24 th International Conference on Electricity Distribution Glasgo, 25 June 207 Paper 007 LINEAR THREEPHASE STATE ESTIMATION FOR LV GRIDS SING PSEDO MEASREMENTS BASED ON APPROXIMATE POWER DISIBTIONS Robert BRANDALIK, Dominik WAERESCH, Wolfram H. WELLSSOW, Jiali T T Kaiserslautern Kaiserslautern, Germany brandalik@eit.unikl.de ABSACT The large increase of distributed generation (DG) of photooltaic (PV) systems in lo oltage (LV) grids results in increasing oltage magnitudes and line loadings. Due to a lack of netork obserability in present LV grids, distribution system operators (DSOs) cannot detect and respond to any limit iolations. Een ith data collected by the expected rollout of smart meters, full netork obserability ill not be achieed. Thus, the netork state ill not be completely knon. LVState Estimation (SE) in combination ith pseudoalue generation can proide a ay to determine the required netork states ith respect to oltage magnitudes and line loadings. This paper presents a linear threephase LVSE approach computed in phase sequences. The performance of the presented SE approach as inestigated on a realistic grid model for different cases ith and ithout pseudoalues. The performance is promising and the approach can be used to proide DSOs ith input data for control actions to aoid limit iolations and thus ill contribute to the further integration of DG. INODCTION The distributed generation (DG) of photooltaic (PV) systems in lo oltage (LV) grids is groing enormously. In Germany, nearly 98 % of all installed PV systems are connected to LV grids []. This corresponds to 60 % of the total installed poer of around 40 GW [2]. Similar alues are present for the hole of Europe []. As a result of the noadays high DG in LV grids, the oltage magnitudes and line loadings are increasing. Limit iolations already occur and ill occur een more frequently ith the further increase of DG. Due to a lack of netork obserability in present LV grids, distribution system operators (DSOs) cannot detect and respond to any limit iolations. With the expected rollout of smart meters, some data from LV grids ill be collected, but not enough to achiee netork obserability. Thus, the netork state is not fully knon. LVState Estimation (SE) in combination ith actie and reactie poer pseudoalues proides a ay to determine the required netork states ith respect to limit iolations. The paper presents a ne LVSE approach and determines the performance of the approach for different cases ith and ithout pseudoalues on a realistic LV grid model. For the performance ealuation, the maximum errors for oltage magnitudes and line loadings hae been determined, as they need to be considered for aoiding limit iolations, thus calculating on the safe site. First a brief reie of existing LVSE approaches is gien. After that, the mathematical background of the ne LVSE is shon. Then, the testbed used to determine the performance of the LVSE for different cases ith and ithout pseudoalues is presented. Finally, the performance is determined and a conclusion is gien. It has been confirmed that a LVSE based only on oltage measurements and pseudoalues shos good performance to detect oltage iolations of upper limits. STATE OF THE ART Lo oltagestate Estimation LVSE should meet the folloing conditions: (i) Be applicable for threephase calculation. LV grids are in general unbalanced. Symmetric LVSE is not able to detect singlephase limit iolations. Thus, symmetric LV SE does not calculate on the safe side. (ii) Proide results alays. For the case of limit iolations, the results of LV SE is the input data for triggering control actions as generation or demand side management. Taking the high number of LV grids into consideration, control actions cannot be done by operators, they hae to be done closed loop. Thus, LVSE alays needs to proide results. Standard SE algorithms use iteratie methods, as the SE problem is by definition nonlinear. These algorithms can lead to conergence problems, thus not proiding results. Hence, it is better to use a less accurate method (such as a linearized method), that alays proide results. (iii) Be highly computationally efficient. It ould be too expensie to install highperformance computers in each lo oltage grid. The LVSE algorithm has to be as efficient as possible. In the field of SE for distribution systems, a lot of research as done in recent years. A good reie of different SE methods for distribution systems is gien in [4]. Hoeer, most of the methods are not focusing on LV grids. In this paper, only the methods suggested for LV grids ill be discussed. Most of the suggested methods are based on the eighted least square (WLS) approach, as in [5], [6] and [7]. In [4] a threephase SE method using hybrid particle sarm optimization is presented. The method meets condition (i), but fails condition (ii) and (iii), as for the case study 000 iterations ere necessary. The suggested method in [5] is focusing on meter placement, but fails to meet any of the aboementioned conditions. A linear threephase LVSE approach computed in symmetrical components has been presented in [6] and [7]. It meets all CIRED 207 /5
24 th International Conference on Electricity Distribution Glasgo, 25 June 207 Paper 007 conditions, but condition (iii) only partly as for each time step all measurements first need to be transformed into symmetrical components and after the SE calculation transformed back to phase sequences. To oercome these draback, a linear threephase SE approach computed in phase sequences has been deeloped. The ne SE approach is also based on the WLS method, but applies a linear Taylor approximation of the measurement functions [8]. Pseudoalues for lo oltage grids In [9] it as shon that accurate pseudoalues for PV system can be obtained if one PV system in the area of the LV grid is measured. Hence, pseudoalues for PV systems ill not be inestigated in this paper. Methods for the generation of pseudoalue for loads can be categorized in (a) Methods based on load profiles, (b) Probabilistic methods and (c) Adanced mathematical methods. Methods based on load profiles hae the draback that alues for all loads at the same time step usually are similar, hat in reality is not the case. Such a method is presented in [0]. Probabilistic methods assume that load alues follo a certain probability distribution. The pseudoalues are obtained from these distributions. Such a method is presented in []. Adanced mathematical methods are all methods that use extensie calculations. They are usually not efficient enough for grid operation. Such a method is presented in [2]. The method uses artificial neural netorks for the pseudoalue generation. A separation of loads into different types (households, industry, electric ehicles etc.) is not discussed, as each method can be applied for all types of loads. The focus of this paper is on the pseudoalues for household loads, as they are by far the most common in LV grids. NEW LINEAR THREEPHASE STATE ESTIMATION APPROACH Mathematical background The idea behind SE is to calculate the statistically most probable alues for a set of state ariables, based on a set of measurements ith hom they are related. The SE problem is defined by [] as soling the equation for the measurement model () here z is the measurement ector of m independent measurements, x the state ector of n ariables, h the measurement function ector relating x to z and e the error ector of measurements. zh x e In poer systems, the state ector is defined as the oltage magnitudes and angles of all nodes. The measurement ector and the measurement function ector depend on the existing measurements. The measurements can be diided into measurements of oltage and current magnitudes and actie, reactie and apparent poer. Voltage angles can also be measured ith phasor measurement unit (PMs), but this is too expensie for lo oltage grids and ill not be further considered. The measurement model is nonlinear as all of the measurement types, except the oltage magnitudes, are nonlinear functions of x. The measurement model can be linearized if Taylor series of the measurement functions are applied. nfortunately, a straightforard linearization of measurement functions for apparent poer and current magnitudes is not possible. An approach for their linearization is gien in [4]. In this paper, they are not considered further. Assuming the symmetrical component parameters of a threephase line connecting node i ith node j is knon, the admittance matrix of the line in symmetrical components 02 can be built. This matrix can be transformed into the admittance 2 matrix in phase sequences. No the relation beteen complex current flos and node oltages can be expressed ith (2). i j I i j I 2 2 2 2 i j I The complex poer flo for phase (), here is the element of column., [,2,] 2 * i * i i j S I, is gien ith at ro and i With the introduction of (4), here is the oltage angle for node i and phase, the actie and reactie poer flo for phase are gien ith (5) and (6), respectiely. and are the conductance and the susceptance of the admittance matrix at ro and column, respectiely. As it can be seen, the equations are nonlinear. B, c 2,,,2, i j, s cos, sin,,,, i i ii ii,,,, P G c B s... j G, c, B, s, i i ii ii,,,, Q G s B c... j G, s, B, c, G, Assuming the ealuation point (7) and applying Taylor approximation on (5) and (6), the linearized approximation for the actie and reactie poer flo for phase can be expressed after some mathematical deriations as (8) and (9), respectiely. ref, 0 if 0 ii,,,,ref 2 / if 2 2 / if 2 CIRED 207 2/5
24 th International Conference on Electricity Distribution Glasgo, 25 June 207 Paper 007 i j ref,,,ref,,,ref P G c B s... 2 i j ref G, s,,ref B, c,,ref i j ref,,,ref,,,ref Q G s B c... 2 i j ref G, c,,ref B, s,,ref For, e.g. the nominal oltage of the grid or the oltage at the transformer can be chosen. The expressions can be extended for poer injections, as shon ith (0). Where N is the number of grid nodes. ref N N i i j j P P Q Q With the linearization, all measurements are linear functions of the state ector, thus the measurement model () can be expressed ith (), here H is the measurement function matrix, formed based on (8), (9) and (0). zhxe With the application of WLS, the estimated state is gien ith (2), here R is a diagonal matrix of the corresponding measurement ariances []. T T ˆ, diag 2 2,..., m x H R H H R z R Application of pseudoalues A necessary condition for the application of SE is a positie redundancy. This means, the number of measurements must be higher than the number of state ariables, as seen from the redundancy definition (). m n, n 2 N As mentioned before, the number of measurements in LV grids are too lo and positie redundancy cannot be achieed ith measurements only. Hence, pseudoalues for loads are necessary. In this paper, the application of pseudoalue generation based on approximate poer distributions for loads as tested. The generation process is presented in []. The results of [] sho, that for each time step the distribution of poer alues for all loads in a LV grid can be approximated ith sufficient accuracy and good properties for use ith the LVSE. TESTBED Model of the LV grid The LVSE approach as tested on the actual models of the LV grids from the projects SmartSCADA and CheapFlex. Information about the projects can be found in [7] and []. In this paper the results for the CheapFlex grid are presented. Fig. shos the CheapFlex grid. The ˆx Figure. Aerial ie of the LV grid from the CheapFlex project, the transformer position is indicated. grid has 258 nodes, 260 lines, 28 loads and 8 PV systems. It is supplied ith a 400 kvatransformer ith eight feeders. Time series for loads and photooltaic systems Threephase time series for loads and PV systems hae been gathered in a 0minute measurement interal during a toyear measurement campaign on around 00 households ithin the SmartSCADA project. The time series for actie and reactie poer for a year period from st January 205 till st January 206 ere used. Benchmark The time series ere randomly assigned to the loads and PV systems of the LV grid. With the assigned alues, poerflo calculations ere performed. The results of the poerflo calculations are used as a benchmark for the estimated results. Test cases Four different cases ere defined to determine the performance of the LVSE approach. Tab. gies an oerie of the inestigated cases. For each case, the alues or the structure of the measurement ector z are different. In other ords, the assumed measurement scope is different. A separation beteen the transformer node (), household nodes () and zero injection nodes () as made. Zero injection nodes are grid connection nodes ithout poer injection or consumption. In LV grids, they are mostly underground nodes ithout the possibility to be measured. The subscript B+ means that input measurements are chosen as equal to the corresponding benchmark alues superimposed ith N noise. The alues for ere chosen based on the accuracy of smart meters. These alues are the representation of real measurements. The subscript AD means that input CIRED 207 /5
24 th International Conference on Electricity Distribution Glasgo, 25 June 207 Paper 007 Table. Oerie of inestigated test cases for z Case Case 2 Case Case 4 B+ 0. B+ B+ 0. 0. measurements are pseudoalues chosen randomly from the approximate actie poer distribution ith a poer factor of 0.9 from []. Their alues for are equal to the assumed pseudoalue accuracy. If there is no alue for in a ro, the corresponding measurements do not occur in z. The symbol means that all oltage angles ere applied to z. If this is the case, the oltage angles of each node are assumed equal to the oltage angle of the transformer (slack) node. Case represents the situation here the oltage magnitude, actie and reactie poer alues of all nodes are measured. The purpose of this case is to inestigate the sole accuracy of the ne LVSE approach. Case 2 represents an extended case. The only difference to case is that all oltage angles occur in z, ith the assumption that all oltage angles are the same as the slack oltage angle. This leads to more redundancy, but also to some error. The purpose of this case is to inestigate this error. Case represents a case that really can be achieed ith measurement equipment. The oltage of the zero injection nodes can in most case not be measured, as they are usually underground. About half of the nodes in a LV grid are zero injection nodes, so the redundancy is reduced by 0.25 (onequarter of the number of state ariables). The purpose of this case is to inestigate hat ould be the accuracy of the approach if smart meters ould measure oltage magnitudes, actie and reactie poers of all households. Case 4 is a modified case. In this case, the actie and reactie poer alues for households are replaced ith pseudoalues. The reason for this case is, that in Germany it is only alloed to measure oltage magnitudes for households [5]. B+ 0. B+ B+ 0. 0. 0.0 B+ 0. B+ B+ 0. 0.0 P AD 60 0.5 Q AD 60 0.5 B+ 0. B+ B+.5 2.75.75 0. 0.0 nits of measurements: [P] = W, [Q] = ar, [] = V, [] = rad. Superscript meaning: Transformer node, Household node, Zero injection node. Subscript meaning: B+ noisy benchmark alues, AD alues from approximate distributions. RESLTS As mention before, the maximum errors for oltage magnitudes and line loadings are of interest. They are calculated by (4). Where the subscript Case indicates the case alues and Benchmark the benchmark alues. error Case Benchmark, Ierror ICase IBenchmark Tab. 2 shos the error range for the different cases oer all time steps. A separation beteen the maximum positie and the maximum negatie alues as made to find out if the LVSE approach has a certain tendency. Another reason for this separation is that today DSOs are interested in the detection of higher oltage magnitudes or line loadings. For this detection, positie errors are not in the scope of interest as they lead to results on the safe side. In the future, hen automatic control actions ill be performed in LV grids, also the loer oltage magnitudes and line loading can be in the scope of interest. For this reason, the hole error range as inestigated. It can be seen that cases, 2 and hae ery similar and small errors. This leads to the conclusion that the LVSE algorithm ithout pseudoalues is accurate. For the case ith pseudoalues (case 4), an acceptable alue of. V for the maximum negatie oltage magnitude error and an acceptable alue of 27.25 A for the maximum positie line loading error as calculated. The maximum positie oltage magnitude error and the maximum negatie line loading error are too high and not acceptable. The reason for this is that the used pseudoalue generation has a limit for actie poer pseudoalues of 2 kw. In reality, higher alues may occur, for example for households ith heat pumps. Thus the pseudoalues are too small and lead to noticeable smaller calculated oltage drops and line loadings. The same can be noticed ith Fig. 2, here the range of oltage magnitude and line loading errors for different daytimes for case and 4 are shon. The highest errors occur for time steps ith high loads. The pseudoalue generation has to be improed to generate actie poer alues higher than 2 kw. Another option is to apply bad data detection and in this ay find loads ith too small alues. First tests ith bad data detection shoed promising results. CONCLSION The paper presents a noel LVSE approach computed in phase sequences. The performance of the approach is excellent if all loads of a LV grid are measured. As this is Table 2. Error range for the different cases Case: 2 4 error max 0.97 V 0.925 V 0.969 V 5.724 V error min 0.86 V 0.8 V 0.400 V.0 V error max I.724 A.74 A.80 A 27.250 A error min I.62 A.296 A.98 A 4.254 A CIRED 207 4/5
24 th International Conference on Electricity Distribution Glasgo, 25 June 207 Paper 007 Figure 2. Range of oltage magnitude and line loading errors for different daytimes for case and 4. neer the case, the approach as also tested ith the use of pseudoalues. The pseudoalue generation based on approximate poer distributions for loads as chosen. The results ith pseudoalues sho that the pseudoalue generation needs to be improed for higher loads or a bad data detection needs to be applied to get applicable results. Neertheless, as the maximum negatie oltage error is an acceptable. V, the approach can at least be used to detect oltage iolations of upper limits caused by DG. Acknoledgments This ork has been sponsored by the German Federal Ministry of Economic Affairs and Energy as part of the 6 th Energy Research Programme of the Federal Goernment ithin the projects SmartSCADA and CheapFlex. REFERENCES [] Fraunhofer Institute for Solar Energy Systems ISE, "Aktuelle Fakten zur Photooltaik in Deutschland," Report, Freiburg, October 206. [2] Deutsche Gesellschaft für Sonnenenergie e.v., "Die Karte der Erneuerbaren Energien," Accessed (December 206) from: http://.energymap.info. [] M. Vandenbergh et al., "Prioritization of technical solutions aailable for the integration of PV into the distribution grid," Report, June 20. [4] S. Nanchian, A. Majumdar and B. Pal, "Threephase state estimation using hybrid particle sarm optimization," 206 IEEE Poer and Energy Society General Meeting (PESGM), Boston, MA, 206. [5] A. AbdelMajeed, S. Tenbohlen, D. Schöllhorn and M. Braun, "Meter placement for lo oltage system state estimation ith distributed generation," 22nd International Conference and Exhibition on Electricity Distribution (CIRED 20), Stockholm, 20. [6] D. Waeresch, R. Brandalik, W. H. Wellsso, J. Jordan, R. Bischler and N. Schneider, "State estimation in lo oltage grids based on smart meter data and photooltaicfeedinforecast," 2rd International Conference on Electricity Distribution (CIRED 205), Lyon, 205. [7] D. Waeresch, R. Brandalik, W. H. Wellsso, J. Jordan, R. Bischler and N. Schneider, "Linear state estimation in lo oltage grids based on smart meter data," 205 IEEE Eindhoen PoerTech, Eindhoen, 205. [8] A. Cate, "Simultaneous OneStep Approximations of Real and Reactie Poer Flo," Journal of Poer and Energy Engineering 2, 204, pp. 28. [9] M. Cramer, P. Goergens, F. Potratz, A. Schnettler and S. Willing, "Impact of threephase pseudomeasurement generation from smart meter data on distribution grid state estimation," 2rd International Conference on Electricity Distribution (CIRED 205), Lyon, 205. [0] M. Hasheminamin, V. G. Agelidis and A. Heidari, "Impact study of high PV penetration in lo and mediumoltage netorks hen considering residential and industrial load profile," 20 International Conference on Reneable Energy Research and Applications (ICRERA), Madrid, 20, pp. 4752. [] R. Brandalik, D. Waeresch and W. H. Wellsso, "Approximate actie poer distributions for standard household loads," 206 International Conference on Probabilistic Methods Applied to Poer Systems (PMAPS), Being, China, 206. [2] A. AbdelMajeed, C. Kattmann, S. Tenbohlen and R. Saur, "sage of Artificial Neural Netorks for pseudo measurement modeling in lo oltage distribution systems," 204 IEEE PES General Meeting Conference & Exposition, National Harbor, MD, 204. [] A. Abur, Poer System State Estimation, CRC Press, Boca Raton, SA, 2004. [4] D. Waeresch, R. Brandalik, W. H. Wellsso, J. Jordan, R. Bischler and N. Schneider, "Bad data processing for lo oltage state estimation systems based on smart meter data," CIRED 206 Workshop: Electrical netorks for society and people, Helsinki, 206. [5] German Federal Ministry of Economic Affairs and Energy, "Gesetz zur Digitalisierung der Energieende (English: The Act on the Digitisation of the Energy Transition)", Berlin, August 206. CIRED 207 5/5