On the Determination of Meshed Distribution Networks Operational Points after Reinforcement

: 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 o ﬀ er 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.


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 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.

System under Examination and Problem Formulation
Tables 1-3 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 mm 2 , R = 1.071 Ω/km and X = 0.393 Ω/km for ACSR 35 mm 2 and R = 0.215 Ω/km and X = 0.334 Ω/km for ACSR 95 mm 2 . 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 mm 2 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.
Appl. Sci. 2019, 9, x  5 of 15   20  100  34  21  2  1  69  250  85  52  6  4  22  250  85  52  6  4  67  175  59  37  4  3  25  1490  504  312  36  22  12  160  54  34  4  2  26  100  34  21  2  1  16  100  34  21  2  1  28  50  17  10  1  1  71  160  54  34  4  2  27  360  122  75  9  5  73  160  54  34  4  2 100  114  100  109  100  72  100  111  100  113  500  74  100  112  100  115  20  76  100  39  100  107  100  21  500  106  100  86  100  13  100  47  100  88  1274  103  100  55  470  116  1815  105  100  56  700 108 50    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.

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 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]: where: v f , v t , i f and i t are the terminal voltages and currents. Equation (1) connects voltages at all nodes and currents. The impedance matrix (Y br ) expresses the impedances across all branches forming a table that is unique for each network.
The admittance matrix Y br is as follows: Eventually, the balance equation based on Kirchhoff's laws can be written as follows [35], f(V, Sg) needs to equal to zero: where S g , and S d are the generators' and loads' apparent power, then (3) becomes [35] f p (Θ, V m , P g ) and fq(Θ, V m , P g ) that also need to equal to zero: and: where vector x equals to: The objective function to be minimized is: P L stands for the total active load of the line, V min is the minimum voltage observed at any node and w 1 and w 2 are the weight factors. In this work, four different cases are examined according to the following Table 4.

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 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.

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 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].

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.

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".