1.1 Research Motivation

Nowadays, with the expansion of control technologies and power electronics, the utilization of FACTS devices in the network is considered a suitable candidate for solving the challenges of network operation. Recently, the proposal to install this equipment around the world has increased compared to a few years ago, and also extensive studies for the installation and operation of this equipment in the research departments of regional power companies in different countries have escalated. Although the presence of this equipment is very desirable in terms of operation, stability and dynamics, reactive power control, loss reduction, congestion management, reliability, and so on, challenges arise due to the presence of this equipment in the network. One of those challenges is the protection of this equipment and the transmission lines in which this equipment is installed. Analyzing the behavior of these equipment in fault conditions is considered one of the basic challenges in various protection problems. When a fault occurs in the transmission line, the behavior and performance mode of this equipment during the fault cannot be predicted under any conditions because of the divergence of the control system. Thus, the prediction and estimation of the behavior of this equipment is considered the main challenge of this paper.

1.2 Literature Review

So far, various issues of design, modeling, and different applications of UIPC have been discussed in various articles and reports. This equipment was proposed for the first time by Qarehpetian et al. in 2012 to improve the performance of IPC [1]. After the publication of [1], due to the benefits and very suitable efficiency of IPC, it quickly attracted the attention of researchers and scholars of the electrical industry and a vast amount of research was published with the main focus of using this equipment. A comparison between the performance of basic IPC and UIPC in various operating conditions based on relationships and mathematical analyses is provided in [2, 3]. The results presented in these references show that UIPC can achieve diverse values of the desired current transfer for voltage angles. In [4-9], in general, the problem of UIPC influence on active and reactive power control of wind and photovoltaic renewable generations, improvement of LVTR capability mode, increase of transient stability margin, and damping of generator output oscillations have been discussed. In [4-6], the WF connection scheme based on FSWT provides the power system through UIPC to improve the transient stability. The direct connection of WFs to the power system suffers from two aspects: the uncontrollable flow of active and reactive power, as well as the influence of the state of the power system on the operation of the WF. Connecting the WF to the power system via UIPC assists in controlling the power flow and isolating the WF from the system. The UIPC control scheme proposed in these references contains control loops for active and reactive power flow. The reactive power loop injects the reactive power so that the voltage of connection point is restored according to the LVRT specification and it controls the active power injected by the WF to the power system by controlling the active power control loop, which helps the stability of the WF. By adding the modified control system, the output power fluctuation and the rotor speed fluctuation of the adjacent synchronous generators are effectively damped. In continuation of the discussion of improving the stability of the generator, the plan of using UIPC for the purpose of protecting synchronous generator in the event of a fault is presented in [7]. It is shown in this reference that The UIPC system ensures generator stability by regulating the load angle to stay within safe operating limits and inhibits the occurrence of high-amplitude currents in the stator windings. According to the results presented in this reference under several fault conditions, it shows that UIPC disconnects the generator from the fault location. This not only accelerates the stabilization of the generator's load angle but also enhances the efficiency of limiting its swing magnitude. This feature enhances the stability margin of the generator, allowing the system to operate near its maximum capacity without compromising system stability. In addition, it is shown in this reference that the use of UIPC boosts the LVRT capability of the generator. In another study, the plan of using UIPC and supercapacitor to solve the remaining challenges in the literature, including the issue of damping the generator output power fluctuations and also generator performance in dynamic transient conditions, has been proposed [8]. To reach this goal, a new power control design is presented to deal with output power oscillations. The validity of the proposed scheme in smoothing the output power of the wind power plant and also enhancing the LVRT capability has been shown in the output results of this reference. In the continuation of the proposed studies, by taking advantage of the performance of UIPC in improving the LVRT mode, the plan of using this equipment in a multi-machine power system equipped with a photovoltaic system in a power system has been reviewed by researchers [9]. In addition to wind generation, large-scale inverter-based photovoltaic generation causes the phenomenon of LVRT and imposes inertia with different time constants compared to generations based on rotating machines, which differentiates this reference from previous research that was based on WF. In another group of studies, the utilization of UIPC has been proposed to improve the performance of AC-DC MGs from different aspects [10-18]. The power flow control scheme of AC-DC MGs linked to the grid-connected hybrid MGs using modified UIPC is presented by Gharehpetian et al. [10, 11]. This new development considered has one power converter called LPC for each of the phases and one power converter called BPC to adjust the DC-bus voltage. A fuzzy logic controller is used in the control system of LPCs in these studies and the fuzzy inference system based on the H_∞ filter method is optimized to diminish errors that appear when designing the membership functions. In relation to the BPC, DC MGs provide the DC voltage of LPCs, and to stabilize DC bridge oscillations, a new robust multilevel sliding mode control strategy using the nonlinear disturbance observer is discussed in these studies to control the DC side of the BPC. In the continuation of the studies, other control schemes such as fractional-order PI control [12] and ANFIS [13, 14] were presented to use UIPC in AC and DC hybrid MGs to achieve the optimal control and power flow. In [15], an adaptive control scheme of reference model UIPC is presented in hybrid MGs in island mode with the presence of flexible loads and energy storages. This reference presents the development of a novel control design for UIPC, which is based on the concept of adaptive control of the reference model. The harmonic-oriented modeling technique has been employed to simulate the DC-side power converter in order to streamline the control design process. In other complementary studies related to this field, a UIPC controller DC-link robust control scheme based on a quasi-Levenberg observer for flexible control of power exchange in hybrid MGs with heterogeneous structures is presented [16]. This reference discusses a nonlinear dynamic modeling of the modified model DC-link of the UIPC with an observer-based DC-link control scheme and proposes a quasi-Levenberg observer to predict DC-link dynamics. This controller eliminates the redundant metering links that are essential in conventional DC-link control schemes and further boosts the Plug-And-Play feature for MGs. Then, the estimated modes are realized in a robust sliding mode controller that reduces the disturbances' effect on dynamics of the DC-link and controls the DC-side power converter of the UIPC. Finally, in the recent studies published in this field, to control power fluctuations, voltage, frequency, and optimal power flow in hybrid MGs with the presence of controllable loads, quasi-affine optimal control schemes [17] and sliding mode control [18] were proposed and evaluated by Gharehpetian et al. In another group of studies, the UIPC's impact on other issues including distance protection, state estimation, and transmission network development planning is presented [19-22]. In [19], the performance of distance relays in UIPC-compensated transmission lines is shown based on the analysis of faulty network impedance equations for different faults. According to the simulation results, as the UIPC can limit the fault current when the fault occurs in the area beyond the UIPC, the relay will experience a reduction in the protection area during the impedance measurement, and its effect is much more destructive than the case where the fault is near the UIPC. In [21, 22], a power flow control and state estimation approach for the power system equipped with UIPC is presented using the weighted least squares algorithm and the maximum absolute magnitude of the spanning tree. The methods presented in these references have reduced the calculation time and simplified the state estimation for UIPC by providing a new formulation and using fewer variables. The transmission network of a robust multi-period model for TEP is presented as a bilevel optimization problem in the presence of UIPC to reduce the level of short circuits [22]. UIPC modeling in the multi-cycle TEP problem considered in this reference reduces the capacity and rating of circuit breakers, enhances flexibility, and reduces investment and operation costs. The lower-level optimization problem describes UIPCs using a centralized mechanism within a pooled power market to operate the power system optimally in all cases. A powerful symphonic orchestra search algorithm was used to address the large-scale mixed-integer nonlinear bilevel model. According to the review of references, no reference has specifically addressed the problem of estimating current and voltage phasors of UIPC's series and parallel converters so far. According to the prominent features of this equipment, its use is considered very favorable for improving network performance and especially microgrid control. The problem of estimating the current and voltage phasors of the converters of this equipment at the time of short-circuit fault, as the necessary parameters for formulating the distance relay equations based on the information of the current and voltage phasors measured by the protective CT and CVT of the distance relay, has been proposed as the basic challenge of this article. In general, a parameter estimation problem can be divided into three basic categories, (1) methods based on statistical techniques [23-28], (2) methods based on physical techniques [29], and (3) methods based on training techniques [30-34]. According to the classification presented in different references, the methods presented in each technique and category can be further divided. The first category (statistical methods): Markov chain [23], hidden Markov [24], Kalman filter [25], Gaussian process [26], Bayesian network [27], and Gaussian process regression [28]. The second category (methods physical): spatial correlation [29]. The third category (training methods): feed-forward neural networks [30], radial basis neural networks [31], support vector machine regression [32], logistic regression [33], and nearest neighbor [34]. The main purpose of these tools is to estimate a set of unknown parameters based on a set of known parameters. Each of these categories includes different techniques that are very efficient for prediction and estimation in a specific problem. In this article, to estimate the necessary parameters, the training-based technique and the feed-forward neural network method are used, and finally, the obtained results are compared and evaluated with those of the radial basis neural network method.

1.3 Research Necessity and Literature's Research Challenges

In case of faults occurring on transmission lines, distance relays protect the faulty line by estimating the impedance of the fault location matching it with the set zoning of the relay itself, and issuing a command to disconnect the breakers at the beginning of the line according to the timing defined for them. The projected equations of the distance relays are established using the symmetrical components of the current and voltage measured by the protective CT and CVT connected to the relay and the line parameters under protection. In these studies, UIPC equipment is considered in the middle of the line. This equipment is placed in series–parallel in a transmission line, and it includes two series VSCs in the line in terms of topology, which are installed in parallel, and also includes a parallel VSC linked to the common bus of the two series converters.

Therefore, according to the mentioned topology, if the distance protection equations of the desired line are planned, the effect of the series and parallel converters of the UIPC equipment will be included in the equations of the distance protection plan and cause deviations in estimating the impedance of the fault location. This aspect has not been addressed in any previous studies on this problem. Reference [19] is the sole article addressing the impact of UIPC on distance protection, highlighting solely the detrimental effects of this equipment on the formulation of distance relays without proposing a solution to this issue. In light of the issues associated with power transmission in power system operations, the utilization of FACTS devices is progressively rising. Their utilization and enhancement of network flexibility are the most viable solutions for addressing the power management issue in the power network. This study proposes the utilization of an phasor estimator for UIPC converters to address the challenges associated with distance relay protection in lines equipped with UIPC.

1.4 Contributions and Novelty

In this article, a scheme for estimating the sequence current and voltage phasor of 72-pulse UIPC voltage source converters at the time of short-circuit fault in transmission lines is presented. Among the prominent points of the proposed design is that there is no need to design and update the new formulation of the distance relay and it can work with the same initial format and the unknown parameters are considered as input. The approach suggested in this research adopts artificial neural network trained to estimate phasors. To implement this model, different scenarios of short circuits in the transmission lines on both sides of the UIPC have been used for different locations, in different phases, for different resistances, and at different times. The input data of this network are in the form of 12 vectors, and these 12 inputs include the size and phase angle of the symmetrical components of voltage and current of all three phases measured by the relay. The output data is a 12 vector, which includes the size and phasor angle of the symmetrical current and voltage components of all three phases of a series voltage source equivalent circuit and a parallel current source equivalent circuit. A total of 3660 fault scenarios have been used for FFN training and modeling in this article. Network modeling under study is implemented in Simulink/MATLAB software and the desired network program is coded in a MATLAB M-file.

1.5 Paper Organization

This article comprises seven general sections. The UIPC-based system is elucidated in Section 2. Section 3 examines and evaluates the impact of UIPC on the distance relay formulation. In Section 4, the theory of the proposed method is defined in three subsets. This section initially introduces the network under investigation, subsequently derives the artificial neural network model for phasor estimation, and concludes with a flowchart of the proposed methodology. Section 5 presents the testing and evaluation of various fault scenarios. Section 6 presents the results of the comparison of the suggested method utilizing two solvers, while Section 7 provides the article's conclusion.

4.1 Introducing the Network Under Study

4.2 Extracting the Model of an Artificial Neural Network for Phasor Estimation

4.2.2 ANN Implementation and Model Extraction

Neural networks are mathematical structures composed of interconnected neurons that mimic the process that humans use to make predictions and estimates in various problems such as pattern recognition, data analysis, and modeling, given the training they receive. There are various kinds of neural networks, which are characterized by the number of neurons and different learning processes. One of these types is the feedforward neural network, which is used for estimation in this article. According to Figure 7, the proposed neural network has three layers: an input layer with 12 neurons, a hidden layer with 12 neurons, and an output layer with 1 neuron. Each neuron in the hidden layer has its weights and biases that are adjusted during the training process. The outputs of the hidden layer neurons are combined with the new weights and biases, and the final output of the network is found through the Purelin linear activation function. This neural network is used for the fitting problem, and its purpose is to predict and estimate the outputs based on the given inputs. The necessary formulation for training the feedforward neural network is provided in Equation (13).

$$$$ \left\{\begin{array}{ll}\ \mathrm{X}={\left[{\mathrm{x}}_1,{\mathrm{x}}_2,\dots, {\mathrm{x}}_{12}\right]}^{\mathrm{T}}& \kern1em \mathbf{Input}\ \mathbf{Layer}\\ {}\begin{array}{l}\kern1em \mathrm{Input}\ \mathrm{to}\ \mathrm{Neuron}\ \mathrm{j}:\\ {}\kern1em {\mathrm{z}}_{\mathrm{j}}=\sum \limits_{\mathrm{i}=1}^{12}{\mathrm{w}}_{\mathrm{j}\mathrm{i}}{\mathrm{x}}_{\mathrm{i}}+{\mathrm{b}}_{\mathrm{j}}\\ {}\ \mathrm{The}\ \mathrm{Output}\ \mathrm{of}\ \mathrm{Neuron}\ \mathrm{j}\\ {}\kern1em \mathrm{using}\ \mathrm{the}\ \mathrm{hyperbolic}\ \mathrm{tangent}\\ {}\kern1em \mathrm{activation}\ \mathrm{function}:\\ {}\kern1em {\mathrm{a}}_{\mathrm{j}}=\tanh \left({\mathrm{z}}_{\mathrm{j}}\right)=\frac{{\mathrm{e}}^{{\mathrm{z}}_{\mathrm{j}}}-{\mathrm{e}}^{-{\mathrm{z}}_{\mathrm{j}}}}{{\mathrm{e}}^{{\mathrm{z}}_{\mathrm{j}}}+{\mathrm{e}}^{-{\mathrm{z}}_{\mathrm{j}}}}\end{array}& \kern1em \mathbf{Hidden}\ \mathbf{Layer}\\ {}\begin{array}{l}\mathrm{Network}\ \mathrm{Output}:\\ {}y=\sum \limits_{\mathrm{j}=1}^{12}{\mathrm{w}}_{\mathrm{k}\mathrm{j}}{\mathrm{a}}_{\mathrm{j}}+{\mathrm{b}}_{\mathrm{k}}\\ {}\mathrm{The}\ \mathrm{output}\ \mathrm{activation}\\ {}\mathrm{f}\mathrm{unction}\ \mathrm{purelin}\ \mathrm{is}\\ {}\kern1.5em \mathrm{applied}\ \mathrm{directly}\ \mathrm{to}\ \mathrm{y}:\\ {}\mathrm{f}\ \left(\mathrm{y}\right)=\mathrm{y}\end{array}& \kern1em \mathbf{Outeput}\ \mathbf{Layer}\end{array}\kern1.25em \right. $$$$ (13)

After training the desired FFN network model, information about its settings for software and hardware implementation is obtained. The desired network information obtained in this article is given in Table 2. Using this information, it is possible to implement the desired FFN without the need for training and test data information.

TABLE 2. Data related to settings of the FFN for implementation on the software model.

Code written in MATLAB
Parameter	Description	Value
Data loading	The data contains 3660 rows including samples and 24 columns, the first 12 columns are the features and the remaining 12 columns are labels, i.e. outputs	AA = 3660 × 24
Data normalization	Data normalization formula (data normalization to the range [−1,1])	((AA—min(AA))./(max(AA)—min (AA))) × 2–1
Data dimensions for neural network	In each step, only one label (output) is estimated according to the input	Inputs  =3660 × 12 Outputs = 3660 × 1
Network creation function	The function is used to create the network	Fitnet (hiddenLayerSize)
Input layer	The primary layer that receives the input data	Number of input layers = 1
Input neurons	The number of input neurons (equal to the number of features)	12
Hidden layers	Intermediate layers between input and output layers	Number of hidden layers =1
Hidden layer activation function	Hyperbolic tangent (tansing)	disp ([‘Hidden Layer Activation Function:’, net. layers {1}. transferFcn])
Hidden layer neurons	The number of hidden layer neurons	12
Output neurons	The number of output neurons	1
Output layer activator function	Pureline	disp ([‘Output Layer Activation Function:’, net. layers {2}. transferFcn])
Input preprocessing functions	Preprocessing functions for inputs	{‘removeconstantrows’, ‘mapminmax’}
Output preprocessing functions	Preprocessing functions for outputs	{‘removeconstantrows’, ‘mapminmax’}
Data division function	All data divider function	‘dividerand’
Data sharing mode	All data divider mode	‘sample’
Training data ratio	Proportion of data allocated to training	80%
Validation data ratio	Proportion of data allocated to validation	10%
Test data ratios	Proportion of data allocated to testing	10%
Training function	The function used to train the network (Levenberg–Marquardt)	‘trainlm’
Performance function	Network performance function	‘mse’
Graph drawing functions	Functions used to draw performance analysis graphs	{‘plotperform’, ‘ploterrhist’, ‘plotfit’, ‘plotregression’}
Network save file	The name of the saved file of the trained network	fitnet.mat
Outputs return formula	Formula to restore outputs from normalized state to original values	(((outputs +1)/2) × (max (AA (: 13)) − min (AA (: 13)))) + min (AA (: 13))
Error and performance	Formula for calculating errors and network performance	gsubtract (targets_new, outputs_new), perform (net, targets_new, outputs_new)

4.2.3 Output Results of the Suggested Model

The purpose of this subsection is to test and evaluate the final FFN. At this stage, the proposed neural network has predicted 12 outputs. Based on 12 input characteristics, each output is individually predicted. These predictions have been evaluated using statistical criteria. RMSE, MSE, R, StD, ME, and regression indices can be used to evaluate and compare the results. Equations (14-19) can be adopted to describe the mentioned indicators quantitatively. The graphical results of these evaluations based on the equations presented are given in Figure 8. According to the results obtained, as can be seen, the accuracy of the proposed method in both training and testing data is very high. The accuracy in estimating values based on the extracted model based on training the FFN model to solve this challenge is considered very desirable.

$$$$ \mathrm{RMSE}=\sqrt{\frac{1}{n}\sum \limits_{i=1}^n{\left({y}_{i-}{\hat{y}}_i\right)}^2} $$$$ (14)

$$$$ \mathrm{MSE}=\frac{1}{n}\sum \limits_{i=1}^n{\left({y}_i-{\hat{y}}_i\right)}^2 $$$$ (15)

$$$$ \mathrm{R}=\frac{\sum \limits_{i=1}^n\left({y}_i-{\overline{y}}_i\right)\left({\hat{y}}_i-\overline{\hat{y}}\right)}{\sqrt{\sum \limits_{i=1}^n\Big({y}_i}-\overline{y}\Big){}^2\sum \limits_{i=1}^n{\left({\hat{y}}_i-\overline{\hat{y}}\right)}^2} $$$$ (16)

$$$$ StD=\sqrt{\frac{1}{n-1}\sum \limits_{i=1}^n\Big(\left({y}_i-{\hat{y}}_i\right)-\overline{e}}\Big){}^2\kern2.25em \mathrm{Where}\ \overline{e}=\frac{1}{n}\sum \limits_{i=1}^n\left({y}_i-{\hat{y}}_i\right) $$$$ (17)

$$$$ \mathrm{ME}=\frac{1}{n}\sum \limits_{i=1}^n\left({y}_i-{\hat{y}}_i\right) $$$$ (18)

$$$$ \mathrm{Output}=b\times \mathrm{target}+a $$$$ (19)

Table 3 tabulates the information on the results of the FFN training and testing for all 12 intended outputs.

TABLE 3. Output results of training and testing the FFN for all 12 output parameters.

Results	Iteration	Time	Performance	Gradient	Error	Validation
$$$ {FFN}_1 $$$	1000	0:00:17	2.58e-10	3.77e-6	e-8	0
$$$ {FFN}_2 $$$	134	0:00:02	0.00373	0.0174	e-5	6
$$$ {FFN}_3 $$$	594	0:00:09	1.81e-5	0.000123	e-7	6
$$$ {FFN}_4 $$$	52	0:00:01	0.00160	0.00676	e-5	6
$$$ {FFN}_5 $$$	256	0:00:04	5.86e-5	0.000556	e-7	6
$$$ {FFN}_6 $$$	48	0:00:01	0.0306	0.0138	0.000100	6
$$$ {FFN}_7 $$$	490	0:00:08	8.49e-5	0.000950	e-8	6
$$$ {FFN}_8 $$$	41	0:00:01	0.0292	0.0223	e-5	6
$$$ {FFN}_9 $$$	39	0:00:01	0.00814	0.00329	e-5	6
$$$ {FFN}_{10} $$$	36	0:00:01	0.0253	0.0309	0.000100	6
$$$ {FFN}_{11} $$$	1000	0:00:15	2.43e-7	4.31e-7	e-8	6
$$$ {FFN}_{12} $$$	21	0:00:00	0.0559	0.123	e-6	6

4.3 Final Flowchart of the Proposed Method

Figure 9 displays the complete flowchart of FFN training steps. Based on the provided flowchart, all training and testing steps as well as output results for 12 parameters are given.

5.1 Evaluation of Usual Fault Scenarios

In this part, the goal is to test and evaluate the designed algorithm in a simulated network. For implementation, the network presented in Figure 5 has been used. To test and evaluate the proposed algorithm, 10 different scenarios have been used. To ensure the performance of this proposed plan, these 10 scenarios considered in the neural network training and testing database have not been included. The results presented in Table 4, fault scenarios, show the values recorded by the PMUs at the bus A location. As can be seen in the table, the measured values in bus A are given as the input of the proposed model and the estimation results for 12 output parameters of the model, which include the magnitude and angle of voltage and current of the UIPC converters, are calculated. Each parameter's estimation error is also shown. As can be seen, the accuracy of the proposed estimation method is very suitable at the time of occurrence of any type of short-circuit fault with a variety of changeable parameters. The proposed method in this paper, for the first time, uses the idea of estimating the parameters of the FACTS devices to solve the distance relay challenge. The method includes an expandable compensator for various types of networks.

5.2 Sensitivity Analysis

In this part, the goal is to investigate the sensitivity of the suggested algorithm to seven critical scenarios. The conditions of these seven scenarios are given in Table 5. The estimation error results of 12 output parameters are listed in this table. Figure 10 shows the estimation error of ±0 sequence voltage and current phasors of UIPC's converters for seven error scenarios. According to the obtained results, the average parameter estimation error for scenarios S2 and S7 are the lowest and highest values of this sensitivity analysis, respectively. As can be seen, the proposed method can be developed with very good accuracy in various critical conditions because it uses FFN and does not require special adjustments. The robustness of the proposed method with respect to the proposed sensitivities indicates the successful performance of the proposed method.