A new control strategy of SMES for mitigating subsynchronous oscillations

Physica C 483 (2012) 34–39

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A new control strategy of SMES for mitigating subsynchronous oscillations Mohsen Farahani Bu-Ali Sina University, Department of Electrical Engineering, Hamedan-Iran, Iran

a r t i c l e

i n f o

Article history: Received 1 February 2012 Received in revised form 28 May 2012 Accepted 22 June 2012 Available online 1 July 2012 Keywords: Superconducting magnetic energy storage (SMES) unit Torsional oscillations Subsynchronous resonance (SSR) Chaotic optimization algorithm (COA)

a b s t r a c t This paper proposes a new strategy to mitigate the subsynchronous oscillations in power systems compensated by series capacitors via control of active power of superconducting magnetic energy storage (SMES) unit. The strategy is based on the generator acceleration signal. So, the SMES absorbs or generates the energy imbalance caused by different disturbances in the power system and suppresses the subsynchronous oscillations. The chaotic optimization algorithm (COA) is used to achieve the optimal parameter of the proposed controller. To validate the capability of the SMES in damping oscillations, some simulations with different disturbances are performed on the first model of IEEE second benchmark model. All the simulation results show that the subsynchronous resonance as well as low frequency oscillation (LFO) is satisfactorily mitigated by the SMES controlled by the proposed strategy. Ó 2012 Elsevier B.V. All rights reserved.

1. Introduction Early 1950, series capacitors were widely installed in long AC transmission lines (250 km or more) in order to compensate part of the inherent inductive reactance of power transmission lines. Until 1971, up to 70% of the 60-Hz inductive reactance was compensated by series capacitors in some long transmission lines with little concern for side impacts. In 1970, and again in 1971, a turbine-generator at Mohave Power Plant in southern Nevada experienced shaft damage that required repairs for several months. Torsional oscillations between the two ends of the generator–exciter shaft led to the shaft damage. Shortly after the second event, it was discerned that the torsional oscillations were caused by torsional interaction, which is a type of subsynchronous resonance. After carrying out the investigations on the damaged power plant, the series capacitor was diagnosed as the main problem. Investigations showed that turbine-generator systems including several masses located on a long shaft (non-rigid shaft) can be treated as lumped spring-mass model where individual masses are connected with massless springs. When a small disturbance is applied to in this model, the individual masses oscillate at frequencies which are a function of their natural frequencies known as modal frequencies. Similarly, when a disturbance occurs in the shaft system it makes the rotor masses rotate at subsynchronous frequencies along with the base synchronous speed. This disturbance could originate anywhere including the load side (i.e., a sudden drop in load connected to the electrical power transmission network). If these oscillations are not restrained, the shaft will certainly break.

E-mail address: [email protected] 0921-4534/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physc.2012.06.009

It has been clearly established that subsynchronous resonance can be damped using controllers, thus making it possible to benefit from the distinct advantages of series capacitors. Many controllers have been successfully applied such that there has been no reported subsynchronous resonance event since 1971. Most of these controllers were designed using excitation system of generators [1–8] and FACTS devices [9–12]. In many papers, SMESs have been used as a power system stabilizing in power systems [13–18]. Reported results show that SMESs are a proper alternative to stabilize power systems. In addition, SMESs can be used to damp the torsional oscillations [19–21]. For this purpose, different strategies such as PID controller [19], adaptive neural network [19,20], and fuzzy controller [21] have been used to control SMESs. In this study, this approach is followed. This paper proposes a new strategy to control the active power of a SMES unit using the generator acceleration signal in order to mitigate the subsynchronous resonance in power systems. In order to achieve the robust control, the chaotic optimization algorithm is used to optimize the parameter of the proposed controller. The first model of IEEE second benchmark is used to demonstrate the performance of the SMES in suppressing the oscillations.

2. Model of system under study In this study, the first model of IEEE second benchmark model shown in Fig. 1 is used to evaluate and analyze the risk of SSR [22]. In this model, a 600 MVA synchronous generator via two 500 kV transmission lines is connected to a large grid which is approximated by an infinite bus. The masses located on the long shaft of turbine-generator system as shown in Fig. 2 are: exciter

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M. Farahani / Physica C 483 (2012) 34–39

X1

Bus1

XC

R1

Line-1

600MAV 22kV

Xsys Rsys

X2

T Qsm Psm

Infinite

R2

Bus Bus2

Line-2

SMES Fig. 1. The first model of IEEE second benchmark model for the SSR studies.

EXC

Gen

LP

Fig. 5. SMES with active power controller (KAP).

HP

Fig. 2. Modeling of the turbine-generator system.

Electric Torque (pu)

10 Low Frequency Oscillations

5

1.5 1 0.5 1.5

2

0 Subsynchronous Oscillations

2 1 0

−5

8 −10

0

2

4

6

8.05 8

10

Time (s)

Rotor Speed Deviation Δω (pu)

Fig. 3. Variations of electric torque.

0.4

0.2

0

−0.2

−0.4 0

2

4

6

8

10

Time (s) Fig. 4. Rotor speed deviation of generator.

mass (EXC), generator mass (Gen), low pressure turbine mass (LP) and high pressure turbine mass (HP). Figs. 3 and 4 show the electric torque and rotor speed deviation after a 100 ms three-phase to ground fault applied to bus 2, respectively. As seen in these figures, there is a growing vibration on the different sections of the shaft (between masses located on the shaft). If such a situation continues, the shaft of turbine-generator system will eventually break. 3. Overview of SMES The SMES inductor–converter unit is composed of a dc superconducting inductor, a type AC/DC converter and a step down transformer [19]. With the control of the converter firing angle, the dc voltage V appearing across the inductor can be continuously varied between a wide range of positive and negative values. Gate turn off thyristors (GTO) provide such a technology to build this

kind of converter. The converter dc output current Ism being unidirectional, the control for the direction of the inductor power flow Psm, is achieved by continuously regulating the firing angle a. For initial charging of the SMES unit, the bridge voltage Vsm is kept constant at a proper positive value depending on the desired charging period. The inductor current Ism rises exponentially and magnetic energy Wsm is then stored in the inductor. When the inductor current approaches its rated value Ism0, it is maintained by decreasing the voltage across the inductor to zero. In this time, the SMES unit can be coupled with the power system to mitigate torsional oscillations. Due to different disturbances, the generator speed oscillates. When the system load is increased, the generator speed falls at the first instance, but due to the governor action, the speed begins to oscillate around the pre-specified value. The converter will act as an inverter (90 < a(degree) < 180) if the generator speed is less than the pre-specified speed, in this case, energy is drawn from the SMES unit (Psm negative). However, the energy is recovered when the speed swings to the other side. The converter then acts as a rectifier (0 < a(degree) < 90) and the power Psm becomes positive [13]. Several reasons can be mentioned for the use of superconducting magnetic energy storage. The main feature of SMES is that the time delay during charge and discharge is quite short. Power is available almost instantaneously and very high power output can be provided for a brief period of time. Another feature is that the power loss is less than other storage methods, since the resistance of SMES coil is negligible. Meanwhile, the main parts in a SMES are stationary, which results in high reliability. Fig. 5 draws the SMES model with simultaneous active and reactive power (P–Q) modulation control scheme [13]. In the model, KP which is the SMES active power controller can be expressed by

K AP ¼ KðPm  Peo Þ

ð1Þ

where K is the gain of active power controller and should be determined; Pm and Peo are input mechanical power and output active power of generator, respectively. It should be noted that the difference of input mechanical power and output active power of generator is known as the generator acceleration signal. According to Fig. 5, Klsm is the SMES coil current controller and represented by

  1 K sm ðIsm  Ism0 Þ K lsm ¼ K p þ Tis

ð2Þ

where KP, Ti and Ksm denote the proportional gain, the time constant (s) and the SMES coil controller gain, respectively; Ism and Ism0 are also the SMES coil current (p.u) and the initial value of SMES coil current (p.u), respectively. In order to model the SMES, the effect of Ism should be considered, since the dynamic behavior of Ism has a significant impact on overall performance of SMES. In practice, Ism is not allowed to reach zero to prevent the possibility of discontinuous conduction under unexpected disturbances. On the other

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M. Farahani / Physica C 483 (2012) 34–39

hand, high Ism which is above the maximum allowable limit, may lead to loss of superconducting properties. According to the hardware operational constraints, the lower and upper coil current limits are considered and assigned as 0.3Ism0 and 1.38Ism0, respectively [13]. Here, Ism can be calculated from the PEI block which has a relation as

Ism ¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi I2sm0  2Eout =ðLsm  I2sm;base Þ

Eout ¼

Z

Psm dt  Ssm;base

ð3Þ ð4Þ

where Eout is the SMES energy output (J); Lsm is the SMES coil inductance (H); Ism,base is the SMES current base (A); Psm is the SMES active power output and Ssm,base is the SMES MVA base (MVA). Subsequently, the energy stored in a SMES unit (Esm) and the initial energy stored (Esm0) can be obtained from

Esm ¼ Esm0  Eout 1 Lsm  I2sm0  I2sm;base 2

Esm0 ¼

ð5Þ ð6Þ

Also, KV is the voltage controller and represented by

K V ¼ K Vsm ðV t0  V ts Þ

ð7Þ

where KVsm is the controller gain; Vt0 and Vts are the initial value of the terminal bus voltage of the SMES unit (p.u.) and the bus voltage of SMES (p.u.), respectively. The following equations represent the desired active and reactive power output of SMES (Pd and Qd).

Pd ¼ V ts Ism cos h

ð8Þ

Q d ¼ V ts Ism sin h

ð9Þ

As seen in Fig. 5, the SMES active and reactive power outputs (Psm and Qsm) are the output of the SMES controlled converter (CONV). The following first-order time–lag compensator represents the converter transfer function [13].

CONV ¼

1 1 þ TC s

ð10Þ

where TC denotes the time constant of converter (s). 4. Design of SMES controller 4.1. Optimization problem It should be noted that the design objective of KAP is to minimize the torsional modes. Therefore, the objective can be formulated as the minimization of the following objective function f.

f ¼ J¼

Z

t¼t sim

tðjPm  P eo jÞdt

t¼0 m X

ð11Þ

fi

i¼1

In the above equations, tsim and m are the time range of the simulation, the total number of operating conditions for which the optimization should be carried out, respectively. To compute the objective function, the time-domain simulation of the system model incorporating all saturation limits of control signals is carried out for the simulation period. The purpose is to minimize this objective function to damp the torsional oscillations. The design problem can be formulated as the following constrained optimization problem, where the constraint is the K parameter bounds:

K min 6 K 6 K max

ð12Þ

In this paper, the chaotic optimization algorithm (COA) is used to solve this optimization problem and search for the optimal parameter. 4.2. Chaotic optimization algorithm As mentioned in the previous subsection, the chaotic optimization algorithm based on Lozi map is implemented and used to optimize the parameter of KAP. The Lozi map can be represented as [23]:

y1 ðkÞ ¼ 1  ajy1 ðk  1Þj þ yðk  1Þ

ð13Þ

yðkÞ ¼ b  y1 ðk  1Þ

ð14Þ

zðkÞ ¼

yðkÞ  a ba

ð15Þ

where k is the iteration number. In this work, the values of y are normalized in the range [0, 1] to each decision variable in the n-dimensional space of optimization problem. Thus y 2 ½0:6418; 0:6716 and [a, b] = (0.6418, 0.6716). Many unconstrained optimization problems with continuous variables can be formulated as the following functional optimization problem.

Find X to minimize f ðXÞ; X ¼ ½x1 ; x2 ; . . . ; xn  where f and X are the objective function and the decision solution vector, respectively. The decision solution vector consists of n variables xi which are bounded by lower (Li) and upper limits (Ui). The chaotic optimization algorithm based on the Lozi map is implemented as follows [23]:

Step 1: Initialize the variables: Set k = 1. y1(0), y(0), a = 1.7 and b = 0.5 for the Lozi map. Set the initial best objective function f ⁄ = +1 Step 2: Algorithm of chaotic global search: Begin While k 6 Mg do xi(k) = Li + zi(k)  (Ui  Li) i = 1, . . . n If f (X(k)) < f⁄ Then X⁄ = X(k) f⁄ = f(X(k)) End if k=k+1 End while End Step 3: Algorithm of chaotic local search: Begin While k 6 Mg + Ml do For i = 1 to n If r < 0.5 Then (where r is a uniformly distributed random variable with range [0, 1]) xi ðkÞ ¼ xi þ k  zi ðkÞ  jU i  xi j Else if xi ðkÞ ¼ xi  k  zi ðkÞ  jxast i  Li End if End for If f(X(k)) < f⁄ then X⁄ = X(k) f⁄ = f(X(k)) End if k=k+1 End while End

37

M. Farahani / Physica C 483 (2012) 34–39

where Mg, Ml, f⁄ and X⁄ are number of iterations of the chaotic global and local searches, the best objective function and the best solution of the current run of the chaotic search, respectively. The impact of the current best solution on the generating of a new trial solution is controlled by the step size k. A small k tends to perform exploitation to refine results by local search, while a large one tends to facilitate a global exploration of search space. In this study, we have n = 1 and X = [x1] = [K]. The chaotic optimization algorithm based on the Lozi map is completely explained in [23].

Table 2 Eigenvalues analysis of the power system in three different situations. Torsional modes

No controller (J)

SMES Without KAP controller (J)

With KAP controller (J)

Mode 1 Mode 2 Mode 3

0.04 ± 154.92 0.06 ± 203.45 0.04 ± 318.05

0.04 ± 153.11 0.03 ± 203.71 0.04 ± 318.00

1.18 ± 153.30 0.63 ± 203.55 0.07 ± 318.01

5. Simulations

5.2. Time-domain simulation In this subsection, the computer simulation results are provided for different operating conditions and compensation levels of line1 given in Table 3 under various disturbances. (A) Case 1 As the first simulation, it is assumed that a two-phase to ground fault is occurred at t = 0.2 s at the beginning of line-2 and cleared at t = 0.32 s. The response of the system to this fault including the

Table 1 Operating conditions used for the optimization (in p.u). Light

Gen

Nominal

Heavy

P

Q

P

Q

P

Q

0.60

0.14

0.82

0.25

0.97

0.70

Δθ (rad) Δω (p.u)

(p.u)

TGen−LP

P

Vt

0.80 0.96

1.00 1.05

Compensation level (%)

55 35

0 −1 −2

0

1

2

3

4

0

1

2

3

4

0

1

2

3

4

0

1

2

3

4

0

1

2

3

4

0.02 0 −0.02 5 0 −5 2

(p.u)

To better understand the effect of SMES controller on torsional modes, the eigenvalues analysis is performed in three different situations of the power system. Table 2 provides the eigenvalues analysis of the power system in 35% compensation of line-1 and operating condition P = 1 p.u and Vt = 1 p.u. As seen in Table 2, two torsional modes 1 and 2 in the absence of controller are unstable, because of being positive the real part of torsional modes. There is such a situation even in the presence of the SMES without KAP controller. This shows that the SMES without the proposed controller is unable to stabilize torsional modes. In third situation, the KAP controller is added to the SMES. It is clear that SMES with the proposed controller can enhance the damping rate of unstable torsional modes.

Case 1 Case 2

TLP−HP

5.1. Eigenvalues analysis

Operating condition (in p.u)

0 −2 0.01

Psm

 Three different operating conditions given in Table 1 are used to achieve a robust SMES controller.  To cover a wide range of compensation levels, compensation levels of 35%, 55% and 70% are considered.  It is assumed that three-line-to ground fault is occurred at bus 1 at t = 0.1 s and cleared at t = 0.24 s. According to the above assumptions, there are nine different simulations (m = 9) for which the optimization should be carried out. To achieve better performance, 2000 and 500 iterations are considered for the global search and the local search, respectively. After repeating the COA for several times, the optimal parameter of KAP is selected from the best repetition. The final value of KAP parameter is K = 3.901. To show the effectiveness of SMES with the proposed KAP, the eigenvalues analysis, time-domain simulations and fast Fourier Transform (FFT) analysis are performed in MATLAB/SIMULINK environment.

Table 3 Different cases used in the simulations.

(p.u)

The optimization of KAP parameter is carried out based on the following initial operating condition and assumptions.

0 −0.01

Time (s) Fig. 6. Response of system to a 120 ms two-phase ground fault applied to the beginning of line-2.

rotor speed deviation, the rotor angle deviation, torsional torque of Gen-LP and LP-HP sections as well as the output active power of SMES are shown in Fig. 6. The pervious simulation is again repeated for a 150 ms single-phase to ground fault applied to the end of line-1. The response of power system to this fault is illustrated in Fig. 7. It is clear from these results that the SMES controlled by the proposed active power controller is able to mitigate the subsynchronous and low frequency oscillations such that the vibrations on the shaft will be minimal. (B) Case 2 To demonstrate the robustness and effectiveness of proposed approach, the performance of the SMES controlled by the active power controller is evaluated in new case. It is assumed that a 120 ms three-phase to ground fault is occurred at the beginning of line-1. The response of the system to this fault including the rotor speed deviation, the rotor angle deviation, torsional torque of Gen-LP and LP-HP sections are shown in Fig. 8. To verify the robustness of the SMES controlled by the proposed controller, it

Δθ (rad) 1

2

3

1

2

3

4

TGen−LP

2 1 0

1

2

3

TLP−HP

0.5 0

0

1

2

3

2

3

4

0

1

2

3

4

0

1

2

3

4

0

1

2

3

4

0

1

2

3

4

10 0 −10 5 0 −5 0.01

Psm

Psm

(p.u)

−0.05

4

0.01 0 −0.01

1

0

4

1

0

0.05

(p.u)

0

−1

4

Δω (p.u)

0

0 −0.01

0 −0.5

(p.u)

−1

0

(p.u)

TLP−HP

−0.8

(p.u)

0.01

(p.u)

−0.6

TGen−LP

Δθ (rad)

M. Farahani / Physica C 483 (2012) 34–39

Δω (p.u)

38

0 −0.01

0

1

2

3

4

Time (s)

Time (s)

−2

0

1

2

3

4

0.05 0 −0.05

0

1

2

3

4

5

0

1

2

3

6000 4000

Mode 0

Mode 2

2000 0

0

10

20

30

40

50

60

4

0 0

1

2

3

4

0.01

Psm

0−3 sec

Frequency (Hz)

2

0 −0.01

Mode 1

8000

0

−2

(p.u)

Mag (% of Fundamental)

−1

Fig. 9. Response of system to a 150 ms three-phase ground fault applied to the middle of line-1.

0

1

2

3

4

Time (s) Fig. 8. Response of system to a 120 ms three-phase ground fault applied to the beginning of line-1.

Mag (% of Fundamental)

(P.u)

0

−5

(p.u)

TLP−HP

TGen−LP

Δω (p.u)

Δθ (rad)

Fig. 7. Response of system to a 150 ms single-phase ground fault applied to the end of line-1.

15000

Mode 1

3−6 sec

10000

0

Mode 2

Mode 0

5000

0

10

20

30

40

50

60

Frequency (Hz) Fig. 10. FFT analysis of rotor speed deviation in two three-second intervals in the absence of SMES.

is assumed that a 150 ms three-phase to ground fault is occurred at the middle of line-1. Fig. 9 draws the response of the power system to this disturbance. It is evident from all these figures that torsional oscillations are satisfactorily minimized by the SMES such that the vibration on the shaft of turbine-generator is negligible and the torsion contingency of the shaft is minimal.

5.3. Impact of the proposed active power controller on each torsional mode In this subsection, the effect of proposed scheme on each torsional mode is investigated using the fast Fourier transform (FFT)

analysis. For this purpose, the FFT analysis of the rotor speed deviation signal for a three-phase to ground fault is provided. Figs. 10 and 11 depict the FFT analysis of the selected signal in the absence and in presence of SMES controlled by the proposed approach in two three-second intervals, respectively. As seen in Fig. 10, in 0–3 s interval, each mode has a specified magnitude, but in 3–6 s interval, this magnitude is increased in time, while in the presence of SMES, the magnitude of torsional modes in 3–6 interval is decreased in time. Therefore, the result of FFT analysis verifies the result obtained from the eigenvalues analysis and time-domain simulations.

M. Farahani / Physica C 483 (2012) 34–39 4

Mag (% of Fundamental)

x 10 15

0−3 sec Mode 1

10 5 0

Mode 2 0

10

20

30

40

50

60

Mag (% of Fundamental)

Frequency (Hz)

3−6 sec

6000 Mode 1

Mode 2

4000 2000 0

0

20

40

60

Frequency (Hz) Fig. 11. FFT analysis of rotor speed deviation in two three-second intervals in the presence of SMES controlled by the proposed approach.

6. Conclusion This study introduces a new strategy in order to control the active power of a SMES unit to damp the subsynchronous and low frequency oscillations. This strategy is to modulate the output active power of SMES by using the generator acceleration signal. The parameter of the proposed controller is optimized by using the chaotic optimization algorithm. In order to achieve a robust controller, several operating conditions and compensation levels are used. Three different analyses are performed to validate the performance of SMES controlled based on the proposed scheme. All the simulations show that the SMES controlled by the proposed controller can mitigate the oscillations caused by different disturbance in a wide range of operating conditions. Appendix A In the SMES model, the fixed parameters are set as follows: Kp = 40, Ti = 0.4, Ksm = 1, KVsm = 1 TC = 0.01, Lsm = 10 Ssm,base = 100 MVA, Vt,base = 22 kV References [1] R.G. Farmer, Al Schwalb, Katz Eli, Navajo project report on subsynchronous resonance analysis and solution, IEEE Trans. Power Apparatus Syst. 96 (4) (1977) 1226–1232.

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