Smart Meter Data-based Three-Stage Algorithm to Calculate Power and Energy Losses in Low Voltage Distribution Networks

In the paper, an improved smart meter data-based three-stage algorithm to calculate the power/energy losses in the three-phase low voltage (LV) distribution networks was proposed. In the first stage, an loading procedure of input data was built, being able to work simultaneously with files containing the active and reactive power profiles provided by smart meters and typical profiles associated to consumers without smart meters, based on the energy consumption categories, day type (weekend and working), and season type, knowing the daily energy indexes, in the second stage, a structure vectors-based algorithm was implemented to recognize the network topology, and in the third stage, an improved version of forward/backward sweep-based algorithm was proposed to calculate fast the power/energy losses to three-phase LV distribution networks in balanced and unbalanced regime. A real LV rural distribution network from a pilot zone belonging to a Distribution Network Operator (DNO) from Romania was used to verify the accuracy of the proposed algorithm. The results were compared with those obtained using the DigSilent PowerFactory Professional Software, the MAPE being by 0.94%.


Introduction
Until a few years ago, electric distribution networks were generally characterized by a lack of technical possibilities represented by smart devices that can help the Distribution Networks Operators (DNOs) in the supervisory, control, and decision-making processes.Although the low voltage (LV) distribution networks feed a high number of consumers, little information could be gathered from inside (from the consumers and producers), with a delayed response time.In order to obtain as much data as possible from the network, it is necessary to install smart meters, which allow the recording of the supervised data (energy consumptions, active and reactive powers, voltages, power factors, harmonics etc.) and their transmission to the DNOs level.
The Smart Metering technology is essential for achieving targets regarding the energy efficiency and renewable energy set for 2020, as well as the delineation of future smart grids.The introduction of smart metering systems (SMS) in the European Union is finished in some countries and it is in different stages in others [1][2][3][4][5].Thus, special attention should be paid to the management of databases built

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Stage I is based on the online work, with files from two different databases, as follows: The database of the SMS, including the consumption and production profiles for the integrated consumers and producers and the database containing the characteristic load profiles (CLPs) obtained from the profiling process, which are assigned to the consumers with installed conventional meters, non-integrated in the SMS.This work mode enables the algorithm to work online to estimate the power losses.

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Stage 2 implements a recognition function of the network topology based on two structure vectors.

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Stage 3 is based on an improved version of a forward/backward sweep-based algorithm to quickly calculate fast the power/energy losses in three-phase LV distribution networks with balanced and unbalanced operating regimes.Regarding the forward/backward sweep-based algorithm, it was mainly used in the medium voltage distribution networks to calculate the balanced symmetric steady-state regime [25][26][27][28].However, the proposed version was adapted to the LV distribution networks that most often operate in unbalanced regimes due to the chaotic allocation of the single-phase consumers on the phases.
Taking into account the aforementioned references, a brief characterization taking into account the two main advantages (the online estimation of the power losses and the consideration of the unbalance regime) of the proposed algorithm compared with some other approaches is presented in Table 1.
There is not a discussion about online estimation of power losses in any paper, very few papers treat the unbalanced regime, and the simultaneous consideration of both advantages is not addressed.
Besides the two main advantages, our algorithm uses real data regarding the active and reactive powers for both consumers and small-scale sources integrated in the LV distribution networks.Additionally, the calculation of the power/energy losses is made using a modified branch and bound (forward backward sweep) method.A pilot LV distribution network, from a rural area belonging to a DNO from Romania, was chosen to demonstrate the performance of the proposed algorithm.
A comparison with the results obtained using the DigSilent PowerFactory (DSPF) simulation package certified the accuracy of algorithm.Even if the DSPF package is one of the most powerful packages in processes simulations from the generation, transmission, and distribution levels, it presents some disadvantages.In the DSPF Simulation Package the implementation of the LV electrical network, in the form of a scheme and an individual introduction of elements (bus, line, transformer, load) represented by conventional symbols in order to perform the calculations of steady-state regimes, is necessary.The general and electrical parameters must be entered separately in the graphic interfaces, which are different in function by element.In addition, the active and reactive power profiles for each consumer and producer must be read from more comma-separated values (CSV) files that have a specific format.To build this format, the user should process supplementary files from the SMS and files with CLPs, which leads to increased calculation time and the inability to work online.
The structure of paper is organized as follows: Section 2 reveals the stages of the proposed algorithm, detailing the load profiling process used for the non-integrated consumers in the SMS, Section 3 presents the results obtained in the case of a LV network from a pilot rural zone of a DNO from Romania and a comparison with simulations made using the DSPF package, and Section 4 highlights the conclusions and the future works.

Three-Stage Algorithm to Calculate Power/Energy Losses
Steady-state regime calculations using the very well-known iterative methods (Seidel-Gauss or Newton-Raphson), in order to obtain power/energy losses, can be difficult to perform for LV distribution networks.This occurs due to the following particular features: The ill-conditioning given by the radial topologies, resistance with high values, and reactance with small values (depending on the cross-sections of conductors), which often operate in the unbalanced regimes due to the chaotic allocation of the single-phase consumers on the phases.
Taking into account the above features, a different approach to eliminate these drawbacks, based on the three-stage algorithm, is presented as follows:

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Stage 1.The input data of the consumers, referring to the energy characteristics, are read from the databases of the DNO, which contain the load profiles of each consumer integrated in the SMS or the CLPs, if the consumer has a conventional meter non-integrated in the SMS.Additionally, the production profiles of the producers from the network are loaded by the algorithm.
• Stage 2. The architecture of network is established using an efficient algorithm based on two structure vectors.

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Stage 3. The power/energy losses are determined using an improved variant forward/backward sweep algorithm, which can work in the balanced and unbalanced operating regimes, with or without distributed generation.

The First Stage
Whatever the type of consumer (residential, commercial, or industrial), they have their own consumption pattern, which can be identified based on a load profile representing the consumed active and/or reactive power in a time frame.However, access to these data can be available only if the consumer is integrated in the SMS.In this regard, the vast majority of the DNOs from the UE countries implemented pilot projects to identify the efficiency of the integration in the SMS of the consumers.The expected results should refer to the following [1]: The energy consumption is monitored online with benefits for both parts, the DNOs can implement the energy efficiency measures, and the consumers can establish their pricing mode in function by the energy consumption behaviour.

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The analysis of recorded data must lead to optimal strategies regarding the increase of energy efficiency in the LV distribution networks of the DNOs.

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Extending the processed data (as load type profiles) to the networks from the same area, but without SMS implementation, to analyse their operation regime.
The algorithm accepts the input data using an available format in the database of the DNOs.The records with the associated fields from the input file are indicated in Table 2.
Each field of a record is detailed as follows: • Number represents the allocated record for a certain consumer in the database of the DNO.

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Pillar represents the identification number of each pillar made by the DNO for a rural LV distribution network.The pillars are numbered in all rural LV distribution networks to know where the consumers are connected.For example, in Table 1 consumer 1 is connected at pillar 1 and consumer 4 is connected at pillar 3.

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Branching identifies the type of electric branching for each consumer, single-phase or three-phases.These can be identified in the database with 1-P (single-phase) or 3-P (three-phases).

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Phase allows for identification of the phase(s) at which a consumer is allocated (the notations a, b, or c can be seen for a 1-P consumer, and the notation abc can be observed for a 3-P consumer).

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Type emphasizes if the consumer belongs in the following consumption patterns: Residential (ID is 1); non-residential, namely community buildings, hospitals, town halls, schools, etc. (ID is 2); commercial (ID is 3); and industrial (ID is 4).

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Class belongs to a certain Type, identified by the annual electric energy consumption of the consumer.The DNO can classify the consumers in a given number of consumer classes in function of different criteria.As an example, a division into five classes (made by a DNO from Romania) for the consumers from residential/non-residential types [28] is the following: Class_1 (0-400 kWh), Class_2 (400-1250 kWh), Class_3 (1250-2500 kWh), Class_4 (2500-3500 kWh), and Class_5 (>3500 kWh).

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Integration allows the user to know if the meter is (value is equal to 1) or is not (value is equal to 0) in the database of the SMS.If the meter is integrated, based on the ID of the meter, the active and reactive power profiles of the consumer can be loaded from the database.If a meter is not integrated, then the daily energy indexes will be loaded from the database.In this last case, a CLP will be allocated to the consumer using the approach presented in the next section in function of the records Type and Class.The associated active and reactive power profile is finally obtained based on the loaded energy indexes.
A matrix, with a number of rows equal to the sampling size of the active and reactive power profiles (usually one hour) and a number of columns, with the size 2 × 3 × total number of consumers, is loaded.The signification of the 2 × 3 columns is given by the fact that three columns for the active power and three columns for the reactive power is allocated for each consumer.Only columns associated with the connection phase of the consumers will have values different by 0 in the input matrix.Additionally, the algorithm can be used in the online calculations, with the data being read as soon as they reached in the data center.

Load Profiling Process Based on Smart Meters Data
Load Profiling represents a procedure that allows the energy consumption history of consumers not equipped with smart meters to be converted into a series of estimated load profiles, named "characteristic load profiles" (CLPs), for a certain type of consumer (residential, non-residential, commercial, and industrial).Thus, through the profiling process, the total energy consumption of a consumer for a time interval (one day) is distributed at all hourly levels.CLPs are derived from the processing of active and reactive profiles, with a sampling by 1 h, on a statistical sample belonging to a consumer type (residential, non-residential, commercial, industrial) and belonging to an energy consumption class.The consumption classes are established by DNOs in function of the annual energy consumption, because this is different from consumer to consumer inside of each type.In addition, the energy consumption is influenced by the following factors: Season (winter, spring, summer, and autumn) and week days (weekend or workdays).All mentioned factors are considered in the profiling process and in the case when the consumer has a technical failure at the communication support or the smart meter or is not yet integrated in the SMS in function of consumption class, consumption type, season, and day of the wee, a CLP will be assigned to be used in the steady-state regime calculations.The profiling process can be implemented as an offline procedure (after the update of the database at the end of day) or an online procedure straight after all data are collected from the smart meters.In our approach, the process is implemented as an offline procedure.The term "load profiling" mainly refers to the use of CLPs in special procedures related to the calculations of the steady state regime.
In this context, if a consumer is not integrated in the SMS, the DNO will assign a CLP depending on the different consumer' types (residential, commercial, and public), energy consumption class, and seasons (spring, summer, autumn, and winter), which is obtained based on the available processed data from the consumers with smart meters [29,30].
Using the CLPs and the daily energy consumption for each consumer without a smart meter implemented, the load profiles could be computed using the following algorithm.The denormalized load profile at consumer l is calculated with the following relation: where P l (h) -the denormalized load profile at consumer l for each hour h = 1, . . ., 24, l = 1, . . ., N c ; tc-the type of the l-th consumer, l = 1, . . ., N c ; CLP tc (h) -the characteristic load profile for the tc type of consumer (tc can be residential, non-residential, commercial or industrial), for each hour h = 1, . . ., 24; W l -the daily energy consumption for the consumer l; N c -total number of consumers without smart meter installed or with missing data in the SMS.Next, the denormalized profiles calculated above are adjusted based on the hourly values recorded by the smart meter from the electric substation, as follows: where P m (h) -the three-phase feeder measured load profile for the analysed period; P (h) sm,n -the active power measured with the smart meter at the consumer n, n = 1, . . ., N SM ; N SM -the total number of consumers integrated in the SMS.∆P (h) -the deviation between the measured and computed load profiles for the analysed period; P (h) cor,l -the denormalized load profiles adjusted by measured load profiles for the analysed period at the consumer l, for each hour h = 1, . . .24, l = 1, . . ., N c .

The Second Stage
The topology of the analysed network is very easily identified based on an approach which builds two structure vectors (VS1 and VS2).The approach is explained hereinafter.
The process allows the clustering of each section at a hierarchical level, starting with the first section.To exemplify the procedure, a radial LV distribution network with 8 nodes (pillars) and 7 sections was considered (see Figure 1).The steps for the network from Figure 1 are described below.
where Pm (h) -the three-phase feeder measured load profile for the analysed period; P (h) sm,n-the active power measured with the smart meter at the consumer n, n = 1, …, NSM; NSM-the total number of consumers integrated in the SMS.ΔP (h) -the deviation between the measured and computed load profiles for the analysed period; P (h) cor,l-the denormalized load profiles adjusted by measured load profiles for the analysed period at the consumer l, for each hour h = 1, …24, l = 1, …, Nc.

The Second Stage
The topology of the analysed network is very easily identified based on an approach which builds two structure vectors (VS1 and VS2).The approach is explained hereinafter.
The process allows the clustering of each section at a hierarchical level, starting with the first section.To exemplify the procedure, a radial LV distribution network with 8 nodes (pillars) and 7 sections was considered (see Figure 1).The steps for the network from Figure 1 are described below.If the following order is adopted in numbering the sections, 1-2 (I), 1-3 (II), 3-4 (III), 4-5 (IV), 5-6 (V), 5-8 (VI), and 5-7 (VII), then the size of the vector VS1 is equal with identified levels and the elements represent the sections assigned at one certain level (1, 2, 3, or 4).The correlation between vectors VS1 and VS2 can be observed in Table 3, where the structure vectors are shown.If the following order is adopted in numbering the sections, 1-2 (I), 1-3 (II), 3-4 (III), 4-5 (IV), 5-6 (V), 5-8 (VI), and 5-7 (VII), then the size of the vector VS1 is equal with identified levels and the elements represent the sections assigned at one certain level (1, 2, 3, or 4).The correlation between vectors VS1 and VS2 can be observed in Table 3, where the structure vectors are shown.

The Third Stage
The calculations for the steady state regime from each hour, h, h = 1, . . ., H (in our case H = 24), are made using an improved variant of the forward/backward sweep algorithm, which can work both in the balanced and unbalanced regimes, with or without distributed generation.The following steps are used to calculate the power and energy losses: Step 1.The loads from each node (pillar) are aggregated for all consumers using n i c , allocated at the pillar i.On each phase, {p} = {a, b, c}, the data are loaded from the database of the SMS or result from the profiling process, as follows: where N p represents the total number of pillars from the analyzed networks.If a generator is located in a node j (it can be at the same time and the consumer), connected at the pillar i, then: P Q where P i{p} g,j ,Q i{p} g,j are the active and reactive power injected by the generator from the node j, connected at the pillar i, on the phases p = {a, b, c} and P i{p} c,j , Q i{p} c,j are the active and reactive consumed power in the node j.
Step 2. The phase voltages are initialized at each node (pillar) from the distribution network with the recorded values on the LV side of electric substation (U s {p} ).The values could be different by the nominal voltage: Step 3. Backward sweep: The currents at the level of the nodes (pillars) are calculated: Energies 2019, 12, 3008 9 of 27 where k is the index of current iteration and K max expresses the maximum value of iterations initially introduced by the decision maker.

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Step 3.2.The current flow on each section (v-i) of the network are calculated: where v is the pillar in up stream of pillar i, Next (i) is the set of pillars next to the pillar i, and (v-i) is the section.
Step 4. Forward sweep: The voltage drop on the phases {p} of all sections is calculated: where Z v,i and Z v,i 0 are the impedances of the phase {p} = {a, b, c} and neutral conductors (0).The value I v,i 0 represents the current flows on the neutral conductor.

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Step 4.3.The total apparent power injected to the network is calculated:

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Step 4.4.Testing the stopping condition of iterative process: where ε S represents the imposed error by the decision maker to stop the iterative process.
Step 5.If the iterative process is finished (the relation ( 19) is accomplished), the power loss on each section (v-i) is calculated: where R v,i and R v,i 0 are the resistances of the phase and neutral conductors.
The flow-chart of the proposed algorithm with the three steps is presented in Figure 2a (the first and second stages) and Figure 2b (the third stage).

Case Study
The proposed algorithm was tested on a real pilot LV electric distribution network belonging to a DNO from Romania.The topology of the analyzed network can be seen in Figure 3.

Case Study
The proposed algorithm was tested on a real pilot LV electric distribution network belonging to a DNO from Romania.The topology of the analyzed network can be seen in Figure 3.
The electric substation MV/LV supplies 3 distribution feeders.The three feeders have 189 pillars together.The pillars represent points where the consumers are connected using single-phase (1-P) or three-phase (3-P) branching at the network, these are identified through black circles.Each section has 40 meters, representing the distance between two pillars.
The primary characteristics (number of pillars, total length, cable type, cable size, length of sections using the cable types, and the consumers' number) are shown in Table 4. Additionally, consumers' characteristics can be identified in Table 5.The primary characteristics (number of pillars, total length, cable type, cable size, length of sections using the cable types, and the consumers' number) are shown in Table 4. Additionally, consumers' characteristics can be identified in Table 5.The details regarding the allocations at pillars and phases and the type of the consumers are indicated in Appendix A, Table A1.
The connection phase of each consumer reflects the real situation and this aspect helps to establish the true-to-reality unbalanced model.The hourly load records (active and reactive power profiles) for each consumer integrated in the SMS were imported from the database of DNO for the day when the analysis was made.Based on these profiles, the phase loading at the LV level of the electric substation was calculated for each feeder (see Figures 4-6).The details regarding the allocations at pillars and phases and the type of the consumers are indicated in Appendix A, Table A1.
The connection phase of each consumer reflects the real situation and this aspect helps to establish the true-to-reality unbalanced model.The hourly load records (active and reactive power profiles) for each consumer integrated in the SMS were imported from the database of the DNO for the day when the analysis was made.Based on these profiles, the phase loading at the LV level of the electric substation was calculated for each feeder (see Figures 4-6).
From Figure 4, it can be observed that all consumers from Feeder 1 are allocated on the phase b.Feeder 2 has a high unbalance, the phase b is more loaded than the other two phases (a and c) (see Figure 5).In this case, the current flow on the neutral conductor will lead to the high additional losses.For Feeder 3, the allocation of consumers on the phases of the feeder is more balanced (see Figure 6).The details regarding the allocations at pillars and phases and the type of the consumers are indicated in Appendix A, Table A1.
The connection phase of each consumer reflects the real situation and this aspect helps to establish the true-to-reality unbalanced model.The hourly load records (active and reactive power profiles) for each consumer integrated in the SMS were imported from the database of the DNO for the day when the analysis was made.Based on these profiles, the phase loading at the LV level of the electric substation was calculated for each feeder (see Figures 4-6).
From Figure 4, it can be observed that all consumers from Feeder 1 are allocated on the phase b.Feeder 2 has a high unbalance, the phase b is more loaded than the other two phases (a and c) (see Figure 5).In this case, the current flow on the neutral conductor will lead to the high additional losses.For Feeder 3, the allocation of consumers on the phases of the feeder is more balanced (see Figure 6).The calculations of the steady-state regime were performed at each hour, h = 1, …, H (where H = 24).The total energy losses calculated with the proposed algorithm for each feeder, on the phase and neutral conductors and on the branching and the main conductors are presented in Tables 6.The obtained results with the DSPF software are presented in Table 7 to emphasize the accuracy of the proposed algorithm.
The detailed results, obtained with the proposed algorithm for each feeder, are presented in Tables A2, A3, and A4 from Appendix A. From Figure 4, it can be observed that all consumers from Feeder 1 are allocated on the phase b.Feeder 2 has a high unbalance, the phase b is more loaded than the other two phases (a and c) (see Figure 5).In this case, the current flow on the neutral conductor will lead to the high additional losses.For Feeder 3, the allocation of consumers on the phases of the feeder is more balanced (see Figure 6).
The calculations of the steady-state regime were performed at each hour, h = 1, . . ., H (where H = 24).The total energy losses calculated with the proposed algorithm for each feeder, on the phase and neutral conductors and on the branching and the main conductors are presented in Table 6.The obtained results with the DSPF software are presented in Table 7 to emphasize the accuracy of the proposed algorithm.The detailed results, obtained with the proposed algorithm for each feeder, are presented in Table A2, Table A3, and Table A4 from Appendix A.
The absolute errors (ε) and percentage errors (δ) between both approaches, DSPF software, and the proposed algorithm (PA), are presented in Table 8, Figure 7, and Figure 8.The calculation relations are the following: The absolute errors (ε) and percentage errors (δ) between both approaches, DSPF software, and the proposed algorithm (PA), are presented in Table 8, Figure 7, and Figure 8.The calculation relations are the following:    From Table 8, it can be observed that the percentage errors of the energy losses in conductors are in the range (1.62-5.17)and below 1 percent (0.94) for the total energy losses.In addition, a high value of energy loses in the neutral conductor can be highlighted.These represent about 25% of the From Table 8, it can be observed that the percentage errors of the energy losses in conductors are in the range (1.62-5.17)and below 1 percent (0.94) for the total energy losses.In addition, a high value of energy loses in the neutral conductor can be highlighted.These represent about 25% of the total energy losses, which means that the DNO should apply the balancing measures (especially in the case of Feeder 2).
In terms of phase voltages, these were calculated for each pillar.The obtained values for the farthest pillars are represented in                 The detailed results obtained with the proposed algorithm for each pillar are presented in Table A5 from Appendix A.
An analysis of Figures 9-14 highlighted that at the pillar P95 the phase voltages were inside of admissible limits (nominal voltage ± 10 %) and, at the pillar P188, only the voltage on the phase b corresponded, but was equal with the minimum value (nominal voltage -10%).The voltages on the phases a and c are slightly below the minimum limit with 0.02%.The nominal phase voltage in The detailed results obtained with the proposed algorithm for each pillar are presented in Table A5 from Appendix A.
An analysis of Figures 9-14 highlighted that at the pillar P95 the phase voltages were inside of admissible limits (nominal voltage ± 10 %) and, at the pillar P188, only the voltage on the phase b corresponded, but was equal with the minimum value (nominal voltage -10%).The voltages on the phases a and c are slightly below the minimum limit with 0.02%.The nominal phase voltage in Romania is 230 V. Thus, the DNO should apply the measures to improve the voltage level in this final node (tap changing of transformer from the electric substation).It can be observed that the MPEs is below 0.3 % on each phase at both pillars (P95 and P188).
Nomenclature: The phase impedance of each section ( The daily energy consumption for the consumer l = 1, . . ., N c , [kWh] ∆P (h)  The deviation between the measured and computed load profiles,

Figure 1 .
Figure 1.The topology of a radial LV distribution network.

Figure 1 .
Figure 1.The topology of a radial LV distribution network.

Figure 2 .
Figure 2. (a) The flow-chart of the proposed algorithm (the first and second stages); (b) The flow-chart of the proposed algorithm (the third stage).

Figure 3 .
Figure 3.The analyzed LV distribution network.

Figure 3 .
Figure 3.The analyzed LV distribution network.The electric substation MV/LV supplies 3 distribution feeders.The three feeders have 189 pillars together.The pillars represent points where the consumers are connected using single-phase (1-P) or three-phase (3-P) branching at the network, these are identified through black circles.Each section has 40 m, representing the distance between two pillars.The primary characteristics (number of pillars, total length, cable type, cable size, length of sections using the cable types, and the consumers' number) are shown in Table4.Additionally, consumers' characteristics can be identified in Table5.

Figure 4 .
Figure 4.The phase loading on the first section of Feeder 1.

Figure 5 .
Figure 5.The phase loading on the first section of Feeder 2.

Figure 4 .
Figure 4.The phase loading on the first section of Feeder 1.

Figure 4 .
Figure 4.The phase loading on the first section of Feeder 1.

Figure 5 .
Figure 5.The phase loading on the first section of Feeder 2.Figure 5.The phase loading on the first section of Feeder 2.

Figure 5 .
Figure 5.The phase loading on the first section of Feeder 2.Figure 5.The phase loading on the first section of Feeder 2.

Figure 6 .
Figure 6.The phase loading on the first section of Feeder 3.
Energies 2019, 12, x 16 of 26 total energy losses, which means that the DNO should apply the balancing measures (especially in the case of Feeder 2).In terms of phase voltages, these were calculated for each pillar.The obtained values for the farthest pillars are represented in Figures 9-11 (pillar P95-Feeder 2) and Figures 12-14 (pillar P188-Feeder 3).
The mean percentage errors (MPE) of the phase voltages are presented in Figures15 and 16.These were calculated with the following relation:Energies 2019, 12, x 18 of 26Romania is 230 V. Thus, the DNO should apply the measures to improve the voltage level in this final node (tap changing of transformer from the electric substation).The mean percentage errors (MPE) of the phase voltages are presented in Figures15 and 16.These were calculated with the following relation: observed that the MPEs is below 0.3 % on each phase at both pillars (P95 and P188).

Figure 15 .
Figure 15.The MPE of the phase voltages, Pillar P95.Figure 15.The MPE of the phase voltages, Pillar P95.

Figure 15 .
Figure 15.The MPE of the phase voltages, Pillar P95.Figure 15.The MPE of the phase voltages, Pillar P95.

Table 2 .
The format of input data.

Table 3 .
The structure vectors for the LV distribution network from Figure1.

Table 4 .
The characteristics of the feeders.

Table 4 .
The characteristics of the feeders.

Table 5 .
The characteristics of the consumers.

Table 5 .
The characteristics of the consumers.

Table 5 .
The characteristics of the consumers.

Table 6 .
The energy losses calculated with the proposed algorithm, [kWh].

Table 7 .
The energy losses calculated with the DSPF software, [kWh].
6.The phase loading on the first section of Feeder 3.

Table 6 .
The energy losses calculated with the proposed algorithm, [kWh].

Table 7 .
The energy losses calculated with the DSPF software, [kWh].

Table 8 .
Comparison between both approaches (the values of energy losses and the errors).

Table 8 .
Comparison between both approaches (the values of energy losses and the errors).