Optimal selection of metering points for power quality measurements in distribution system

Quality of power delivery in power distribution systems requires continuous measurement using power quality analyzers installed in a large number of nodes of the network. Therefore the problem of selection of metering points arises so the number of meters is kept minimal. The paper reviews three methods for selecting the metering points in a distribution grid. Performance of the methods is compared using IEEE 37-node test network and a typical MV feeder in a real-word urban area.


I. INTRODUCTION
One of the main tasks of a Distribution System Operator (DSO) is to maintain high power quality in connection points of customers. This task is supported by metering campaigns using mobile power quality (PQ) meters or analysers. In order to control power quality in the entire network in a continuous manner DSO needs a large monitoring system covering the distribution grid. The system uses a great number of PQ meters installed in selected nodes. Installing a meter in each node of the grid is not economically nor technically suitable, therefore an issue of selecting metering points appears. The points should be carefully selected so the metering system would be useful without excessive costs of installation and maintenance.
Based on general rules of generation and distribution of PQ disturbances it is possible to formulate some recommendations for selection of the metering points. Such recommendations are proposed by e.g. CIGRE (joined working group JWG C4.112) and CEER working groups [1][2][3]. In order to keep PQ parameters in MV grids substations with HV to MV transformation should be considered first. In the station MV sections should be selected for PQ monitoring. Connection points of significant customers in the grid should be selected next. This comes from the need for monitoring individual emission and possible dispute settlement when customers complain about supply quality. Following those recommendations would require installation of PQ meters in every MV substation and large customer and still would not guarantee full information about PQ parameters in the entire grid. Consequently a more analytical framework for selecting metering points is needed.
The paper is organised as follows: The 2 nd section describes shortly the problem of optimal selection of metering points, the 3 rd section presents three selected methods for selection of the nodes and their comparison using an IEEE test feeder, the 4 th section describes results of the methods in application to a typical MV distribution grid, section 5 th gives conclusions.

II. OPTIMAL SELECTION OF METERING POINTS
The problem of optimal selection of metering points can be divided into two subproblems: 1. Creation of an equivalent model and formulation of an optimisation problem. The model should allow for expressing measurement goal in an analytical form. Usually, it requires a simplified model of the grid. In order to define the optimisation problem, a criterion should be selected and formulated in an analytical form.
2. Solving the optimisation problem -which requires selecting the solving method. In most cases, the problem does not have an analytic solution so utilisation of numerical methods is needed. Due to numerical complexity heuristic methods are preferred.
For optimal selection of metering points the theoretical framework of operational research is used. Due to inherent properties of power distribution system, it may still be difficult to find a reasonable solution even if the model is proper. There may be constraints that cannot be embedded easily into the analytical form of the optimisation problem.
Full literature review excesses the framework of this paper. However, it can be concluded, that the problem of optimal selection of metering points has many solutions. Those solutions are strictly related to the assumed goal of the measurement. The problem is secondary to the more general problem e.g. state estimation (SE) or fault identification. SE framework seems to be the most appropriate for PQ metering therefore methods related to the optimal selection of metering points for SE would be also useful for PQ measurements.

METERING POINTS
Considering the type of the measurements and the tree-like topology resulting from the radial structure of the distribution system some methods should be selected for further examination. In the paper, three methods have been chosen to test their performance when applied to the selection of metering points for PQ measurement.
Method no. 1 developed by Don-Jun Won and Seung-Il Moon [4,5] tries to combine expert knowledge with observability analysis. The expert knowledge is expressed in a weighting system to define importance of nodes based on experience. Therefore for each grid element a numerical weight is defined so the priority of the element in PQ analysis is introduced. Observability analysis ensures that full SE is possible. The method can be extended by defining new weights and usually does not require complex numerical algorithms to find a solution.
The grid is modelled as a rooted tree structure which contains information about the type of grid elements and theirs connection. For each element, weighting factors can be defined according to: 1. Kirchhoff current law criterion, which states that current in a line can be computed by summation of currents in other lines. It also means that in a node comprising of n lines only n-1 can be monitored without losing observability of the system.
2. Customer connection point -when a PQ parameter exceeds limits it may affect customers. Therefore a branch with connected customers should be selected to monitor with high priority.
3. The number of branches fed form a node. Elements near the supply source are more important for monitoring due to the total number of elements connected to them.

Connection point (the beginning) of a branch -allows
for including the branch and all its descendants into a meter's coverage area installed in the node, which further increases observability of the system.
By application of the aforementioned rules weighting factors are defined and total weight is computed as a product of all partial weighting factors. The weight is a numerical value that describes the importance of the PQ measurements of the element. A hierarchy of elements can be built in this way so meters should be installed in elements having as higher total weight as possible. In order to ensure observability, an ambiguity index is introduced next. The index describes how large is the fragment of the grid that cannot be. The value of the index equals zero means that the entire grid is observed so it is possible to find a source of a disturbance if it is detected by the nearby meters.
Application of the method is as follows: first total weight for each element is computed, then an iterative procedure starts. The procedure places a meter to monitor element with the highest total weight and compute ambiguity index. If the index is greater than zero, the next meter is placed and the index is recomputed. The procedure stops when the index reaches zero which means that the grid is observable and meters monitor grid elements which give measurements of the highest importance possible.
The method is fast and easy to implement. It can be easily extended e.g. to include preinstalled meters. The method introduces also the concept of meter's section which can be useful in further analysis of the metering system e.g. by supporting measurements using mobile meters or by dividing implementation of the metering system into stages. [6] focuses on harmonics metering and considers harmonic phasor measurement. Voltage phasor meters placed in nodes selected according to the method allows for locating sources of distortion in the power system. The method also requires knowledge (or measurement) of active and reactive power of each load.

Method no. 2 developed by Saxena, Bahaumik and Singh
Application of the method is divided into two stages: 1. Observability analysis by means of iterative procedure referred to as index method. Nodes are selected based on mutual connection analysis in a way that the total observability is maximised. This stage decreases the number of nodes to analyse in the next stage. This comes from the assumption that the optimal solution can be found from a reduced set of nodes.
2. Optimisation procedure which finds a minimal set of nodes to monitor, having preselected those chosen in the stage 1. The procedure minimises a fitness function which depends on the number of used meters (in this stage) and metering redundancy i.e. the number of meters that can monitor a single node. The fitness function is nonlinear and the optimisation procedure also has to keep constraints related to observability. Therefore there is no analytical solution and heuristic algorithms should be used for the performance reason. The source paper [6] uses binary particle swarm optimisation (BPSO) procedure for this task but any other solver for binary problems can also be used.
The method guarantees total observability of the system. This allows for harmonic state estimation and also the location of harmonic current sources. [7,8] for harmonic state estimation in the system. The method focuses on analysing connections between nodes in order to provide full observability. This allows for computing harmonic voltages and current in every point of the network based on the measurements and known grid parameters. The analysis uses Kirchhoff's current and voltage laws to check whether it is possible to compute quantities in nodes or branches without any metering. The method considers voltage and current measurement separately. Although a typical meter measures voltage in one node and current in one branch, the method can include multichannel meters e.g. performing current measurement in several branches connected to that node.

Method no. 3 developed by Carlos Frederico M. Almeida and Nelson Kagan
The optimisation problem is formulated in a way that the cost of the entire metering system is minimised. The cost can include voltage and current transducers, data transmission and acquisition equipment etc. The problem is solved by using the branch and bound approach or genetic algorithm (GA) [7,8].
The source papers do not specify whether phasor or rms value of voltage and current is required to measure. If harmonic SE is required, this needs to be clarified. However, when only location of meters is considered the issue is of minor importance.

A. Method comparison using the IEEE 37-node test feeder
Performance of the described methods can be analysed by application to a common test grid. The IEEE 37-node test feeder [9] is used for this task. The test grid has been chosen due to its radial structure, typical for a distribution system. Fig. 1 shows the simplified diagram of the test feeder.
In method no. 1 a grid is represented in the form of a graph. The graph contains each grid element i.e. lines, transformers, loads etc. Due to the radial structure, the graph is a form of a tree with one root and multiple branches. The root of the graph represents the main supply which is HV/MV substation in the case. Full observability is achieved by 22 meters which monitor elements shown in Fig. 2a. When an element is chosen to monitor it requires measurement of voltage in upstream node and current in the element's branch apart of the other PQ parameters. The method prefers monitoring lines over loads in proximity of the main supply point. This is related to rule 3 of the method, which maximises observability.
The source articles leave some implementation choices to the user. This involves a situation when weighting factors are equal. The situation may be common in networks similar to the test feeder especially when the application of rule 1 is considered. Therefore proper implementation according to [4,5] may give different results.
Method no. 2 requires two stages of computation. In stage 1 (the index method) 11 nodes are selected. In stage 2 two extra nodes are added to those found in stage 1. Stage 2 of the method requires solving the optimisation problem using a heuristic algorithm. In this paper a GA is used instead of BPSO. Finally, the method selects 13 nodes for voltage monitoring.
It is worth to note that the current measurement is not considered by the method, the method requires measurement of voltages phasors only. However, in order to achieve full observability also currents of loads should be monitored, which gives extra 25 meters. The final result is visualized in Fig. 2b. It is worth to note that constrains and fitness function defined in [7] do not give a unique solution in the result. Instead, several solutions (optimal in the sense of the method) exist and an heuristic algorithm can usually find only one of them. Solution found by an implementation of GA for the purpose of this paper is presented in Fig. 3. It is expected, that utilisation of a different algorithm gives different result. From Fig. 3 it can be noticed, that full observability is achieved by voltage metering in 14 nodes and current metering in 16 branches. Harmonic SE requires load current metering which adds extra 25 meters, resulting in 41 meters in total. Usually current measurement is done in a branch connected to the node with voltage measurement. There are nodes with two branches selected for current monitoring e.g. node 713 and 710. The situation enables multichannel current metering which can decrease total number of meters needed. Multichannel metering can be enabled or disabled by modification of the cost function.
In the source articles the optimisation procedure has been classified as linear programming. However, the problem contains constraints in a form of a highly nonlinear function without analytical form. This makes utilisation of typical linear programming algorithms impossible. To solve the issue the optimisation problem can be redefined by introducing nonlinear fitness function similar to the one in method no. 2. This however changes the problem into nonlinear one and limits further the choice of solving algorithms. Among the methods described above, this one is the most computationally demanding.

B. Application to a typical MV feeder in distribution grid
In order to check performance of the methods in a realworld case a typical MV feeder has been selected. The feeder is based on a distribution system in urban area of a large city in Poland. Fig. 4 shows simplified diagram of the feeder. There are 11 nodes, 10 nodes contain MV/LV transformer which supplies mostly residential buildings. Nodes are connected by means of underground cable lines. There is also one node with significant nonlinear load i.e. a load causing a flow of distorted current. In some places a substation meter is installed. The meters provide energy metering and reduced subset of PQ parameters. The meters may be further considered as a part of the PQ metering system. Effect of application of method no. 1 is presented in Fig.  5a. Total observability of the system is provided by 10 meters. The elements selected for monitoring are marked with grey. When a line is selected for monitoring, it involves measurement of voltage in the upstream node and measurement of the line currents. Monitoring of a load involves measurement of voltage of the secondary side of the transformer and the transformer total current. Fig. 5a shows also the position in the hierarchy of measurements. Smaller numbers indicate the more important elements to monitor which results in higher priority to install a meter in the nodes. The method can be extended to include preinstalled meters if needed.
Effect of application method no. 2 is shown in Fig. 5b. The method places 4 voltage phasor meters in nodes marked in grey circles. The solution is found in stage 1 so there is no need to apply numerical optimisation procedure. To achieve total observability also currents of all loads should be measured. If preinstalled substation meters can be used for this task, the number of meters increases by 5, yielding 9 meters in total.
The method no 3 considers voltage and current metering separately. There are 20 possibilities for metering voltage and current. The method heavily relies on numerical optimisation procedure and also formulation of the cost function. Due to the low number of combinations both GA and complete enumeration (CE) method has been tested. It has been found from application of CE that observability is achieved by 3 meters which can be placed in 16 different configurations. It is expected that GA (and any other heuristic method) can find near-optimal solution which is still applicable from practical point of view. The solution found both by CE and GA is shown in Fig. 5c. Nodes selected for voltage monitoring are marked with grey circles, lines selected for current monitoring are marked with grey rings. Loads also should be monitored, which involves extra 5 meters, provided that meters preinstalled in substations can be utilised.

V. CONCLUSIONS
Utilisation of the described methods in order to select PQ measurement points is possible, however its performance varies depending on the test grid. For a simple feeder the method no. 3 gives the smallest number of required meters, however for a complex, tree-like grid, method no. 1 is better.
The research allows to draw some general conclusions. The existing methods have been developed for other purposes than PQ measurements. Extension to PQ metering is still possible but is not straightforward. Only method no. 1 has been designed for PQ metering, however without referring to specific PQ parameters that can be obtained by means of the method.
Definition of observability in the context of PQ measurement should also be reviewed and possibly formulated anew. Observability in the meaning of SE is often defined as the possibility to compute voltages and currents based on measurements and general knowledge of the grid parameters. It is not clear whether observability in this sense is sufficient to provide PQ parameters computation. Practical considerations including technical, organisational or other limitations also adds an additional level of complexity. Such issues are not usually included into the analysis. It must be concluded that there are different requirements for a method easy to apply in real-word grid than for analysis. The former should result in a metering system easy to implement under local conditions of the grid. For the latter, the solution have to be consistent with all constraints and prerequisites defined under the framework of the method.
For distribution grids with relatively simple structure i.e. one main feeder with few short lateral branches, the sufficient locations for metering include load connection points, starting with those of confirmed sensitivity to voltage disturbances or emitting excessive disturbances. Continuous PQ metering in the point would be necessary for keeping voltage quality and would be useful in case of complain settlements.
For distribution systems with a complex tree-like structure is should be necessary to apply an analytical method. Method no. 1 can be utilised due to its original purpose. However, some properties of the method have to be taken into account e.g. relatively big number of meters to achieve total observability or tendency to select a branch instead of loads for monitoring in proximity of the main supply node (HV/LV substation).

ACKNOWLEDGMENT
The research has been carried out under the project "The propagation assessment and power quality parameters improvement system in power distribution grids -SOPJEE", implemented under the "PBSE" Power Sector