real-time voltage stability indicators based on phasor …psrcentre.org/images/extraimages/8...

Abstract— In this paper a Methodology is proposed for the

online monitoring and assessment of voltage stability margins (VSM), using artificial neural networks and input data from the local phasor measurement units in power system. In this methodology, first the system model is simulated using digisilent 14. Then Optimal PMU placement was carried out considering outage line operating conditions whit application of GA algorithm and supervised learning of artificial neural networks is carried out on the basis of this model. Finally, on the basis of trained network and the set of system variables, monitoring is carried out along with the assessment of voltage stability margins for power system buss. Results for Zanjan 400kv Power Systems have been obtained to demonstrate the effectiveness of the algorithm.

Keywords— Voltage Stability Margin, PMU, Artificial Neural Networks.

I. INTRODUCTION OLTAGE instability-related outage events have occurred around the world and resulted in recent years in major system failures (blackouts). A number of these collapse

phenomena were reported in France, Belgium, Sweden, Germany, Japan, and the United States [1, 2]. Voltage stability has become an important concern for utilities. Static voltage stability can be assessed using continuation power flow calculations [1–4]. Much static voltage assessment methods have been proposed so far, such as the minimum singularity value method, sensitivity method and mode analysis method [5, 6]. The voltage stability evaluation determines if a given operating condition is voltage secure. Furthermore, it is desirable to know how far the system can move away from its current operating point and still remain secure [7]. For this kind of quasi-steady state voltage stability studies, the system load is slowly increased along a certain direction to the point of voltage collapse. The variation of load voltage magnitude with loading P is plotted as the P-V curve. The MW-distance from the base operating point to the critical collapse point, namely load active power margin, is a good measure of proximity to voltage stability. Continuation power flow (CPF)

Saed. Jalilzadeh is with the Electrical Engineering Department, University of Zanjan, Iran, (corresponding author to provide phone:09122419261; e-mail: [email protected]).

Reza. Abbasi was with Zanjan University (e-mail: Reza.abbasi @znu.ac.ir).

Reza. Noroozian is with the Electrical Engineering Department, University of Zanjan, Iran, (e-mail: [email protected]).

is a powerful algorithm to trace the power flow solution, starting at a base load leading up to the steady state voltage stability limit, for determining the load P margin. There are two methods available: Chiang method [8] and by Ajjarapu- Christy [9]. So the last few years, several methodologies for detecting the voltage collapse points (saddle-node bifurcations) in power systems using steady-state analysis techniques have been modified and applied for the determination of analyzing voltage stability of power systems for example Q-V curves and sensitivity-based indices [10]. Other methods, such as bifurcation theory [11], energy function [12], singular value decomposition [13], and so forth, have been also reported in the paper.

On the other hand, machine learning techniques together with traditional analytical techniques can significantly contribute in the solution of the related problems. The techniques, such as: pattern recognition, expert systems, artificial neural networks, fuzzy systems and evolutionary programming have been proposed in an impressive number of publications in the power system community [14]. Artificial intelligence techniques have been used in several power system applications. A feed forward neural network is used to evaluate L index for all buses [15]. Ref [16] for online voltage stability assessment of each vulnerable load bus an individual feed forward type of ANN is trained. In this method, ANN is trained for each vulnerable load bus and for a wide range of loading patterns. For this purpose by using the singular value decomposition method, a Radial Basis Function (RBF) neural network is trained to map the operating conditions of power systems to a voltage stability indicator and contingency severity indices corresponding to transmission lines.

A measurement approach to voltage stability monitoring and enhancement is simple and appears to be quite effective. In the wake of increasing interest, development and deployment in wide area monitoring system (WAMS) in power system, the research effort in the measurement approach to the solution of the problem is being pursued actively. Realizing that network phasor measurements contain enough information for monitoring voltage stability at local load supply nodes, researchers have developed some algorithms that only use voltage and current phasor measurements to monitor system voltage stability [17, 18]. However, these tools can produce results after the system is disturbed by significant network events, i.e they are reactive rather than being proactive or predictive. It is very important that a voltage instability situation is predicted before it really

Saed. Jalilzadeh, Reza. Abbasi, and Reza. Noroozian

Real-Time Voltage Stability Indicators Based on Phasor Measurement Unit Data by Application

of ANN technique

V

International Conference on Electrical, Electronics and Instrumentation Engineering (EEIE'2013) Nov. 27-28, 2013 Johannesburg (South Africa)

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mailto:[email protected]




appears so that control measures can be put in place to avoid the problem.

In this paper, a new voltage stability monitoring scheme based on neural network application is proposed. The proposed scheme utilizes output from Phasor Measurement Units (PMU) installed at determined buss. Time synchronized measurements of voltage are adequate to estimate the Voltage Stability margin (VSM) in real time with application neural network.

II. VOLTAGE INSTABILITY ASSESSMENT Fig.1. illustrate, Load P margin can be directly obtained

from the P-V curve. P-V analysis is a steady-state tool that develops a curve, which relates voltage at a bus (or buses) to load within an area or flow across an interface. Bus voltages are monitored throughout a range of increased load and real power flows into a region. The benefits of this methodology is that it provides an indication of proximity to voltage collapse throughout a range of load levels or interface path flows for the simulated system topology. The nature of voltage collapse is that as power transfers into a well-bounded region are increased, the voltage profile of that region will become lower and lower until a point of collapse is reached. The voltages at specific buses in the region can vary significantly, and some specific bus voltages could appear acceptable. The point-of-collapse at all buses in the study region, however, will occur at the same power import level, regardless of the specific bus voltages. The current operating value of real power delivered to the load (base operating point) is P0 and the maximum possible power transfer is Pmax. The load P margin is defined as the difference between these two quantities and Voltage Stability Margin (VSM) is [19]:

i

ii

PPP

VSM imax

0max −=

(1)

Fig. 1 Typical P-V curve showing power margin.

III. 2BOPTIMAL PMU PLACEMENT CONSIDERING NORMAL AND CONTINGENCY CONDITIONS

In this paper, proposed approach for the optimal PMU placement is implemented in two sequences. At first, the optimal placement is carried out with the goal of minimizing the total number of required PMUs for complete system observability during normal conditions, i.e. line outage. Then, the derived placement set is modified so that the network regains its observability during of contingency, (i.e. a branch outage). Both of the problems are solved using the described modified BGA algorithm.

A. Optimal PMU placement in normal conditions The purpose of this section is to minimize the total number

of PMUs required for complete system observability assuming normal conditions. The optimization problem can be described mathematically as:

B

k

i Bii NK

NKXCFC 02

1

1 ... ++= ∑=

(2)

B=A.X P

TP (3)

Where k is the number of system's buss, CRiR is the cost of

PMU installation on the bus i, it is 3500, XRiR is the binary variable which is 0 or 1, regarding whether PMU has been placed on bus i or not, A: is the matrix of branch connections to the buses that is defined as follows:

�1 𝑖𝑓 𝑏𝑟𝑎𝑛𝑐ℎ 𝑗 𝑖𝑠 𝑖𝑛𝑐𝑖𝑑𝑒𝑛𝑡 𝑡𝑜 𝑏𝑢𝑠 𝑖 0 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒

B is system's observability matrix, KR1R is constant

coefficient of observability, KR2R is constant coefficient of penalty factor, NRBR is sum of the B matrix’s elements (show number of system's observability), NR0BR is number of the B matrix’s zero elements.

B. Optimal PMU placement in loss of a single branch In this stage, an algorithm is developed in which the

placement configuration derived in normal conditions is modified to maintain network observability during a line outage. The objective function of this part can be expressed mathematically as follows:

).(1.. 0211 1

1Bm

n

m

k

i

n

m Bmii NK

NK

nXCFC ∑∑ ∑

== =

++= (4)

In this relation, the observability analysis is performed to

consider the impact of a branch outage on network observability. In order to maintain network observability during a line outage, each bus of the system must be observable from two paths. It is clear that if one of the paths is lost (single line outage), that bus is still observable through the other path. Note that observability of buses with one incident line is not of interest during single line outage, because those buses become isolated from the network after the line outage. For attention this subject, in every iteration after primary placement of PMUs, outage one by one all lines and calculate cost function in (4).

IV. 3BPROPOSED APPROACH In this paper, for fast estimating voltage stability margin a

new approach base on the application of neural network is proposed. The conceptual structure of the proposed approach is shown in Fig. 2. In the proposed approach, at any given operating condition including both phase and magnitude of bus voltages is provided by PMUs. By feeding the network voltage profile to ANN, the system VSM corresponding to the current operating point is estimate.


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Fig. 2 Conceptual structure of the proposed approach.

V. NUMERICAL RESULTS The proposed ANN based approach for voltage stability

margin estimation is applied to the Zanjan 10-bus 400kv system shown in Fig. 3. The system consists of 6 load buses, 4 generator buses, and 11 transmission lines.

Fig. 3 Zanjan 400 Kv system.

For PMU placement, we use the method explained in

section 3. The genetic algorithm was used for optimization and the characters of the algorithm and constant coefficient of cost function are shown in table.I. The results are as follows:

TABLE I .CHARACTER OF GA ALGORITHM AND CONSTANT COEFFICIENT OF COST

FUNCTION Value parameter

10000 K 1 100000 K 2

1000 Max iteration of BGA

50 Number of BGA population

0.3 Probability of mutation

0.7 Probability of crossover

A. 9BOptimal PMU placement in normal conditions: The optimization model (2) would assign four PMUs to

buses 1, 2, 5 and 7. Table.II. are shown number of observability of buses in normal condition and outage lines in this case. Whit due attention to table.II, buss 8, 9 and 10 be unobservable whit outage lines 8, 6 and 11 respectively. For solution this problem we used cost function (3) in next section.

VI. 5BOPTIMAL PMU PLACEMENT IN LOSS OF A SINGLE BRANCH The optimization model (3) would assign five PMUs to

buses 2, 5, 7, 9 and 10. Table.III. are shown number of observability of buses in normal condition and outage lines in this case Just as table.III. are shown the mean of observability in this case than amount 1.4 in before state to 1.6 to be increased. The proposed neural network has been shown in Fig. 4, which consists of an input layer, a hidden layer and an output layer. To obtain the best combination of number of neurons, training and transfer function a test system is developed and the toolbox parameters are applied. The following Toolbox functions are analyzed (i) neural network architecture and types, (ii) training functions, (iii) activation functions, (iv) learning function, (v) initialization functions, and (vi) performance functions. Initially from the selected input data set, the minimum and maximum values are found. Then the network training parameters such as number of epochs (1000), parameter goal (1e_5), number of neurons (15), minimum and maximum gradient (1e_10 and 1e_10 respectively) have been set based on the extensive analysis done and four performance measures are used in this paper to evaluate the performance of the testing data, mean square error (MSE) in (5) , mean absolute error (MAE) in (6) and maximum error in (7):

(5)

(6)

(7)

Here, VSMRactualR is the target P margin obtained from the CPF program and VSMRANNR is the P margin estimated by the ANN, n is the number of unseen cases. After training the network for the set of samples, network performance is evaluated with a new set of non-simulated data and the output with the VSM values obtained from the conventional algorithm is compared. The trained network nomenclature is then assigned and further a new set of NN is trained for contingencies. In order to train the ANN, 1000 random operating points were generated using the model described in Section 4 and verified by a power flow program. Another 100 cases were created and verified through the same method to be used as the testing data to verify the ANN performance. Addition to training, validating and testing errors, another post-training analysis denoted as regression analysis has been performed relating ANN response to the actual values to investigate the performance of the trained ANN. For this purpose, linear regression between ANN outputs and exact values is used to determine the accuracy of ANN. The variations of mean square error (MSE) for ANN method is shown in Fig. 5.


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TABLE II

THE NUMBER OF OBSERVABILITY OF BUSES IN NORMAL CONDITION AND OUTAGE LINES IN FOUR PMUS TO BUSES 1, 2, 5 AND 7. outage

L11 outage

L10 outage

L9 outage

L8 outage

L7 outage

L6 outage

L5 outage

L4 outage

L3 outage

L2 outage

L1 Normal

condition Bus

number 2 2 2 2 2 2 2 2 2 2 1 2 B1 2 2 2 2 2 2 2 2 2 2 1 2 B2 2 2 2 2 2 2 1 2 2 1 2 2 B3 2 1 2 2 2 2 2 1 2 2 2 2 B4 1 1 1 1 1 1 1 1 1 1 1 1 B5 2 2 1 2 2 2 2 2 1 2 2 2 B6 1 1 1 1 1 1 1 1 1 1 1 1 B7 1 1 1 0 1 1 1 1 1 1 1 1 B8 1 1 1 1 1 0 1 1 1 1 1 1 B9 0 1 1 1 1 1 1 1 1 1 1 1 B10

Table.II The number of observability of buses in normal condition and outage lines in four PMUs to buses 2, 5, 7, 9 and 10. outage

L11 outage

L10 outage

L9 outage

L8 outage

L7 outage

L6 outage

L5 outage

L4 outage

L3 outage

L2 outage

L1 Normal

condition Bus

number

1 2 2 2 2 2 2 2 2 2 1 2 B1 1 1 1 1 1 1 1 1 1 1 1 1 B2 2 2 2 2 2 2 1 2 2 1 2 2 B3 2 1 2 2 2 2 2 1 2 2 2 2 B4 2 2 2 2 2 1 2 2 2 2 2 2 B5 2 2 1 2 2 2 2 2 1 2 2 2 B6 1 1 1 1 1 1 1 1 1 1 1 1 B7 2 2 2 1 1 2 2 2 2 2 2 2 B8 2 2 2 2 2 1 2 2 2 2 2 2 B9 1 1 1 1 1 1 1 1 1 1 1 1 B10

Fig. 4 Proposed neural network architecture.

In Fig. 6, the outputs of ANN are plotted versus the exact

values, while its slope and correlation coefficient for test, training and validation data are about 1 and 0.99726, 0.99 and 0.99568, 0.99 and 0.99088 respectively which are very close to 1 indicating good performance of ANN. Mean absolute error percent and maximum error percent for the estimated VSM by ANN are 0.7836% and 4.2318% respectively, for 100 samples randomly selected for testing ANN.

Fig. 5 The variations of mean square error (MSE) for ANN method.

VII. 6BCONCLUSION A novel scheme based on output from Phasor Measurement

Units (PMU) base and neural network application is proposed for fast estimating voltage stability margin, in this paper. In this scheme, network voltage profile consisting of both phase and magnitude of bus voltages which are measured synchronously by PMU constitutes the input pattern for artificial neural networks. The use of the trained ANN for voltage stability prediction has been demonstrated by applying it to the Zanjan 400kv electric power system. For this system, the trained ANN was valid for large operating range. The simulations results have been obtained to demonstrate the effectiveness, speed and accuracy of the algorithm.


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Fig. 6 outputs of ANN versus the exact values, for (a) validation, (b)

training and (c) test data.

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[6] G.K. Morison, B. Gao, P. Kundur, Voltage stability analysis using static and dynamic approaches, IEEE Trans. Power Syst. 8 (August (3)) (1993) 1159–1171.

[7] N. Hatziargyriou, Machine Learning Applications to Power Systems. Berlin, Germany: Springer, 2001

[8] H.-D. Chiang, A. J. Flueck, K. S. Shah, and N. Balu, “CPFLOW: A practical tool for tracing power system steady-state stationary behavior due to load and generation variations,” IEEE Trans. Power Syst., vol. 10, no. 2, pp. 623–634, May 1995

[9] V. Ajjarapu and C. Christy, “The continuation power flow: A tool for steady state voltage stability analysis,” IEEE Trans. Power Syst., vol. 7, no. 1, pp. 416–423, Feb. 1992.

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[11] C. A. Canizares, “On bifurcations, voltage collapse and load modeling,” IEEE Transactions on Power Systems, vol. 10, no. 1, pp. 512–522, 1995.

[12] T. J. Overbye and C. L. DeMarco, “Improved techniques for power system voltage stability assessment using energy methods,” IEEE Transactions on Power Systems, vol. 6, no. 4, pp. 1446–1452, 1991.

[13] P. A. L¨of, T. Smed, G. Andersson, and D. J. Hill, “Fast calculation of a voltage stability index,” IEEE Transactions on Power Systems, vol. 7, no. 1, pp. 54–64, 1992

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[18] G. Verbi´e and F. Gubina, “A new concept of protection against voltage collapse based on local phasors,” Proc. Int. Conf. Power Systems Technology, vol. 2, pp. 965–970, Dec 2000.

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