Impact of TCSC on Distance Protection Setting based Modified Particle Swarm Optimization Techniques

Published Online May 2013 in MECS

In recent years, power demand has increased substantially while the expansion of power generation and transmission has been severely limited due to limited resources and environmental restrictions. As a consequence, some electrical transmission lines are heavily loaded and the system stability becomes a power transfer-limiting factor. FACTS controllers have been mainly used for solving various power system steady state control problems [1].

There are two generations for realization of power electronics based FACTS controllers: the first generation employs conventional thyristors switched capacitors and reactors, and quadrature tap-changing transformers while the second generation employs gate turn-off (GTO) thyristors switched converters as voltage source converters (VSCs). The first generation has resulted in the Static Var Compensator (SVC), the Thyristor Controlled Series Capacitor (TCSC), and the Thyristor Controlled Phase Shifter (TCPS) [2,3]. The second generation has produced the Static Synchronous Compensator (STATCOM), the Static Synchronous Series Compensator (SSSC), the Unified Power Flow Controller (UPFC), and the Interline Power Flow Controller (IPFC) [4]. The two groups of FACTS controllers have distinctly different operating and performance characteristics. In the presence of series FACTS devices, the conventional distance relay characteristics such as MHO and quadrilateral are greatly subjected to mal-operation in the form of overreaching or under-reaching the fault point [5,6]. Therefore, the conventional relay characteristics may not work properly in the presence of FACTS device.

Application of PSO technique in power system protection, reported in references [7,8] study the optimal coordination of overcurrent relays using a Modified Particle Swarm Optimization (MPSO) on transmission line. In [9,10] the application a Hybrid Particle Swarm Optimization (H-PSO) technique for optimal coordination of overcurrent relays is presented. The authors in references [11-14] study the application Nelder-Mead Particle Swarm Optimization (NM-PSO) technique for optimal coordination of overcurrent protection. In reference [15] the authors present an adaptive optimal relay coordination scheme for distributed generation based PSO technique, and optimal coordination of overcurrent relays by Mixed

Genetic (MG) and PSO Algorithm and comparison of both is reported in [16].

PSO application technique for transformer protection is reported in [17] where the transformer protection is based on Chaos PSO technique using dissolved gas value as a feature parameter and creates a power transformer fault detection model by support vector machine classifier. In reference [18, 20] applied PSO method trained by ANN algorithm for power transformer differential protection is presented and in reference applied PSO based probabilistic neural network for power transformer protection an algorithm has been developed around the theme of the conventional differential protection of transformer. It makes use of ratio of voltage to frequency and amplitude of differential current for the determination of operating conditions of the transformer.

For motor protection, the authors in paper [21] give a thermal protection technique by applying PSO technique to thermally protect three phases’ induction motors that are being successively starting, from operating beyond the IM thermal limits. This approach is implemented with PSO so as to determine the number of starting and operating times versus the IM thermal capability. This leads to a great improvement in the industry of thermal protection relays, where the output of the modeled induction motor is fed to a developed PSO program to find the optimal number of operating cycles regarding the duration of the duty cycle, the thermal capability is the main limitation for the number of starting cycles.

The effect of compensator TCSC on distance protection of transmission lines has been reported for general research on the influence of TCSC on the transmission lines protection in references [22-24] while the impact on communication-aided distance protection schemes and its mitigation is reported in [25]. Authors in reference [26] study this impact on numerical relay using computational intelligence based ANN method. In reference [27], the impedance measured ( Z_seen ) by distance relay for inter phase faults with TCSC on a double transmission line high voltage is being studied and in [28], the variation of Z_seen by distance relay for inter phase faults in presence of TCSC on adjacent transmission line by considering MOV operation is investigated. The effects of voltage transformers connection point on Z_seen at relaying point for inter phase faults is reported in reference [29]. Comparing TCSC placements on double circuit line at mid-point and at ends from Z_seen point of view is mentioned in reference [30].

The authors report in [31] a comparative study of GCSC and TCSC effects on MHO distance relay setting in single 400 kV Algerian transmission line. In reference [32] the authors is study the impact of TCSC on Z_seen by MHO distance relay on 400 kV Algerian transmission line in presence of phase to earth fault based analytical method, and in reference [33]

modified setting numerical distance protection of transmission line 400 kV in presence TCSC using IEC 61850 communication protocol is reported. However, there is no work reported on mitigation of the impact of midpoint TCSC compensated transmission lines on distance protection.

In this paper two techniques : AM and MPSO for setting zones of an MHO distance protection on a 400 kV single transmission line installed in Algerian electrical networks in presence TCSC are investigated.

• II.    Apparent Reactance Injected by Thyristor Controlled Series Capacitor (TCSC)

The series compensator TCSC mounted on figure 1.a is a type of series FACTS compensators. It consists of a capacitance ( C ) connected in parallel with an inductance ( L ) controlled by a valve mounted in antiparallel thyristors conventional ( T₁ and T₂ ) and controlled by an extinction angle ( α ) varied between 90° and 180°.

(a)

(b)

Fig. 1: Transmission line with TCSC system. (a). System configuration, b). Apparent reactance.

This compensator injects in the transmission line a variable reactance ( X_T CSC ) indicated by figure 6.b. Its value is function of the line reactance X L where the device is located. The apparent reactance X_T CSC is defined by the following equation [34, 35, 36]:

XTCsc (a) = Xc. [1 — A + B ]

Where,

. K2  ^ о + sin(o)A =

K2 -11 п

А =

L.C

_R   4. K²     2Г о

B =       cos

K ²- 1      ( 2

And, о = 2.(п - а)

.

K .tan

The о is a part of a cycle during which a thyristors valve is in the conducting state and the firing angle a is the time expressed in electrical angular measure from the capacitor voltage ( V_C ) zero crossing to the starting of current conduction through the thyristors valve [36]. The curve of X TCSC as a function of angle a is divided into three different regions which are inductive, capacitive and resonance as shows in figure.2.

K=А

to

Fig. 2: Characteristic curve X tcsc = /(a) for TCSC.

The Vernier mode allows the TCSC to behave either as a continuously controllable capacitive reactance or as a continuously controllable inductive reactance. It is achieved by varying the thyristors firing angle in an appropriate range. However, a smooth transition from the capacitive to inductive mode is not permitted because of the resonant region between the two modes [34, 37]. A variant of this mode is the capacitive vernier mode, in which the thyristors are fired when the capacitor voltage and capacitor current have opposite polarity.

This condition causes a TCR current that has a direction opposite to that of the capacitor current, thereby resulting in a loop-current flow in the TCSC controller. Another variant is the inductive vernier mode, in which the TCSC can be operated by having a high level of thyristors conduction. In this mode, the direction of the circulating current is reversed and the controller presents net inductive impedance.

• III.    Settings Zones for Distance Relays Protection

• 3.1    Selectivity protection

Since the impedance of a transmission line is proportional to its length, for distance measurement it is appropriate to use a relay capable of measuring the impedance of a line up to a predetermined point (the reach point). Such a relay is described as a distance relay and is designed to operate only for faults occurring between the relay location and the selected reach point thus giving discrimination for faults that may occur in different line sections [37-39].

The basic principle of distance protection involves the division of the voltage at the relaying point by the measured current. The apparent impedance so calculated is compared with the reach point impedance.

If the measured impedance is less than the reach point impedance, it is assumed that a fault exists on the line between the relay and the reach point as shown in figure 3.

Fig. 3: Principle operation for distance protection

Time selectivity protection is given by the staggered trip time depending on the distance between measurement point and the fault [37,  38],  [40].

Following the setting philosophy of the distance protection in Sonelgaz group, three zones (Z1, Z2 and Z3) are considered [41]: The first zone covers about 80% of the protected transmission line AB and trips the circuit breaker in t1.

The second zone extends to 100% of the protected line AB and 20% of the adjacent line and trips circuit breaker in the t 2 while the third zone extends to 100% of the protected line AB+40% of the adjacent line and trips the circuit breaker in the t 3 as indicated in figure 4.

Fig. 4: Selectivity of distance protection.

Fig. 5: Settings zones of distance protection.

• 3.2    Setting zones

Line impedances are proportional to the line lengths and this property is used to calculate the distance from the relay location to the fault. The relay, however, is fed with the current and voltage measured signals from the primary system via current transformers (CT) and voltage transformers (VT). Therefore, the secondary measured value by relay is used for the setting and is obtained by the following expression:

Z,^ = Zab-l = [(Rl + jX )-l] (k  k J

Where,

k

I pri

' CT    т sec

k

V pri

and,

'VT   v sec

The setting zone of distance zone for transmission line is indicated by figure 5.

The setting zones for protected electrical transmission line without series FACTS i.e. TCSC is [40, 41]:

is initialized with a population of random solutions, called particles.

Unlike in the other evolutionary computation techniques, each particle in PSO is also associated with a velocity. Particles fly through the search space with velocities which are dynamically adjusted according to their historical behaviors. Therefore, the particles have a tendency to fly towards the better and better search area over the course of search process.

Where, Z L-AB and Z L-BC is real total impedance of line AB and BC respectively. K VT and K CT is ratio of voltage and current respectively. The characteristic curves X ( R ) for MHO distance relay are represented in figure 6.

Fig. 6: Characteristic curves of MHO distance relay.

^Z 1 — 0, 8. [ R AB ^{+ JX}AB ^{+ JX}tcsc ^{( a ) ]}

Z 2 — R ab + JX ab + JX tcsc ( a ) + 0,2.( R bc + JX bc ) ₍₁₃₎

3      AB      AB      TCSC        ,  . BC      BC )   (14)

• 4.1    Original particle swarm optimization algorithm

The original PSO algorithm is discovered through simplified social model simulation. PSO was introduced by Kennedy and Eberhart [43, 44], has its roots in swarm intelligence. The motivation behind the algorithm is the intelligent collective behavior of organisms in a swarm (e.g., a flock of birds migrating), while the behavior of a single organism in the swarm may seem totally inefficient. The bird would find food through social cooperation with other birds around it.

PSO represents an optimization method where particles collaborate as a population to reach a collective goal. Each n-dimensional particles xi is a potential solution to the collective goal, usually to minimize a function f . Each particle in the swarm can memorize its current position that is determined by evolution of the objective function, velocity and the best position visited during the search space referred to the personal best position ( pbest ), this search is based on probabilistic, rather than deterministic, transition rules. A particle x i has memory of the best solution y i that it has found, called its personal best ; it flies through the search space with a velocity v i dynamically adjusted according to its personal best and the global best ( gbest ) solution y’ found by the rest of the rest of the swarm (called the gbest topology) [45-47].

Let i indicate a particle’s index in the swarm, such that, S = { x₁, x₂, ..., x_s } is a swarm of s particles. During each iteration of the PSO algorithm, the personal best y_i of each particle is compared to its current performance, and set to the better performance. If the objective function to be minimized is defined as function f. R " > ' , then [48].

^ xi t)        if      f ( xi t) )< f ( У( t-1))

Traditionally, each particles velocity is updated separately for each dimension j, with:

• IV. Particle Swarm Optimization (PSO) Technique

PSO technique based approach is considered as the one of the most powerful methods for solving the nonsmooth or smooth global optimization problems [42, 43]. PSO is the population based search algorithm and

vit;1) — wvC + ci.ri.(pbest'j't* -xi,^)

⁺ c 2 . r 2 . ( gbest S - x it) )

The stochastic nature of the algorithm is determined by r 1 and r 2 , two uniform random numbers between zero and one. These random numbers scaled by acceleration coefficient c 1 and c 2 . The inertia weight w was introduced to improve the convergence rate of the PSO algorithm [46-48].

Usually, the value of the velocity is clamped to the range: [- v_max , v_max ] to reduce the possibility that the particle might fly out the search space. If the space is defined by the bounds: [ x min , x max ], then the value of v max is typically set so that:

v max

h.x

. max

Where 0,1 ≤ h ≤ 1 [49]. After that, each particle is allowed to update its position using its current velocity to explore the problem search space for a better solution as follows:

.( t +1)

i , j

( t )         ( t )

i , j          i , j

The search mechanism of the PSO using the modified velocities and position of individual i based on equations (16) and (18) is shows in figure 7.

the possibility of finding an optimal or close to optimal solution.

The original PSO is therefore modified to overcome the aforementioned problems. Initializing the pickup currents randomly does this, thus the problem becomes linear and the reactance injected by TCSC values is calculated using the interior point method. The initial feasible solutions are then applied to the PSO algorithm.

The method is implemented to handle constraints of the relay coordination optimization problem and is found to be more efficient while updating the solution into a feasible solution (inductive and capacitive operation mode).

If any particles of an individual violate its constraints then it is fixed to its maximum/minimum value (cut down value of X_TCSC ) according to its objective function minimum/maximum.

This method is used for handling the constraints for modified particle swarm optimization to solve MHO distance relay coordination.

x^k    if satidfying constraints

Fig. 7: Search mechanism of the PSO technique.

k

^k i ,min

x^k i ,max

if no satidfying constraints (max)

if no satidfying constraints (min)

The PSO or MPSO algorithm doesn’t require any initial feasible solution for iterations to converge instead the initial position of the particles generated randomly for the MPSO is considered.

The particles positions are then verified with the constraints before passing it to the objective function for optimization. Thus there is no need of the penalty value calculation. It reduces the time and increase the convergence rate also [50]. The velocity update in MPSO is taken care of by inertia weight w, usually calculated with the following if-then-else statement:

if iter_m „ <  iter .then max

• 4.2    Modified particle swarm optimization algorithm

The standard PSO algorithm is used for unconstrained optimization tasks. PSO in its standard form is not capable of dealing with the constrained optimization problem like relay coordination of distance relay. The repair algorithm gives the PSO algorithm capability of tackling the coordination constraints imposed on the relays, while searching for an optimal setting three zones.

The PSO algorithm also has limitation in terms that, during the updating process, where each particle modifies its position, the resultant particle position could be outside the feasible search space. This reduces w =

ML — ML min     max

iter„ — 1 max

. ( iter ^- 1 ) + w max

else w =   ■ min

The inertia weight starts at w_max and its functional value in equation (17) reduces as the number of iterations increases till iter_max (maximum iteration count) and after that maintains a constant value of w_m i _n for remaining iteration. Where the w_max and w_m i _n are the maximum and minimum weight value that are constant and iter_max is maximum iteration [51].

Figure 8 represent the flow chat for the MPSO algorithm used to calculate the optimal setting three zones ( Z 1 , Z 2 , and Z 3 ) of the MHO distance relay.

Stop

Start

| Evaluation objective function j

________________________i_______________________, Ц /to >/(?»"■) then pu»i = x

[ Ц /to >№=) Чип g^; = x ]

Yes

Find the initial searching point (with constraint satisfies. evaluation objective function) and also get initial рь#» and gs».-

Checks the particles are within the constraints allow it or otherwise reelect it

"                         4

Initialize the swarm using random generation

Update the position using the equation x,"'

Update the velocity using the equation v"1

Display the best result (Zt, Zs, Zs)

Perform position check

Fig. 8: Flow Chart of MPSO technique proposed.

• V. Case Study and Simulation Results

The power system studied in this paper is the 400 kV Algerian electrical transmission networks at group Sonelgaz (Algerian Company of Electrical and Gas) which is shows in figure 9 [52, 53]. The MHO distance relay is located in the busbar at Ramdane Djamel substation to protect transmission line between busbar A and busbar B respectively at Ramdane Djamel and Oued El Athmania substation in Mila. The busbar C is located at Salah Bay substation in Sétif.

The TCSC is installed in midline where maximum injected voltage V TCSC is equal 20 kV and maximum reactive power Q TCSC is +80 / -10 MVar. The parameters of transmission line are summarized in the annexes.

Figure 10 show the X_TCSC characteristics curves on two modes inductive and capacitive mode as function of the firing angle ( α ) of the TCSC used in case study.

The figures 11.b and 11.b show the impact of TCSC insertion (capacitive and inductive modes) on the active and reactive power variation of P_L and Q_L transited respectively with angle line ( δ ) varied between 0° to 180°.

Fig. 9: Electrical networks study in presence TCSC.

Fig. 10: Characteristic curve X TCSC ( α ).

Table 1: Settings Zones without TCSC based AM.

Settings	Zones of Protection
	Zone 1	Zone 2	Zone 3
Reactance ( Ω )	72,00	99.50	109,00
Resistance ( Ω )	1,7467	2,4139	2,6443

• 5.2    Settings zones based analytical method

Figures 12.a and 12.b represented the impact of the parameters of TCSC on the settings three zones reactance ( X₁ , X₂ and X₃ ) respectively for MHO distance relay based AM.

(a)

(a)

О 20     40     60     80     100    120 UO 160    180

а (■)

(b)

Fig. 11: Impact of TCSC on power transmission line. a). Active power P L ( δ ), b). Reactive power Q L ( δ ).

(b)

Fig. 12: Settings zones reactance with respect to α and X TCSC . a). X Zones = f ( α ), b). X Zones = f ( X TCSC ).

• 5.1    Settings zones without TCSC

  The total impedance measured by the distance relay without TCSC is: Z_L = 43,668 + j 1800 ( Ω ), the settings zones are summered in table 1.

2.5 -

Figures 13.a and 13.b represented the impact of the parameters of TCSC on the settings three zones resistance ( R 1 , R 2 and R 3 ) respectively for MHO distance relay based analytical method.

(a)

§

2 --

0.5

О*—

-500

500         1000

W^)

(b)

Fig. 13: Settings zones resistance with respect to α and X TCSC . a). R Zones = f ( α ), b). R Zones = f ( X TCSC ).

• 5.3    Settings zones based MPSO technique

The specified parameters for the proposed algorithm are summered in the appendix. The testing data of the proposed MPOS algorithm to calculate the setting distance relay on two boost mode, i.e. Inductive and capacitive are indicated respectively in table 2.a in table 2.b with their percentage error (ε) between the accurate values based AM and the estimated based MPOS.

Table 2: Setting Zones for Distance Relay based MPOS.

a). Inductive Mode

	а (°)
	95	115	125	135	145	147
X i (П)	68,710	69,0418	69,1219	69,843	72,111	79,0112
R i (П)	1,6731	1,67396	1,67404	1,6838	1,6661	1,6647
ε r (%)	4,2098	4,1642	4,1596	3,5995	4,6128	4,6931
X 2 (П)	96,109	96,1131	96,321	97,034	100,01	109,127
R 2 (П)	2,3396	2,33050	2,3332	2,34080	2,3214	2,3285
ε r (%)	3,0789	3,4546	3,3430	3,0280	3,8315	3,5358
Х з (П)	105,124	105,541	105,241	105,433	109,491	118,88
R 3 (П)	2,5582	2,5591	2,5495	2,54460	2,5509	2,5636
ε r (%)	3,2559	3,2195	3,5830	3,7700	3,5301	3,0494

b). Capacitive Mode

	а (°)
	149	155	160	165	170	180
X i (П)	53,111	68,011	69,021	69,143	67,711	68,011
R i (П)	1,7043	1,7188	1,7248	1,7210	1,6824	1,6874
ε r (%)	2,4268	1,5935	1,2497	1,4685	3,6800	3,3931
Х 2 (П)	75,109	93,113	93,321	94,034	95,013	96,127
R 2 (П)	2,3382	2,3439	2,3254	2,3348	2,3554	2,3799
ε r (%)	3,1351	2,8964	3,6629	3,2740	2,4231	1,4077
Х з (П)	86,124	103,54	103,24	104,43	105,49	105,51
R 3 (П)	2,6164	2,5978	2,5665	2,5877	2,6101	2,6074
ε r (%)	1,0523	1,7549	2,9409	2,1401	1,2925	1,3925

As can be seen, application of the MPO technique for       3, 0280 and 4,6931 from table 2.a and between 1,05238

optimal new settings results in the error varied between       and 3,68004 from table 2.b.

• 5.4    Comparison and interpretations

Table 3 presents a comparison between the proposed and usual algorithms for two operations mode (inductive and capacitive). In the proposed algorithm, it is obvious that the execution time and iteration numbers is lesser than usual algorithm, where t_exe is the execution time and N I _ter is the number of iterations.

proposed method can be adopted for determining the optimum settings of zones.

For future research, the application a new hybrid MPSO trained by ANN multiple layers (PSO-ANN) to minimize the execution time, number of iterations and error can be investigated.

Table 3: Comparison between AM and MSOP Method.

a). Inductive Mode

Method	AM		MPSO
a (°)	t exe (sec)	N Iter	t exe (sec)	N Iter
95	1541	542	93	61
115	1498	476	82	55
125	1382	381	74	47
135	1254	239	61	32
145	1193	191	52	28
147	1106	147	43	19

b). Capacitive Mode

Method	AM		MPSO
a (°)	t exe (sec)	N Iter	t exe (sec)	N Iter
149	1608	768	143	81
155	1543	643	126	61
160	1441	539	97	52
165	1389	378	81	43
170	1233	266	69	38
180	1104	197	54	26

It is clear from simulation results in table 3, the other advantages of MPOS as compared with AM, the proposed MPSO is capable of controlling the variation angle α and reactance X TCSC permanently which is an advantage in calculating new settings zones of the network at a very high speed with an acceptable error.

• VI. Conclusion

This paper analyzes and demonstrates the modified particle swarm optimization algorithm application associated with protective distance relay for 400 kV protected transmission line in presence of TCSC compensator witch affects three settings zones. MPOS techniques could be used as an effective tool for realtime and implement digital relaying purposes. This might allow distance relay work more accuracy and precision.

In this paper also a new MPOS algorithm is proposed in terms of computation speed, rate of convergence, and objective function value for reduction in the distance relay operating time. The results demonstrate that the