13-IJAEST-Volume-No-3-Issue-No-2-TRANSMISSION-LINE-STABILITY-IMPROVEMENT-USING-TCSC-165-173 by ISERP ISERP

MUSTHAFA. P et al. / (IJAEST) INTERNATIONAL JOURNAL OF ADVANCED ENGINEERING SCIENCES AND TECHNOLOGIES Vol No. 3, Issue No. 2, 165 - 173

TRANSMISSION LINE STABILITY IMPROVEMENT USING TCSC

MUSTHAFA. P *

Assistant Professor, Electrical and Electronics Engineering, Veltech Multitech Dr.RR Dr. SR Engineering College. #42,Avadi-Veltech Road, Chennai-600062, India. Email id: musthafapeelippuram@gmail.com.

Abstract A steady state analysis is applied to study the voltage collapse problem. The Modal Analysis method is used to investigate the stability of the power system. Prediction of the stability margin or distance to voltage collapse is based on the reactive power load demand. The load is connected to several selected buses. The analysis is performed for IEEE 14 Bus system. Then, the most critical mode is identified for each system. After that, the weakest bus, which contributes the most to the critical mode, are identified using the participation factor. The remedial measure is proposed to prevent the voltage collapse. TCSC is used to improve the voltage profile of the system. The voltage profile obtained after the incorporation of the TCSC is compared with the same before the incorporation of the TCSC and the improvement is verified. Keywords: N-R method, voltage collapse, Participation factor, TCSC, MATLAB INTRODUCTION Voltage collapse problem has been one of the major problems facing the electric power utilities in many countries. The problem is also a main concern in power system operation and planning. It can be characterized by a continuous decrease of the system voltage. In the initial stage the decrease of the system voltage starts gradually and then decreases rapidly.

ISSN: 2230-7818

MURUGESAN.G*

Lecturer, Electrical and Electronics Engineering, Veltech Multitech Dr.RR Dr.SR Engineering College. #42,Avadi-Veltech Road,Chennai-600062,India. Email Id : murugesan_g84@yahoo.co.in

The following can be considered the main contributing factors to the problem 1. Stressed power system; i.e. high active power loading in the system. 2. Inadequate reactive power resources. 3. Load characteristics at low voltage magnitudes and their difference from those traditionally used in stability studies. 4. Transformers tap changer responding to decreasing voltage magnitudes at the load buses. 5. Unexpected and or unwanted relay operation may occur during conditions with decreased voltage magnitudes. This problem is a dynamic phenomenon and transient stability simulation may be used. However, such simulations do not readily provide sensitivity information or the degree of stability. They are also time consuming in terms of computers and engineering effort required for analysis of results. The problem regularly requires inspection of a wide range of system conditions and a large number of contingencies. For such application, the steady state analysis approach is much more suitable and can provide much insight into the voltage and reactive power loads problem . So, there is a requirement to have an analytical method, which can predict the voltage collapse problem in a power system. As a result, considerable attention has been given to this problem by many power system researchers.

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The problem of reactive power and voltage control is well known and is considered by many researchers. It is known that to maintain an acceptable system voltage profile, a sufficient reactive support at appropriate locations must be found. Nevertheless, maintaining a good voltage profile does not automatically guarantee voltage stability. On the other hand, low voltage although frequently associated with voltage instability is not necessarily its cause. 2.1 METHODS OF VOLTAGE STABILITY ANALYSIS: Many algorithms have been proposed in the literature for voltage stability analysis. Most of the utilities have a tendency to depend regularly on conventional load flows for such analysis. Some of the proposed methods are concerned with voltage instability analysis under small perturbations in system load parameters. The analysis of voltage stability, for planning and operation of a power system, involves the examination of two main aspects: 1.How close the system is to voltage instability(i.e.Proximity). 2.When voltage instability occurs, the key contributing factors such as the weak buses, area involved in collapse and generators and lines participating in the collapse are of interest (i.e. Mechanism of voltage collapse). Proximity can provide information regarding voltage security while the mechanism gives useful information for operating plans and system modifications that can be implemented to avoid the voltage collapse. Many techniques have been proposed in the literature for evaluating and predicting voltage stability using steady state analysis methods. Some of these techniques are P-V curves, Q-V curves, modal analysis, minimum singular value, sensitivity analysis, reactive power optimization, artificial neural networks , neuro-fuzzy networks, reduced Jacobian determinant, Energy function methods and thevenin and load impedance indicator and loading margin by multiple powerflow solutions. Some of these methods will be discussed briefly as follow. 2.1.1

Q-V Curve

Q-V curve technique is a general method of evaluating voltage stability. It mainly presents the sensitivity and variation of bus voltages with respect to the reactive power injection. Q-V curves are used by many utilities for determining proximity to voltage collapse so that operators can make a good decision to avoid losing system stability. In other words, by using Q-V curves, it is possible for the operators and the planners to know the maximum reactive power that can be achieved or added to the weakest bus before reaching minimum voltage limit or voltage instability. Furthermore, the calculated Mvar margins could relate to the size of shunt capacitor or static var compensation in the load area.

Figure 2.1: A Typical QV Curve

2.1.2

P-V curve

The P-V curves, active power-voltage curve, are the most widely used method of predicting voltage security. They are used to determine the MW distance from the operating point to the critical voltage.

2.2

MODAL OR EIGEN VALUE ANALYSIS METHOD It can predict voltage collapse in complex power system networks. It involves mainly the computing of the smallest eigen values and associated eigenvectors of the reduced Jacobian matrix obtained from the load flow solution. The eigen values are associated with a mode of voltage and reactive power variation, which can provide a relative measure of proximity to voltage instability. Then, the participation factor can be used effectively to find out the weakest nodes or buses in the system. 2.3 POWER FLOW PROBLEM The power flow or load flow is widely used in power system analysis. It plays a major role in planning the future expansion of the power system as well as helping to run existing systems to run in the best possible way. The network load flow solution techniques are used for steady state and dynamic analysis programs . The power-flow problem solves the complex matrix equation: I = YV = S*/V* where, I = Nodal current injection matrix. Y = System nodal admittance matrix. V = Unknown complex node voltage vector. S = Apparent power nodal injection vector representing specified load and generation at nodes where, S=P + jQ The Newton-Raphson method is the most general and reliable algorithm to solve the power-flow

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problem. It involves iterations based on successive linearization using the first term of Taylor expansion of the equation to be solved. 3. METHOD OF ANALYSIS 3.1 MODAL ANALYSIS 3.1.1 REDUCED JACOBIAN MATRIX The linearized steady state system power voltage equations are given by. ∆P

JPθ

JPV

∆θ

= ∆Q

JQθ

JQV

∆V [3.1]

Where, ∆P =

Incremental Change in Bus Real Power.

∆Q =

Incremental Change in Bus Reactive Power. ∆θ = Incremental Change in Bus Voltage Angle. ∆V = Incremental Change in Bus Voltage Magnitude.

If the conventional powerflow model is used for voltage stability analysis

 P   J P    Q   J Q

J PV     the Jacobian matrix in (3.1) is  J QV   V 

the same as the Jacobian matrix used when the powerflow equations are solved using the Newton-Raphson technique. With enhanced device models included, the elements of the Jacobian matrix in (3.1) are modifled as discussed as follows. System voltage stability is affected by both P and Q. However. at each operating point we keep P constant and evaluate voltage stability by considering the incremental relationship between Q and V. This is analogous to the Q-V curve approach. Although incremental changes in P are neglected in the formulation, the effects of changes in system load or power transfer levels are taken into account by studying the incremental relationship between Q and V at different operating conditions.

To reduce [3.1], let ∆P = 0, then, ∆Q =

JQV - JQθ

[3.2] JR-1 ∆Q

ISSN: 2230-7818

JQV - JQθ

JPθ-1 JPV

[3.4]

JR is called the reduced Jacobian matrix of the system. JR is the matrix which directly relates the bus voltage magnitude and bus reactive power injection. Eliminating the real power and angle part from the system steady state equations allows us to focus on the study of the reactive demand and supply problem of the system as well as minimize computational effort. The program developed also provides the option of performing eigen-analysis of the full Jacobian matrix. If the full Jacobian is used, however, the results represent the relationship between (∆θ. ∆V) and (∆P, ∆Q). Since ∆θ is included in the formulation, it is difficult to discern the relationship between ∆V and (∆P, ∆Q) which is of primary importance for voltage stability analysis. Also modal analysis using the full Jacobian matrix is computationally more expensive than using the reduced Jacobian. For these reasons we have chosen the reduced Jacobian approach. Modes of Voltage Stability: Let JR =

[3.5]



Where; 

 = 

Right Eigenvector Matrix of JR. Diagonal Eigenvalue Matrix of JR. Left Eigenvector Matrix of JR.

And JR-1 =

 -1 

[3.6]

From [3] and [6] we have; ∆V =

 -1  ∆Q

[3.7]

∆V =

 (i i / i ) * ∆Q

[3.8]

Or i

Where i is the ith column right eigenvector and i, the ith row left eigenvector of JR. Similar to the concept used in linear dynamic system analysis each eigenvalue A, and the corresponding right and left eigenvectors i , and i d e h e the ith mode of the system. The ith modal reactive power variation is. =

Ki i

[3.9]

Where,

and ∆V =

∆Qmi

JPθ-1 JPV

= JR ∆V

Where,

[3.3]

Ki2  ji2

[3.10]

with  ji the jth element of i. The corresponding ith modal voltage variation is.

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∆Vmi

(1/i) * ∆Qmi

[3.11]

It is seen that, when the reactive power variation is along the direction of El. the corresponding voltage variation is also along the same direction and the magnitude is amplified by a factor which is equal to the magnitude of the inverse of the ith eigen value. In this sense the magnitude of each eigenvalue i, determines the weakness of the corresponding modal voltage. The smaller the magnitude of i, the weaker the corresponding modal voltage. If i = 0. the i* modal voltage will collapse because any change in that modal reactive power will cause inflnite modal voltage variation. let ∆Q = ek where ek has all its elements zero except the kth one being 1. Then. ∆V

 (i ik / i )

[3.12]

with ik ( the kth element of i; V-Q Sensitivity at Bus k, Vk / Qk

 (ik ik / i )

 (Pki / i)

[3.13]

A system is voltage stable if the eigenvalues of the Jacobian are all positive. Those who are used to small signal stability analysis using eigenvalue techniques may find the requirement for the eigenvalues of the Jacobian to be positive for voltage stability a little confusing because in the study of small signal stability, an eigenvalue with positive real part indicates that the system is unstable. The relationship between system voltage stability and eigenvalues of the Jacobian J, is best understood by relating the eigenvalues of J, with the V-Q sensitivities, (which must be positive for stability), at each bus. For practical purposes, J, can be taken as a symmetric matrix and therefore, the eigenvalues of JR are close to being purely real. If all the eigenvalues are positive, J, is positive definite thus V-Q sensitivities are also positive indicating that the system is voltage stable. As the system is stressed, the eigenvalues of JR become smaller at the critical point of system voltage stability, at least one of the eigenvalues of J R, becomes zero. The application of modal analysis is to help in determining how stable the system is. How much extra load or power transfer level should be added and, when the system reaches voltage stability critical point, to determine the voltage stability critical areas and to describe the mechanism of instability by iden-g elements which participate in each mode. Bw Participations The participation factor of bus k to mode i is defined as. Pki = ik * ik [3.14] Pki indicates the contribution of the ith eigenvalue to the V-Q sensitivity at bus k. The bigger the value of PM, the more A, contributes in determining V-Q sensitivity at bus k. For all the small eigenvalues. Bus participation factors determine the areas close to voltage instability.

ISSN: 2230-7818

3.2.1

CALCULATION OF EIGENVALUES AND EIGENVECTORS OF JR:

An algorithm for calculating the minimum singular value and the corresponding left and right singular vectors, for both the full Jacobian and the reduced Jacobian has been developed. a. Select m initial trial vectors R=[R1, R2…… &Rm]. b. Premultiply R by A. S = AR. c. Determine G = RHR, H = RHS. d. Solve GB = H for B. e. Do full eigen-solution of B. f. Determine W = ST.with T the right eigenvector matrix of B. g. Set R = W', where W' is W normalized such that all the vectors have their largest element equal to unity. h. Check convergence by comparing the last two solutions of R. If converged, stop. Otherwise go back to b. Upon convergence the eigenvalues of B give the m largest eigenvalues of A. and R contains the corresponding right eigenvectors. The same procedure applied to AT provides the m largest eigenvalues of A and the associated left eigenvectors. Since we are interested in the smallest eigenvalues of JR-1, which correspond to the largest eigenvalues of JR-l, the simultaneous iteration algorithm has to be applied to JR-l. At each iteration, the premultiplication is. S = JR -1R

-------------[3.15] JQ J P-l

Recall JR = JQv JQv, which is not sparse due to the reduction. To fully exploit the sparsity of the Jacobian matrix S in (3.15) is obtained by solving the following sparse linear equations,

 J P   J Q

J PV   Z   0   J P    J QV   S   R   J Q

J PV   Z   0    J QV   S   R 

----------------[3.16]

The method is applied to JR and [JR] T in turn to calculate the smallest eigenvalues and the corresponding right and left eigenvectors. An alternative approach is to solve for the right and left eigenvectors simultaneously. Which requires in each iteration loop the solutions of JR, S = R and [JR]T S' = R'. Because JR is very close to being symmetric, the iteration for left eigenvectors converges very fast starting with the right eigenvectors as trial vectors. Also, there may exist cases where only the right eigenvectors are of interest. We believe. Therefore, that the lop-sided approach is more efficient and flexible than iterating on the right and left eigenvectors simultaneously. 1. If i = 0, the ith modal voltage will collapse because any change in that modal reactive power will cause infinite modal voltage variation.

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2. If i 0, the ith modal voltage and ith reactive power variation are along the same direction, indicating that the system is voltage stable. 3. If i 0, the ith modal voltage and the ith reactive power variation are along the opposite directions, indicating that the system is voltage unstable. The system response is the combination of the system response to each of the N modes. 1.The eigenvalues determine the system stability. A real( positive or negative) eigen value determines a exponentially increasing (decreasing) behavior. 2. A complex eigenvalue of positive (negative) real part results in an oscillatory (increasing or decreasing) behavior. 3. The components of the right eigenvector measure the relative activity of each variable in the i-th mode. 4. The components of the left eigenvector weight the initial conditions in the i-th mode. Appropriate effective indicators could be based on reduced load flow Jacobian matrix. The general load flow analysis can be formulated as

 P      Q    J   V      J

 J    J1 

J1 

J2   J4 

[3.17]

[3.18]

P P Q Q , J2  , J3  , J4   V  

[3.19]

where J represents the load flow Jacobian matrix. It contains the first derivatives of active and reactive power mismatch equations, ∆P=∆P(θ,V) and ∆Q=∆Q(θ,V), with respect to the voltage magnitude V and angles θ. it is proposed to reduce the Jacobian to the first derivative of reactive power equations in relation to voltage magnitude by assuming that the generator and load buses present no active power variation, i.e. ∆P=0. Jacobian matrix J can be reduced as follows:

JR, then the participation factor measuring the participation of the kth bus in ith mode is defined as Pki = ki ki 3.4 Q – V Curve Q–V or voltage-reactive power curves are generated by series of power flow simulation. They plot the voltage at a test bus or critical bus versus reactive power at the same bus. The bus is considered to be a PV bus, where the reactive output power is plotted versus scheduled voltage. Most of the time these curves are termed Q–V curves rather than V–Q curves. Scheduling reactive load rather than voltage produces Q–V curves. These curves are a more general method of assessing voltage stability. They are used by utilities as a workhorse for voltage stability analysis to determine the proximity to voltage collapse and to establish system design criteria based on Q and V margins determined from the curves. Operators may use the curves to check whether the voltage stability of the system can be maintained or not and take suitable control actions. The sensitivity and variation of bus voltages with respect to the reactive power injection can be observed clearly. The main drawback with Q–V curves is that it is generally not known previously at which buses the curves should be generated. 3.5 MODAL INDICATORS The modal analysis approach has the added advantage that it provides information regarding the instability procedure. Voltage stability characteristics of the system can be identified by computing the eigenvalues and eigenvectors of the reduced Jacobian matrix JR . J R   .. [3.22]

   1 where, Λ =

Diagonal Eigenvalue Matrix.

Right Eigenvector Matrix. Left Eigenvector Matrix.

Q  J R .V

[3.20]

J R  J 4  J 3 J11 J 2

[3.21]

ξi

where JR is reduced Jacobian matrix. The singular value of this reduced matrix can be used to determine proximity to voltage collapse .

[3.23]

ηi

ith right eigenvector, ith column of right eigenvector matrix. = ith left eigenvector, ith row of left eigenvector matrix.

3.3 Identification of the Weak Load Buses 3.3.1

Participation factors

The participation factor of the j-th variable in the i-th mode is defined as the product of the j-th´s components of the right and left eigenvectors corresponding to the i-th mode. If i and i represent the right- and left- hand eigenvectors, respectively, for the eigenvalue i of the matrix

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4. THYRISTOR CONTROLLED SERIES COMPENSATOR

4.3 ASYMMETRICAL THYRISTOR CURRENT

4.1 DEFINITION FOR TCSC

Figure 4.3: Asymmetrical Thyristor Current Figure 4.1: TCSC Model

TCSC is a Capacitive Reactance Compensator which consists of a series capacitor bank shunted by a Thyristor Controlled Reactor (TCR) in order to provide a smoothly variable series capacitive reactance.

4.4 TCSC MODEL FOR TRANSIENT VOLTAGE STABILITY ANALYSIS

OPERATION OF TCSC When the TCR firing angle is 180 degree the reactor becomes non-conducting and the series capacitor now has the normal impedance. As the firing angle approaches from 180 degree to less than 180 degree, the capacitor impedance increases. On the other hand, when the TCR firing angle is 90 degree, the reactor becomes fully conducting, and the total impedance becomes inductive, because the reactor impedance is designed to be much lower than the series capacitor impedance with 90 degree firing angle, the TCSC helps in limiting fault current. The TCSC may be a single large unit, or may consist of several equal or different sized smaller capacitors in order to achieve a superior performance. Thus the TCSC can vary the impedance continuously to levels below and above to the lines’ natural impedance. On the other hand adding a TCSC means of adding a variable positive impedance to a value above the lines’ natural positive impedance. Once installed, either it will respond to rapidly to control signals to increase or decrease the capacitance or inductance thereby damping those dominant oscillation frequencies that would otherwise breed instabilities or unacceptable dynamic conditions during or after disturbance.

Figure 4.4: TCSC Model for Transient Voltage Stability Analysis

4.5 TEST SYSTEM DESCRIPTION

4.2 TRANSIENT AND LONG TERM TCSC OVERLOAD CAPABILITY

Figure 4.2: Transient and Long Term TCSC Overload Capability

ISSN: 2230-7818

Figure 4.5: IEEE 14 Bus System.

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4.6 VOLTAGE PROFILE FOR ALL BUSES:

4.8 PARTICIPATION FACTOR FOR SELECTED BUSES:

Graph 4.6: Voltage Profile for all Buses

Graph 4.8: Participation factor for Selected Buses

4.7 TABULAR REPRESENTATION OF VOLTAGE PROFILE : Bus Number

Voltage (pu)

Angle (p.u)

Generation (p.u)

Load (p.u)

Real

Reactiv e

1.060

0.000

1.354

0.329

0.000

1.040

-2.239

0.804

0.434

0.217

0.127

1.010

-4.554

1.045

0.114

0.942

0.190

0.979

-7.758

0.000

0.967

0.338

0.983

-6.482

0.000

0.049

0.392

1.070

-12.935

0.101

0.328

0.112

0.075

1.046

-10.960

0.000

1.080

-10.951

0.001

0.186

0.000

1.050

-12.570

0.000

0.339

-0.142

1.049

-12.806

0.000

0.059

0.032

1.056

-12.895

0.000

0.020

0.028

1.024

-15.838

0.000

0.367

0.027

1.044

-14.225

0.000

0.135

0.058

1.029

-13.314

0.000

0.004

0.002

4.9 TABULAR REPRESENTATION OF PARTICIPATION FACTORS:

Load bus numbers

Participation Factor

0.0091

0.0045

0.0691

0.1912

0.2319

0.1095

0.0225

0.0351

0.3270

Table 4.9: Participation factor for Selected Buses

Table 4.7: Voltage Profile for all Buses

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5.1 TEST SYSTEM WITH TCSC INCLUDED:

5.3: PV CURVE FOR BUS 14 BEFORE REMEDY

5.4: PV CURVE FOR BUS 14 AFTER REMEDY:

Figure 5.1: Test System with TCSC included

6. CONCLUSION& RECOMMENDATIONS 6.1 CONCLUSION

5.2: PV Curve and Power Margin

2. 3. 4.

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The Modal analysis technique is applied to investigate the stability of IEEE 14 Bus system. The method computes the smallest Eigen value and the associated Eigen vectors of the reduced Jacobian matrix using the steady state system model. The magnitude of the smallest Eigen value gives us a measure of how close the system is to the voltage collapse. Then, the participating factor can be used to identify the weakest node or bus in the system associated to the minimum Eigen value. The obtained results agreed about the weakest buses that contribute to voltage instability or voltage collapse. TCSC is used as the compensator so as to improve the voltage profile after the prediction of the voltage collapse. PV curves are plotted for the bus more sensitive to voltage collapse both before and after compensation and the improvement is verified.

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6.2

RECOMMENDATIONS FOR FUTURE RESEARCH The following recommendations are made for the future research: 1. Consideration of improved (exact) modelling of the power system devices such as generators and static VAR compensators, in the voltage collapse analysis. 2. Consideration of SVC also as a remedial measure for the voltage collapse problem in the analyzed system. REFERENCES 1.

P.Kundur, ― Power System Stability and Control‖, Tata McGraw Hills, ISBN Series No: 0-07—035958X.

P.Kundur, G.K Morrison, B.Gao, Voltage Stability Evaluation using Modal Analysis, IEEE transactions on Power Systems, Vol.7, No.4, Nov 1992.

P. Pal, "Voltage Stability Conditions Considering Load Characteristics", IEEE Trans. on Power Systems, Vol. 7, No. 2, pp. 243-249, Feb. 1992.

M. Suzuki, S. Wada, T. Asano, and K. Kudo, "Newly Developed Voltage Security Monitoring System", IEEE Trans. On Power System, Vol. 7, No. 3, pp. 965-972, August 1992.

P. Kessel and H. Glavitsch, "Estimating the Voltage Stability of a Power System,‖ IEEE Trans. on Power Delivery, vol. 1, pp. 346-353, July 1986.

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