EE 653 Power Distribution System Modeling Optimization and

EE 653 Power Distribution System Modeling, Optimization and Simulation Distribution System State Estimation and Smart Meter Data Analytics GRA: Yuxuan Yuan Advisor: Dr. Zhaoyu Wang Department of Electrical and Computer Engineering Iowa State University

Contents • Introduction to Distribution System State Estimation (DSSE) - • DSSE Research Topics - - • • The concept of SE Conventional SE method The concept of DSSE The challenges of DSSE - Observability problem - Metering device placement - Unbalanced problem - Topology configuration - Renewable integration - Cyber security Robust DSSE Smart Meter (SM) Data Analytics Conclusion 2 ECE

Contents • Introduction to Distribution System State Estimation (DSSE) - • DSSE Research Topics - - • • The concept of SE Conventional SE method The concept of DSSE The challenges of DSSE - Observability problem - Metering device placement - Unbalanced problem - Topology configuration - Renewable integration - Cyber security Robust DSSE Smart Meter (SM) Data Analytics Conclusion 3 ECE

The Concept of SE What is the state in the power system? • In general, power system has normal, emergency, and restorative states. • To monitor system states, different measurements from all parts of the system need to be utilized. • In the transmission system SE, voltage magnitudes and phase angles are considered as the states of systems. Fig. 1 State Diagram for Power System Operation [1] Gomez-Exposito A, Abur A. Power system state estimation: theory and implementation[M]. CRC press, 2004. 4 ECE

The Concept of SE State estimation (SE) function processes redundant measurements in order to provide an optimal estimate of the current operating state [1]. At present, SE is a widely-used tool in transmission systems. Fig. 2 On-line Static Security Assessment: Functional Diagram [1] 5 ECE

The Concept of SE Why is it important to use SE in the power system? Various constrains make it impossible to have a good picture of the power system [2]: • Because of the economical constraints, measurement devices can not be installed in every place where the measurements are needed, so the data is incomplete. • Because of the meter malfunction and the communication problem, the measurements are subject to error or lost, so the data is inaccurate, unreliable and delayed. [2] H. Wang and N. N. Schulz, “A revised branch current-based distribution system state estimation algorithm and meter placement impact, ” IEEE Trans. Power Syst. , vol. 19, no. 1, pp. 207– 213, Feb. 2004 6 ECE

The Concept of SE Types of Measurement Errors • Random errors – depend on the class of precision of the measurements (PMU, SM, etc. ). • Intermittent errors – large noise or temporary failures due to the communication failure or meter malfunction. • Systematic errors – deterioration of measurements due to age, temperature, weather, and other environmental effects [3] Zhong, Shan, and Ali Abur, “Combined state estimation and measurement calibration, ” IEEE Trans. Power Syst. , vol. 20, no. 1, pp. 458– 465, Feb. , 2005 7 ECE

Conventional SE Method Traditionally, bus voltage magnitudes and phase angles have been used as state variables in transmission systems. So the basic equation of SE can be obtained: 8 ECE

Conventional SE Method Weighted Least Square (WLS) optimization method [1]: 9 ECE

Conventional SE Method [4] F. F. Wu, “Power system state estimation: a survey, ” International Journal of Electrical Power & Energy Systems, vol. 12, no. 2, pp. 80– 87, Apr. 1990. 10 ECE

Conventional SE Method State Variables Measurement Variables Jacobian Matrix of the State Equations Weight matrix For the pseudo load For the actual measurements 11 ECE

The Concept of DSSE Why is it important to develop DSSE? In the past, most distribution systems were not monitored. Therefore, there was no need for SE technique. But, nowadays, due to the rapid growth of SCADA and Advanced Metering Infrastructure (AMI) in distribution systems, DSSE is expected to become a significant function in monitoring and power management of smart grids by estimating the high accurate system states [5]-[6]. [5] “FERC staff report: Assessment of demand response and advanced metering - Dec. 2017. ” [Online]. Available: https: //www. ferc. gov/legal/ staff-reports/2017/DR-AM-Report 2017. pdf. [6] A. Primadianto and C. N. Lu, “A review on distribution system state estimation, ” IEEE Trans. Power Syst. , vol. 32, no. 5, pp. 3875– 3883, Sep. 2017. 12 ECE

The Concept of DSSE Distribution System Real-time Measurements Fig. 3 Percent of Smart meter installation from 2011 -2016 [7] Energy Information Administration. (2017) Annual Electric Power Industry Report. [Online]. Available: https: //www. eia. gov/electricity/data/eia 861/ 13 ECE

The Concept of DSSE Differences between transmission system and distribution system Fig. 5 IEEE 34 Bus Test System. Fig. 4 IEEE 24 Bus Test System. Meshed topology Uni-directional power flows Balanced lines and loads Radial topology Bi-directional power flows Unbalanced lines and loads 14 ECE

The Concept of DSSE is the process of inferring the values of distribution system’s state variables using a limited number of measured data at certain locations in the system [8]. Fig. 6 DSSE function in smart grid environment [9]. [8] A. Monticelli, State estimation in electric power systems: a generalized approach. Springer Science & Business Media, 1999. [9] K. Dehghanpour, Z. Wang, J. Wang, Y. Yuan and F. Bu, "A Survey on State Estimation Techniques and Challenges in Smart Distribution Systems, " in IEEE 15 Transactions on Smart Grid, vol. 10, no. 2, pp. 2312 -2322, March 2019. ECE

The Concept of DSSE Except for the bus voltage magnitudes and phase angles, the branch current magnitudes and phase angles have been used as state variables in DSSE. a) Voltage-Based DSSE [10]-[12] b) Branch Current-Based SE (BCSE) [13]-[15] [10] M. E. Baran and A. W. Kelley, “State estimation for real-time monitoring of distribution systems, ” IEEE Trans. Power Syst. , vol. 9, no. 3, pp. 1601– 1609, Aug. 1994 [11] D. A. Haughton and G. T. Heydt, “A linear state estimation formulation for smart distribution systems, ” IEEE Trans. Power Syst. , vol. 28, no. 2, pp. 1187– 1195, May 2013. [12] C. N. Lu, J. H. Tang, and W. H. E. Liu, “Distribution system state estimation, ” IEEE Trans. Power Syst. , vol. 10, no. 1, pp. 229– 240, Feb. 1995. [13] M. E. Baran and A. W. Kelley, “A branch-current-based state estimation method for distribution systems, ” IEEE Trans. Power Syst. , vol. 10, no. 1, pp. 483– 491, Feb. 1995. [14] M. Pau, P. A. Pegoraro, and S. Sulis, “Efficient branch-current-based distribution system state estimation including synchronized measurements, ” IEEE Trans. Instrum. Meas. , vol. 62, no. 9, pp. 2419– 2429, Sep. 2013. [15] M. E. Baran, J. Jung, and T. E. Mc. Dermott, “Including voltage measurements in branch current state estimation for distribution systems, ” In 16 IEEE Power & Energy Society General Meeting, pp. 1– 5, Jul. 2009. ECE

Contents • Introduction to Distribution System State Estimation (DSSE) - • DSSE Research Topics - - • • The concept of SE Conventional SE method The concept of DSSE The challenges of DSSE - Observability problem - Metering device placement - Unbalanced problem - Topology configuration - Renewable integration - Cyber security Robust DSSE Smart Meter (SM) Data Analytics Conclusion 17 ECE

The Challenges of DSSE Compared to the SE in transmission systems, DSSE is still a challenging problem since distribution systems have many features that are different from transmission systems [2]. These factors include： • Low observability due to the lack of measurement devices • Higher R/X ratio • Three-phase unbalanced system • Topology identification problem • Renewable energy integration 18 ECE

Observability Problem • Unlike transmission systems that have a high level of data redundancy, the distribution systems are generally undetermined with low observability. • “Observability” refers to the system operator’s ability to solve the SE problem. That depends on the number of metering devices. • Observability problem is one of the main challenge in applying transmission SE techniques to distribution systems directly [2]. • In the traditional WLS-based SE method, the number of measurements is required to be larger than the states being estimated. • The bad/missing measurement data also causes the observability problem. 19 ECE

Observability Problem At presents, distribution systems can be divided into three groups according to the observability: fully observable systems, partially observable systems and fully unobservable systems. Fig. 7 Distribution Systems with different observability. 20 ECE

The Concept of DSSE Distribution System Real-time Measurements Fig. 8 Percent of Residential Smart meter installation rate by state, 2016 [7]. 21 ECE

Observability Problem [16] A. Angioni, T. Schlosser, F. Ponci, and A. Monti, “Impact of pseudo-measurements from new power profiles on state estimation in low-voltage grids, ”IEEE Trans. Instrum. Meas. , vol. 65, no. 1, pp. 70– 77, Jan. 2016. 22 ECE

Observability Problem Existing data-driven pseudo-measurement method can be roughly separated into two categories: • Probabilistic and Statistical Approaches: These methods employ spatial/temporal correlation and historic probability distribution data to generate reasonable pseudo-measurements and assessing their uncertainty [17]-[20]. [17] C. Muscas, M. Pau, P. A. Pegoraro, and S. Sulis, “Effects of measurements and pseudo-measurements correlation in distribution system state estimation, ” IEEE Trans. Instrum. Meas. , vol. 63, no. 12, pp. 2813– 2823, Dec. 2014. [18] A. K. Ghosh, D. L. Lubkeman, M. J. Downey, and R. H. Jones, “Distribution circuit state estimation using a probabilistic approach, ”IEEE Trans. Power Syst. , vol. 12, no. 1, pp. 45– 51, Feb. 1997. [19] R. Singh, B. C. Pal, and R. A. Jabr, “Statistical representation of distribution system loads using Gaussian mixture model, ”IEEE Trans. Power Syst. , vol. 25, no. 1, pp. 29– 37, Feb. 2010. [20] R. Singh, B. C. Pal, and R. A. Jabr, “Distribution system state estimation through Gaussian mixture model of the load as pseudo-measurement, ” IET Gener. Transm. Distrib. , vol. 4, no. 1, pp. 50– 59, Jan. 2009. 23 ECE

Observability Problem Existing data-driven pseudo-measurement method can be roughly separated into two categories: • Learning-Based Approaches: Multiple machine learning algorithms have also been utilized to generate active/reactive power pseudo-measurement and uncertainty assessment [21][25]. [21] B. P. Hayes, J. K. Gruber, and M. Prodanovic, “A closed-loop state estimation tool for MV network monitoring and operation, ”IEEE Trans. Smart Grid, vol. 6, no. 4, pp. 2116– 2125, Jul. 2015. [22] D. Gerbec, S. Gasperic, I. Smon, and F. Gubina, “Allocation of the load profiles to consumers using probabilistic neural networks, ”IEEE Trans. Power Syst. , vol. 20, no. 2, pp. 548– 555, May 2005. [23] E. Manitsas, R. Singh, B. C. Pal, and G. Strbac, “Distribution system state estimation using an artificial neural network approach for pseudo measurement modeling, ” IEEE Trans. Power Syst. , vol. 27, no. 4, pp. 1888– 1896, Nov. 2012. [24] Y. Yuan, K. Dehghanpour, F. Bu, and Z. Wang, "A Multi-Timescale Data-Driven Approach to Enhance Distribution System Observability, " IEEE Transactions on Power Systems, vol. 34, no. 4, pp. 3168 -3177, July 2019. [25] K. Dehghanpour, Y. Yuan, Z. Wang and F. Bu, "A Game-Theoretic Data-Driven Approach for Pseudo-Measurement Generation in Distribution System State Estimation, " in IEEE Transactions on Smart Grid. 24 ECE

Observability Problem – Case Study [24]: A Multi-Timescale Data-Driven Approach to Enhance Distribution System Observability Problem Statement: Inferring hourly consumption data from customer monthly billing information as pseudo-measurements. Challenges: • Absence of high penetration of real-time smart meters (SMs) and availability of a sizable data history. • Loss of correlation between consumption time-series at different timescales • Dependency of customer daily consumption on typical behavior • Unobserved customers’ unknown typical behavior [24] Y. Yuan, K. Dehghanpour, F. Bu, and Z. Wang, "A Multi-Timescale Data-Driven Approach to Enhance Distribution System Observability, " IEEE Transactions on Power Systems, vol. 34, no. 4, pp. 3168 -3177, July 2019. 25 ECE

Observability Problem – Case Study [24]: (I): Using data clustering for capturing customer typical behavior (II): Multi-timescale load inference (stage by stage inference chain) (III): Using state-estimation-based Bayesian learning for inferring unobserved customers’ typical behavior Fig. 9 Overall structure of the proposed method. [24] Y. Yuan, K. Dehghanpour, F. Bu, and Z. Wang, "A Multi-Timescale Data-Driven Approach to Enhance Distribution System Observability, " IEEE Transactions on Power Systems, vol. 34, no. 4, pp. 3168 -3177, July 2019. 26 ECE

Observability Problem – Case Study [24]: (I): Using data clustering for capturing customer typical behavior • Typical daily load profiles are classified and stored in a databank using a spectral clustering (SC) algorithm trained by the SM dataset of observed customers (i. e. , customers with SMs). • Typical load behaviors are extracted for different types of customers for weekdays and weekends. 27 ECE

Observability Problem – Case Study [24]: Data Cluster: • Unsupervised machine learning tasks. • Discover structures and patterns in data. • Group data with similar patterns together. Fig. 10 Example of K-means algorithm [26] Wikipedia contributors. "K-means clustering. " Wikipedia, The Free Encyclopedia, 3 Oct. 2019. Web. 328 Oct. 2019. ECE

Observability Problem – Case Study Fig. 11 Performance of the spectral clustering [27]. • SC is a graph theory-based clustering technique. • SC is robust and outperforms traditional clustering techniques, such as kmeans. [27] L. Zelnik-Manor and P. Perona, “Self-tuning spectral clustering, ” Proceedings of the 17 th International Conference on Neural Information Processing System, pp. 1601– 1608, 2004. 29 ECE

Observability Problem – Case Study [24]: • Fig. (a) shows the typical load patterns for different types of customers for weekend. (a) • Fig. (b) shows the typical load patterns for different types of customers for weekdays. • Red represents Industrial, blue represents commercial, and black represents residential customers. (b) Fig. 12 Typical pattern banks for weekday and weekend. 30 ECE

Observability Problem – Case Study [24]: (II): Multi-timescale load inference (stage by stage inference chain) • Near-zero correlation between customer monthly consumption and hourly load data. • Keep the high correlation level between different time resolution data. • Utilize artificial neural networks (ANNs) to develop the structure of inference model. Fig. 13 Correlation between Consumption at Different Time-Scales. 31 ECE

Observability Problem – Case Study [24]: Fig. 14 Multi-timescale learning structure. • A three-layer structure is developed for each type of customer. • Each layer corresponds to the total consumption at different timescales. • Total monthly consumption is set as the input of the first layer. • Hourly consumption is set as the output of the final layer. 32 ECE

Observability Problem – Case Study [24]: Fig. 15 ANN generalized structure. • Each ANN includes input layer, multiple hidden layers, and output layer. • Each layer has an activation function (Sigmoid function, Tanh function, Relu). • Levenberg-Marquardt (LM) backpropagation method is used to update the network weight and 33 bias variables. ECE

Observability Problem – Case Study [24]: • For each ANN, the dataset is randomly divided into three separate subsets for training (70% of the total data), validation (15% of the total data), and testing (15% of the total data). • Several hyper-parameters are calibrated using the grid search methods. • • • The number of hidden layer. The number of neurons. The value of learning rate. Fig. 16 Calibration result for ANN. 34 ECE

Observability Problem – Case Study [24]: (III): Using state-estimation-based Bayesian learning for inferring unobserved customers’ typical behavior • Determine the typical load profiles of unobserved customers. • Utilize a limited number of feeder-level measurements by leveraging a Branch Current-based SE (BCSE) aided recursive Bayesian learning (RBL) approach [20]. 35 ECE

Observability Problem – Case Study [24]: Fig. 17 Performance of BCSE-aided RBL pattern identification method. 36 ECE

Observability Problem – Case Study [24]: • Utilize the mean absolute percentage error (MAPE) criterion to evaluate the accuracy of estimation methods. • The MAPE values for the proposed method are {7. 4%, 10. 02%}. • The existing methods in [28] and [29] show average MAPE of {19. 74%, 20. 32%} and {13. 79%, 21. 16%} over the test set. Fig. 18 Comparison of load inference results. [28] Y. R. Gahrooei, A. Khodabakhshian, and R. A. Hooshmand, “A new peudo load profile determination approach in low voltage distribution networks, ” IEEE Trans. Power Syst. , vol. 33, no. 1, pp. 463– 472, Jan. 2018. 37 [29] D. T. Nguyen, “Modeling load uncertainty in distribution network monitoring, ” IEEE Trans. Power Syst. , vol. 30, no. 5, pp. 2321– 2328, Sep. 2015. ECE

Observability Problem – Case Study [24]: • Utilize the mean absolute percentage error (MAPE) criterion to evaluate the accuracy of BCSE based on the proposed pseudo load estimation. • The MAPE values for the voltage magnitude and phase angle around 0. 704% and 0. 24%, respectively. • In the previous work [2], the MAPE values are around 0. 73% and 0. 36%, respectively with 20% maximum Gaussian error for pseudo measurements. Fig. 19 BCSE-based state estimation performance using the proposed load inference model. 38 ECE

Observability Problem – Case Study [25]: Game-Theoretic Data-Driven Approach for Pseudo-Measurement Generation in DSSE Problem Statement: Providing observability with Advanced Metering Infrastructure (AMI) against missing data. Challenges: • Capture seasonal correlations in customer behavior • Bid-data challenge for large AMI datasets • Improve machine learning performance using DSSE data [25] K. Dehghanpour, Y. Yuan, Z. Wang and F. Bu, "A Game-Theoretic Data-Driven Approach for Pseudo-Measurement Generation in Distribution System State Estimation, " in IEEE Transactions on Smart Grid, 2019 39 ECE

Observability Problem – Case Study [25]: Game-Theoretic Data-Driven Approach for Pseudo-Measurement Generation in DSSE Fig. 20 Overall structure of the proposed method. [25] K. Dehghanpour, Y. Yuan, Z. Wang and F. Bu, "A Game-Theoretic Data-Driven Approach for Pseudo-Measurement Generation in Distribution System State Estimation, " in IEEE Transactions on Smart Grid, 2019 40 ECE

Observability Problem – Case Study [25]: • Utilize the Relevance vector machine (RVM) to inference the pseudo measurements. • A parallel computational framework is applied to alleviate the high cost of training • A game-theoretic framework is employed to exploit the seasonal changes in customer behavior. • A close-loop mechanism is developed to improve the accuracy of pseudomeasurement generation. 41 ECE

Observability Problem – Case Study [25]: Relevance vector machine (RVM): • RVM is a machine learning technique that uses Bayesian framework to infer the value for regression and classification [30]. • RVM is capable of quantifying the uncertainty of pseudo-measurements. • The inherent pruning mechanism of RVM introduces robustness against bad data points. • Compared to the support vector machine (SVM), RVM has a high computation cost of training and a low cost of testing. [30] M. E. Tipping, “Sparse Bayesian learning and the relevance vector machine, ” The Journal of Machine Learning Research, vol. 1, pp. 211– 244, 2001. 42 ECE

Observability Problem – Case Study [25]: Fig. 21 Pseudo-measurement accuracy demonstration. 43 ECE

Observability Problem – Case Study [25]: Fig. 22 DSSE performance in estimating state variables in open- and closedloop conditions. 44 ECE

Metering Device Placement Optimizing the location of meter in distribution systems is a significant subject for research, given the size of the system and potentially limited financial resources [9]. Objective Function Constraints Solution Algorithm Meter cost [31] Estimation accuracy Heuristic search Estimation accuracy [32] Meter number Mixed integer semidefinite optimization Network observability [33] NA Heuristic search Meter cost & estimation accuracy [34] Estimation accuracy Multi-Objective evolutionary [31] M. E. Baran, J. Zhu, and A. W. Kelley, “Meter placement for real-time monitoring of distribution feeders, ” IEEE Trans. Power Syst. , vol. 11, no. 1, pp. 332– 337, Feb. 1996. [32] T. C. Xygkis, G. N. Korres, and N. M. Manousakis, “Fisher information based meter placement in distribution grids via the d-optimal experimental design, ” IEEE Trans. Smart Grid, vol. 9, no. 2, pp. 1452– 1461, Mar. 2018. [33] B. Brinkmann and M. Negnevitsky, “A probabilistic approach to observability of distribution networks, ” IEEE Trans. Power Syst. , vol. 32, no. 2, pp. 1169– 1178, Mar. 2017. [34] S. Prasad and D. M. V. Kumar, “Trade-offs in PMU and IED deployment for active distribution state estimation using multi-objective evolutionary algorithm, ” IEEE Trans. Instrum. Meas. , vol. 67, no. 6, pp. 1298– 1307, Jun 2018. 45 ECE

Three Phase unbalanced Problem In distribution systems, loads can be three-phase, two-phase or single-phase. Hence it is desirable to use a three-phase model in DSSE [14]. The basic WLS SE method was adapted for three-phase analysis to address the phase unbalanced problem [35]. Fig. 23 Three-phase branch model [34]. [35] U. Kuhar, M. Pantos, G. Kosec, and A. Svigelj, “The impact of model and measurement uncertainties on a state estimation in three-phase distribution networks, ” to appear in IEEE Trans. Smart Grid. 46 ECE

High R/X Ratio • Except the phase unbalanced, distribution line with high r/x ratio is another challenge for SE [6]. • Conventional estimators may not work satisfactorily for networks with high R/X ratio [36] • In DSSE, to address this challenge, branch current have been adopted as state variables, which turns out to be a more natural way of DSSE formulation [9]. This method is known as BCSE. [36] Mohamed Ben Ahmed and Anouar Abdelhakim Boudhir. 2018. Innovations in Smart Cities and Applications: Proceedings of the 2 nd Mediterranean Symposium on Smart City Applications (1 st ed. ). Springer Publishing Company, Incorporated. 47 ECE

High R/X Ratio - BCSE • BCSE is more insensitive to line parameters than the conventional nodevoltage-based SE methods [9]. • BCSE is based on the WLS approach and can be expressed as a three-phase model. • BCSE has better performance compared to conventional node-voltage-based SE methods both in computation speed and memory usage [2]. Fig. 24 Equivalent circuit of one phase of a branch line [2]. 48 ECE

High R/X Ratio - BCSE Table 2. Variable explanation [2]. For different real measurements z, the non-linear measurement function h() can be written as follows [2]: 1) Branch Power Measurements: The power of phase p from bus k to bus m at the bus k end can be stated as: 49 ECE

High R/X Ratio - BCSE When km=st & p=q, the Jacobain matrix entries can be written as: 50 ECE

High R/X Ratio - BCSE (2) Current Magnitude Measurements: The current of phase p from bus k to bus m can be stated as: The corresponding Jacobian matrix entries are: 51 ECE

High R/X Ratio - BCSE (3) Power Injection Measurements: The injection power of phase p at bus k can be stated as: The Jacobian matrix entries are divided into two categories since the related state variables can be upstream or downstream of the measurement. Fig. 25 One-line diagram of part of system for illustrating power injection measurements [2]. 52 ECE

High R/X Ratio - BCSE (A) When the related state variables are upstream of the measurements: 53 ECE

High R/X Ratio - BCSE (A) When the related state variables are downstream of the measurements: 54 ECE

High R/X Ratio - BCSE (4) Voltage Magnitude Measurements: Based on the tree structure of distribution system, the voltage magnitude of bus k can be computed using the voltage of root bus 0. The voltage of phase p at bus n+1 can be stated as: Fig. 26 One-line diagram of part of system for illustrating voltage magnitude measurements [2]. 55 ECE

High R/X Ratio - BCSE The corresponding Jacobian matrix entries can be stated as: If the line segment is not on the way from the measurement bus, the related entries are all zero. 56 ECE

High R/X Ratio - BCSE Detailed Algorithm: -Step 1 Initialization: Ø Ø Set the initial value of voltage at every node, such as 1 pu. Backward Step: Using the injected power at every node, the values of state variables (branch current magnitudes and phase angles) are computed starting from the end of networks. -Step 2 WLS Ø Ø Using the WLS method, the state variable increments are obtained. Update the value of state variables. 57 ECE

High R/X Ratio - BCSE Detailed Algorithm: -Step 3 Forward Step: Ø Using the new values of state variables, the values of nodal voltages are calculated starting from the substation. -Step 4 Convergence Analysis Ø If the increments are smaller than the tolerance: stop. If not, return to step 2. 58 ECE

High R/X Ratio - BCSE Case Study [13]: A branch-current-based state estimation method for distribution systems Fig. 27 One-line diagram of the test feeder. • The first measurement case Z 1: The unobserved loads are presented by perturbing the actual load data by about 30%. • The second measurement case Z 2: Same pseudo load except the value of capacitor at node 33 is reduced by 50 k. Var/phase to simulate a case with a bad measurement. 59 ECE

High R/X Ratio - BCSE Case Study [13]: Fig. 28 Test results between BCSE and voltage-based SE based on Z 1. Fig. 29 Test results between BCSE and voltage-based SE based on Z 2. • The small differences in the results are mainly due to the different convergences criteria used in the two methods. • BCSE is computationally more efficient. 60 ECE

Topology Configuration DSSE relies on the basic assumption that we know the exact network model so that we can write the measurement functions h(x). Hence, it is necessary to perform topology configuration process to identify the current topology. Fig. 30 DSSE and possible associated applications into a DMS. 61 ECE

Topology Configuration Existing topology configuration method can be roughly separated into two categories: • System Identification Approaches: These methods assume the basic topology of the network is known to the system operator. However, due to local events, such as faults, line disconnections, switching events, etc, the basic topology will undergo local changes over times. [37]-[41]. [37] G. N. Korres and N. M. Manousakis, “A state estimation algorithm for monitoring topology changes in distribution systems, ” in Proc. IEEE Power Energy Soc. Gen. Meeting, San Diego, CA, USA, Jul. 2012, pp. 1– 8. [38] M. E. Baran, J. Jung, and T. E. Mc. Dermott, “Topology error identification using branch current state estimation for distribution systems, ” In IEEE Transmission & Distribution Conference & Exposition: Asia and Pacific, pp. 1– 4, Oct. 2009. [39] D. Singh, J. P. Pandey, and D. S. Chauhan, “Topology identification, bad data processing, and state estimation using fuzzy pattern matching, ” IEEE Trans. Power Syst. , vol. 20, no. 3, pp. 1570– 1579, Aug. 2005. [40] G. Cavraro and R. Arghandeh, “Power distribution network topology detection with time-series signature verification method, ” IEEE Trans. Power Syst. , vol. 33, no. 4, pp. 3500– 3509, Jul. 2018. [41] W. Luan, J. Peng, M. Maras, J. Lo, and B. Harapnuk, “Smart meter data analytics for distribution network connectivity verification, ” IEEE Trans. Smart Grid, vol. 6, no. 4, pp. 1964– 1971, Jul. 2015. 62 ECE

Topology Configuration Existing topology configuration method can be roughly separated into two categories: • Topology learning Approaches: These methods assume that the system operator has very limited or no knowledge of the basic topology of the network [15]. Hence, the objective is to learn the topology of the network using nodal and branch measurements [42][45]. [42] M. Babakmehr, M. G. Simões, M. B. Wakin, and F. Harirchi, “Compressive sensing-based topology identification for smart grids, ” IEEE Trans. Ind. Informat. , vol. 12, no. 2, pp. 532– 543, Apr. 2016. [43] Y. Weng, Y. Liao, and R. Rajagopal, “Distributed energy resources topology identification via graphical modeling, ” IEEE Trans. Power Syst. , vol. 32, no. 4, pp. 2682– 2694, Jul. 2017. [44] S. J. Pappu, N. Bhatt, R. Pasumarthy, and A. Rajeswaran, “Identifying topology of low voltage distribution networks based on smart meter data, ” IEEE Trans. Smart Grid, vol. 9, no. 5, pp. 5113– 5122, Sep. 2018. [45] J. Yu, Y. Weng, and R. Rajagopal, “Pa. To. Pa: A data-driven parameter and topology joint estimation framework in distribution grids, ” IEEE Trans. Power Syst. , vol. 33, no. 4, pp. 4335– 4347, Jul. 2018. 63 ECE

Topology Configuration – Case Study [38]: Topology Error Identification Using Branch Current State Estimation for Distribution Systems • Develop a bank that includes all topology candidates. • Perform BCSE for all topology candidates. • Use the normalized residuals from the BCSE to identify the topology. Fig. 31 Flowchart of Topology Error Processing [38]. 64 ECE

Topology Configuration – Case Study [38]: • A reduced IEEE 34 node radial test feeder is tested. • Test feeder is assumed to have six switches. Fig. 32 One-line diagram of the test feeder with switch. • Fig. 33 shows the error values in each case. • By checking the smallest value, the algorithm detects the topology error correctly. Fig. 33 Topology detection result when switch 2 open. 65 ECE

Renewable Energy Integration • The higher penetration of renewable power resources introduces a higher level of uncertainty in DSSE. • The non-Gaussian distribution of renewable generation would adversely affect WLS-based DSSE methods [9]. • Fast changes in system states can result in unreasonable errors of the WLS-based DSSE [46] Y. Weng, R. Negi, C. Faloutsos, and M. D. Ilic, “Robust data-driven state estimation for smart grid, ” IEEE Trans. Smart Grid, vol. 8, no. 4, pp. 1956– 1967, Jul. 2017. 66 ECE

Renewable Energy Integration • Probabilistic methods represent the major group of techniques for modeling the impacts of renewable uncertainty on DSSE [9]. • Use GMM technique to obtain the non-Gaussian distribution of renewable power [47]. • Use Beta distribution function to generate renewable pseudo -measurement [48]. [47] G. Valverde, A. T. Saric, and V. Terzija, “Stochastic monitoring of distribution networks including correlated input variables, ” IEEE Trans. Power Syst. , vol. 28, pp. 246– 255, Feb. 2013. [48] A. Angioni, T. Schlosser, F. Ponci, and A. Monti, “Impact of pseudo measurements from new power profiles on state estimation in low voltage grids, ” IEEE Trans. Instrum. Meas. , vol. 65, no. 1, pp. 70– 77, Jan. 2016. 67 ECE

Renewable Energy Integration – Case Study [49] A Probabilistic Data-Driven Method for Photovoltaic Pseudo-Measurement Generation in Distribution Systems • Generate the pseudo-load values of unmeasured PV based on the output power of observed solar distributed generators that are located nearby. • Estimate solar power probability density function in a nonparametric method, kernel density estimation (KDE) • Determine the kernel bandwidth of KDE by minimizing the overall modeling bias. [49] Y. Yuan, K. Dehghanpour, F. Bu, and Z. Wang, “A Probabilistic Data-Driven Method for Photovoltaic Pseudo-Measurement Generation in Distribution Systems, ” 2019 IEEE PES General Meeting, Atlanta, August 4 -8, 2019. 68 ECE

Renewable Energy Integration – Case Study [49] Fig. 35 Comparison of PV power inference and real data. Fig. 34 Flow chart of the proposed probabilistic data-driven method. Fig. 36 State estimation performance using the proposed method. 69 ECE

Cyber Security Due to the vulnerability of the power system against cyberattacks has been observed in practice, several common types of cyber-attack related to SE have been modeled in the literature: • False data injection [50]-[53] • Topology attacks [54]-[55] • Data privacy attacks [56] [50] Q. Yang et al. , “On false data-injection attacks against power system state estimation: Modeling and countermeasures, ” IEEE Trans. Parallel Distrib. Syst, vol. 25, no. 3, pp. 717– 729, Mar. 2014. [51] S. Li, Y. Yilmaz, and X. Wang, “Quickest detection of false data injection attack in wide-area smart grids, ” IEEE Trans. Smart Grid, vol. 6, no. 6, pp. 2725– 2735, Nov. 2015. [52] J. Liang, L. Sankar, and O. Kosut, “Vulnerability analysis and consequences of false data injection attack on power system state estimation, ” IEEE Trans. Power Syst. , vol. 31, no. 5, pp. 3864– 3872, Sep. 2016. [53] Y. Chakhchoukh and H. Ishii, “Enhancing robustness to cyber-attacks in power systems through multiple least trimmed squares state estimations, ” IEEE Trans. Power Syst. , vol. 31, no. 6, pp. 4395– 4405, Nov. 2016. [54] Y. Chakhchoukh and H. Ishii, “Coordinated cyber-attacks on the measurement function in hybrid state estimation, ” IEEE Trans. Power Syst. , vol. 30, no. 5, pp. 2487– 2497, Sep. 2015. [55] J. Zhang and L. Sankar, “Physical system consequences of unobservable state-and-topology cyber-physical attacks, ” IEEE Trans. Smart Grid, vol. 7, no. 4, pp. 2016– 2025, Jul. 2016. [56] H. Li, L. Lai, and W. Zhang, “Communication requirement for reliable and secure state estimation and control in smart grid, ” IEEE Trans. 70 Smart Grid, vol. 2, no. 3, pp. 476– 486, Sep. 2011. ECE

Robust DSSE • WLS estimator is a quadratic form of the maximum likelihood estimator and can be stated as the minimization of the weighted sum of squares. It is a fast and widely-used mathematical formulation. However, the susceptibility of WLS to bad data should be noted. • To handle the uncertainty of measurement data, alternative mathematical formulations have been proposed to increase the robustness of state estimator. 71 ECE

Robust DSSE [57] R. Jabr, B. Pal, and R. Singh, “Choice of estimator for distribution system state estimation, ” IET Generation, Transmission & Distribution, vol. 3, no. 7, pp. 666– 678, Jul. 2009. 72 ECE

Contents • Introduction to Distribution System State Estimation (DSSE) - • DSSE Research Topics - - • • The concept of SE Conventional SE method The concept of DSSE The challenges of DSSE - Observability problem - Metering device placement - Unbalanced problem - Topology configuration - Renewable integration - Cyber security Robust DSSE Smart Meter (SM) Data Analytics Conclusion 73 ECE

Smart Meter Data Analytics Why is it important to perform SM data analytics? • The widespread popularity of SMs enables an immense amount of fine-grained electricity consumption data to be collected [58]. • High-resolution data from SM provide rich information to understand the consumption behaviors of the consumers. • SM data provides an unique opportunity to develop a dataenabled modernized power system [59]. [58] Y. Wang, Q. Chen, T. Hong and C. Kang, "Review of Smart Meter Data Analytics: Applications, Methodologies, and Challenges, " in IEEE Transactions on Smart Grid, vol. 10, no. 3, pp. 3125 -3148, May 2019. [59] H. Sun, Z. Wang, J. Wang, Z. Huang, N. Carrington and J. Liao, "Data-Driven Power Outage Detection by Social Sensors, " in IEEE Transactions on Smart Grid, vol. 7, no. 5, pp. 2516 -2524, Sept. 2016. 74 ECE

Smart Meter Data Analytics Fig. 37 Number of publication about SM data analytics [58]. Fig. 38 Number of publication in nine most popular journals [58]. • In 2010, the number of SM data analytics publications was at a low level. • The number of publications increased rapidly from 2012. 75 ECE

Smart Meter Data Analytics Fig. 39 Taxonomy of SM data analytics [58]. 76 ECE

Smart Meter Data Analytics – Case Study [60] A Data-Driven Framework for Assessing Cold Load Pick-up Demand in Service Restoration • In distribution systems, thermostatically controlled loads (TCLs) are diversified during normal operation, and undiversified in restoration. • The phenomenon of losing load diversity is called Cold load pick-up (CLPU) and can cause considerable demand increase [60] F. Bu, K. Dehghanpour, Z. Wang, and Y. Yuan, “A Data-Driven Framework for Assessing Cold Load Pick-up Demand in Service Restoration, ” IEEE Transactions on Power Systems, accepted for publication. 77 ECE

Smart Meter Data Analytics – Case Study [60] • Develop a data-driven framework to assess the deviation of CLPU demand from normal demand, • • • At the feeder level: A nonlinear auto-regression model is applied to estimate the normal demand in restoration phase to obtain CLPU ratios, and then a CLPU ratio regression model is developed At the customer level: Probabilistic reasoning methods are employed to estimate customer normal demand in restoration phase, and then the customer demand increase due to CLPU is identified Advantage: No need for modeling specific houses 78 ECE

Smart Meter Data Analytics – Case Study [60] • Obtain CLPU ratio at feeder-level, using learning-based demand prediction approach • Determine customer demand increase, using probabilistic reasoning (GMM) • Obtain useful statistics at feeder- and customer-level to fully quantify CLPU demand Input Output Fig. 40 Flowchart of the proposed method [59]. 79 ECE

Smart Meter Data Analytics – Case Study [60] 80 ECE

Smart Meter Data Analytics – Case Study [59] Fig. 41 Distributions of estimated normal customer demand increase. Fig. 42 Distributions of aggregated demand increase of groups of customers. 81 ECE

Contents • Introduction to Distribution System State Estimation (DSSE) - • DSSE Research Topics - - • • The concept of SE Conventional SE method The concept of DSSE The challenges of DSSE - Observability problem - Metering device placement - Unbalanced problem - Topology configuration - Renewable integration - Cyber security Robust DSSE Smart Meter (SM) Data Analytics Conclusion 82 ECE

Conclusions • The goal of DSSE is to infer the values of distribution system’s state variables using a limited number of measured data. The DSSE is basically a numerical process to map data measurements to system state variables. • Technically, conventional transmission level SE approaches cannot be directly applied to the DSSE due to various challenges. • To address these challenges, different methods are proposed for DSSE. Most recent works are concentrated on using SM data analytics-based approaches to improve the conventional DSSE. • How to take advantage of massive SM data to enhance the efficiency of the demand side has become an important topic. 83 ECE

Thank You! 84 ECE