An ANN-Based Method for On-Load Tap Changer Control in LV Networks with a Large Share of Photovoltaics—Comparative Analysis

Abstract

The paper proposes a new local method of controlling the on-load tap changer (OLTC) of a transformer to mitigate negative voltage phenomena in low-voltage (LV) networks with a high penetration of photovoltaic (PV) installations. The essence of the method is the use of the load compensation (LC) function with settings determined via artificial neural network (ANN) algorithms. The proposed method was compared with other selected local methods recommended in European regulations, in particular with those currently required by Polish distribution system operators (DSOs). Comparative studies were performed using the model of the 116-bus IEEE test network, taking into account the unbalance in the network and the voltage variation on the medium voltage (MV) side.

1. Introduction

In recent years, most European countries have fundamentally changed their approach to the methods and sources of electricity generation, gradually reducing the share of high-emission sources in favor of renewable energy sources. There have also been changes in the entire power generation sector—replacing centralized systems with distributed ones in which the operation of power plants is supported by small energy sources installed close to customers. These changes can be seen in, among other things, the increasing number of prosumer sources installed in households and connected to the low-voltage grid. The vast majority of energy sources operating in LV networks are photovoltaic installations. However, the increasing share of photovoltaics in distribution networks is the cause of undesirable phenomena in the network, mainly problems with too-high voltage during peak hours of generation from solar panels [1,2].

Many publications have discussed the methods of reducing the negative impact of PV sources on voltage in a low-voltage network. These methods can be divided into local, decentralized and centralized categories [3,4]. These groups differ, among others, in the necessary communication range and the degree of coordination of individual elements of the control system.

Local methods do not require communication infrastructure; they are based only on values measured locally, at the place of installation. Thanks to this, they are fast and reliable, and they do not require large initial financial outlays. The disadvantage of local methods is the lack of the possibility of coordinating the operation of the network.

Local methods include the autonomous control of PV installation using its own inverters by selecting a predefined operating mode. As a result, control is achieved by reactive power consumption/generation (e.g., in standard modes: Q(V), cosφ(P) or cosφ fixed) or by limiting the generated active power (e.g., in P(V) mode). In Q(V) mode, the current value of the inverter’s reactive power depends on the voltage measured at the point of common coupling (PCC). In cosφ(P) mode, when the PV source exceeds the set threshold of generated active power, the inverter starts to draw reactive power from the network, reducing the cosφ factor. This mode operates independently of the voltage value measured at the PCC, which means the consumption of reactive power at a given moment may be unjustified or even inadvisable. On the other hand, in the situation of too-high voltage in the network, the cosφ(P) mode often turns out to be more effective than Q(V) because a larger number of inverters in the network draw reactive power, affecting the voltage value. The mode with a constant value of the power factor, cosφ fixed, also has similar properties to cosφ(P). In this mode, the power factor is imposed from above, and its value does not depend on either the voltage or the generated power. This results in the least flexibility of all modes and usually the largest reactive power flows. The last of the standard modes, P(V), is a mode of limiting the generated active power as a function of an increasing voltage. Studies considering various aspects of predefined inverter operation modes and comparative analyses for different network configurations can be found in [3,4,5,6,7]. Combined inverter operation modes are also considered in publications. They can be based, for example, on simultaneous active and reactive power control (Q(V) + P(V) [8,9], cosφ(P) + P(V) [8]), or they can combine the properties of different reactive power control modes (cosφ(P, V) mode [10]).

Local strategies also include methods using an on-load tap changer. In [11,12], an OLTC control algorithm based on reactive power measurement was developed. In [13], a method based on estimating voltages in distant points of the network, using time-series Monte Carlo analysis, was proposed. In [14], solar radiation data were used to select the OLTC position. In [15,16], the results of the method combining OLTC operation with the Q(V) mode of inverters were presented. In [16], an OLTC operation allowing for independent voltage control in each phase was additionally proposed.

Relatively new and technically advanced solutions can also be used as local means of mitigating negative voltage phenomena, including, e.g., line voltage regulators (LVRs), hybrid distribution transformers [17] and static compensators (STATCOM, SVC). The obvious disadvantage of these solutions is their high cost and the associated low implementation potential. In [18], the use of LVR allowed for increasing the PV hosting capacity by both minimizing overvoltages and reducing voltage unbalance in the network. In [19,20], a combination of LVR with an inductive voltage divider implemented on magnetically controlled inductors (MCIs) was proposed, which ensures the continuous and uninterrupted operation of the regulator. In [21], very good results for the use of STATCOM were demonstrated, including the elimination of problems with large voltage changes in generation and load peaks, the speed of operation and a reduction in voltage unbalance. The authors of [22] proposed a new compensator design, ensuring, among other things, the ability to shape the injected current waveforms, as well as the ability to absorb and generate active and reactive power and limit higher-current harmonics.

The next group of voltage control methods is centralized methods. They enable the full coordination of network operation, thanks to an appropriately developed communication structure and a hierarchical control system. This system collects measurement data from many points in the network and uses it to manage the connected sources, loads and control devices. The group of centralized methods ensures the highest level of network optimization, but at the cost of high requirements for the level of component automation and the expansion of telecommunications infrastructure. Processing information at so many levels can also introduce delays in the control process. An example of a centralized control system is the microgrid central energy management system (MCEMS) described in [23], which relies on a day-ahead operational planning and an online adjustment procedure during operation. Another example is the active network management system (ANM), the concept of which is described in [24]. The ANM system controls the output of distributed generation in real time, managing voltages at constraint points within the network. This system has been deployed to facilitate the connection of 200 kW of generation in the LV network in the UK. In [25], another centralized system is described, based on the cooperation of sensors distributed in the network and smart meters with controllers placed in MV/LV stations, from where the data are transmitted to the network operator.

Decentralized voltage control methods combine the features of local and centralized methods. The main idea of decentralized control is the partial coordination of groups of automated network components, but without control from the system operator center. As in the case of centralized strategies, in these methods, it is necessary to ensure communication between selected network elements. Examples of decentralized methods can be found in [26,27,28,29]. The basic assumption of the decentralized method described in [26] is the cooperation of the inverter with the PV installation controller, which can operate in five modes, differing in the method of controlling the output active and reactive power. A similar method of voltage control is presented in [27]. In addition to controlling the active and reactive power of the inverter, energy storages were also introduced here, which are intended to regulate the voltage value in the network. The method is based on local voltage measurement, and the communication implemented as power-line communication (PLC) is used to send information about the voltage increase to other controllers located in neighboring nodes. The use of energy storage was also proposed in [28]. Controllers monitoring the state of charge of energy storage receive commands from the master controller, which also controls the operation of the OLTC of the transformer installed in the network. In [29], a method was proposed to control a larger group of PV sources in such a way as to obtain the same ratio of output power—reactive and active—to the maximum power for each of them. In the described method, a data exchange between neighboring PV sources is required, but these data are not provided continuously, thus simplifying the communication.

Of the many methods considered in this research, only a few have entered into wide use. One of the most important documents for EU member states concerning distributed energy sources is Commission Regulation (EU) 2016/631 of 14 April 2016, establishing a network code on requirements for the grid connection of generators (NC RfG—Network Code Requirements for Generators) [30]. However, the NC RfG focuses on those requirements that are of particular importance in the connections between the power systems of individual European countries (e.g., frequency stability). The regulation lacks requirements for the management of the distribution network with connected energy sources, including voltage regulation methods. These issues are governed by the regulations of individual countries. These, in turn, are based on the European standard EN 50549-1:2019 Requirements for generating plants to be connected in parallel with distribution networks [31]. In terms of voltage control, the standard recommends equipping the generating installation with Q fixed, Q(V), cosφ fixed and cosφ(P) modes. In order to avoid a disconnection of the energy source caused by overvoltage protection, the standard recommends reducing the active power generation as a function of the increasing voltage. Both in the reactive power and active power control modes, as well as in the selection of settings and the method of operation of overvoltage protection, the EN 50549 standard leaves a lot of freedom to the DSOs of individual countries.

In Polish regulations (e.g., [32]), the recommended operating mode of the inverter is the reactive power control mode as a function of the voltage at the PCC (Q(V) mode). The remaining modes (cosφ fixed and cosφ(P)) are defined as additional. The Q(V) mode cannot cause the cosφ value of 0.9 (inductive/capacitive) to be exceeded. Although the DSO regulations recommend activating the generated power limitation mode when the Q(V) control capabilities are exhausted, imposing such restrictions on prosumers currently has no legal basis. The final measure to counteract excessive voltage levels is two-stage overvoltage protection. The first stage operates with a delay, with a threshold of 1.1 V_n, and responds to the 10-min mean voltage value. The second stage is to immediately switch off the photovoltaic installation when the voltage at the connection point exceeds 1.15 V_n.

As experience from several years shows, the methods currently implemented are ineffective in networks with a large share of photovoltaics, and prosumers report frequent disconnections of inverters due to excessively high voltage [33,34]. However, the implementation of more effective methods is associated with large-scale investments related to, for example, network modernization, the installation of additional regulating devices, as well as the implementation, testing and operation of complex control systems. The lack of readiness to bear such costs results in a top-down limitation to the number of sources connected to the low-voltage network by introducing less favorable billing systems for prosumers or limiting support programs.

This research proposes a voltage regulation method based on the use of an on-load tap changer with a load compensation (LC) function in an MV/LV transformer station. The innovative approach seeks to determine the load compensation settings using an artificial neural network. This solution can be classified as a local method, based only on measurements performed in the MV/LV station. It is a simple and reliable method that does not require a real-time data exchange between any devices in the network. The proposed method has demonstrated high effectiveness in preventing overvoltage while, at the same time, achieving good results in terms of limiting reactive power flows and the level of energy losses in the network. The authors are aware of the fact that OLTC is not commonly used in low-voltage networks [35,36]. It is worth noting, however, that the increase in the number of renewable energy sources forces network operators to undertake investment activities that improve the quality of the supplied power energy. One such investment may be the replacement of fixed-ratio transformers with OLTC transformers. The differences in the costs of a fixed-ratio transformer and an OLTC transformer are not so high at present, and the scale effect in implementations covering a larger number of networks will certainly reduce these costs further. In addition, OLTCs are commonly used in higher-voltage networks, making the solution well-known and widely tested, so its implementation and operation in LV networks should not pose any difficulties.

The major contributions of this paper can be highlighted as follows:

• Simulation models for overvoltage protection of the PV inverter according to EN 50549, as well as models for the Q(V) mode of the inverter, were developed. These models allow for the performance of dynamic and quasi-dynamic simulations using the PowerFactory software (2024 version).
• An original, ANN-based method for determining load compensation settings in the OLTC of a distribution transformer was developed.
• The proposed method was tested in a 116-bus IEEE test network with different voltage levels on the MV side while the asymmetry of sources and loads was taken into account. The method was compared with other selected local methods: cosφ fixed, Q(V) and Q(V) + P(V) modes.

The rest of the paper is structured as follows. Section 2 describes the basic research assumptions and simulation models. Section 3 presents the basics of the author’s ANN-based OLTC control method. Section 4 presents the research results in the form of daily voltage curves and other quantities characterizing the network operation under different control strategies. Quantitative data are also presented. Section 5 contains a summary and conclusions.

2. Simulation Models

In this section, a model of a 116-bus IEEE low-voltage test network, additionally extended with connected PV sources, is presented. In addition, DSL and QDSL (DIgSILENT Simulation Language and Quasi-Dynamic Simulation Language) models are presented, enabling simulation implementation of the PV inverter and OLTC control strategy in the DIgSILENT PowerFactory software.

2.1. Test Network Model

The IEEE European low-voltage test feeder model was used in the study, from which the data and basic assumptions were derived [37,38]. The network diagram is presented in Figure 1. The network consists of 115 lines (of various lengths and cross-sections) supplied from an 800 kVA MV/LV transformer. Customers are connected to 55 network buses, for which separate load profiles were loaded in the form of 24-h active power waveforms (data with a resolution of 1 min.) at a constant power factor cosφ = 0.95 (inductive). All customers are connected in a single-phase manner. The detailed data needed to build the model, including parameters of individual line sections and load profiles, are available in [38].

For the purposes of the research described in this paper, the network model was supplemented by adding single-phase PV sources in 30 nodes. The same daily waveform of power generated in all PV installations was assumed. This results from the small extent of the low-voltage network, which makes the solar radiation conditions similar throughout the network. However, the nominal power of the PV installation was varied; it was adjusted to the maximum active power consumed in a given node. The total installed power in PV sources is approximately 186 kW, while the powers of individual installations range from 3 to 13 kW.

Single-phase PV sources, which introduce unbalance into the low-voltage network, contribute to the deepening of problems with excessively high voltage [14,16]. Therefore, it seems necessary to include such sources in this research. It is worth mentioning, however, that national regulations usually contain restrictions on the connection of single-phase sources. In Poland, sources with rated power above 3.68 kW are connected only in a three-phase manner [32]; in most other European countries, the power limit for single-phase installations ranges from 3.68 to 5 kW [39]. The rated power of individual sources was adjusted to the maximum power drawn in a given node during the considered day. This is not a rule; in the real network, the sources are often oversized, which makes the disproportion between the consumed and generated power significant. This intensifies the negative voltage phenomena in the network, which could be mitigated or even eliminated via the self-consumption of energy generated in the PV installation.

In order to quantitatively assess the power of PV sources connected to the grid, one can use the PV penetration indicator. This indicator does not have a uniform and consistent definition. In [40], PV penetration is understood as the ratio of the number of households with photovoltaic installations to the total number of customers connected to the grid. In [41], PV penetration is defined as the ratio of total peak PV power to peak-load apparent power on the feeder. In other works [42,43,44,45], this indicator is defined as the ratio of the maximum active power generated in PV sources to the maximum (peak) active power demand, e.g., annual or averaged for a given season. Other publications [14,46] assume the ratio of the total installed PV power to the rated load power as the definition of PV penetration. This indicator can be determined individually for each node [46], each line or the entire network. In this article, due to the available data for the IEEE test network, PV penetration (ppv%) is defined as the percentage ratio of the total installed power in photovoltaic installations (P_PVinstalled) to the maximum total load power (P_LOADmax):

$$ppv\%={\displaystyle \frac{P_{\mathrm{PVinstalled}}}{P_{\mathrm{LOADmax}}}}·100\%={\displaystyle \frac{186\mathrm{kW}}{330\mathrm{kW}}}·100\%\approx 56\%$$

(1)

PV penetration at this level can be assessed as an average; in real conditions, one can find networks with a much higher share of PV. The presented case is, therefore, not an extreme case. Also, the parameters and properties of the model network used in the research seem to be averaged against the background of real European LV networks. A transformer with a relatively high rated power of 800 kVA, as well as a small network area (the total line length is approx. 1.2 km) indicate that this is not a network particularly exposed to problems with large voltage changes. Looking at the unit reactance values of individual line sections, which are within the range of 0.076 Ω/km to 0.093 Ω/km, one can state that this is a cable network. The R/X ratio for the vast majority of line sections is high, and it ranges from approx. 4 to almost 15. This parameter determines the effectiveness of the influence of reactive power control on the voltage value in the network. The lower the proportion of line reactance relative to line resistance, the higher the reactive power drawn from the network must be to achieve the same regulatory effect. This is described in the following equation [3]:

$$\Delta V_{\%}={\displaystyle \frac{P_{\mathrm{PV}}·R}{V^2}}\left(1+\mathrm{tg}\phi ·{\displaystyle \frac{X}{R}}\right)$$

(2)

where ΔV_% is the relative voltage change, V is the voltage at the PV source connection point, tgφ = Q_PV/P_PV is the power factor of the PV source, P_PV and Q_PV are the generated active power and reactive power consumed by the PV source, and R and X are the line resistance and reactance.

It follows that reactive power control to reduce voltage will be much less effective in a low-voltage network (especially a cable network) than in higher-voltage networks.

2.2. Overvoltage Protection Model

In order to model the operation of overvoltage protections in PV inverters, a two-stage relay model was made, compliant with the requirements of the EN 50549-1:2019 standard. The implementation of the first, delayed stage (V>) was based on the measurement of the 10-min mean voltage value. This value was determined using the moving window method as the root of the arithmetic mean of the squared input values over 10 min. In addition, 10-min aggregation should be used, in accordance with EN 61000-4-30 class S. According to this standard, the basic measurement time of the effective voltage value should be a 10-period interval (for a 50 Hz system), i.e., 0.2 s. The set trip value of the first protection stage (V>) is 1.1 V_n. The second protection stage (V>>) was configured as instantaneous, with a set trip value of 1.15 V_n. The reconnection of the PV system (after the tripping of the protective relay) can occur when the voltage at the connection point is maintained within the limits of 0.85 V_n ≤ V ≤ 1.1 V_n for an observation time of 60 s (default value according to EN 50549-1:2019). The above settings are in accordance with the requirements of Polish DSOs [32]. The thresholds and tripping time required in other countries (including Italy, Germany, China and New Zealand) can be found in [47].

The structure of the protection model for a three-phase installation, along with the description of individual elements, is shown in Figure 2. An example of the operation of the first level of protection is presented in Figure 3. It shows that, after a step increase in voltage from 230 V to 257 V (exceeding the threshold of 1.1 V_n, 253 V), the 10-min average voltage value increases, and as a result, the first protection level is activated after a delay of more than 8 min.

For the purposes of conducting the research described in the article, due to the relatively low resolution of the input data for the IEEE network (1 min), the operation of the overvoltage protections was simplified, while the basic operation logic was maintained.

2.3. Model for Q(V) Inverter Mode

The reactive power control mode as a function of voltage is currently the basic mode set by default in inverters of new prosumer PV installations in Poland [32], as well as in some other European countries (e.g., Germany [48]). The Q(V) mode is also recommended in the conclusions of most studies comparing individual reactive power control modes [3,5]. The EN 50549 standard does not specify the exact settings of the Q(V) characteristic, leaving a lot of freedom to the DSOs of individual countries. However, the shape of the characteristic is always similar, and it can be expressed as Function (3). The graph of this function is shown in Figure 4.

$${\displaystyle \raisebox{1ex}{$Q$}\!\left/ \!\raisebox{-1ex}{$P$}\right.}=\left\{\begin{array}{cc}-\mathrm{tg}{\phi }_{\max },\hfill & V>V_4\hfill \\ {\displaystyle \frac{\mathrm{tg}{\phi }_{\max }}{V_4-V_3}}\left(V_3-V\right),\hfill & V_3\le V\le V_4\hfill \\ 0,\hfill & V_2\le V\le V_3\hfill \\ {\displaystyle \frac{\mathrm{tg}{\phi }_{\max }}{V_1-V_2}}\left(V-V_2\right),\hfill & V_1\le V\le V_2\hfill \\ \mathrm{tg}{\phi }_{\max },\hfill & V<V_1\hfill \end{array}\right.$$

(3)

The implementation of the Q(V) mode in the simulation required the creation of a QDSL model (Figure 5).

For more accurate simulations that take into account medium- and long-term transients, which are possible with the RMS Simulation module in PowerFactory software, the Q(V) characteristic can be realized using the DSL model, the diagram of which is presented in Figure 6.

In the research described in this paper, the characteristic settings were adopted in accordance with the requirements of Polish DSOs [32]. These settings and—for comparison—the settings required in the grid codes of other European countries are presented in

Table 1. Q(V) characteristic settings in accordance with the requirements of Polish, German and Italian DSOs [47].

Q(V) Settings	Poland [32]	Germany [49]	Italy [50]
V1, pu	0.92	0.93	0.90
V2, pu	0.94	0.97	0.92
V3, pu	1.06	1.03	1.08
V4, pu	1.08	1.07	1.10
cosφmax (tgφmax)	0.9 (0.4843)	0.9/0.95 1 (0.4843/0.3289)	0.9 (0.4843)

¹ Value depends on generator power.

.

2.4. Model for P(V) Inverter Mode

Activating the mode of reducing the active power generated in the PV installation as a function of voltage is intended to avoid the need to trigger overvoltage protections. The EN 50549 standard stipulates that this mode must not cause surges or fluctuations in output power. The detailed logic of the P(V) mode is not imposed in the standard. However, it should certainly be a compromise solution: on the one hand, it should provide the smallest possible generation restrictions for the prosumer, but on the other hand, it should effectively reduce the voltage in the network.

This paper assumes that the P(V) characteristic will be activated only when the capabilities of the Q(V) mode are exhausted, i.e., above the V₄ threshold. The course of the P(V) function is presented below (Figure 7 and Equation (4)). This study assumed the maximum limitation of the generated power at the level of max_lim_P = 0.85. The voltage thresholds are V₄ = 1.08 pu and V₅ = 1.1 pu.

$${\displaystyle \raisebox{1ex}{$P$}\!\left/ \!\raisebox{-1ex}{$P_{\max }$}\right.}=\left\{\begin{array}{cc}max\_li{m}_{\mathrm{P}},\hfill & V>V_5\hfill \\ 1+{\displaystyle \frac{max\_li{m}_{\mathrm{P}}}{V_5-V_4}}\left(V-V_4\right),\hfill & V_4\le V\le V_5\hfill \\ 1,\hfill & V<V_4\hfill \end{array}\right.$$

(4)

The research used the QDSL model available in [51] after appropriate adjustment to the simulation conditions and with (4) taken into account.

3. Proposed ANN-Based OLTC Control Method

The standard operation of the on-load tap changer is based on local measurements, i.e., values measured on the transformer station busbars. In the case of a network with a high PV penetration, such a strategy seems to be insufficient. The voltage in nodes located close to the transformer is rigid, and its small changes do not reflect the situation in the depth of the network, where the most important aspect is the mutual relationship between load and generation. In order to adapt the operation of the OLTC to the conditions in a network with a high share of PV sources, the tap changes should be made dependent on the voltages in the depth of the network, measured or estimated. The measurement of electrical parameters in the depth of the network has been proposed in decentralized methods, described in [28,40,52,53], among others. All the proposed methods require reliable real-time communication between the station and distant network nodes. The solutions that do not require the expansion of the network with communication infrastructure are local methods. They can be based, for example, on estimating voltages in distant buses using non-deterministic methods [13], making the OLTC setting dependent on solar radiation [14] or using historical data [54].

The method proposed in the article can also be classified as local, and its basic idea is to use the functionality usually available in on-load tap-changer controllers, i.e., the load compensation function. This function makes the OLTC operation dependent on voltage conditions in the depth of the network by correcting the voltage measured at the station for the decrease/increase caused by the current drawn/injected via loads and sources:

$$V_{\mathrm{LC}}=\left|V_{\mathrm{T}}+\left(R_{\mathrm{LC}}+\mathrm{j}{X}_{\mathrm{LC}}\right)·{\underset{\_}{I}}_{\mathrm{T}}\right|$$

(5)

where V_LC is the load compensation voltage, R_LC and X_LC are, respectively, the resistance and reactance of load compensation (set in the controller), and I_T and V_T are, respectively, the load current and voltage (values measured in the transformer station).

For real power grids, the proper selection of R_LC and X_LC values is a complex issue. This problem results from the complexity of distribution network systems and the variability in load and generation of individual feeders and nodes. For this reason, load compensation is rarely used in OLTC controllers. The article proposes and tests a solution that allows for avoiding the need for troublesome parameterization of load compensation. This was possible thanks to the use of an artificial neural network.

Artificial neural networks are currently a common tool for classifying patterns, predicting and making decisions based on past data. They enable solving practical problems without the need to create a mathematical model and provide any theoretical assumptions about the problem. Artificial neural networks can be used to support the operation of power grids with photovoltaic sources, e.g., for forecasting the power generated in PV systems [55,56], detecting disturbances in the operation of sources and networks [57] or developing various strategies to improve the operating conditions of networks with distributed generation [58].

The neural network used in the research was intended to determine the pattern between the values measured in the transformer station (load current or power) and the tap changer position that would provide the best voltage conditions in the entire network. Therefore, the ANN allows for configuring load compensation without the need to directly determine the resistance, R_LC, and the reactance, X_LC. The settings for load compensation are determined in the form of a characteristic, illustrating the relationship between the voltage set in the OLTC controller and the current/power measured in the transformer station. The OLTC operates according to the set characteristic, without the participation of the ANN and based only on measurements performed locally, in the transformer station. In this way, the OLTC operation is dependent on voltages in the depth of the network while avoiding the need to perform remote measurements.

The STATISTICA Automated Neural Networks tool was used to design the ANN, select its structure and conduct the training, testing and validation process. A single-input, single-output neural network was selected. The active power measured in the transformer station (P_B1) was defined as the ANN input, and the output was the voltage set in the OLTC (V_B1set) (i.e., indirectly, the OLTC tap number). In order to prepare data for the training set, i.e., appropriate pairs containing input data and corresponding output reference data, it was necessary to determine the optimal OLTC position for different cases of the test network operation. This was achieved using the on-load tap changer operation algorithm in the form of the QDSL model available in [59] (Figure 8). This algorithm reads the voltage values in all network nodes at a given simulation step and then determines the maximum and minimum voltage. If the minimum value is lower than the assumed threshold, the transformer tap is reduced by one position. Similarly, if the maximum voltage is higher than a specified value, the OLTC position is increased by one tap. This action is repeated in the subsequent simulation steps.

In order to obtain the widest possible set of data in the training set, simulations were carried out in many variants, differing in load and generation levels, with a disconnected part of the PV installation and at different voltage levels on the MV side. Data from the training set, i.e., active power values measured in the station (P_B1) and the assigned voltage values measured in node 1 (V_B1), are shown in Figure 9.

The next stage was to select the structure and parameters of the neural network. A multilayer perceptron was selected as the network architecture, and the sum square error (SOS and SSE) value was selected to assess the fit of the network results to the reference values. The remaining network parameters (the number of neurons in the hidden layer, the activation functions of neurons in the hidden and output layers, and the learning algorithm) were selected using the STATISTICA Automated Neural Networks tool after several hundred different configurations were tested. This enabled the selection of parameters that allowed for the highest possible quality of learning, testing and validation. The summary of network parameters and the obtained learning results are shown in

Table 2. Structure, parameters and quality of the designed neural network.

Feature/Parameter	Results for Designed ANN
Network architecture	MLP 1-11-1 (1 input, 1 output, 11 neurons in hidden layer)
Quality (training/testing/validation)	0.751/0.732/0.726
Error (training/testing/validation)	0.000265/0.000308/0.000282
Learning algorithm	BFGS 324 (Broyden–Fletcher–Goldfarb–Shanno algorithm) [60]
Error function	SOS (sum square errors)
Activation function (neurons in the hidden and the output layer)	Logistic (sigmoid)

.

The last stage comprised loading the subsequent active power values into the created neural network as input data and retrieving the network response in the form of estimated values of the voltage set in the OLTC. The characteristic created in this way (Figure 10) was loaded into the OLTC simulation model as a load compensation setting.

4. Results

This section presents the results of the simulation studies for the 116-bus IEEE test network. Five cases are considered:

• Case 1: This is the base case, where no voltage control methods were implemented. All PV sources operated at maximum power, depending only on the current solar radiation conditions (according to the loaded generation curve).
• Case 2: PV sources operated in the cosφ fixed mode with a cosφ = 0.9 (inductive).
• Case 3: PV sources operated in Q(V) mode (as described in Section 2.3).
• Case 4: PV sources operated in Q(V) + P(V)) mode (as described in Section 2.3 and Section 2.4).
• Case 5: This case presents the implementation results of the proposed ANN-based OLTC control method. The PV sources operated in Q(V) mode.

Each case was repeated at three voltage levels on the MV side: 0.95 pu (Scenario I), 1.0 pu (Scenario II) and 1.05 pu (Scenario III). Voltage variation in the MV network is a natural phenomenon that is additionally intensified due to distributed generation, and it is also connected to MV networks.

The simulation results are presented graphically in the form of daily waveforms of characteristic values (including voltages, generated active power, reactive power and OLTC tap positions). Due to the large number of cases, the article presents waveforms only for Scenario III, i.e., at the highest voltage level on the MV side. This is the scenario in which the problem with a voltage increase will occur on the widest scale. For the sake of clarity, the figures show only the voltages in the buses where extreme voltage values were observed (buses 66, 77, 103 and 114), as well as the voltage in the node with the transformer (bus 1). Daily waveforms of active and reactive power generated/consumed via PV sources are shown only for node 114. This is the end node of one of the feeders, and the voltage conditions are the worst there.

In addition to the graphical presentation of the results, a tabular summary of the results for the entire network is provided below the description of each case. The following comparative criteria were taken into account:

• Number of nodes in which the upper voltage threshold, set to 1.1 V_n (value in accordance with EN 50160 [61]), was exceeded.
• Number of nodes in which the lower voltage threshold was exceeded. The threshold was set to 0.95 V_n (the EN 50160 standard [61] allows for a value of 0.9 V_n, but a more stringent requirement was adopted in the studies).
• Total time of exceeding the upper and lower voltage thresholds in relation to the total simulation time (expressed as a percentage).
• Maximum and minimum voltage recorded during the simulation.
• Total reactive energy consumed or fed into the network via all PV installations.
• Total energy losses in the network.

4.1. Case 1

The base case is a reference for the remaining cases presenting different methods of improving voltage conditions in the network. The results obtained in case 1 (

Table 3. Summary of simulation results—case 1.

Comparison Criterion	Scenario I (VMV = 0.95 pu)	Scenario II (VMV = 1.0 pu)	Scenario III (VMV = 1.05 pu)
V > 1.1 Vn: number of nodes; time of exceedances (%)	0; 0%	21; 0.22%	90; 3.76%
V < 0.95 Vn: number of nodes; time of exceedances (%)	116; 50.31%	0; 0%	0; 0%
Maximum voltage (pu)	1.076	1.121	1.166
Minimum voltage (pu)	0.914	0.966	1.018
Reactive energy (kvarh)	0	0	0
Network energy losses (kWh)	43.97	40.07	36.66

) are strongly dependent on the voltage on the MV side. At the lowest voltage (Scenario I), the lower voltage threshold (0.95 pu) was exceeded in all nodes, and the total exceedance time was over 50% of the entire simulation time. The scale of exceedances is, therefore, high. In the second extreme case (Scenario III, Figure 11), when the voltage V_MV was the highest, the threshold of 1.1 V_n was exceeded in 90 nodes out of all 116.

Although the total exceedance time was not high (3.76% of the total simulation time), the maximum voltage of 1.166 pu means the network would experience multiple disconnections of PV sources via overvoltage protections, by both the first and second stages of protection. In all scenarios, PV sources operated in cosφ = 1 mode, so they did not consume or generate reactive power.

The operation of overvoltage protections for Scenario III is shown in Figure 12. Although the activation of protections visibly decreased the voltage in the network, it did not completely solve the problem of too-high voltage—voltage exceedances occurred in the same 90 network nodes, but their total time was lower (2.90% of the total simulation time). The maximum voltage was also reduced to 1.136 pu. However, this effect was achieved by significantly reducing the power generated in PV sources. Considering the energy generated via all PV installations during the entire day in the base case, which amounted to 1193.5 kWh, the operation of protections caused its reduction to 899.7 kWh. This was a loss of 24.62%. Moreover, these restrictions were not evenly distributed among all prosumers but only concerned those installations that were connected at the most distant points of the network. The most extreme case is shown in Figure 12c. In bus 114, the loss of generated PV energy was 66.47%.

4.2. Case 2

In the cosφ fixed mode, the maximum permissible value of the power factor specified in the EN 50549 standard [31], i.e., 0.9 (inductive), was set. This solution is already inflexible by design. One fixed cosφ value will always have the same effect, in this case by reducing the voltage in the network, regardless of the voltage currently measured in it. As the results show (

Table 4. Summary of simulation results—case 2.

Comparison Criterion	Scenario I (VMV = 0.95 pu)	Scenario II (VMV = 1.0 pu)	Scenario III (VMV = 1.05 pu)
V > 1.1 Vn: number of nodes; time of exceedances (%)	0; 0%	1; 0%	79; 2.53%
V < 0.95 Vn: number of nodes; time of exceedances (%)	116; 54.48%	0; 0%	0; 0%
Maximum voltage (pu)	1.055	1.101	1.147
Minimum voltage (pu)	0.914	0.966	1.018
Reactive energy (kvarh)	577.94	577.94	577.94
Network energy losses (kWh)	60.73	55.23	50.43

, Figure 13), in the case of the highest voltage value on the MV side (Scenario III), this solution caused a small improvement, limiting, to some extent, the scale of exceeding the upper voltage limit of 1.1 V_n. In Scenario II, it can be assumed that the operation of the inverters in the cosφ fixed mode completely solved the problem of excessive voltage, but even in the base case, this problem was minor in this scenario. The worst results are—as expected—at the lowest V_MV value, i.e., in Scenario I. In this case, the inverter setting has an unfavorable effect, additionally unnecessarily reducing the voltage in the network. It is worth noting that, regardless of the scenario, high reactive power consumption was recorded, which contributed to the increase in energy losses in the network. This increase can be described as high, amounting to about 38%. It is also visible that the impact of reactive power on the voltage in the network is not very significant. Despite the relatively high reactive power consumption, the results (e.g., total exceedance time) do not differ significantly from the base case. This confirms Formula (2) and the conclusion that, in the case of low-voltage lines, reactive power control for voltage regulation is not as effective as for higher-voltage lines (with higher unit reactance).

4.3. Case 3

In case 3, the reactive power of PV sources depends on the voltage measured at the inverter terminals. When the voltage is too high (above 1.06 pu), the inverter starts to consume reactive power, and when the voltage is too low (below 0.94 pu), the inverter injects reactive power into the grid, as shown in Figure 4. The limit value is still the reactive power injected/consumed at a level that ensures the power factor of the PV installation is not lower than 0.9 (inductive/capacitive). As shown by the results (

Table 5. Summary of simulation results—case 3.

Comparison Criterion	Scenario I (VMV = 0.95 pu)	Scenario II (VMV = 1.0 pu)	Scenario III (VMV = 1.05 pu)
V > 1.1 Vn: number of nodes; time of exceedances (%)	0; 0%	0; 0%	51; 2.26%
V < 0.95 Vn: number of nodes; time of exceedances (%)	116; 50.29%	0; 0%	0; 0%
Maximum voltage (pu)	1.073	1.100	1.136
Minimum voltage (pu)	0.914	0.966	1.019
Reactive energy (kvarh)	3.49	74.35	354.57
Network energy losses (kWh)	44.03	43.47	46.60

), in Scenario I, with the lowest V_MV value, there is almost no visible effect from the Q(V) mode on the grid voltage. This is due to the fact that the lowest voltage values occurred at night. The active power generated in the PV sources is then zero, and the inverter usually switches off, and thus, there is no possibility of controlling reactive power. For Scenario II, activating the Q(V) mode resulted in the complete elimination of voltage exceedances. In Scenario III (Figure 14), the exceedances of the upper voltage limit were only slightly limited compared to the base case. This is a result comparable to that obtained in case 2. However, a significant difference compared to the cosφ fixed mode can be seen in the value of reactive energy. In each of the scenarios, the Q(V) mode contributed to its significant reduction, which also resulted in a reduction in energy losses in the network.

4.4. Case 4

Case 4 presents the results obtained after the combined Q(V) + P(V) characteristic was implemented. According to (2), for a network with a high R/X value, the control of the active power of PV sources is much more effective than the control of reactive power. However, it is associated with the limitation of the generation capabilities of PV sources and, therefore, with a decrease in the profitability of the installation for the prosumer. For this reason, the shape of the P(V) characteristic shown in Figure 7 was selected, with a maximum limitation of only 15% of the maximum power. The results (

Table 6. Summary of simulation results—case 4.

Comparison Criterion	Scenario I (VMV = 0.95 pu)	Scenario II (VMV = 1.0 pu)	Scenario III (VMV = 1.05 pu)
V > 1.1 Vn: number of nodes; time of exceedances (%)	0; 0%	0; 0%	37; 0.89%
V < 0.95 Vn: number of nodes; time of exceedances (%)	116; 50.29%	0; 0%	0; 0%
Maximum voltage (pu)	1.073	1.096	1.120
Minimum voltage (pu)	0.914	0.966	1.019
Reactive energy (kvarh)	3.49	70.98	359.79
Network energy losses (kWh)	44.03	42.73	41.64

) showed that the activation of the P(V) mode had no effect on the operation of the network in Scenario I. The mode of limiting the generated power is activated after exceeding the voltage threshold of 1.08 pu, and the maximum recorded voltage does not exceed this value. Minor changes are also visible in Scenario II. However, the P(V) mode improved the results at the highest V_MV voltage, in Scenario III. The upper voltage limit was exceeded only in 37 nodes out of all 116, and their total time was less than 1% of the total simulation time. However, limiting the voltage increase was achieved at the cost of reducing the power generated by some prosumers, an example of which is shown in Figure 15c. To assess the scale of generation limitations, the simulation in case 4 was performed again with active overvoltage protections. These protections still switched off the PV sources several times a day. The total energy lost due to the operation of protections and limitations imposed by the P(V) mode was 24.79%. This is a value comparable to that obtained in the base case with active protections (24.62%), but in this case, the scale of voltage exceedances is much lower.

4.5. Case 5

In the last case, it was proposed to replace the supply transformer with a unit with an on-load tap changer. The standard operation of OLTC is based on voltage measurement in the transformer station. In simple terms, when the measured voltage exceeds the imposed limits, the transformer ratio is changed, which causes a change in the voltage on the transformer buses. In the situation presented in the article, when a large number of distributed energy sources are connected to the network, such a control strategy turned out to be insufficient. This is because the voltage measured at the power source (transformer) does not reflect the phenomena occurring deep in the network (e.g., in node 114). These phenomena result from the mutual relationship of the power consumed and generated in individual nodes, and they do not have to affect the voltage on the station buses. Moreover, the OLTC operating in the traditional way required changes in settings, depending on the voltage on the MV network side.

The above disadvantages are devoid of the original OLTC control method, the results of which are presented in case 5. In the proposed method, the load compensation function was activated in OLTC, the settings of which were determined by the neural network. The OLTC model has nine taps (from position –3 to +5), and changing the tap by one position causes a voltage change of 1%. Additionally, all PV inverters have the Q(V) mode activated. The results, presented in

Table 7. Summary of simulation results—case 5.

Comparison Criterion	Scenario I (VMV = 0.95 pu)	Scenario II (VMV = 1.0 pu)	Scenario III (VMV = 1.05 pu)
V > 1.1 Vn: number of nodes; time of exceedances (%)	0; 0%	0; 0%	0; 0%
V < 0.95 Vn: number of nodes; time of exceedances (%)	79; 0.66%	0; 0%	0; 0%
Maximum voltage (pu)	1.091	1.096	1.100
Minimum voltage (pu)	0.943	0.956	0.966
Reactive energy (kvarh)	27.81	45.33	73.77
Network energy losses (kWh)	43.32	43.21	43.25

, show that the proposed solution is characterized by the greatest flexibility: for each voltage level, V_MV, the best results were obtained. Although, in Scenario I, the lower voltage limit was exceeded in as many as 79 nodes, the total time of these exceedances is already acceptable (0.66% of the total simulation time). Compared to case 1 (base), this time was reduced by more than 75%. In the other two scenarios, neither the upper nor the lower voltage limits were exceeded. However, in Scenario III (Figure 16), the OLTC operates at the maximum tap during the peak PV generation period, and despite this, the maximum voltage is almost at the same level as the upper threshold (1.1 pu). This means that the method’s control capabilities in this case are already exhausted. In such a situation, it is possible to consider additionally activating the P(V) mode in the inverters. In case 5, in none of the scenarios did the PV installation protections operate, so no losses of generated energy related to this were recorded. The proposed method also yields good results in terms of total reactive energy (consumed or generated) and energy losses in the network.

4.6. Summary of Simulation Results

The results of the comparison of the proposed method against other selected local methods are presented below in graphical form (Figure 17, Figure 18 and Figure 19). The comparison includes all three research scenarios, assuming changes in the voltage level on the MV side. The comparisons include such criteria as the number of nodes and the time of exceeding the lower and upper voltage limits, the voltage range recorded in all network nodes, the total reactive energy consumed and injected into the network, and the total energy losses in the network.

In Scenario I, with the lowest voltage on the MV network side, neither the base case (case 1) nor any of the tested methods (cases 2–5) recorded any exceedances of the upper voltage limit (Figure 17a). The proposed method (case 5) provided the best results among all tested methods (cosφ fixed, Q(V), and Q(V) + P(V) modes) in terms of limiting exceedances of the lower voltage limit (Figure 17b), maintaining the voltage within the imposed range (Figure 17c) and limiting energy losses in the network (Figure 17e).

In Scenario II, with the MV network side voltage of 1.0 pu, the authors’ OLTC control method allowed for the complete elimination of the exceedances of the upper voltage limit; however, even in the base case, these exceedances did not occur on a large scale (Figure 18a,c). The lower voltage limit was not exceeded in any of the cases (Figure 18b). In case 5, the lowest reactive energy value was recorded, while the energy losses in the network were at a similar level as in the base case and in the Q(V) and Q(V) + P(V) modes, but they were significantly lower than in the cosφ fixed mode.

In Scenario III, with the highest voltage on the MV network side, the proposed method allowed for the complete elimination of voltage exceedances in all nodes, which was not possible with the other methods tested in this research (Figure 19a,c). In case 5, the lowest reactive energy values were recorded. The energy losses in the network were at a level comparable to those of the rest of the cases.

5. Discussion

This paper proposes a local OLTC transformer control method to overcome voltage problems in LV networks with a large share of PV installations. The method uses the load compensation function, the settings of which were determined via artificial neural network algorithms. A 116-bus IEEE network was used for testing. The LV network unbalance and voltage variation on the MV network were taken into account.

The following are the key conclusions:

• The authors’ method achieved the best results in terms of maintaining the voltage within the imposed limits (0.95–1.1) V_n. Good results were also obtained in terms of limiting the flow of reactive power and power losses in the network. The described method showed great flexibility in terms of voltage changes in the MV network.
• The proposed method can be classified as a local voltage control strategy that does not require ensuring a data exchange between network nodes and the OLTC controller. Thanks to this, it is possible to reduce the implementation costs and failure rate of the method to a certain extent. In addition, the use of a transformer with an on-load tap changer means that the method is based on solutions that are well known and have been used for many years in higher-voltage networks.
• The presented method involves limitations. Methods using OLTC are less effective when several feeders with a large source and load imbalance are supplied from one transformer station. In such a situation, when trying to reduce the voltage in one line with high PV generation, an undesirable voltage reduction may occur in the more heavily loaded lines, where there are no or few energy sources. These methods also may not cope with large voltage asymmetry in individual phases, resulting from the operation of single-phase loads and sources.
• The implementation of the method is facilitated via the use of a simple tool in the form of an artificial neural network. An ANN does not require any initial assumptions or information regarding the nature of the forecasted phenomena, and it can also be retrained while taking into account new data, for example, when the network configuration changes. The data needed for the ANN training process may be incomplete and, therefore, may come from the smart energy meter system installed for some customers and prosumers.
• The DSL and QDSL models developed and presented in the paper are universal, and they can be used for further simulation studies in PowerFactory, taking into account other network configurations, and for testing other voltage control strategies.