Active Disturbance Rejection Control – Based Load Frequency Controller of Interconnected Power

Systems Involving Wind Power Penetration

Emad Abu Khousa Projects Manager - Glory Horizons

Dubai Silicon Oasis, P.O.Box 18881 Dubai, United Arab Emirates

emad@emadak.com

Abdulla Ismail Professor of Electrical Engineering

RIT- Dubai, P.O.Box 341055 Dubai, United Arab Emirates

axicad@rit.edu

Abstract— The load frequency control (LFC) problem is becoming more significant today in accordance with increasing grid size, changing structure, integration of renewable energy sources, and complexity of interconnected power systems. In this paper the assessment of Active Disturbance Rejection Controller (ADRC) based LFC is presented. This control algorithm offers a new design concept and inherently robust controller building block that requires very little information about the system. It actively estimates and compensates for the effects of the unknown dynamics and disturbances. The control strategy was applied to a single isolated power area and then to three interconnected control areas. The simulation results showed that the used controller was able to maintain a robust performance and grid stability by minimizing the effect of disturbances caused by load variation and wind power penetration.

Keywords- Load Frequency Control, Active Disturbance Rejection Controller, Interconnected Power Systems, Renewable Energy Resources, Wind Power Penetration.

I. INTRODUCTION

Whether it is to diversify the energy sources or to reduce

the environmental impact of the conventional electrical energy generation, renewable energy sources are increasingly attracting high interest on international levels. The driving motives behind deploying environmentally friendly energy sources and distribution mechanisms call for higher power generation/transmission efficiency as well as maintaining overall power grid reliability and capacity. Nowadays, the wind energy is the fastest growing utilized renewable energy [1]. Although it is considered as a very prospective energy source, wind power fluctuation caused by randomly varying wind speed is still a serious problem. This is because the random variation of wind speed causes the wind farm output power. These power variations interact with the network and thus initiate voltage and frequency fluctuations in interconnected power system [2]. Therefore, this makes the power system frequency regulation a very challenging task in systems with high penetration level of wind power production. The impact of wind power fluctuations on the power system frequency has been addressed in [3][4]. An extensive literature review and

open problems regarding frequency regulation in power systems with renewable energy sources are presented in [5].

Power system load frequency control (LFC) has been one of the important control problems in electric power system design and operation [6]. The goal of LFC is to reestablish primary frequency regulation capacity, return the frequency to its nominal value and minimize unscheduled tie-line power flows between neighboring control areas [7]. There are volumes of research articles regarding LFC of single area/interconnected areas power system considering various control strategies [8]. Many control strategies like integral control, discrete time sliding mode control, optimal control, intelligent control, adaptive and self-tuning control, and robust control, have been reported in the literature [9]. Some reports have recently addressed the power system frequency control issue in the presence of wind power generation [1][2], [10]-[12].

Active disturbance rejection control (ADRC) is a new robust control design concept that shows promising power in dealing with the uncertainties of control systems [13]. It was systematically proposed by Han and colleagues in their pioneer works [14]-[16]. ADRC compensates dynamical uncertainty as a kind of disturbance [17], and it has been successfully applied in many challenging domains such as aerospace, aviation, electricity, chemical industry and other fields to improve system dynamics with simple algorithm, short response time and little overshoot [18][19]. ADRC based decentralized LFC for interconnected power systems have been successfully employed in [20]-[22].

This paper first explores the ADRC-based LFC problem for an isolated area power system as a disturbance rejection problem and discusses the effect of load disturbance and wind power penetration on the control performance, then the same control method is applied to three-area connected power systems. The control objective is to regulate frequency error and net tie-line power deviations in the presence of power load changes and wind power penetration. The simulation results demonstrate that the ADRC controller is robust and has desirable performance in comparison of classical control design in all of the performed test scenarios.

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II. LOAD FREQUENCY CONTROL

A. LFC in Isolated Power Systems

In order to conduct a frequency response analysis for an isolated power system in the presence of sudden load changes, all generators of a power system are represented by an equivalent generator, which has an equivalent inertia constant and is driven by the combined mechanical output of the individual turbines [6]. In this case, the proposed model can be used as an equivalent frequency response model for the whole multi-machine power system. A block diagram of a synchronous generator equipped with frequency control loops in an isolated power system is shown in Fig. 1.

Pc Pm f++

- -

PL

_____sTg + 1

1 _____2Hs + D

1_____sTt + 1

1IN OUT

_R 1

Controller Governor Turbine Rotating mass & Load

Speed drop characteristic

Figure 1. Block diagram model of governor with frequency control loops for a non-reheat steam generator unit.

In this model the overall generator–load dynamic relationship between the incremental mismatch power (∆ − ∆ ) and the frequency deviation (∆ ) can be expressed as

∆ ( ) − ∆ ( ) = 2 ∆ ( ) + ∆ ( ) (1)

Where ∆ is the frequency deviation, ∆ is the mechanical power change, ∆ is the load change, H is the inertia constant and D is the load damping coefficient. The system consists of two loops, primary and secondary loops. The primary loop provides the primary speed control function, and all generating units contribute to the overall change in generation, irrespective of the location of the load change, using their speed governing. However, primary control action is not usually sufficient to restore the system frequency and the secondary control loop is required to adjust the load reference set point through the speed-changer motor. The secondary loop performs a feedback via the frequency deviation and adds it to the primary control loop through a dynamic controller. The resulting signal (∆ ) or the control effort is used to regulate the system frequency. In real-world power systems, the dynamic controller is usually a simple integral (I) or proportional integral (PI) controller [6]. According to Fig. 1, the system frequency experiences a transient change ( ∆ ) following a change in load ( ∆ ). Thus, the feedback mechanism comes into play and generates an appropriate signal for the turbine to make generation (∆ ) track the load and restore the system frequency.

B. LFC in Interconnected Power Systems

A multi-area power system comprises of power areas that are interconnected by high voltage transmission lines or tie-lines. The trend of frequency change measured in each control area is an indicator of the mismatch power in the interconnection and not in the control area alone. The LFC system in each control area of an interconnected (multi-area) power system should control the interchange power changes with the other control areas as well as its local frequency changes. Therefore, the described dynamic LFC system model in Fig. 1 must be modified by taking into account the tie-line power signal. This is generally accomplished by adding a tie-line flow deviation (∆ ) to the frequency deviation in the secondary feedback loop. A suitable linear combination of frequency and tie-line power changes for area i, is known as the area control error (ACE) is given as = ∆ , + ∆ (2)

Where is the area bias factor. Each control area monitors its own tie-line power flow and frequency at the area control centre. The ACE signal is computed and allocated to the controller. Finally, the resulting control action signal is applied to the turbine–governor unit. Therefore, it is expected that the secondary control can ideally meet the basic LFC objectives and maintain area frequency and tie-line interchange at scheduled values. A complete model is given in [6].

Pc Pm++

- -

PL

_____sTg + 1

1 _____2Hs + D

1_____sTt + 1

1IN OUT

_R 1

Controller Governor Turbine

Rotating mass & Load

ACE

+

+

β

__s

2π

f1

T12 +T13

+

+

+

-

f3

f2

Ptie

-

.

Figure 2. Block diagram model of control area 1 with secondary control.

In this study we illustrate the LFC system behavior for a multi-area power system using the dynamic model of three interconnected control area.[6]. The complete block diagram of the LFC system of Area 1 is shown in Fig. 2, where each area consists of one generator, one governor, and one turbine unit.

III. ACTIVE DISTURBANCE REJECTION CONTROL

The basic principle of ADRC is that it uses the extended state observer (ESO) to estimate the total disturbances, and forces the system changing in a canonical way. Then it employs a new control input for the remainder of the system. Because of its strong ability to reject disturbances, it has been widely expanded [23].

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A. Mathematical Modeling of ADRC The model of ADRC and ESO is driven in [15] [20] [21].

Although we aim to develop ADRC for a high-order power plant, we will introduce the design idea of ADRC on a second order plant for the convenience of explanation.

Let’s consider a dynamical motion system that can be

described as ( ) + ( ) + ( ) = ( ) + ( ) (3)

Where u(t) is the input force of the system, y(t) is the

position output, ( ) represents the external disturbance of the system, , and are the coefficients of the differential equation. Equation (3) can be written as ( ) = ( ) + ( ) − ( ) − ( ) (4)

The internal dynamics of the system combined with the external disturbance w(t) can form a generalized disturbance, denoted as d(t). Then (4) can be rewritten as ( ) = ( ) + ( ) (5)

The generalized disturbance contains both the unknown external disturbance and the uncertainties in internal dynamics. So as the generalized disturbance is observed and cancelled by ADRC, the uncertainties included in the disturbance will be canceled as well. In order to cancel the generalized disturbance after modifying the plant (5), we will treat the generalized disturbance as an extra state of the system and we will use an ESO observer to estimate its value. Let = , = , and = , The inclusion of as an additional third state is what motivated the name Extended State. The augmented state space form of (5) is

= + + = (6) = [ ] , where = , = , = . = 0 1 00 0 10 0 0 , = 00 , = 001 , and = [1 0 0].

It is assumed that has local Lipschitz continuity and is bounded within domain of interests. From (6) the ESO is derived as

= + + ( − ) = (7)

where = [ ] is the estimated state vector of , and is the estimated system output and the observer gain vector is

= [ ] (8)

This observer is denoted as the linear extended state observer (LESO). The observer gains are chosen such that the characteristic polynomial + + + is Hurwitz. For tuning simplicity, all the observer poles are placed at − . It results in the characteristic polynomial of (7) to be ( ) =+ + + = ( + ) , where is the observer bandwidth, and = [3 3 ] .

Generally, the larger the observer bandwidth the more

accurate the estimation will be. However, a large observer bandwidth will increase the noise sensitivity. Therefore a proper observer bandwidth should be selected in a compromise between the tracking performance and the noise tolerance [18]. With a well tuned ESO will track closely. Then we will have

≈ = (9)

From (9), this generalized disturbance ( ) can be approximately removed by the time domain estimated value .

With the control law = (10)

the system described in (5) becomes = + ≈ ( − ) + = (11)

From (11), we can see that with accurate estimation of

ESO, the second-order LTI system could be simplified into a pure integral plant. Then a classic state feedback control law could be used to drive the plant output y to a desired reference signal. The state feedback control law for the simplified plant = is chosen as

= ( − ) − (12)

From (7) will track , and will track . Then substituting in ≈ with (12) yields

( ) = − − (13)

where is the desired trajectory. The closed-loop transfer function from the reference signal to the position output can be driven from (13)

( )( ) = 14)

Let = and = 2 . We will have ( ) = = ( ) (15)

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where represents the bandwidth of the controller. With the increase of , the tracking speed of the output of ADRC controlled system will increase as well while the tracking error and overshoot percentage of the output will be decreased.

B. Model of ADRC-Based LFC for Power Control Area

The ADRC-based FLC controlled interconnected power system is shown in Fig. 2. The ADRC controller is placed in each area acting as local LFC. Non-reheat turbine units are considered in all areas of this study. The third-order plant model requires a 4th order ESO [20][21]. In summary, an ADRC for area 1 can be designed and represented by the following equations: ( ) = ( − ) ( ) + ( ) + ( ) (16) ( ) = ( ) − ( ) − ( ) − ( ) (17) ( ) = ( ) ( ) (18)

Where ( ) = ( )( )( )( ) , = 0 1 0 00 0 1 00 0 0 10 0 0 0 , = 000 ,

= [1 0 0 0], = ⎣⎢⎢⎡464 ⎦⎥⎥

⎤, = , = 3 , = 3 .

The other two areas have a similar structure and

parameters as for the ADRC of Area 1.

IV. SIMULATION STUDY

To demonstrate the effectiveness of the chosen control design, some selected simulations were carried out. In these simulations, the proposed controller was applied to a single isolated area (Fig. 1) and to a three-areas power system. The simulation parameters of the systems are given in Table I in the Appendix.

The design parameters of ADRC were tuned to:

= 8, = 40.

A. Case study 1: Step load change in a single isolated area

The performance of ADRC was tested on a single isolated area shown in Fig. 1. The dynamic response of the closed-loop system for a step load disturbance of 0.02 pu is plotted in Fig. 3. For the sake of comparison, the frequency deviation response of different controllers is also plotted on the same figure. The I, PI, and PID parameters were tuned using

MATLAB and are given in Table II in the Appendix. From the simulation results, we can notice that the ADRC outperformed the other controllers and the frequency deviation has been smoothly driven to zero by ADRC in the presences of power load changes in less than 2.5 seconds.

Figure 3. Dynamic response of the closed-loop system of an isolated area.

.

B. Case study 2: ADRC response to wind power penetration in a single isolated area

This case provides a simulation study on the impacts of

wind power units on the power system frequency and the responses of ADRC and conventional controllers. For the sake of simulation, random variations of wind speed (ws) between 10 m/s and 14 m/s have been taken into account and simulated. Dynamics of the windmill including the pitch angle control of the blade is also considered. The variation of produced powers by wind turbine due to change in wind velocity performs the source of frequency variation in the study systems. The load is assumed constant in this case (∆ = 0). A simulated wind power response to wind speed variations in 300 seconds is shown in Fig.4.

Figure 4. Wind power system response to random wind speed (ws).

To augmentation of our power system with the incoming

wind generation the following assumptions are considered.[10] i) the wind turbines to be installed do not respond to network frequency deviations, and the total load of

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the system remains the same; ii) an x% wind penetration means an x% reduction in the existing generating units, i.e., an x% reduction in the system inertia. Furthermore, the droop settings of the individual generators remain the same; and iii) the spinning reserve in the power system is enough to take up any generation deficit. The way to consider the excess active power injection from the wind turbine into the power system is done by multiplying the wind power deviation (∆ ) with the penetration level ( ) to convert ( ∆ ) from the wind farm (WF) base to the system MVA base. The effective load step in the presence of the wind power is: ∆ , = ∆ − ∆ . (19)

In this case wind power is penetrated into the isolated power system given in case study 1 with 20% penetration level. The ADRC, I, PID controllers responses of the system in the first 60 seconds are shown in Fig. 5. The ADRC was able to stabilize the system and brought the frequency deviation to zero. The performance of the ADRC shows superiority over the conventional controllers.

Case Study C: ADRC response to Wind Power Penetration in three connected control areas

In this case a wind power is penetrated in Area 1 of the connected power system with 20% penetration level. The responses of the conventional and ADRC controllers in the three areas are illustrated in Fig. 6 and Fig. 7 respectively. For comparison purposes the first 60 seconds of ADRC and a conventional I controllers’ responses are shown in Fig. 8. It is clear from the system responses that the ADRC was able to settle down the system and bring the frequency deviation (∆ ) and the tie-line flow deviation (∆ ) to 0 in response to each wind power deviation.

Figure 5. ADRC, I, and PID responses to 20% penreation level of wind power .in a single isloated area.

Figure 6. Conventional controller responses to 20% penreation level of wind power in Area 1 of the interconncted power system.

Figure 7. ADRC controller response to 20% penreation level of wind power in Area 1 of the interconncted power system.

Figure 8. ADRC and convesional controllers responses to 20% penreation level of wind power in Area 1 of the interconncted power system.

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V. CONCULSION

This study presents an assessment of the application of ADRC-based LFC for both an isolated power area and a three-area interconnected power system. The ADRC has been selected to improve the performance and stability of the system with the existence of wind power generation. The used control strategy was able extract the information of the disturbance from input and output data of the system and actively compensate for the disturbance. The control method was tested with load change and penetration of wind power scenarios. Simulation results demonstrated the effectiveness of the controller. It was shown that ADRC controller can guarantee the robust performance, such as precise reference frequency tracking and disturbance attenuation under disturbances cased by change of power demand or the penetration of fluctuated renewable energy resource.

APPENDIX

TABLE I. CONTROL AREAS PARAMETERS

Area Area 1 /isolated power system

Area 2 Area 3

I controller -0.3/s -0.2/s -0.4/s D (pu/Hz) 0.015 0.016 0.015 2H (pu s) 0.1667 0.2017 0.1247 R (Hz/pu) 3.00 2.73 2.82 Tg (s) 0.08 0.06 0.07 Tt(s) 0.40 0.44 0.30 β (pi/Hz) 0.3483 0.3827 0.3692

(pu/Hz) = 0.20 = 0.25 = 0.20 = 0.12

= 0.25 = 0.12

TABLE II. PARAMETERS OF THE CONVENTIONAL CONTROLLERS

Controller Gains Kp Ki Kd

I -0.3 PI -0.26 -0.34 PID -0.59 -0.79 -0.1

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