Implementation of PMU Based Distributed Wide Area Monitoring in Smart Grid

Determination of accurate operating states of the power system is one of the most challenging tasks due to integration of large number of solar PVs into the power system. Since these sources of energy are inertialess generations, hence may cause instability issues if highly penetrated. Hence, precise monitoring and control of such systems with higher PV penetration is a critical issue to address both in terms of the total number of PV sources in the system and the percentage of penetration. Phasor Measurement Units (PMUs), with their time synchronizing abilities, have made this task a bit easier. However, traditional centralized data handling architecture at control centers are becoming redundant due to various limitations such as data handling, computational constraints etc. To overcome this, a distributed PMU-PDC architecture approach is utilized in this paper. Since local PDC (Phasor Data Concentrator) in an n-area power system can run separate optimization algorithms, by combining the results of these optimization algorithms of n-area PDCs, we can get a much more accurate global consensus about the current operating state of the system. The presented work is divided into two parts. First, the analysis of power system stability is performed in terms of the total number of Photovoltaic Source (PV) in the system and the percentage of PV penetration. Then, the accuracy of the method is tested both in terms of the number of PMUs in each area along with their channel capacities. Low-frequency oscillations have been simulated on IEEE-68 standard bus system using MATLAB, and the modes of oscillation are estimated using the Alternating Direction Method of Multipliers (ADMM) algorithm.


I. INTRODUCTION
Following the power outage of July 2012 in the northern and north-eastern portions of India, PMUs with their ability to provide time-synchronized measurements, are gaining popularity and momentum. The government of India has initiated the various projects for the deployment of PMUs across the grid on a larger scale. These synchronized measurements from different locations are sent to the PDC installed at load centres through proper communication for the aim of analysis and usage [1], [2]. The most serious concern about such a system is the generation of gigantic PMU data generated, which are perhaps unattended so far. Therefore, instead of concentrated data storage and analysis, distributed physical architecture needs to be developed under such conditions. This distributed architecture contains dedicated local PMUs and PDC that determines the operating states of the power system locally [3]. Decisions towards any perturbation in the power system can be accurately done by assessing the locally attained measurements at central PDC sent via proper communication channels. Such a distributed architecture ensures the robustness of the system compared to centralized architecture in terms of computational complexity as well as data handling [1], [4]. Several advanced signal processing methods analyze lowfrequency oscillations using centralized approach. These techniques are Fast Fourier Transform (FFT) [5], Matrix Pencil (MP) [6], [7],Prony Analysis (PA) [8], [9], Principal Component Analysis (PCA) [10],Empirical Mode Decomposition (EMD) [11], [12],Multivariate Empirical Mode Decomposition (MEMD) [13], Hilbert Transform (HT) [14], wavelet transform(WT) [15],robust recursive least square (RRLS),regularized robust recursive least square (R3LS) algorithm [16], Eigensystem Realization Algorithm (ERA) [17], Dynamic Mode Decomposition (DMD) Algorithm [18] etc. All these methods suffer computational challenges due to data handling at a centralized stage. To overcome such challenges, distributed PMU-PDC architecture is used in [19]- [27] to analyze instability caused by low-frequency oscillations due to various faults occurring in the system. Such a system consist of several regions, which might or may not be symmetric, and belong to several companies as shown in Figure 1. Each wide-area contain PMUs that communicate their data in real-time to PDCs position at the control station by a Virtual Private Network (VPN). These PDCs can send data into each other and with a main PDC placed at the separate system operators while monitoring such a wide-area using Software Define Network (SDN). The idea is to utilize this distributed grid to work as global assent at the PDCs into every region, iteratively produce a reliable evaluation of the coefficients of the polynomial, and allow the PDCs to interact with each other to reach the global solution using many variants of the ADMM algorithm [28] [29]. In standard distributed algorithms, local PDCs are performing their respective optimization steps with equal speed, and the communication delays between the local PDCs and the central PDC are also equal, i.e., they are synchronous. However, in reality, the PDCs may not be perfectly synchronized with each other due to differences in their processing speeds as well as due to various communication delays such as routing, queuing, and transfer delays in the SDN. This problem can be overcome by the use of recently developed method called Asynchronous ADMM (A-ADMM). In this method, the central PDC receives the updates only from a subset of the N local PDCs at every iteration k, referred to as active PDCs. Although both the algorithms ensures data privacy between the N PDCs, it is not very resilient as the central PDC is directly amenable to failure under extraneous attacks. This problem can be resolved by resorting to a completely distributed version of Architecture distributed ADMM (D-ADMM). In this formulation, each active PDC at each iteration communicates directly with a subset of other active PDCs determined by a communication graph. Therefore, the need for the central PDC no longer exists. However, if p, the number of PMUs, is large, a better strategy will be to create multiple hierarchical layers of PDCs so that the computational load of the global estimation gets divided. This method is known as hierarchical ADMM (H-ADMM) algorithm [24], [25], [30]- [32]. Since in modern power systems, conventional energy resources are continuously being replaced by renewable energy resources such as solar, wind etc. Continuous efforts are presently being made worldwide to integrate large numbers of solar PV systems into the grid due to the numerous benefits it offers to utility and consumers. The stability of the power system is directly linked with the inertia between generators at the generation side and motors at the load side. Since solar PV system is an inertialess generation replacing it with conventional power sources will cause inertia imbalance, hence can affect the stability of the power system. However, the present power system cannot handle a large amount of solar penetration without the smart renovation of the grid. It is unanimously accepted that more than 30% Renewable Energy Sources (RES) penetration affects grid stability. Although, large-scale integration of energy storage devices will be helpful to improve the grid stability and can enhance the percentage of penetration for safe operation. Therefore, analysis of power system stability under significant PV penetration is a critical issue to address. In this work, stability analysis of the power system is performed with varying PV penetration using distributed PMU-PDC architecture. The analysis performed in this work is divided into two parts. First, the power system stability analysis is performed under different test conditions viz. percentage of PV penetration and number of PV sources in the system. Then performance on the accuracy of the proposed method is also tested based on the total number of PMUs installed along with their channel capacity.
This paper is divided into the following sections. Section II describes the problem formulation and description of the ADMM algorithm, in section III, the communication architecture for obtaining the measurement from multiple PMU-PDC systems is presented, section IV discusses the test results on the IEEE-68 bus system. The conclusions drawn are presented in section V.

II. PROBLEM FORMULATION
ADMM algorithm is a strong algorithm that is well appropriate to control distributed optimization. ADMM algorithm can be utilized for many practical convex optimization problems suitable for analyzing stability properties and decomposability [24], [25]. Let a power system be consisted by synchronous generators and load buses linked by a particular topology. All generators are modelled via a second-order swing equation. The modelling of every bus is obtained by representing active and reactive power buses by two algebraic equations. The linearized element variable type for the machine framework can be expressed as: is the mechanical damping from generator , is the inertia , is the ( × ) matrix, is synchronous speed, is the laplacian matrix. ( ) ∈ , represent collection of phase angle measurements ∆θ Pi (t), p = 1, … , P measured at busses equipped with PMU. is the eigenvalues, denoted by(− ± Ω ), ( ≜ √−1) = 1, … , . The purpose is to evaluate those second eigenvalues of from ( ) in a distributed style utilizing various computational sources. Before this, we need to generalize model assessment algorithm that is well suited for distributed optimization problems [24].
The solution of ∆ ( ) in equation 1 can be written as Where ( ( )) is a uniform sampling with period T, ( ) damping, (Ω ) frequency of ℎ mode & is the remains of the ℎ mode reflected in the ℎ output. A generic expression for the − of ∆ ( ) ≜ ∆ ( )| , ( = 0,1, … , − 1) with measured samples, can be rewritten as Where (b) and (a) are fixed zero polynomial and characteristic polynomial.
Step one: Finding the values of matrix by using Where is an integer satisfying 2 + ≤ − 1 . For PMU = 1, … , , concatenate, cp and Hp and solving by using LS minimization technique.
Where ‖. ‖ indicates the 2 models of a vector.
Step two: after finding a, we calculate the roots of discretetime z transform from the denominator of (3). Suppose roots be denoted by , = 1, … ,2 , after that the eigenvalues of can by find as ln . The LS of (5) can be reformulated as a global consensus problem over a grid of N calculation areas spanning the power grid, as shown in Figure 2. VOLUME XX, 2017 Such that − = , for = 1, … , , ^= ( ) , ^= ( ), = 1, … , ( is the number of sensors in each area), is a vector of the primal variable and z is the local variable. From equation 6, we utilize ADMM algorithm, which reduce the next group of recursive update by utilizing an increased lagrangian. We can write ( ) Where ( ) vector of the dual variables at repetition k, > 0 indicates the penalty factor. ^( ) =^ as determined in (6).

III. Asynchronous ADMM (A-ADMM) Algorithm
One basic consideration in standard ADMM algorithm is that all the local PDCs are obtaining their particular optimization procedure at a similar speed, and the communication latency between the main PDC and the local PDCs are also similar; thus, we can say that they are synchronous. Although the global PDCs might not get totally synchronized together due to variations in their processing speeds and different connection delays like transfer, queuing, and carry delays in the SDN. The solution to take control of this asynchrony is to put the main PDC to stay until it receives all local PDCs.
In this state, the latency for every repetition will be dependent on the slow connection link. Under this condition, the algorithm will become slower. The various alternative method for resolving this problem is an asynchronous version of the ADMM algorithm. In this algorithm, the PDC receives the update data only from N global PDCs at each repetition point as active PDCs. For this algorithm, let this set be signified by And then found + , utilizing the latest local evaluation from all PDCs. At this time instant + , + is computed. The main PDC then transmit ( + , + ) to each local PDC. After accepting + from every local PDC j at that point builds + and + .It can be written as [16], [24], [33], [34].

IV. RESULT AND DISCUSSION
To verify the results, IEEE-68 standard bus system is considered as shown in Figure 3. The whole system is divided into five areas (PDC), and each area contains 3 PMUs and 1 local PDC. Table 1 shows the optimally placed PMU location for each considered area. For simplicity, sixthorder system generator is considered. A three-phase fault is simulated between bus 6 and bus 7, began at 0.4 s, cleared at 0.25 s and 0.8 sec at bus 6 and bus 7, respectively. The optimization iteration is started by considering initial 50 samples. The main objective is to assess different inter-area post-fault oscillations of the system. In this simulation, select 2 = 40 provides satisfying evaluations for inter-area mode. The value of ρ=10 -9 and ε=10 -6 . For each case, PDCs are chosen arbitrarily with equal probability of 0.9. The time per iterations for the algorithm is found to be between 1-2 seconds using MATLAB 2016a tic() toc() command on an Intel(R) Core(TM) i5-7200U CPU @2.50GHz processor with 8.00 GM RAM and 64-bit Windows 10 OS. This is pragmatic since a PMU based communication delay will not be over a few milliseconds if added to the above-mentioned iteration time. The iteration time is comparable to the previous studies. One such study has been reported in [35]. Here Table I to Table V are of specific importance where the number of iterations and the iteration time in seconds are summarized for the ADMM technique against other techniques. Time per iteration in seconds for our study (between 1 to 2 seconds) is at par with the reported studies.
The frequency plot of all the generation buses is plotted in Figure 4.

Case Study
Power system stability using eigenvalues during oscillations in power system after PV penetration is monitored by multichannel PMUs using ADMM technique. Simulation Methodology: The dynamics of the IEEE 68 bus system was analyzed in MATPOWER toolbox in MATLAB. The fault was simulated at various locations, and post-disturbance dynamics was recorded. The recorded dynamics, mixed with PMU error, is portrayed as the PMU data for selective locations. The PMU data is then processed to obtain eigenvalues of the system for stability analysis.
First, the analysis of power system stability is performed in terms of the total number of PV sources in the system and the percentage of penetration. For analysis with varying PV penetration, a certain percentage of total installed capacity of synchronous generators is replaced by PV system and the effect of size of PV penetration on system stability is determined. For analysis with variation in number of PV sources, the synchronous generators are completely replaced by PV sources of the same capacity and the effect of number of PV sources on the system stability is determined. Second, the accuracy of the method is tested both in terms of the number of PMUs in each area along with their channel capacities. The analysis of each case considered is discussed as follows: Case 1: Effect of size of PV penetration on system's vulnerability to disturbances using ADMM technique utilizing PMU data Table 2 shows the effect of the size of PV on the eigenvalues of the system as monitored by Synchrophasors data. The system's vulnerability is increasing with an increase in the size of the PV. The eigenvalues for the post-disturbance dynamics are closer to the origin for higher PV penetration.  Note that due to the absence of techniques like inertial emulation and energy storage devices, the simulations cannot be run for higher PV penetration as it will make the system unstable. PVs do not provide inertial response to the system, which leads to such vulnerability unless energy storage devices or virtual inertia techniques are used.
The results for damping (σ) and frequency (Ω) for each case of varying PV penetration are shown in Figure 5 and Figure  6 respectively. Case 2: Effect of number of PV sources on the system's vulnerability to disturbances using ADMMA The stability of the power system reduces as PV sources replace more conventional generators as these PV sources do not compensate the inertia provided by conventional generators.. The eigenvalues of the system appear to come closer to the origin as evaluated at the PDC end. When the PV sources replace 6 generators, the system becomes unstable post fault. This indicates that the PV penetration seriously affects the inertial response on the power system; hence, this vulnerability of distributed generation connected grid should be addressed. In addition, the study suggests the use of PMU based ADMM technique to find eigenvalues for disturbance analysis in power systems. The results for each case with the integration of different numbers of PV sources are tabulated in Table 3, and the results for damping (σ) and frequency (Ω) for each case of a varying number of PV generation sources are shown in Figure 7 and Figure 8 respectively.  As the number of PMUs are increased in each region, the accuracy of the technique to find eigenvalues using synchrophasor data improves. This is evident from Figure 9, showing the error between the true eigenvalues and those evaluated by ADMM algorithm. However, as the number of PMUs increases in each area, the error margin reduces. This clearly suggests that a trade-off between the installation cost of PMUs and accuracy can be made conveniently. Therefore, the study suggests that no more than 4 PMUs per area are needed as the error margin is not significant as more PMUs are added. However, if redundancy of the monitoring system is intended more PMUs can be placed.
Author Name: Preparation of Papers for IEEE Access (February 2017) VOLUME XX, 2017 9

Case 4: Effect of number of PMU channels in each region on the accuracy of ADMM technique
The effect of PMU channels on the accuracy of the technique has a similar pattern as observed in Case IV. More PMU channels reduce the error between the true eigenvalues and those evaluated using the ADMM technique shown in Figure  10. However, as the number of channels increases, the error margin reduces so much that the 4 PMU channel error curve almost coincides with the 3 PMU channel error curve. Hence, placement of a costly 4-PMU channel will be a needless exercise as 3 channel PMUs will suffice to monitor the system. Further, those locations (buses) which have less than 3 intersecting lines (branches) can have PMUs with lesser channels. For example, a bus having only two interconnections will need only a 2 channel PMU unless redundancy in measurements is intended.

V. CONCLUSION
Power system stability is one of the most severe concerns due to integrating a large number of inertialess renewable energy resources, especially solar PV systems. This paper performs stability analysis under such conditions using distributed PMU-PDC architecture.
The power system stability is tested under different test conditions that include variations of PV penetration and the number of PV generation sources in the system. The performance of the proposed technique is also tested by varying the number of PMUs in the system along with their channel capacity. The study results obtained on the IEEE-68 bus system demonstrate the effectiveness of the proposed work. The proposed work demonstrates how the different PDCs installed across the power system can communicate with each other to avoid data handling issues in centralized PDC architecture. The ADMM algorithm has been presented and the results computed for each mode suggest that the future installation of PMUs and PDCs can be reconfigured into distributed one to enhanced accuracy, reliability and avoid complexity, the most important the data handling.