases.Column 1 corresponds to the parameters of the UFLS scheme used in Case 1, column two presents the parameters of the UFLS scheme used in Case 2, and so on for Cases 3 through 6.To understand the parameters presented in the file, Table 1  .xlsx:This file contains the results of the simulated scenarios considering different system topologies and configurations.Six scenarios are considered, evaluating the response of the electric frequency in the power system to the loss of a generating unit.In Case 1, the system is considered without the operation of the HVDC VSC link, and the UFLS scheme is deactivated.In Case 2, the operation of the HVDC VSC link without inertia emulation is considered, and the UFLS scheme is deactivated.The resulting values for the simulations of Cases 1 and 2 are in Sheet1.
The first column corresponds to the simulation time in seconds, the second column corresponds to the frequency value reached in Case 1, and the third column corresponds to the frequency values reached in Case 2.
In Case 3, the system is considered with the operation of the HVDC VSC link without inertia emulation and a non-optimized UFLS scheme called traditional.In Case 4, the system is considered with the operation of the HVDC VSC link with inertia emulation and a non-optimized UFLS scheme.In Case 5, the operation of the HVDC VSC link without inertia emulation and the UFLS scheme optimized by the genetic algorithm are considered.In Case 6, the operation of the HVDC VSC link with inertia emulation and the UFLS scheme optimized by the genetic algorithm are considered.The results of Cases 3, 4, 5, and 6 are in Sheet2.The first column corresponds to the simulation time in seconds, the second column corresponds to the frequency values reached in Case 3, the third column corresponds to the frequency values reached in Case 4, the fourth column corresponds to the frequency values reached in Case 5, and finally, the fifth column corresponds to the frequency values reached in Case 6.
More detailed information about the study cases can be found in [1].

Methods
The model of the power grid was developed using the simulation software Digsilent Power Factory.The main parameters of the network are found in the file Grid_information.xlsx, as described earlier.
Dynamic simulation was conducted without the UFLS scheme or HVDC VSC link to observe the frequency behavior in response to the loss of a generating unit.The time and electrical frequency data were collected to obtain the results for Case 1.Following this, the HVDC VSC link was activated with the inertial control system deactivated, and the time and frequency data were collected to obtain the results for Case 2.
The non-optimized UFLS scheme was programmed using the characteristics presented in Table 2. Dynamic simulation was performed considering the operation of the traditional UFLS scheme and the HVDC VSC link, with the inertia emulation control turned off.The time and frequency results were collected for Case 3.For the simulation of Case 4, the previous scenario was used, the inertia emulation control was activated, and the time and frequency results were collected.The values of the optimized UFLS scheme were obtained using the simulation methodology shown in Figure 1.The steps comprising this procedure are described below:

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Step 1: A vector X is defined with the parameters of the candidate solution.

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Step 2: The space of possible values is defined for each of the genes of vector X.Thus, vectors X min and X max represent the limits of the parameters associated with the candidate solution.This information is found in the file Vmin_Vmax.xlsx.

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Step 3: The initial population is created by configuring individuals randomly.

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Step 4: The parameters of each individual are sent as configuration inputs for each of the UFR relays that make up the UFLS system implemented in DigSilent Power Factory.

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Step 5: The inertial response control of the HVDC VSC link is activated, and a load flow is executed to determine the total value of active power demanded by the system.• Step 6: The overall active power consumption of the system is transmitted to the Python GA. • Step 7: The initial conditions and dynamic simulation are run in DigSilent Power Factory, taking into account the frequency events defined in the dynamic simulation.The results of the frequency time series and the total value of active power demanded by the system after UFLS action are sent to the Python GA.

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Step 8: The objective function is evaluated by finding the difference between the total consumed active power values.If frequency violation values are evident in the frequency time series, the objective function takes a value that renders this individual unfeasible as a solution.

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Step 9: The selection tournament is conducted.• Step 10: The individuals selected in the selection tournament are crossed over.

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Step 11: A mutation is applied to the resulting individuals from the crossover.• Step 12: With the mutation included in the genes of the individuals, the new generation is ready to be evaluated.

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Step 13: If the stopping criteria are met, the algorithm stops, providing the solution.
Otherwise, the algorithm returns to Step 4 and repeats the cycle until the stopping criteria are met.Once the GA criteria are met and the Digilent Power Factory/Python co-simulation process is completed, a suboptimal solution to the problem of configuring the parameters of the UFR relays that make up the UFLS scheme is obtained.Dynamic simulation was performed considering the operation of the optimized UFLS scheme and the HVDC VSC link with the inertia emulation control turned off.The time and frequency results were collected for Case 5.For the simulation of Case 6, the configuration of the previous case was used, the inertia emulation control of the HVDC VSC link was activated, and the time and frequency results were collected.

Conclusions
This paper provides a comprehensive dataset obtained through simulations of an IEEE 39-bus test system, aimed at evaluating frequency behavior under the loss of a generating unit.This endeavor seeks to optimize Under-Frequency Load Shedding (UFLS) schemes in power systems, with a particular focus on considering the injection of virtual inertia by a Voltage Source Converter based a High-Voltage Direct Current (VSC-HVDC) link.The dataset considers base cases and variations incorporating different combinations of HVDC VSC link operation and UFLS scheme configurations.An optimization approach using a Genetic Algorithm (GA) was employed to determine the optimal UFLS scheme configurations.In each case, the frequency behavior was obtained with and without the injection of virtual inertia by the HVDC VSC link.
The dataset presented paves the way for further research aimed at enhancing the stability and resilience of power systems in the face of generation disturbances.By making the dataset available, this paper encourages reproducibility and facilitates future investigations in the field.Overall, it constitutes a significant contribution to the advancement of power system stability analysis and control strategies.

Figure 1 .
Figure 1.Co-simulation framework using Digsilent Power Factory/Python for the UFLS scheme.

Table 1 .
Position of optimized UFLS scheme parameters.
must be consulted, where the values from rows 1 to 19 (state [On/Off]) correspond to the state of each UFR.A value of 1 indicates the UFR is off (due to the logic of operation of the DigSILENT PowerFactory simulation software), while 0 indicates the device is on.Each UFR consists of six stages, each containing three parameters (threshold [Hz], delay [s], and shed load [%]).As shown in Table1, for UFR_3, the values between positions 20 and 25 correspond to the activation thresholds of each stage.Values between positions 26 and 31 represent the delay times between the activation of one stage and the next.Values between positions 32 and 37 correspond to the percentages of load shed in each of the six operation stages of the UFR.Thus, column one of Table1lists the name of each UFR.Column two represents the location in the Parameters_UFLS.xlsxfile of the states of each UFR (according to the study case).Columns three and four represent the location space of the six activation thresholds of each stage of each UFR.Columns five and six represent the position of the six delay times assigned to each stage in each UFR.Finally, columns seven and eight represent the locations of the six load percentage values corresponding to each stage of each UFR.•File Vmin_Vmax.xlsx:Toreducetheexecution times of the genetic algorithm and delimit the search space of the solutions, minimum and maximum values are set for each parameter of the UFRs in the UFLS scheme.This file contains the values of the search space for each parameter evaluated by the genetic algorithm.The first column corresponds to the minimum value each parameter can take, and the second column to the maximum value.The assignment of each location corresponds to those shown in Table1.•File Results