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Article

On the Determination of Meshed Distribution Networks Operational Points after Reinforcement

1
Department of Electrical and Electronic Engineering Educators, A.S.PE.T.E.—School of Pedagogical and Technological Education, Ν. Ηeraklion, 141 21 Athens, Greece
2
Faculty of Electrical Engineering, University Politehnica of Bucharest, Spaiul independentei 313, RO-060042 Bucharest, Romania
*
Author to whom correspondence should be addressed.
Appl. Sci. 2019, 9(17), 3501; https://doi.org/10.3390/app9173501
Received: 25 July 2019 / Revised: 12 August 2019 / Accepted: 22 August 2019 / Published: 25 August 2019
(This article belongs to the Special Issue Implementation of Vehicular Cloud Networks Using Wireless Sensor)

Abstract

:
This paper proposes a calculation algorithm that creates operational points and evaluates the performance of distribution lines after reinforcement. The operational points of the line are probabilistically determined using Monte Carlo simulation for several objective functions for a given line. It is assumed that minimum voltage at all nodes has to be balanced to the maximum load served under variable distributed generation production, and to the energy produced from the intermittent renewables. The calculated maximum load, which is higher than the current load, is expected to cover the expected needs for electric vehicles charging. Following the proposed operational patterns, it is possible to have always maximum line capacity. This method is able to offer several benefits. It facilitates of network planning and the estimation of network robustness. It can be used as a tool for network planners, operators and large users. It applies to any type of network including radial and meshed.

1. Introduction

Medium and low voltage distribution networks are mostly operated as radial; however, in some exceptional cases, they can be connected as meshed or in loops [1]. Radial circuits have many advantages over networked circuits, including easier fault current protection, lower fault currents over most of the circuit, easier voltage control, easier prediction and control of power flows and lower installation cost [2]. On the other hand, meshed networks demonstrate performance improvements and efficiency increase. The reinforcement of already existing distribution networks is an issue of priority for network operators, in an effort to ensure the uninterruptable power supply. Several works have been developed to investigate reinforcement issues in radial and meshed distribution level and to provide adequate simulation tools and methods. Alvarez-Herault et al. [3] demonstrated the benefits of meshing the network instead of reinforcing it. Novoselnik et al. [4] provided a procedure to improve networks’ performance taking into consideration the advantage of its meshed development. The networks operate in radial mode even if they are built as meshed. This article proposes a control method to optimally rearrange the radial network. Nevertheless, in this case the network continues to operate radially. Moreover, several planning methods take into consideration that optimal solutions can lead to meshed networks [5], even if they are weakly meshed. Recently, optimization for distribution network planning has led to substantial research activity even if part of the researcher community still supports, to a certain degree, the benefits of distribution system radial operation [6].
Added to the above, the increasing use of electric vehicles and the consequent impact on the operation of the network has to be taken into consideration. Note that the penetration level of electric vehicles is higher in the countries where the appropriate infrastructure is widely available [7]. Hence, their charging and their interaction in general with the electricity network can be controlled remotely in a safe manner, maybe by a charging service provider (CSP) [8,9] or on individual vehicle basis [10]. Given the already major resources provided to build the infrastructure, their charging can be prioritized on grid requirements. This would on one hand meet possible infrastructure constraints and on the other hand improve electricity system performance, even though new significant load is added. Furthermore, this procedure would offer time for system reinforcements, if these are needed.
However, system inertia exists in the system, and hence, controlled charging has to be achieved gradually [11]. It can start from lower penetration of electric vehicles and random charging when needed, up to the level where electric vehicles would charge only when grid has the essential capacity to allocate in this exercise. In this way, electric vehicles are behaving as battery storage [12]. The proposed procedure would also be enhanced in the future from improved battery performance connected to enhanced electric vehicle range that would reduce driver anxiety. However, in any case, this approach could decrease vehicle owners’ satisfaction who are used to a continued service currently offered from fossil fuel powered vehicles. This approach could also possibly deteriorate battery condition. Of course, on the other hand, drivers’ behavior affects, in a different manner, electricity systems [13].
Additionally, it could create discomfort to the industry [14] that is going to implement the incentive, but the benefits are more important to the effort. It has to be mentioned that electricity companies already have the experience in operating demand side management programs, restricted by the limited communication resources of the past. These demand side management programs are not considered as suitable for electric vehicles optimal charging [15]. Building upon this direction, bibliography proposes electric vehicle charging regulation that is organized on the transmission system or to the level of the distribution network based on a range of decision factors [16] that have to do with operational conditions or production from intermitted renewables.
Having mentioned the above, electric vehicles are to be charged in a way to provide always the necessary load [17]. This approach would contribute in achieving grid operational optimization as it is also projected in this study. This optimization would be based on the incoming intermittent energy from renewables connected to the distribution grid and the voltage profile of the line under investigation.
Except from the electric vehicles, the already widely developed connection of distributed generation [18] affects the operation of the grid. It creates bidirectional power flows [19] and changes network topology. As expected, network planning with distributed generation research applies similar to meshed network planning optimization methods [20,21]. Meshed planning in conjunction to the connection of distributed generation could potentially enhance network’s operation [22]. It has to be mentioned that in our work all components are assumed as functioning; however, in practice there could be malicious and faulty units [23].
Several optimization methods are being used for distribution network analysis, including Tabu search (TS), Simulated annealing (SA), Genetic algorithm (GA), Evolutionary strategy (ES), Artificial immune system (AIS), Ant colony optimization (ACO), Ant colony system (ACS), Particle swarm optimization (PSO) and Hybrid TS/GA (Memetic) [24]. This research is based on the Monte Carlo method [25], which is implemented to a plethora of applications [26], including network planning. On power systems, it is widely used to simulate probabilistic phenomena [27] in general, and power flows for steady state simulations [28]. Active distribution [29] and expansion [30] planning under uncertainty remains an issue of paramount importance. The dynamic programming method is a viable alternative [31]. Monte Carlo is frequently the method of choice to this direction [32]. It requires, even for today’s standards, high computational power; hence, for the simulations of this work, Okeanos cloud computing [33] is used, which is a supercomputing facility, organized on virtual machines available to the research community.
All the proposed methods for distribution network planning seek to optimize a value directly related to grids’ operation. This could be total installation and operational cost, minimum power or copper losses or voltage deviation. The proposed solutions up to today offer a deterministic approach towards solving the given electric vehicle connection capacity problem. However, they lack the capability to enhance user’s decision making capability offering additional information of system robustness, behavior and performance after reinforcement. This could be a useful tool for engineers who engage in network planning, operation and large users of the system. In this paper, a calculation procedure is developed in an effort to upgrade the operation of distribution grids, providing benefits in terms of their optimal point of operation that can be used for demand management purposes. It can be complimentary to any other optimization method for distribution grid planning. Moreover, it aims to demonstrate that distribution medium voltage network is better if operated as meshed and to provide solutions in terms of network planning. Its main contribution is the application of a novel method, based on Monte Carlo and objective functions to evaluate decisions for network reinforcement. This research is organized in three sections. Section 2. ‘System under examination and problem formulation’ describes the network under investigation and the procedure that it was followed to tackle the research question. Section 3, ‘Results and Discussion’ provides the outcome of our analysis and its commenting. Section 4 contains the conclusions and future work.

2. System under Examination and Problem Formulation

Table 1, Table 2 and Table 3 present the technical characteristics and the configuration of the distribution network under study [34]. An abstract graphical representation of the network is provided at Figure 1. The voltage level of the grid is 20 kV, the total length is 55 km and the installed capacity is 12 MVA. The network includes 45 20/0.4 kV distribution transformers and 24 renewable energy sources plants (photovoltaics). The resistance and the reactance of the conductors is R = 1.268 Ω/km and X = 0.422 Ω/km for ACSR 16 mm2, R = 1.071 Ω/km and X = 0.393 Ω/km for ACSR 35 mm2 and R = 0.215 Ω/km and X = 0.334 Ω/km for ACSR 95 mm2. In order to improve the performance of this line [34] and to demonstrate the capability of the proposed method suitable for meshed networks, it is being reinforced in a meshed manner, connecting the nodes 51 and 84 using ACSR 95 mm2 conductors. The distance between these nodes is 8 km, creating a resistance of 1.72 Ω and impedance of 2.672 Ω, or pu resistance and impedance 0.43 pu and 0.668 pu, respectively.
The total load of the line is the sum of all 20/0.4 kV transformers load and the production of renewables is fed to the line through the renewable energy sources connection points. Renewable energy sources connected to this line are located in the relatively proximity with each other. This is to the comparably limited size of a distribution line such as the one under investigation. Plants’ production is considered as analogous to their installed power but the same at each time period across all of the line since solar irradiation can be safely considered as being identical.
Figure 2 depicts the flow chart of the developed calculation procedure. The algorithm creates randomly possible loading for all transformers feeding the low voltage part of the distribution network and perform power flow analysis. Then, the values of the objective functions are calculated, and this algorithm reiterates 4 million times. The above procedure is being repeated for distributed generators production from 0 to full of their installed capacity in 1/10 steps of the maximum value.
AC power flow is used to perform the calculations for this analysis [35], by using an appropriate computer tool [25,26]. All nodes are PQ, being able to offer active and reactive power, except from the slack node. In this case, there is no generator connected. The distributed generators are simulated as negative loads given that based on research questions, their production is known. The following equations used to simulate the branches [36]:
[ i f i t ] = Y br [ v f v t ]
where: vf, vt, if and it are the terminal voltages and currents.
Equation (1) connects voltages at all nodes and currents. The impedance matrix (Ybr) expresses the impedances across all branches forming a table that is unique for each network.
The admittance matrix Ybr is as follows:
Y br = [ y ff i y ft i y tf i y tt i ]
Eventually, the balance equation based on Kirchhoff’s laws can be written as follows [35], f(V, Sg) needs to equal to zero:
f ( V , S g ) = S bus ( V ) + S d C g · S g
where Sg, and Sd are the generators’ and loads’ apparent power, then (3) becomes [35] fp(Θ, Vm, Pg) and fq(Θ, Vm, Pg) that also need to equal to zero:
f P ( Θ ,   V m ,   P g ) = P bus ( Θ ,   V m ) + P d C g · S g
f P ( Θ ,   V m ,   P g ) = Q bus ( Θ ,   V m ) + Q d C g · Q g
and:
g ( x ) = [ f P { i } ( Θ ,   V m , P g ) f Q { j } ( Θ ,   V m , P g ) ]
i I PV I PV ,   j I PQ
where vector x equals to:
x = [ Θ { ι } U m { j } ]
i I ref I PV ,   j I PQ
The objective function to be minimized is:
e = w 1 · P L + w 2 · V min
PL stands for the total active load of the line, Vmin is the minimum voltage observed at any node and w1 and w2 are the weight factors. In this work, four different cases are examined according to the following Table 4.

3. Results and Discussion

Simulation results have shown that in order to achieve the maximum possible total loading without substantially compromising voltages across the line, the transformer that feed the low voltage distribution system has to have the calculated load. Table 5 and Figure 3 show the calculated values for the objective function for each case; the values are increasing when the production from the renewables also increasing, since more load is able to be fed to the low voltage network distribution transformers without decreasing voltage at all points. The production is able to feed nearby loads; hence, the total load served is increasing without severely affecting voltage drop. The higher increase is observed when voltage drop has higher weighting factor for the case 1 and lower for case 4. The graphical representation of this interrelation shall normally provide perfect curves; however, due to the probabilistic approach applied, there could be minor rounding errors that do not substantially affect the results. The source code for this publication has been written on Matpower 6.0 [36,37] and Mathworks Matlab 2017a [38]. The Monte Carlo simulation was run on Aris high performance computing [39].
Table 6, Table 7, Table 8 and Table 9 and their graphical representations Figure 4, Figure 5 and Figure 6 present the recommended loading per node for each examined case, according to the outcomes of the developed calculation procedures. For the case 1 (Table 6 and Figure 4), the obtained results indicate that most of the transformers can be fed near their installed capacity. However, there are connection points that when energy production from renewables is high, they need to keep their load low and vice versa. Other transformers, such as 49 and 15, need to be downscaled if these operational patterns are to be applied. In all cases, its proposed loading does not exceed 60% of their installed capacity. Another solution could be to further reinforce the line at these points.
Considering case 2 (Table 7 and Figure 5), similar results are being observed. The proposed load for several transformers (15, 40, 49, 50, 69, 75, 92, 94, 99, 101) does not exceed 70% of their installed power at any production from the renewable energy sources. Similarly, the proposed load of the transformers 1, 40, 46 and 71 for case 3 (Table 8 and Figure 6) and 1, 7, 10, 12, 14, 16, 59, 61, 64, 66 and 98 for case 4 (Table 9 and Figure 4) does not exceed their installed power capacity. Note that these nodes are the points that are expected to receive more attention for downscaling and/or line reinforcing. Added to the above, it is necessary to highlight the impact of the considered distribution generation (DG) on the obtained results. In cases 1 and 3, the loading per node for DG from 50% to 100% of the installed capacity does not change. In case 2, DG from 20% to 100% provides the same results, since for case 4, the distribution generation does not affect the proposed loading of each transformer.
The proposed method is able to evaluate the performance of the line after reinforcement, even if this is done using meshed networks configuration. It can be used additionally to any other distribution optimization method. The results are able to propose specific operational points of the line based on the production of the connected distributed generations. In this case, the optimal loading of the line at each of its points is predefined. Given that according to the current operational procedures for the distribution lines it is not possible to control loading with such an accuracy, the applicability of the method is restrained.
The connection of new elements such as electric vehicles and storage, on one hand substantially enhances the capability of demand management and on the other hand there are limitations for lines’ expansion. Existing bibliography on the field supports this approach and provides solutions on this direction. Electric vehicles can be aggregated to a virtual power plant, being able to offer ancillary services [40]. This technology can be applied here to always have the operation near the optimal points [41]. However, it has to be mentioned that this procedure would potentially affect customers comfort due to the prioritization of network capacity over user immediate requirements for charging but with substantial benefit to grid flexibility and performance [42].

4. Conclusions

This paper proposes an innovative probabilistic method for evaluating the potential performance of meshed and radial distribution lines, improving electric energy distribution grids reinforcement decisions. It is developed as additional to the existing distribution networks optimization methods, offering a tool for performance evaluation. Furthermore, it serves to the creation of operational points to be used for demand management, if electric vehicle charging is completely controlled. This method is a useful tool for network planners, operators and large users, since they are more able to estimate the robustness of a given network after reinforcement and its capability to host electric vehicle loads. The operational points are loading patterns for the transformers of the low voltage distribution network that minimize voltage drop and maximize total loading. They are calculated for increasing production of the connected to the line distributed generators. Other distribution network lines are expected to have similar behavior. They shall present specific operational patterns and their reinforcement could be also evaluated using this method. Future work includes the investigation of the adoption of the appropriate protection schemes that will ensure the reliable and uninterruptable operation of the network.

Author Contributions

Conceptualization, methodology, V.V.; writing—original draft preparation, writing—review and editing, S.L.; validation, C.A.C.; resources, data curation, G.S.

Funding

The authors acknowledge financial support for the open source publication of this work from the Special Account for Research of ASPETE through the funding program “Strengthening research of ASPETE faculty members” under the project “DECA”.

Acknowledgments

The calculation resources for this research were provided by Okeanos high performance cloud computing [33]. This work was also supported by computational time granted from the Greek Research & Technology Network (GRNET) in the National HPC facility—ARIS—under project ID pa171102 [39]. The authors would like to thank the unknown reviewers, whose comments have improved the quality of this work.

Conflicts of Interest

The authors declare no conflict of interest.

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Figure 1. Abstract graphical representation of the network.
Figure 1. Abstract graphical representation of the network.
Applsci 09 03501 g001
Figure 2. Flow chart of the developed calculation procedure.
Figure 2. Flow chart of the developed calculation procedure.
Applsci 09 03501 g002
Figure 3. Graphical representation of the calculated values.
Figure 3. Graphical representation of the calculated values.
Applsci 09 03501 g003
Figure 4. Graphic representation of the loading per node for case 1.
Figure 4. Graphic representation of the loading per node for case 1.
Applsci 09 03501 g004
Figure 5. Loading per node according for case 2.
Figure 5. Loading per node according for case 2.
Applsci 09 03501 g005
Figure 6. Loading per node for cases 3 and 4.
Figure 6. Loading per node for cases 3 and 4.
Applsci 09 03501 g006
Table 1. Network topology.
Table 1. Network topology.
Line (Node→Node)Length [km]Cross Section [mm2]Line (Node→Node)Length [km]Cross Section [mm2]
1→20.259557→580.48335
1→32.3059558→590.67735
2→40.4889558→600.01416
4→50.9453561→620.595
6→40.5059561→630.195
6→70.3339564→630.64816
6→80.1321665→630.195
7→90.4731665→660.1816
7→1019566→670.52416
10→110.559566→680.16916
11→120.1799568→1170.2216
11→130.0683568→690.01416
11→140.2429570→710.50716
14→150.5219570→720.00835
14→160.3631673→740.0135
15→170.69575→760.0135
17→180.2251675→770.0135
17→190.1979578→790.45135
19→200.2089578→800.04335
20→210.0083580→810.47935
20→220.0069582→830.57135
22→230.3349582→810.0135
22→240.7853584→851.38435
25→262.4193584→860.02235
26→273.1253587→880.07535
26→280.2583589→840.24435
29→300.8711690→820.26616
30→310.141690→910.416
32→330.3049590→920.0616
32→340.3111693→944.96816
32→350.1089595→930.616
35→360.4693596→950.22816
36→370.4653592→970.35916
36→380.6619597→980.00716
38→390.53599→970.36816
38→400.44795100→1010.01816
41→400.32616102→30.00195
42→430.08295103→1040.0735
42→440.316105→1040.19835
42→400.34395106→490.00135
45→461.36516107→830.00635
45→470.02335108→980.0135
48→451.27516109→780.48735
46→490.10235110→280.1435
46→5010.18116111→370.29835
51→520.77735112→370.00135
52→530.28635113→800.12535
52→540.70235114→350.27735
54→550.07635115→810.35635
54→560.41435116→871.29735
Table 2. Installed capacity (S), maximum and minimum active and reactive loads (Pmax, Qmax, Pmin, Qmin) of each 20/0.4kV distribution transformer.
Table 2. Installed capacity (S), maximum and minimum active and reactive loads (Pmax, Qmax, Pmin, Qmin) of each 20/0.4kV distribution transformer.
NodeS [kVA]Pmax [kW]Qmax [kVAr]Pmin [kW]Qmin [kVAr]NodeS [kVA]Pmax [kW]Qmax [kVAr]Pmin [kW]Qmin [kVAr]
15017101146200684253
248516410212749100342121
4720243151171157210714453
61003421215950171011
7320108678560100342121
1092031119322146175251621
1415051314264560189117148
15660223138161066250855264
197525162111741013986106
2010034212169250855264
2225085526467175593743
251490504312362212160543442
2610034212116100342121
285017101171160543442
27360122759573160543442
29810274170201275250855264
3110034212196160543442
94101398610694250855264
3410034212192100342121
4010034212198160543442
4116054344299160543442
455017101110150171011
50545184114138
Table 3. Renewable energy sources at every node.
Table 3. Renewable energy sources at every node.
NodeInstalled Power [kW]NodeInstalled Power [kW]NodeInstalled Power [kW]
110100114100109100
72100111100113500
7410011210011520
7610039100107100
2150010610086100
1310047100881274
103100554701161815
1051005670010850
Table 4. Examined cases.
Table 4. Examined cases.
Casew1w2
10.50.5
20.60.4
30.70.3
40.80.2
Table 5. Calculated value of the objective function. DG: distribution generation.
Table 5. Calculated value of the objective function. DG: distribution generation.
Case 1Case 2Case 3Case 4
without DG0.76830.76110.76110.7689
10% of DG prod0.78720.77720.77590.7795
20% of DG prod0.79970.79180.78710.7879
30% of DG prod0.80970.80450.79660.7949
40% of DG prod0.81750.81550.80480.8009
50% of DG prod0.82610.82510.81240.8061
60% of DG prod0.83510.83030.81940.8107
70% of DG prod0.8430.83610.82550.8148
80% of DG prod0.84990.84340.83090.8117
90% of DG prod0.85210.84830.83460.8143
full DG prod0.85370.84960.83560.8166
Table 6. Loading per node for case 1.
Table 6. Loading per node for case 1.
Node0% DG10% DG20% DG30% DG40% DG50–100% DG
183.8%3.0%83.8%81.8%39.1%15.2%
288.6%90.2%88.6%96.0%94.3%88.5%
490.5%91.1%90.5%86.9%98.9%91.9%
697.6%92.5%97.6%98.0%92.8%99.2%
734.7%94.8%34.7%92.4%92.7%82.6%
1068.7%97.0%68.7%12.4%83.8%47.8%
1482.8%45.2%82.8%76.0%18.5%98.8%
1516.5%61.8%16.5%32.5%27.8%33.0%
1997.3%84.0%97.3%87.1%84.4%82.8%
2051.4%79.1%51.4%26.0%84.6%84.2%
2267.6%91.3%67.6%90.0%86.8%97.1%
2599.3%91.9%99.3%84.6%71.6%93.2%
2690.8%91.7%90.8%82.5%94.4%94.0%
2883.8%78.8%83.8%37.9%28.9%6.7%
2784.1%54.2%84.1%82.4%91.5%95.7%
2989.7%94.7%89.7%84.0%31.4%64.4%
3127.0%61.3%27.0%80.0%82.4%76.7%
974.6%39.7%74.6%42.3%28.7%98.0%
3431.3%90.4%31.3%60.8%92.4%71.1%
4058.6%57.4%58.6%88.7%75.8%11.2%
4184.3%88.7%84.3%32.7%68.6%93.9%
4532.6%82.5%32.6%68.2%54.5%6.7%
5045.6%43.5%45.6%57.6%54.4%56.9%
4638.9%3.6%38.9%80.4%19.6%62.0%
4914.9%16.5%14.9%3.4%30.5%53.3%
537.6%64.4%7.6%80.3%92.2%1.5%
5986.9%44.9%86.9%97.1%49.8%82.2%
6019.5%30.2%19.5%79.6%22.7%87.9%
6169.5%95.7%69.5%81.2%61.9%97.8%
6475.0%12.2%75.0%51.6%28.9%71.5%
6670.9%62.3%70.9%55.8%70.6%91.9%
11735.8%86.7%35.8%75.1%40.8%50.9%
6923.9%40.2%23.9%65.2%71.6%48.6%
6786.1%99.4%86.1%86.3%80.6%91.6%
1271.5%80.7%71.5%64.6%22.3%85.1%
1677.5%24.0%77.5%85.7%83.6%70.6%
7159.6%55.7%59.6%17.8%52.0%45.3%
1824.5%32.6%24.5%11.8%91.6%80.3%
7559.8%84.9%59.8%12.0%89.5%93.5%
9617.9%60.7%17.9%49.8%17.6%91.2%
9478.7%57.3%78.7%74.5%74.7%11.6%
9230.7%67.6%30.7%86.7%79.9%37.4%
9820.1%54.8%20.1%50.9%3.3%84.5%
9946.7%36.9%46.7%18.7%24.7%11.5%
10192.5%0.8%92.5%24.7%43.0%22.8%
Table 7. Loading per node for case 2.
Table 7. Loading per node for case 2.
Node0% DG10% DG20–100% DGNode0% DG10% DG20–100% DG
13.0%3.0%15.2%463.6%3.6%62.0%
290.2%90.2%88.5%4916.5%16.5%53.3%
491.1%91.1%91.9%5364.4%64.4%1.5%
692.5%92.5%99.2%5944.9%44.9%82.2%
794.8%94.8%82.6%6030.2%30.2%87.9%
1097.0%97.0%47.8%6195.7%95.7%97.8%
1445.2%45.2%98.8%6412.2%12.2%71.5%
1561.8%61.8%33.0%6662.3%62.3%91.9%
1984.0%84.0%82.8%11786.7%86.7%50.9%
2079.1%79.1%84.2%6940.2%40.2%48.6%
2291.3%91.3%97.1%6799.4%99.4%91.6%
2591.9%91.9%93.2%1280.7%80.7%85.1%
2691.7%91.7%94.0%1624.0%24.0%70.6%
2878.8%78.8%6.7%7155.7%55.7%45.3%
2754.2%54.2%95.7%1832.6%32.6%80.3%
2994.7%94.7%64.4%7584.9%84.9%93.5%
3161.3%61.3%76.7%9660.7%60.7%91.2%
939.7%39.7%98.0%9457.3%57.3%11.6%
3490.4%90.4%71.1%9267.6%67.6%37.4%
4057.4%57.4%11.2%9854.8%54.8%84.5%
4188.7%88.7%93.9%9936.9%36.9%11.5%
4582.5%82.5%6.7%1010.8%0.8%22.8%
5043.5%43.5%56.9%
Table 8. Loading per node for case 3.
Table 8. Loading per node for case 3.
Node0% DG10% DG20% DG30% DG40% DG50–100% DG
13.0%15.2%15.2%15.2%15.2%53.1%
290.2%88.5%88.5%88.5%88.5%90.5%
491.1%91.9%91.9%91.9%91.9%96.8%
692.5%99.2%99.2%99.2%99.2%94.5%
794.8%82.6%82.6%82.6%82.6%61.8%
1097.0%47.8%47.8%47.8%47.8%61.8%
1445.2%98.8%98.8%98.8%98.8%5.0%
1561.8%33.0%33.0%33.0%33.0%91.7%
1984.0%82.8%82.8%82.8%82.8%85.6%
2079.1%84.2%84.2%84.2%84.2%93.6%
2291.3%97.1%97.1%97.1%97.1%90.0%
2591.9%93.2%93.2%93.2%93.2%91.5%
2691.7%94.0%94.0%94.0%94.0%91.9%
2878.8%6.7%6.7%6.7%6.7%22.3%
2754.2%95.7%95.7%95.7%95.7%76.0%
2994.7%64.4%64.4%64.4%64.4%94.7%
3161.3%76.7%76.7%76.7%76.7%99.3%
939.7%98.0%98.0%98.0%98.0%93.2%
3490.4%71.1%71.1%71.1%71.1%58.5%
4057.4%11.2%11.2%11.2%11.2%3.7%
4188.7%93.9%93.9%93.9%93.9%31.3%
4582.5%6.7%6.7%6.7%6.7%16.2%
5043.5%56.9%56.9%56.9%56.9%77.0%
463.6%62.0%62.0%62.0%62.0%34.8%
4916.5%53.3%53.3%53.3%53.3%85.3%
5364.4%1.5%1.5%1.5%1.5%88.1%
5944.9%82.2%82.2%82.2%82.2%59.2%
6030.2%87.9%87.9%87.9%87.9%79.4%
6195.7%97.8%97.8%97.8%97.8%57.0%
6412.2%71.5%71.5%71.5%71.5%53.9%
6662.3%91.9%91.9%91.9%91.9%66.7%
11786.7%50.9%50.9%50.9%50.9%76.5%
6940.2%48.6%48.6%48.6%48.6%88.3%
6799.4%91.6%91.6%91.6%91.6%96.7%
1280.7%85.1%85.1%85.1%85.1%53.7%
1624.0%70.6%70.6%70.6%70.6%34.3%
7155.7%45.3%45.3%45.3%45.3%8.4%
1832.6%80.3%80.3%80.3%80.3%46.7%
7584.9%93.5%93.5%93.5%93.5%65.0%
9660.7%91.2%91.2%91.2%91.2%48.7%
9457.3%11.6%11.6%11.6%11.6%82.8%
9267.6%37.4%37.4%37.4%37.4%97.5%
9854.8%84.5%84.5%84.5%84.5%45.1%
9936.9%11.5%11.5%11.5%11.5%96.9%
1010.8%22.8%22.8%22.8%22.8%70.3%
Table 9. Loading per node for case 4.
Table 9. Loading per node for case 4.
NodeAll CasesNodeAll CasesNodeAll CasesNodeAll Cases
153.1%2691.9%4985.3%718.4%
290.5%2822.3%5388.1%1846.7%
496.8%2776.0%5959.2%7565.0%
694.5%2994.7%6079.4%9648.7%
761.8%3199.3%6157.0%9482.8%
1061.8%993.2%6453.9%9297.5%
145.0%3458.5%6666.7%9845.1%
1591.7%403.7%11776.5%9996.9%
1985.6%4131.3%6988.3%10170.3%
2093.6%4516.2%6796.7%
2290.0%5077.0%1253.7%
2591.5%4634.8%1634.3%

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Vita, V.; Lazarou, S.; Christodoulou, C.A.; Seritan, G. On the Determination of Meshed Distribution Networks Operational Points after Reinforcement. Appl. Sci. 2019, 9, 3501. https://doi.org/10.3390/app9173501

AMA Style

Vita V, Lazarou S, Christodoulou CA, Seritan G. On the Determination of Meshed Distribution Networks Operational Points after Reinforcement. Applied Sciences. 2019; 9(17):3501. https://doi.org/10.3390/app9173501

Chicago/Turabian Style

Vita, Vasiliki, Stavros Lazarou, Christos A. Christodoulou, and George Seritan. 2019. "On the Determination of Meshed Distribution Networks Operational Points after Reinforcement" Applied Sciences 9, no. 17: 3501. https://doi.org/10.3390/app9173501

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