Big Data-Based Approach to Detect, Locate, and Enhance the Stability of an Unplanned Microgrid Islanding
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Huaiguang Jiang 1; Yan Li 2; Yingchen Zhang 3; Jun Jason Zhang 4; David Wenzhong Gao 5; Eduard Muljadi 6; and Yi Gu 7
Abstract: In this paper, a big data-based approach is proposed for the security improvement of an unplanned microgrid islanding (UMI). The proposed approach contains two major steps: the first step is big data analysis of wide-area monitoring to detect a UMI and locate it; the second step is particle swarm optimization (PSO)-based stability enhancement for the UMI. First, an optimal synchrophasor measurement device selection (OSMDS) and matching pursuit decomposition (MPD)-based spatial-temporal analysis approach is proposed to significantly reduce the volume of data while keeping appropriate information from the synchrophasor measurements. Second, a random forest-based ensemble learning approach is trained to detect the UMI. When combined with grid topology, the UMI can be located. Then the stability problem of the UMI is formulated as an optimization problem and the PSO is used to find the optimal operational parameters of the UMI. An eigenvalue-based multiobjective function is proposed, which aims to improve the damping and dynamic characteristics of the UMI. Finally, the simulation results demonstrate the effectiveness and robustness of the proposed approach. DOI: 10.1061/(ASCE)EY.19437897.0000473. © 2017 American Society of Civil Engineers. Author keywords: Smart grid; Big data; Unplanned microgrid islanding; Synchrophasor measurement device; Ensemble learning; Random forest; Particle swarm optimization.
Introduction Featured by increasing penetration of distributed energy resources (DERs), microgrids, and various measurement devices such as synchrophasor measurement devices (SMDs), the emerging smart grid reveals a new era for electrical power generation, storage, transmission, and distribution (Fang et al. 2012; Wang et al. 2016a; Gu et al. 2014; Cui et al. 2016b; Wu et al. 2015). Various DERs such as photovoltaics (PV), microwind turbines, and batteries can highly penetrate 1
Postdoctoral Researcher, National Renewable Energy Laboratory, 15013 Denver West Pkwy., Golden, CO 80401 (corresponding author). E-mail:
[email protected] 2 Ph.D. Student, Dept. of Electrical and Computer Engineering, Univ. of Connecticut, 371 Fairfield Way, Storrs, CT 06269. E-mail:
[email protected] 3 Senior Engineer, National Renewable Energy Laboratory, 15013 Denver West Pkwy., Golden, CO 80401. E-mail:
[email protected] 4 Assistant Professor, Daniel Felix Ritchie School of Engineering and Computer Science, Dept. of Electrical and Computer Engineering, Univ. of Denver, 2155 East Wesley Ave., Denver, CO 80208. E-mail: jun.
[email protected] 5 Associate Professor, Daniel Felix Ritchie School of Engineering and Computer Science, Dept. of Electrical and Computer Engineering, Univ. of Denver, 2155 East Wesley Ave., Denver, CO 80208. E-mail:
[email protected] 6 Principal Engineer, National Renewable Energy Laboratory, 15013 Denver West Pkwy., Golden, CO 80401. E-mail:
[email protected] 7 Ph.D. Student, Daniel Felix Ritchie School of Engineering and Computer Science, Dept. of Electrical and Computer Engineering, Univ. of Denver, 2155 East Wesley Ave., Denver, CO 80208. E-mail:
[email protected] Note. This manuscript was submitted on November 22, 2016; approved on March 23, 2017; published online on June 28, 2017. Discussion period open until November 28, 2017; separate discussions must be submitted for individual papers. This paper is part of the Journal of Energy Engineering, © ASCE, ISSN 0733-9402. © ASCE
in distribution sides, which increases the system robustness and reduces the transmission costs (Fang et al. 2012; Cui et al. 2016a, 2015; Wang et al. 2016c; Wu et al. 2013). Conversely, the massive data can be collected with heterogeneous sources such as phasor measurement units (PMUs), fault disturbance recorders (FDRs), and micro-PMU, which brings a big data challenge for smart grids (Fang et al. 2012; Wang et al. 2016b; Jiang et al. 2014a). For example, by 2013 the PMU installation number is more than 2,500 in China (Cheng et al. 2015). In North America, the supervisory control and data acquisition (SCADA) systems have also been widely implemented in many utilities with different SMDs (Zhang et al. 2010; Fang et al. 2012; Jiang et al. 2014a). And more than 2,000 PMUs are installed in the North America power system grid (Overholt et al. 2015; Banavar et al. 2015). One evolving trend of the modern power grid is to have the capability to operate with multiple microgrids so that the smart grids are more reliable and economical (Lasseter 2002; Lasseter et al. 2002; Carrasco et al. 2006). Unplanned microgrid islanding (UMI) issues caused by transmission line outages or unplanned maneuvers are major reasons for the UMI (Borghetti and Peretto 2012; Bahrani et al. 2011). In this paper, a big data-based approach is proposed to detect and locate the UMI quickly, and enhance its stability to smooth the power fluctuations and avoid blackouts. Currently, the signals of smart grids can be collected by pervasively located SMDs, which provide critical information for system control and stability enhancement (Bose 2010; Gu et al. 2016). However, the meaningless data usually take a large part in the collected big data, which causes a big computational and transmission burden. In this paper, a spatial-temporal approach is proposed to detect and locate the UMIs with the collected big data. In the spatial domain, the approach provides the spatial characterization of the synchrophasor measurements with optimal synchrophasor measurement device selection (OSMDS), and in the temporal domain, the massive time series data are characterized by matching pursuit decomposition (MPD)
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Trigger Signal 1
MPD based Feature Extraction
As shown in Fig. 1, the proposed approach consists of two major steps: the big data-based wide-area monitoring and the PSO-based stability enhancement for a UMI. The first step monitors the smart grid and triggers the second step to optimize stability when a UMI is detected and located. © ASCE
Occurrence Time and Position
Spatial-Temporal Characterization
No
UMI Detection Yes
System Modeling Operation Range Estimation & Calculation Eigenvalues Calculation
PSO Initialization
PSO Optimization
Location End
Fig. 1. Flowchart of the proposed approach; Block 1 is wide-area monitoring and Block 2 is PSO-based stability enhancement
In the first major step, the multimodal signals, such as bus voltage and current, are collected by the optimally selected SMDs in smart grid. The MPD with the Gaussian atom dictionary is then used to extract the time-frequency feature of the signals. The amplitude, time-shift, frequency-shift, and variance of the signals are extracted, and with the extracted feature data, the random forest–based approach is used to detect the UMI issues from the normal operation conditions. Combined with the topology of the smart grid, the fault contour map is generated with the clustered result of the MPD features for locating the UMI. If a UMI is detected and located, the occurrence time and position will be transmitted to the second major step. In the second major step, the feature of the UMI system is modeled and analyzed based on typical operational ranges. Thus, the objective function of the stability optimization is built, and both damping and dynamic characteristics are included. Subsequently, the PSO-based stability enhancement approach is used to improve the damping ratio and enhance the dynamic characteristics.
Spatial-Temporal Data Characterization Spatial Domain Characterization: OSMDS The OSMDS is used to characterize the big data in the spatial domain, where the objective function is designed to minimize the selected number of SMDs with the constraint of smart grid topologically observable. In this section, the concept of topological observability is adopted, and the basic Ohm’s law-based observation is applied (Jiang et al. 2014a) for the OSMDS. For a topologically observable smart grid, every bus must be observed at least once. Considering a smart grid with n buses, the OSMDS issue can be formulated as a mixed-integer linear programming problem as follows: n X minF ¼ ci 1 u 0 i 1 ð1Þ Pn
Architecture of the Proposed Approach
2
Optimal Synchrophasor Measurement Devices Selection
PSO Based Stability Enhancement
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Start
Wide Area Monitoring
(Mallat and Zhang 1993; Jiang et al. 2014b). In addition, it is demonstrated that the machine learning–based method is an effective way to detect faults in smart grids and many other areas (Tate and Overbye 2008; Aggarwal and Song 1998; Axelberg et al. 2007; Jiang et al. 2015; Yu et al. 2009). Using the generated spatial-temporal characteristics, a random forest is used to detect the UMI issues from the normal operation conditions. Combined with the spatial-temporal characteristics and topology information, a UMI can be detected and located. In a UMI, DERs such as wind turbine generators, PV arrays, batteries, and microturbine generators are usually connected to the system through power electronic interfaces (Lasseter 2002; Lasseter et al. 2002; Bai et al. 2015). Many approaches are developed to enhance the stability and reliability of the distribution systems and microgrids (Weber et al. 2015; Ding et al. 2016; Zhao and Low 2014; Ding and Loparo 2015). Although the power electronic devices provide the possibility for a fast controller response, the lack of inertia poses difficulties in preserving the stability of the UMI in autonomous mode (Carrasco et al. 2006; Pogaku et al. 2007). Moreover, the intermittent nature of some DERs bring negative impacts on system stability as well (Gautam et al. 2009; Bai et al. 2016; Lin et al. 2015). The stability of power electronics in autonomous mode is a critical issue for the UMI. When a UMI is detected and located, all the dispatchable DERs are responsible for maintaining the system voltage and frequency on acceptable levels and ensuring stability of the UMI. This study is focused on addressing the stability issues of the UMIs using the flexibility of the controllable DERs. The stability enhancement problem is formulated as an optimization issue where an eigenvalue-based multiobjective function aimed toward improving the damping characteristics and enhancing dynamic characteristics under disturbances in a UMI is proposed. Compared with other optimization algorithms, particle swarm optimization (PSO) has attracted the most attention in parameter optimization because of its flexibility, simplicity, efficiency, and robustness (Hassan and Abido 2011; Abido 2002). In each iterative step of PSO, mode analysis is conducted to reveal variations of system stability characteristics. Finally, the effectiveness and robustness of the proposed approach have been tested through the small signal stability analysis and nonlinear temporal domain simulations of a benchmark under various disturbances and loading conditions. In the future, the proposed approach can be a multifunctional platform to cooperate with many other aspects such as electrical vehicle, intelligent transportation, and smart city (Chen and Borken-Kleefeld 2014; Chen and Fan 2014). This paper is organized as follows. In the section “Architecture of the Proposed Approach,” the flowchart of the proposed approach is introduced. In the section “Spatial-Temporal Data Characterization,” the spatial-temporal data characterization approach is proposed with the OSMDS and MDP-based timefrequency analysis. In the section “UMI Detection and Location,” the random forest–based detection and fault contour map based location is introduced for a UMI microgrid. In the section “Optimization of the Stability Characteristics of a UMI,” the PSObased stability enhancement approach is presented. In the section “Simulation and Results,” the numerical results are presented. Finally, the proposed approach is concluded in the last section.
i1 ¼1
u0
subject to fi1 ¼ j1 ¼1 ai1 ;j1 j1 ≥ 1; i1 ¼ 1; 2; 3; : : : ; n, where ci1 = cost of a select SMD at bus i1 , such as economic cost and communication cost. The selection cost at each bus is assumed to be equal to 1 per unit in the present study. The f i1 is the number of times that the i1 th bus is observed through synchrophasor measurements; ai1 ;j1 = ði1 ; j1 Þth entry of smart grid connectivity matrix; and u 0 i1 = binary that can be defined as
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u 0 i1 ¼
1 if a synchrophasor measurement device is selected at bus i1
In addition, considering the rules of zero injection buses (ZIBs), a zero injection cluster (ZIC) is observable when the ZIC has at most one unobservable bus (Jiang et al. 2014a). In summary, considering the effect of ZIBs, the number of SMDs can be further reduced in the OSMDS.
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Temporal Domain Characterization: Time-Frequency Characterization of Synchrophasor Measurements In this section, the MPD is used to characterize the data in the temporal domain. Through the MPD analysis, the feature of the signals (collected by the optimal selected SMDs), can be represented by the Gaussian atoms with the information of amplitude, time-shift, frequency-shift, and variance. In Mallat and Zhang (1993), the MPD is first introduced with Gabor functions. In this paper, the MPD is used to decompose the voltage signals and extract their features. On Bus i1 , the voltage signal si1 ðtÞ can be decomposed as a weighted summation of the Gaussian atoms (Mallat and Zhang 1993; Jiang et al. 2014b) as si1 ðtÞ ¼
∞ X
κp 0 gp 0 ðtÞ
ð3Þ
p 0 ¼1
where gp 0 ðtÞ = Gaussian atom and selected from a given Gaussian atom dictionary D with a coefficient κp 0 . The convergence of this representation is defined in Mallat and Zhang (1993). Considering real engineering applications, a remainder rN 1 ðtÞ is introduced with finite iterations as follows: si1 ðtÞ ¼
N 1 −1 X p 0 ¼1
κp 0 gp 0 ðtÞ þ rN 1 ðtÞ
ð4Þ
where gp 0 ðtÞ can be computed with the maximum magnitude of the projection in rp 0 ðtÞ Z ∞ rp 0 ðtÞgðeÞ ðtÞdt gp 0 ðtÞ ¼ arg max ð5Þ gðeÞ ðtÞ∈D
ð2Þ
0 otherwise
−∞
where e ¼ fς; ϱ; ϕg are the time-shifting, frequency-shifting, and variance parameters for the Gaussian atoms. The coefficient κp 0 can be computed as Z ∞ κp 0 ¼< rp 0 ðtÞ; gp 0 ðtÞ >¼ rp 0 ðtÞgp 0 ðtÞdt ð6Þ −∞
Then the voltage signals can be decomposed in the temporal domain, and their feature vectors ½κ; ς; ϱ; ϕT can be extracted with limited iterations (Jiang et al. 2016).
UMI Detection and Location
overfits the training sets, brings high variance, and is hard to generalize. From a computational perspective, a single decision tree can be easily trapped into local minimum, which brings a risk for future detection (Breiman 2001; Yang et al. 2017). Random forest provides a way to average the multiple deep decision trees and reduce the high variance. Based on decision trees, the proposed random forest-based UMI detector is an ensemble learning-based approach, which is more stable and robust to detect the UMI issues. As the flowchart in Fig. 1 illustrates, in the UMI detection part, Λ0RF and Λ1RF are used to indicate the data set of normal operating conditions and the data of UMI issues, separately. The random forest is implemented as follows (Ho 1998; Pal 2005): • Random sample with replacement (bagging) from the data set Λ0RF and Λ1RF to generate the training sets; • For each random sample set, train a decision tree to fit the pattern; and • For the detection, the averaging approach is used to generate the results of the random forest. In random forest, the bagging approach is used to generate different decision trees to learn the pattern comprehensively. The averaging approach is used to reduce the variance without increasing the bias. Then, the proposed UMI detector is used to detect the UMI issues from the normal operation conditions in the smart grid. In this paper, the proposed random forest–based UMI detector is built with 100 decision trees. In considering different algorithms (Ho 1998; Pal 2005; Banfield et al. 2007), the number of decision trees for the random forest can be decided with the test accuracies. Fault Contour Map–Based Location for a UMI If a UMI is detected, the fault contour map is used to locate the position of the UMI. The coefficient amplitude of the feature Gaussian atom in the MPD results is used to represent the impact of the UMI at the bus where the signal is recorded (Jiang et al. 2014b). The test bench system is based on the IEEE New England 39-bus system. The microgrids are used as active loads of Buses 12, 18, 21, 23, 26, 28, 29, 31, and 39. With the clustering algorithm, the 39 buses are classified into several different impact levels that indicate the fault impact from heavy to light (Jiang et al. 2014b). Combined with the topology information of the smart grid, the fault contour map can be generated to locate the UMI. The UMI location approach is demonstrated as follows using the example of transformer fault. Two three-phase transformer faults occur in two transformers between Bus 12 and Bus 13, Bus 12 and Bus 11, which are similar to the transmission line outages. The result is that the microgrid located on Bus 12 operates in UMI mode. After the MPD, the k-means clustering algorithm is used to cluster the coefficients of feature Gaussian atoms and the corresponding 39 buses into five different impact levels as shown in Table 1. The k-means clustering algorithm is an unsupervised learning approach, which
Random Forest–Based Detection for a UMI
Table 1. Impact Level of Transformer Faults
Using the spatial characterization obtained by OSMDS and temporal characterization by MPD, the power system situational awareness can be analyzed and achieved. In this section, a random forest–based UMI detector is trained to detect the UMI issues. From a statistical perspective, a single decision tree can fit deeply to learn the highly unique patterns of a single feature, which usually
Impact level
© ASCE
1st (nearest to fault) 2nd 3rd 4th 5th
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Bus number 12 5, 6, 11, 13, 14, 15 3, 4, 7, 8, 9, 10, 16, 17, 18, 21, 24, 27 1, 2, 23, 25, 26, 28, 29 19, 20, 22, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39 J. Energy Eng.
G8
Distribution Network
Distribution Network
G10
Distribution Network
G8
Distribution Network
Distribution Network
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G1
Distribution Network
Distribution Network
G6
Distribution Network
G7
G5
G2 Distribution Network
G4
G3
Fig. 2. Fault contour map for locating the UMI; the impact levels 1–5 are indicated with different circles
can be used for data clustering with a given number of clusters and a given distance function (Jiang et al. 2014a, b). Combined with the topology information of the IEEE 39-bus system, it is noticed that Bus 12 has the greatest amplitude of the feature Gaussian atom. In Table 1, Bus 12 belongs to the first level. The UMI caused by the two transformer faults is located with an ellipse. Levels from 2 to 5 indicate different fault impact levels. Combining the topology information of the smart grid with Table 1, the fault contour map can be generated, as shown in Fig. 2. The change in color indicates the fault impact from heavy to light. The fault contour map can be used to locate the UMI and indicate different impact areas.
where x ∈ Rn1 represent integral variables, (e.g., state of charge in battery, y ∈ Rt1 represents algebraic variables; bus voltage, p ∈ Rp1 are the parameter variables; control parameters in controller, and n1 , t1 , and p1 are the dimensions). Eq. (7) can be linearized at the point of ðx0 ; y0 Þ as follows:
Optimization of the Stability Characteristics of a UMI
Δ˙x ¼ fA − BD−1 CgΔx ¼ Asys Δx
For an detected and located UMI, it is essential to ensure the small signal stability of the microgrid under different operation conditions (Wang et al. 2013).
Δ˙x ¼ f x jðx0 ;y0 Þ Δx þ f y jðx0 ;y0 Þ Δy 0 ¼ gx jðx0 ;y0 Þ Δx þ gy jðx0 ;y0 Þ Δy
where fx ; fy ; gx ; gy represent ∂f=∂x; ∂f=∂y; ∂g=∂x; ∂g=∂y, respectively; and A ≜ f x jðx0 ;y0 Þ ; B ≜ fy jðx0 ;y0 Þ ; C ≜ gx jðx0 ;y0 Þ ; D ≜ gy jðx0 ;y0 Þ . For a normal operating system, the matrix D is nonsingular, and Eq. (8) can be rewritten as
Asys zi ¼ λi zi
x˙ ¼ fðx; y; pÞ 0 ¼ gðx; y; pÞ © ASCE
ð7Þ
ð9Þ
where Asys represents the system state matrix. It is assumed that the small signal stability problem of the islanding microgrid is described as follows:
Small Signal Stability Analysis of a UMI In a UMI, the comprehensive analysis on DERs, inverters, loads, and network show that their mathematical models can be generally expressed in state equations and algebraic equations. Therefore, a UMI with multiple DERs can be described by a set of differential and algebraic equations as (Wang et al. 2013)
ð8Þ
ðAsys ÞT ui ¼ λi ui
ð10Þ
where λi ¼ τ i þ jζ i = ith generalized eigenvalue of the system described in Eq. (10) with τ i = real part and ζ i = imaginary part; and zi and ui = generalized eigenvectors, respectively. Systems are considered to be stable when there is no eigenvalue that has a real part equal to or larger than zero. Further sensitivity analysis also shows that eigenvalues are usually impacted by some critical parameters in a system such as parameters in DER inverter controller (Wang et al. 2013). Therefore, the critical parameters can be optimized to obtain better system stability characteristics.
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Table 2. Comparison of OSMDS Results in IEEE 30-Bus, 39-Bus, and 118-Bus System Test system IEEE 30-bus system IEEE 39-bus system IEEE 118-bus system
Scenario
Number
Location of measurement devices
Selection rate (%)
I II I II I
10 7 13 8 32
33.3 23.3 33.3 20.5 27.1
II
28
2, 4, 6, 9–10, 12, 15, 18, 25, 27 2, 4, 10, 12, 15, 18, 27 2, 6, 9–10, 13–14, 17, 19–20, 22–23, 25, 29 3, 8, 10, 16, 20, 23, 25, 29 3, 5, 9, 12, 15, 17, 21, 23, 28, 30, 34, 37, 40, 45, 49, 53, 56, 62, 64, 68, 71, 75, 77, 80, 85-86, 90, 94, 102, 105, 110, 115 3, 8, 11–12, 17, 21, 27, 31-32, 34, 37, 40, 45, 49, 53, 56, 62, 72, 75, 77, 80, 85–86, 91, 94, 102, 105, 110
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Objective Function for Stability Optimization of a UMI To improve the system robustness within its operating range, critical parameters such as droop coefficients in the DER’s inverter controller are optimized based on analysis of massive system operation data (Wang et al. 2013). Specifically, the eigenvalue-based objective function in Eq. (11) is proposed to optimize the critical parameters in terms of small signal stability of a UMI under an operating range X X X min γ μj;m ½ξ 0 − ξ j;m ðpÞ þ η χk;m δ k;m ðpÞ p
m
j
k
s:t: ξ j;m ðpÞ < ξ 0
ð11Þ
where m = number of operation scenarios; j = number of eigenvalues whose damping ratios are less than the given value; and k = kth dynamic oscillation mode. The damping and dynamic characteristics of Eq. (11) are presented as follows. Damping Characteristics Based on Data Analysis P In the first item, γ j μj;m ½ξ 0 − ξ j;m ðpÞ, the damping ratio ξ j;m ðpÞ is less than the given value ξ 0 . The γ denotes the weight coefficient for this term, which is a set value. The ξ j;m ðpÞ can be obtained by ξ j;m ðpÞ ¼ jζ i =τ i j, which is a function of the control parameter p. The μj;m is the weight coefficient of the corresponding damping ratio, and its value is given by the following expression: μj;m ¼ L½ξ 0 − ξ j;m ðpÞα
value. The χk;m is the weight coefficient of the dynamic characteristics, and its expression is given as follows: χk;m ¼ ½δ 0 − δ k;m ðpÞβ
Particle Swarm Optimization Compared with the genetic algorithm and simulated annealing approaches in previous studies (Jiang et al. 2013; Wang et al. 2013; Panigrahi et al. 2010), PSO is an effective algorithm for solving nonlinear problems. In this paper, PSO is used to optimize the critical parameters and improve the stability characteristics of a system. To improve the robustness of the optimized parameters, the boundary conditions of the islanded area are considered in the system modeling and initialization during the optimization process (Wang et al. 2013). Massive data, e.g., bus voltage, current, and DERs statuses are metered, collected, and analyzed to generate particle swarm, which is needed for the parameter optimization. It is assumed that the size of the swarm is N, and each particle is represented as an M-dimensional real valued vector characterized by the velocity ν i2 ¼ ½ν i2 ;1 ; ν i2 ;2 ; : : : ; ν i2 ;M and the position oi2 ¼ ½oi2 ;1 ; oi2 ;2 ; : : : ; oi2 ;M . The iterative procedure of velocity and position is given in the following equations: þ1 ν ni22;m ¼ ωn2 þ1 · ν ni22;m2 þ c10 · r10 · ðqni22;m2 − oni22;m2 Þ 2
þ c20 · r20 · ðgni22;m2 − oni22;m2 Þ
where α is given positive integer, making μj;m a power function of ξ j;m ðpÞ; and L = positive constant.
IEEE 30-bus system IEEE 39-bus system IEEE 118-bus system
Detection rate (%) Detection rate with noise (%) 100 (260/260) 100 (260/260) 100 (260/260)
98.9 (335/350) 98.9 (338/350) 97.6 (338/350)
Table 4. UMI Detection Rates with OSMDS Test system IEEE 30-bus system IEEE 39-bus system IEEE 118-bus system © ASCE
ð15Þ
þ1 þ1 oni22;m ¼ oni22;m2 þ ρ · ν in22;m 2 2
ð16Þ
where n2 = current iterative step; and n2 þ 1 = next step. Eq. (14) is the iterative formula for the particle velocity. The first term of Eq. (14) shows that the current velocity is affected by the history value, that is the inertial motion influenced on the particle own velocity. The coefficient ωn2 þ1 is an inertia weight. Eq. (15) shows the iterative procedure, where ωstart is the value of velocity weight at the beginning, which is usually smaller than but close to 1; ωend is the value of velocity weight at the end of iterations; and
Table 5. Comparison of Detection and Identification
Detection rate (%) Detection rate with noise (%) 100 (260/260) 100 (260/260) 100 (260/260)
ð14Þ
ωstart − ωend N iteration
ωn2 þ1 ¼ ωn2 −
Dynamic Characteristics Based on Data Analysis P The second item, η k χk;m δ k;m ðpÞ, indicates the system dynamic characteristics. The η denotes the weight coefficient, which is a set
Test system
ð13Þ
where δ 0 = given dynamic oscillation mode; and β = positive integer, making χk;m a power function of δ k;m ðpÞ.
ð12Þ
Table 3. UMI Detection Rates with Synchrophasor Measurement Devices Fully Selected
23.3
97.3 (335/350) 98.1 (338/350) 97.3 (338/350)
Method ANN SVM Proposed method
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Detection (%)
Detection 10 dB (%)
95.7 93.1 99.4
89.4 85.8 97.5 J. Energy Eng.
Main Grid 1 (PCC)
2 Circuit Breaker 1 3
Microgrid
5
4
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Battery1
Load 1
+
7
6
20
8
Circuit Breaker 2
PV1
9 13
10
Battery2
+
12
11 Load 3
PV2 14 Load 2
MT1 15 Load 4
Load 5 16 MT2
19
PV3
17 +
18
Battery3
Fig. 3. Benchmark LV unplanned area network
N iteration is the maximum allowable iterations of PSO in one experiment, which is an empirical value and can be decided based on Panigrahi et al. (2010). As shown in Eq. (15), the velocity weight is decreasing during the iteration procedure, avoiding the problem of fly over near optimization efficiently. Eq. (14) shows the influence caused by the personal best position qni22;m2 . The coefficient c10 is known as cognitive acceleration, representing the self-experience of each particle. The third term of Eq. (14) is related with the group best position gni22;m2 . The coefficient c20 is called social acceleration, representing the experience of other particles in the swarm. In Eq. (14), r10 ; r20 are the uniformly distributed random numbers in (0,1). Eq. (16) gives the iterative formula for the particle position. The first term shows the effect of the current position and the second part represents the influence of the current velocity. In this expression, ρ is the velocity weight.
Simulation and Results Big Data-Based UMI Detection and Location To demonstrate the proposed spatial-temporal synchrophasor measurement system characterization approach and its application on fault detection and identification, the IEEE 30, 39, and 118-bus systems are used for experiments on numerical simulations. All
60
Eigenvalue before optimization Eigenvalue after optimization
40 20 0
Table 6. Optimization Results of Droop Coefficients Kf DERs Battery1 Battery2 Battery3 MT1 MT2 © ASCE
-20
Kν
Initial values
Optimization
Initial values
Optimization
15.3402 8.1315 10.1054 8.2347 2.2605
9.2368 3.8367 6.8795 1.5347 0.7468
13.6575 6.2243 7.8276 4.5059 6.6108
9.1345 8.0110 4.7686 1.8987 6.6784
-40 -60 -7
-6
-5
-4
-3
-2
-1
0
Fig. 4. Eigenvalues for initial condition and parameter optimization 04017045-6
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1.5
Reactive power(p.u.)
Active power(p.u.)
1.5 1 Battery1 Battery2 Battery3 MT1 MT2 PV1 PV2 PV3
0.5 0 -0.5 0
5
10
15
20
(a)
25
30
35
40
45
1 0.5 0 -0.5 -1
50
0
10
15
20
25
30
35
40
45
50
Time(s) 1.004
System Frequency (p.u.)
Bus voltagee(p.u.)
1.4 Downloaded from ascelibrary.org by Huaiguang Jiang on 06/28/17. Copyright ASCE. For personal use only; all rights reserved.
5
(b)
Time(s)
1.2 1 0.8
Bus11 Bus12 Bus13 Bus17 Bus19 Bus20 Bus5
0.6 0.4 0.2 0 0
(c)
Battery1 Battery2 Battery3 MT1 MT2 PV1 PV2 PV3
5
10
15
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25
30
35
40
45
Frequency of MT1 system Frequency of MT2 system
1.003 1.002 1.001 1 0.999 0.998 0.997 0.996
50
0
5
10
15
(d)
Time(s)
20
25
30
35
40
45
50
Time(s)
Fig. 5. (a) Active power response of DERs; (b) reactive power response of the DERs; (c) bus voltage; (d) system frequency
the simulations are executed using a computer with 3.00-GHz Intel i7 CPU and 32-GB RAM. The resulting binary integer linear programming is solved by CPLEX Toolbox for MATLAB, and the overall OSMDS is studied with MATLAB with Power System Analysis Toolbox (PSAT). The time consumed for each simulation is less than 1 s. Two smart grid scenarios are simulated by (1) ignoring the effect of ZIB, and (2) considering the effect of ZIB. OSMDS and Data Volume Reduction In Table 2, the OSMDS results for IEEE 30-bus, IEEE 39-bus, and IEEE 118-bus systems are illustrated, respectively. The smart grid requires fewer number of measurement devices if the effect of ZIB is considered. If the power system is larger, the synchrophasor measurement device selection rate might be further decreased. For a simulation period of 10 s, 10,000 data samples are collected with the selected synchrophasors (Xu et al. 2005). Then, the features of the collected data are extracted into 30 four-dimensional feature vectors ½κ; ς; ϱ; ϕT , and the size is 30 × 4 ¼ 120. The data compression rate is 1.20%, which is defined as the feature data volume to the original data volume. Considering the proposed OSMDS, the average synchrophasor device selection rate is 26.8% in Table 2. In summary, the data compression rate of the proposed approach can reach 0.322%, which provides an effective method for smart grid measurement data processing and transmission. UMI Detection and Location Different types of faults, such as transformer faults, and transmission line outage are simulated as the reasons to result in UMI issues. The simulation of each scenario lasts 10 s, and the fault randomly occurs at 2, 2.5, 3, 3.5, and 4 s with duration for 5, 10, and 15 cycles. The Gaussian atom dictionary is built with 1,800,000 Gaussian atoms and the MPD iteration number is 30. The random forest is validated with 10-fold cross validation. To evaluate the fault detection performance, 260, 260, and 260 random faults are simulated to generate training and testing data in the IEEE © ASCE
30-bus, 39-bus, and 118-bus system, respectively. Among the aforementioned data, 90% of the data are used for training and 10% are used for testing. An additive white Gaussian noise (AWGN) with signal-to-noise ratio (SNR) 10 dB is used for evaluating the performance with noisy measurements. With SMDs selected at every bus and OSMDS in the IEEE 30-bus, 39-bus, and 118-bus systems, the results of the UMI detection rates are illustrated in Tables 3 and 4. The UMI detection rate of OSMDS is similar to the SMDs full selection scenario. This indicates that the OSMDS can dramatically reduce the number of synchrophasors and keep high performance in UMI detection. Based on the earlier fault scenarios, 100 UMI issues are randomly generated and simulated at different locations in the IEEE 30-bus, 39-bus, and 118-bus systems, to evaluate the fault location methods performance. The success rate of locating a fault is 100%, and it can be concluded that the proposed location approach is robust given the previous experimental scenarios. Comparison with Other Methods In Aggarwal and Song (1998), and Axelberg et al. (2007), an artificial neural network (ANN) and support vector machine (SVM)
Table 7. Perturbations of Irradiance and Loads Scenario 2
Irradiance of PV1 (W=m ) Irradiance of PV2 (W=m2 ) Irradiance of PV3 (W=m2 )
Initial values
Perturbation
Simulation
1,000.00 1,000.00 1,000.00
900.00 1,050.00 950.00
(1) 15 s (3) 45 s (5) 75 s
Load1
Active power (W) Reactive power (W)
12.75 7.90
14.00 7.50
(6) 90 s (6) 90 s
Load2
Active power (W) Reactive power (W)
61.15 37.90
65.00 36.00
(2) 30 s (2) 30 s
Load3
Active power (W) Reactive power (W)
12.75 7.90
12.00 8.50
(4) 60 s (4) 60 s
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32 PV1 PV2 PV3
Active Power (kW)
30 28 26 24 22
0
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70
80
100
0
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20
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50 Time(s)
70
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100
0
10
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40
50 Time(s)
70
80
100
14.5
Active Power (kW)
14 13.5 13 12.5 12 11.5
68
Active Power (kW)
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20
66
64
62
60
(1)
(2)
(3)
(4)
(5)
(6)
Fig. 6. Response of DERs and loads under different perturbations
are used to detect the UMI issues. Using the same simulation as described at the beginning of section “Simulation and Results,” the UMI detection rates obtained using ANN, SVM, and the proposed approach are demonstrated in Table 5. The proposed method performs better than the other two methods (Aggarwal and Song 1998; Axelberg et al. 2007), especially in low signal-to-noise ratio scenarios. Numerical Results of the UMI Stability After a UMI is detected and located, the numerical results of the UMI are illustrated as follows. The 0.4 kV, 60 Hz typical system prototype shown in Fig. 3 is used to test and verify the proposed approach. In the test system, Bus 1 is connected to Bus 29 in Fig. 2. The parameters of this system are provided in © ASCE
Papathanassiou et al. (2005). The testing system includes three categories of DERs (Wang et al. 2013), namely nondispatchable DER [photovoltaic (Kim et al. 2009)], dispatchable DER unit [microturbine (MT) (Tremblay et al. 2007)], and dispatchable distributed energy storage (battery). Among these DERs, all five dispatchable units are operated with droop control, whereas the three PV units are controlled via a maximum power point tracking strategy (Kim et al. 2009; Chung et al. 2010; Miao et al. 2011). These DERs are integrated into the system through voltage source inverters. In this study, a sparse matrix technology based on an improved cross chain table is applied to the matrix derived for small signal stability analysis of the test system. The initial and optimized values of critical control coefficients in some PSO experiment are listed in Table 6.
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Small Signal Stability Analysis There are 148 state variables in the test UMI system. Under the condition of initial values, all the eigenvalues can be calculated through QR algorithm and critical eigenvalues near to the imaginary axis are shown in Fig. 4. It shows that there exist a complex conjugate pair of eigenvalues with positive real parts, thus the system is unstable in this case. After the parameters optimization, there is no eigenvalue located on the right half of the plane, which leads to a stable system. In the stable case, the least damping ratio is 0.5278, larger than the given damping ratio 0.2. Among the eigenvalues, the largest real part is –0.10102, smaller than the given value –0.01. In Fig. 4, the eigenvalues are placed on three different clusters, i.e., low-frequency modes, medium-frequency modes, and high-frequency modes. The frequency-scale separation among modes is expected because of the interfaces of power electronic devices in the system. A rigorous parameter perturbation analysis on different modes indicates that low-frequency modes are affected primarily by the power controllers and the dominant low-frequency eigenvalues are influenced primarily by the active power controller, particularly by the droop coefficient, whereas medium-frequency and high-frequency modes are primarily dictated by the current controllers and LCL filters in the system. Temporal Domain Simulation Results Two typical simulation cases are provided to confirm the effectiveness and robustness of the proposed approach. The simulations are carried out in DIgSILENT and PowerFactory.
Conclusion With the flourishing development of DERs in distribution systems, it can be foreseen that microgrids will be frequently formed. In smart grid operations, the UMI issues might be caused by many different system faults or unplanned maneuvers that dramatically impact system security. To tackle this issue, a big data-based security approach is proposed to detect and locate the UMI, then enhance the stability for the UMI. The proposed spatial-temporal characterization approach can dramatically reduce the data volume and keep high performance in smart grid monitoring to detect and locate the UMI. This procedure of smart grid security monitoring functions as a trigger for the stability enhancement of the UMI. In the stability enhancement, the PSO is used to improve the damping and dynamic characteristics of the UMI. The effectiveness and robustness of the proposed approach is validated by the simulation results. In real-world applications, the scenarios can be more complicated because many other factors can affect the smart grids and cause UMIs. Based on these, in the next step the authors will further study the proposed approach to provide prompt smart grid security assessment and stability enhancement in future smart grids.
Acknowledgments This work was supported by the U.S. Department of Energy under Contract DE-AC36-08-GO28308 with the National Renewable Energy Laboratory.
Mode Transition Simulation To verify the robustness of the optimized coefficients, Circuit Breaker 1 in Fig. 3 is opened at 5.0 s, realizing the transition from grid-connected mode to island mode; then a three-phase short circuit fault happens at Bus 11 at 15.0 s and then is cleared at 15.1 s; subsequently, Circuit Breaker 2 is opened at 30.0 s, compelling the entire system to two subsystems. Fig. 5 shows the responses during the mode transition and fault. Simulation results show that when Circuit Breaker 1 is opened at 5.0 s, the system will be operated in islanded mode. After the UMI detection and location, the DERs adjust their output power according to the optimized parameters, as shown in Table 6, in order to maintain stable system operation. Simulation results confirm the robustness of the optimization results. Disturbance Simulation Typical simulation cases are provided to test the dynamics of DERs and loads, and to confirm the effectiveness of the proposed approach. The simulation process is settled as shown in Table 7. Taking the active power as an example, Fig. 6 shows the responses of DERs and loads during different operation conditions (under weather disturbances and various loading conditions). Fig. 6 shows that stable power-sharing performance can be obtained under various disturbances. When the system is operated under other different conditions, the same conclusions can be drawn from simulation results, which confirm the effectiveness of the proposed method. Both the small signal stability analysis and temporal domain simulation certify the rationality of the coefficients optimized by the proposed approach. In the autonomous mode, all the DERs in droop control strategy are responsible for sharing the active and reactive power in order to maintain the voltage and frequency within the regulated range and enhance the system performance against disturbances. © ASCE
Notation The following symbols are used in this paper: c10 ; c20 = two positive acceleration coefficients for velocity updates of each particle in PSO; ci1 = cost of select a synchrophasor measurement device at bus i1 ; D = Gaussian dictionary; oi2 ; ν i2 = position and velocity vectors of the i2 th particle in PSO, respectively; r10 , r20 = two independently random variables with uniformly distributed range (0,1) for velocity updates of each particle in PSO; si1 ðtÞ = voltage signal on bus i1 , where t is a time index; ui01 = binary decision variable for a synchrophasor measurement device selected at bus i1 ; κ; ς; ϱ; ϕ = amplitude, time-shifting, frequency-shifting, and variance parameters for Gaussian atoms in MPD; Λ0RF , Λ1RF = Λ0RF and Λ1RF are the training data set of normal operating conditions and the data of UMI issues, respectively; and λi = λi ¼ τ i þ jζ i is the i th generalized eigenvalue of the UMI, where τ i is the real part, and ζ i is the imaginary part.
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