Novel Adaptive Damping Controller for Interline Power Flow Controller to Improve Power System Stability

Subject Areas : International Journal of Smart Electrical Engineering

Naser Taheri ¹ , Hamed Orojlo ² , Hamid Karimi ³ , Farhad Ebrahimi ⁴ , Kaveh Khalifeh ⁵

1 - Faculty Member, Department of Electrical Engineering, Technical and Vocational University (TVU), Tehran, Iran
2 - Faculty Member, Department of Mechanical Engineering, Technical and Vocational University (TVU), Tehran, Iran
3 - Faculty Member, Department of Computer Engineering, Technical and Vocational University (TVU), Tehran, Iran
4 - Department of Computer Engineering, Islamic Azad University, Qeshm Branch, Qeshm, Iran
5 - Department of Mechanical Engineering, Maragheh University, Maragheh, Iran

Received: 2021-08-06 Accepted : 2021-10-29 Published : 2021-11-01

Keywords:

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10                                International Journal of Smart Electrical Engineering, Vol.10, No.1, Winter 2021                      ISSN: 2251-9246        

EISSN: 2345-6221

 

pp. 1:10

 

Novel Adaptive Damping Controller for Interline Power Flow Controller to Improve Power System Stability

Naser Taheri*1 , Hamed Orojlo2,Hamid Karimi3, Farhad Ebrahimi4, Kaveh Khalifeh5

1Department of Electrical Engineering, Technical and Vocational University(TVU), Tehran, Iran, [e-mail]  

2Department of Mechanical Engineering, Technical and Vocational University(TVU), Tehran, Iran, [e-mail]                                                         3Department of Computer Engineering, Technical and Vocational University(TVU), Tehran, Iran, [e-mail]                                      4Department of Computer Engineering, Islamic Azad University, Qeshm Branch, Qeshm, Iran, [e-mail]     5Department of Mechanical Engineering, Maragheh University, Maragheh, Iran, [e-mail]                                                                     

Abstract

Todays, it is well known that using a supplementary controller in FACTS devices can be affective for damping oscillations of electromechanical (EM) mode. In the meantime, appropriate coupling of inputs-outputs signals in the multivariable power system equipped by FACTS can improve the performance of designed supplementary controller. In this paper using of a supplementary controller of interline power flow controller (IPFC) based on input-output signal selection is surveyed to improve power system stability. The proposed controller is added as a supplementary loop to the converter control loops in IPFC and will enhance the damping torque in the power plant by increasing the damping coefficients of the system oscillation modes. Moreover, a solution is provided to use the proposed damping controller in the most optimal path between input-output signals of the system, so that the most controllability on the oscillation modes and the least interference with other channels between the input-output signals are obtained. To increase stability, further Lead-Lag controllers, a novel on-line adaptive controller has been used analytically to identify power system parameters and damp electromechanical oscillations. The simulation results show that the method proposed in this paper not only improves the dynamic stability of the power system but also strengthens the voltage profile.

Keywords: IPFC, Power System Stability, Input-Output Coupling, Adaptive Damping Controller 

Article history: Received -----------; Revised -----------; Accepted -----------.

© 2021 IAUCTB-IJSEE Science. All rights reserved

 

1.       Introduction

 

Today, increasing demand for electricity, economic challenges, and environmental and technical considerations for the establishment of new transmission lines and power plants, power systems are much more loaded than before [1]. Moreover, interconnection between the neighbor power networks has increased the complexity of systems and result rising in the low frequency oscillations. The mentioned issues forced the power system to operate near its stability margins [2-3].

Power system stabilizer (PSS) control provides a positive contribution by damping rotor speed deviation, which are in a broad range (typically 0.1 - 1.0 Hz) of frequencies in the power system. PSS obtains a supplementary damping signal to excitation system and improve the power system stability. However, PSS has a negative effect on the voltage profile and its performance in damping the oscillations caused by severe disturbances is not significant. [5-6].

The concept of FACTS (Flexible Alternating Current Transmission System) refers to a family of power electronics-based devices which are able to improve the power system controllability and stability and increase the capability of power transmission. Recently, researchers demonstrate that FACTS devices can be used to mitigate power system oscillations [7-8]. The possible benefits of FACTS devices can be listed out as below: 

ü       improving voltage profile of power systems.

ü       removing/reducing the overloads of branches.

ü       enhancing transient and dynamic stability of power systems.

ü       reducing energy losses.

ü       effective in mitigating the consequences of contingencies.

 Generally, the power system oscillations damping is not the main reason of using FACTS devices in the power system, but rather power flow control [6-7]. However, by adding a supplementary damping signal to FACTS, these devices can contribute to the power system oscillations damping and the stability improvement. The supplementary damping controller provides the appropriate damping torque for the power system to amplify the damping ratio of the oscillation modes.

In [2], an adaptive design of interline power flow controller (IPFC) using a reinforcement learning (RL) approach is utilized for damping of the low-frequency oscillations (LFOs) in power system. In [3], an IPFC is used as a power suppression carrier and its mechanism is analyzed using the linearized state-space method to improve the system damping ratio. It is shown that although the IPFC can suppress forced oscillation with well-designed parameters, its capability of improving the system damping ratio is limited. In [4], the improvement of the dynamic stability in power system equipped by wind farm is examined through the supplementary controller design in the high voltage direct current (HVDC) based on voltage source converter(VSC) transmission system. In [7], a novel algorithm is proposed to determine the best least number (BLN) and allocation of the thyristor-controlled series capacitor (TCSC) with a goal of improving the transient stability in an optimal manner.

 The adaptive controller is an appropriate choice for controlling a nonlinear dynamic system. The parameters of adaptive controller are tuned based on the dynamic changes of the nonlinear system and accordingly, the control objectives are met. In [1], an adaptive neural damping controller based neural identifier is proposed to improve power system stability which is equipped by VSC HVDC and overcome the drawbacks of conventional phase compensator. In [21], To increase power system stability, further Lead-Lag and LQR controllers, a novel on-line adaptive controller based on UPFC has been used analytically to identify power system parameters and damp the low frequency oscillations.

Interline power flow controller (IPFC) is a new approach of the FACTS devices which is used for series compensation and impressive power flow management of transmission lines. In this paper, implementation of IPFC to improve the stability of power system and damp the low frequency oscillations will be considered. A proposed method based on the controllability and relative gain array(RGA) concepts are proposed to distinguish the most appropriate path between the input-output signals of the power system equipped by IPFC for the damping controller design. Then, the supplementary damping controller based on the self-tuning regulator(STR) is designed and implemented in the selected path to improve the power system stability.  

2.       Modelling of Power System equipped by IPFC

Fig.1 is a single machine infinite-bus power system equipped with a IPFC which consists of a Master voltage source converter (VSC-M) and a Slave voltage source converter (VSC-S) and its two transformers and a DC link capacitor .In Fig. 1,  are the amplitude modulation ratio and phase angle of the control signal of each VSC respectively, which are the input control signals to the IFFC [12].

Fig. 1. Power System equipped by IPFC

 

If the general pulse width modulation (PWM) (or optimized pulse patterns or space-vector modulation approach) is adopted for the GTO-based VSC, the three-phase dynamic differential equations of the IPFC as the three-phase dynamic differential equations of the IPFC are [13] (k=1,2):

	(1)
	(2)

Using Park’s transformation, and ignoring the resistance and transients of the transformers of the IPFC:

	(3)
	(4)
	(5)

The nonlinear model of power system which was shown in Fig.1 is as follow:

(6)

Where

(7)

Writing circuit voltage law and node current law, it is possible to calculate synchronous generator injected currents. Using these currents, following linearized components of power system are obtained:

(8)

Where (Detail of coefficients can be find in appendix)

	(9)
	(10)
	(11)
	(12)

Substitute eqns. 9-12 into eqn. 8, we can show the state variable equations of the power system installed with IPFC (Eq.13).

(13)

The  are input signals of IPFC. The linearized dynamic model of eqn. 8 is shown by Fig. 2, where only one input control signal is demonstrated, with u begin 1 () , 2 () ,  or  and  are the row vectors as defined below:

 

In figure (2), each of the control signals of converters (i.e.  ) in IPFC can be used for adding a supplementary damping signal. However, to increase the effectiveness of the damping controller and reduce control costs, it is necessary to provide the best input signal with the greatest effect in amplifying the damping coefficient of oscillation modes of the power system. Accordingly, in this paper, a novel method for selecting the best coupling of the input-output signals of the power system (described in Equation (13)) is proposed.

Fig. 2. Philips-Heffron model of power system installed with IPFC

3.       Input-output Signal Selection

Controllability is defined as the ability of a control system to reach a definite state from a fixed (initial) state in a finite time. It is considered as an important property of the control system as it defines the behaviour of the control system. In this paper, the concept of controllability is used to measure the damping of oscillation modes over the different work conditions in the power system. In this way, the appropriate path between input-output signals can be selected to apply the damping signal which is produced by supplementary controller. Popov-Belevitch-Hautus (PBH) is a practical approach for achieving this goal [15-17]. Based on this method, for a state space model of a dynamic system () it is required to measure rank of following matrix [15-17]:

(14)

Which  is the kth eigenvalue of the matrix A, I is the identity matrix,  is the column of B corresponding to ith input . The mode  of linear system in state space form is controllable if matrix  has full row rank. The rank of matrices  can be appraised by their singular values. the distance of the matrix C from all the matrices with a rank ofis demonstrated by the minimum singular values. This characteristic can be utilized to determine modal controllability of a mode [14, 15]. The minimum singular value () of the matrix shows the capability of the ith input to control the mode associated with the eigenvalue(in this paper  is electromechanical mode (EM) of power system). Notice that the higherresults the higher controllability ofby the corresponding inputs. Therefore, the controllability of the EM mode can be examined with all inputs in order to identify the most effective one to control the mode.

In this paper, in order to select the best coupling of the input-output signals and design the most effective damping controller, it is proposed to measure the controllability of the system oscillation modes through the each of the input signals and for different operating conditions of the power system. The measurements are performed based on the following proposed algorithm:

1.       The working point of power system is determined.

2.       The electrical components of the power system are calculated through a load flow program.

3.       Using load flow results, the nonlinear model of the power system (Eqs.1-8) is linearized and the state space model is calculated (Eq.13).

4.       The electromechanical mode of the power system is determined and the controllability matrix based on PBH test() is made.

5.       SVD of  are calculated and the smallest SVD () is selected.

6.       Steps 1 up to 5 are performed for the different operating points of the power system and the smallest SVD values of the controllability matrix are stored.

7.       Between the system inputs, the input with the highest amount of  is selected as the best input to apply the damping signal.

Using the proposed method, the effect of each coupling between the input-output signals of the power system (on the controllability of oscillation modes) can be compared with each other. However, an important indicator that can be appropriate to the optimal selection of input-output signals coupling is the degree of interaction of each coupling. Relative gain array (RGA) concept is used to measure the degree of interaction in a dynamical system. The original technique is based upon the open loop steady state gains of the process and is relatively simple to interpret [15,17-18]. The RGA matrix  can be calculated by following equation:

(15)

Where denotes the element ij of the matrixand the operator  denotes the Hadamard or Schur product (element by element product). The ith row sum of the RGA is equal to the square of the ith the output projection, and the jth column sum of the RGA is equal to the square of the jth input projection. So RGA is an effective screening tool for selecting inputs-outputs from  which includes all the candidate inputs and outputs. Essentially for the case of many candidate manipulations (inputs) one may consider not using those manipulations corresponding to columns in the RGA where the sum of the elements is much smaller than 1.

In this paper, in order to select the best input-output signal coupling, in addition to the controllability test, the least interaction index based on RGA will also be considered. Accordingly, the following algorithm is proposed to select the input-output coupling with the least interference:

RGA is used for measuring interactions between the output (rotor speed deviation)-inputs (four input of IPFC) paths by using of the following proposed algorithm:

1.       The working point of power system is determined.

2.       The electrical components of the power system are calculated through a load flow program.

3.       Using load flow results, the nonlinear model of the power system (Eqs.1-8) is linearized and the state space model is calculated (Eq.13).

4.       The system transfer function matrix () is formed and RGA of this matrix is calculated () for steady state.

5.       Sum of the elements in a column ofis calculated.

6.       Steps 1 up to 5 are performed for the different operating points of the power system and all sums are plotted based on work points.

7.       The input-output path with the highest amount of  is selected as the most appropriate path with the lowest interaction with other existence channel between the input-output signals.

2.       Adaptive Damping Controller based on Self Tuning Regulator

The power system is a nonlinear dynamic system whose operating conditions are constantly changing. Accordingly, the use of classic controller (for example lead-lag controller in Fig. 3), which is tuned based on a special operating point, cannot meet the requirements of the power system.

Adaptive controllers change the controller parameters to adapt to changes in the dynamic system that occur with time [20-21]. Therefore, the use of this type of controller in the power system not only increases the efficiency of the controllers but also strengthens the reliability. In this paper an adaptive controller based on self-tuning regulator (STR) is proposed to design the supplementary damping controller based on IPFC.  

As it is shown in Fig. 4 the proposed controller in this paper has two separated parts: (a) estimation and (b) controller. The main function of the estimation block is to estimate the model of the power system in different working conditions using the recursive least-squares (RLS) or the projection algorithms. The block labeled "Controller Design" represents an on-line solution to a design problem for a system with known parameters or with estimated parameters based on minimum degree pole placement method (MDPP). The main task of the controller block is to calculate the required control signal. The controller parameters computed by its proceeding block.

It can be seen that at each time step, the dynamic system is identified by the estimator and then this data is used to calculate the appropriate control signal. The system can be considered as an automation of processing modeling/estimation and design, in which the process model and the control design are updated at each sampling interval.

Fig. 3. Structure of lead-lag controller

Fig. 4. Schematic of STR

 

The transfer function of a path between input-output signals can be assumed as follows (in discrete form):

(16)

A general linear controller can be described by:

(17)

Where R, S and T are polynomials. A block diagram of the closed-loop system is shown in Fig. 5.

Fig. 5. general linear controller with 2 degrees of freedom.

 

General equations of R, S and T are polynomials and have been calculated by MDPP as follows:

(18)

The closed-loop characteristic polynomial is thus:

(19)

The key idea of the design method is to specify the desired closed-loop characteristic polynomial . The polynomial R and S can then be solved from Eq. (19). In the design procedure we consider polynomial  to be a design parameter that is chosen to give desired properties to the closed-loop system. Eq. (19), which plays a fundamental role in algebra, is called the Diophantine equation [21].

The following algorithm shows how to implement the proposed adaptive control:

1.       Data: Give the reference model in the form of a desired closed-loop pulse transfer operator (desire transfer function) and a desired polynomial.

2.       Step 1: Estimate the coefficients of the polynomials A and B using the RLS method.

3.       Step 2: Using the polynomials A and B estimated in step 1; apply the MDPP method, the polynomials R, S and T of the controller are then obtained by solving the Diophantine equation.

4.       Step 3: Compute the control action which is

5.        Repeat steps 1-3 at each sampling period

1.       Simulation Results

The MATLAB-SIMULINK software is used for the simulation. All information about the power system can be found in appendix. In table. 1. Three different working condition are shown.

 

 

First, the most efficient path between input-output signals is selected based on the criteria described in section 3. This path provides the most controllability over the oscillation modes. The results of measuring the controllability of oscillation modes are shown in Fig.6 and Fig. 7. It is observed that the most controllability is provided by the modulation angle in the converters of IPFC. Fig.8 and Fig.9 show the interactions between the output signal (the rotor speed deviation) and IPFC-related inputs. It is observed that the channels containing the converter modulation angle create the least interference with other channels between the inputs-outputs. Therefore, according to Fig. 6 up to Fig. 9, the best input for applying the damper signal is the modulation angle of the converters.

After selecting the best input-output path, it is necessary to design the supplementary damping controller. To design the damping controller, the nominal operating conditions of the power system is selected. The coefficients of the designed lead-lag controllers are shown in Table (2).

Table.1 Work points of power systems(based on pu)
	System				Disturbance
	Linear	0.9	0.1	1
	Linear	1.2	0.4	1
	Nonlinear	1	0.1	1
3phase fault at  for 7 cycles

 

Fig. 6. SVD result with

 

Fig. 7. SVD result with

Fig. 8. RGA result with

Fig. 9. RGA result with

 

The system estimator based on damping STR, which is responsible for identifying the power system, is considered as:

 

The estimation algorithm must determine the coefficients in the mentioned transfer function. The adaptive controller coefficients (R and S polynomials) are adjusted for each working point based on the model provided by the estimator. Note that the polynomials S and R are considered as a second order function. In Fig. 10 deviation of the estimator parameters is shown.

Figures (11) to (14) show the linear system response for the different operating points of the power system. As can be seen, the use of the supplementary controller has caused the damping of power oscillations as well as frequency in the power system. In particular, the use of damping controllers based on STR in the "rotor deviation speed - IPFC modulation angle" path, lead to better response of power system rather than using of the classic lead-lag compensator.

Fig. 15. up to Fig. 18. show the nonlinear system response in the presence of the proposed damping controllers. In nonlinear system simulation, the controller output signal is applied to the system through the converter modulation angle. It can be seen that compared to the classical controller, the adaptive controller damps the power-frequency oscillations in the most optimal time. In addition, the voltage profile has been significantly improved.

Table.2 Parameters of designed Lead-Lag controllers in  condition
M	13.29	0.029	0.059	0.13	0.057
	93.61	0.02	0.027	0.084	0.098

(a)the parameters of estimator

(b)parameters of controller

Fig. 10. The parameters deviation in the damping STR

 

 

Fig. 11. Rotor Speed deviation()

Fig. 12. Generated Active Power()

Fig. 13. Rotor Speed deviation()

 

Fig. 14. Generated Active Power ()

 

Fig. 15. Rotor Speed Deviation ()

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