Optimal feedback path selection for interconnected power systems using load frequency control strategy

The main goal of an interconnected power system is to transfer power from one area to another while the network frequency and tie-line ﬂow remain within the prescribed limits. However, both of these quantities may violate their desired values during this transfer due to disturbances in the network. This paper proposes a stratagem for choosing the right feedback path for an interconnected power system to maintain the system frequency and tie-line ﬂows within the prescribed limits while external disturbances exist. Area control error (ACE), a combination of frequency error and tie-ﬂow deviations, is used as the performance indicator. In the proposed approach, feedback control is designed using active disturbance rejection controller (ADRC) based load frequency control to tackle ACE. It is observed that the individual load change monitoring is sufﬁcient for selecting the right feedback paths rather than the consideration of simultaneous load changes of all load centres. The effectiveness of the proposed controller for selecting the feedback paths has been tested by conducting several case studies. The results demonstrate that the proposed controller can reduce transient magnitude around 57% for ACE, 55% for frequency error and 72% for tie-line error as compared to the PID controller.


INTRODUCTION
Power generation and demand of interconnected power systems should be exactly matched by controlling the speed of synchronous machines. This sense of balance must be kept up during load changes and instabilities, such as equipment disconnecting issues [1]. A system is about an equilibrium point if, when subjected to small perturbation, it remains within a small region surrounding the equilibrium point. Stable frequency and voltage, the two most important equilibrium points in a power system, mainly depend on the balance of active and reactive power supply, respectively. Without balancing these two factors, the system will reset at a new value and, consequently, the equilibrium points will drift. Regulation of real power output of generating units in retort to change in system frequency and tie-line power interchange within specified limits is known as load frequency control (LFC) [2]. The primary task of LFC is to uphold the system frequency to its predetermined value. Many researchers suggested many control strategies for LFC in their pioneer work. Most of the proposed controllers are based on linear quadratic regulator (LQR), fuzzy logic-based techniques, adaptive fuzzy logic, neural network, genetic algorithm, particle swarm optimization, hybrid and other techniques. However, proportional, derivative, integral (PID) controlling techniques are widely used in control techniques [3][4][5][6]. A model free control strategy is offered for the stability of power system frequency in [7].
Active disturbance rejection control (ADRC) technique, introduced by J. Han in 1995, is a very powerful control strategy [5]. This controller is modified for frequency control in interconnected power systems by Z. Gao in [6,8]. ADRC is used to study the frequency deviation problem in multi-area power system and the proposed controller performance is tested on the minimum and non-minimum phase systems [9]. An ADRC based LFC of multi-area power systems considering communication delays is proposed in [10]. ADRC requires only the information of input and output of physical system. The disturbances are generated by ADRC from the incongruities of mathematical model and actual system and finally reject the discrepancies actively using a non-linear feedback controller [11]. Due to its independency from accurate data of the physical model, ADRC is very robust against parameter uncertainties and external disturbances. Recently, ADRC is used in single area and multi-area power system for LFC [12][13][14][15][16].
Interconnected power system is considered to share all power (import and/or export) from one area to another using transmission-line interconnections or tie-lines. The interconnected power system is established over a country or in a specific region of a country. However, in all areas there may not be enough generation to meet the demand. It may be termed as load-rich area. Generation-rich area may have adequate generation regardless of their load.
ADRC-based LFC of multi-area power system is presented using optimal output feedback method and its dynamic responses in [17]. A modified LFC model is proposed for a multi-area power system considering deregulated surroundings using optimal output feedback technique in [18]. Linear matrix inequalities based robust predictive LFC for single area-and multi area-power system with communication delays is demonstrated in [19]. In [20], authors showed that feedback connections from various generation-rich areas to load-rich areas of interconnected power system are very important for its stability. However, the work did not consider the simultaneous load change from the load centres, even though loads always change simultaneously in any power system.
To the best of authors' knowledge, any specific strategy to select the feedback path between generation-rich areas and loadrich areas for load frequency control is not yet reported in the literature. To bridge the research gap, this paper proposes ADRC-based LFC to select optimal feedback paths for improving the performance of the LFC. The main contributions of this work are to design and analyse the ADRC-based LFC model to determine optimal feedback path while considering several effects of the interconnected power system. The reason of conducting this study is to improve the power system stability and reliability that depend on the selection of right feedback path.
The remainder of this paper is structured as follows. The structural design of ADRC and ADRC-based LFC model for selecting feedback path are proposed in section II. ADRC-based LFC model for interconnected power system is also shown in section III. In section IV, the selection of feedback paths and related terms are demonstrated. The simulation results and proposed method for selecting feedback paths is presented in section V.

DESIGN ARCHITECTURE OF ADRC AND ADRC-BASED LFC MODEL
The architecture and mathematical representation of ADRC are presented in this section. Moreover, the ADRC based LFC model is also revealed. The structural design of ADRC is shown in Figure 1. ADRC includes three main parts: tracking differentiator (TD), feedback control system (FCS) and extended state observer (ESO). ESO is the heart of this controller. It follows the output of the plant, y, and approximate of state variable of the plant at a variety of instructions with the ballpark figures of uncertainties. TD generates the tracking output of control object, r. FCS actively rejects the disturbances using a PD controller, and b is considered as the compensation issue.
A system with discrepancy can be represented as follows, where U(s) is the plant input, Y(s) is the output of the system, and W(s) is considered as a simplified disturbances. The transfer function of a physical plant G p (s) can be represented as follows, a n s n + a n−1 s n−1 + ⋯ + a 1 s + a 0 (2) where R(s) is the reference input and a i (i = 1,…., n) and b j (j = 1,…, m) are coefficient of the transfer function.
The algebra of polynomials is modified into a higher order ADRC from the transfer function only to facilitate the analysis. Thus, a corresponding model of Equation (2) is necessary in the polynomial form to execute ADRC for the system of Equation (1). The discrepancies involving these two models are considered as generalized disturbance.
The polynomial long division is derived as simplified equivalent model as follows, 1 G p (s) = a n s n + a n−1 s n−1 + ⋯ + a 1 s In Equation (3), c i (i = 0,…, n-m) are coefficients of polynomial division result, and the G left (s) is a reminder, which can be signified by where, Equation (5) can be rewritten as Finally, we have, where, From Equation (3), it can be seen that It is seen from Equations (3) and (4) that, coefficients c i and d i are real. But it is hard to obtain the expressions of the other coefficients in Equations (2) and (3). For the development procedure of ADRC, D(s) is termed as the generalized disturbance and will be anticipated in time domain so that we do not actually need the exact expressions for the c i and d j . The high frequency gain (denoted as b) is still the ratio between the coefficients of the highest-order terms of the numerator and the denominator. The relative order n-m may be employed rather than using n order of the controller system and Equation (7) can be rewritten as: An ADRC-based LFC model is presented using the block diagram in Figure 2. Each area in an interconnected power system is composed of a turbine, a generator and a governor. The foremost function of ADRC is to reduce ACE to zero where the ACE is produced by the linear combination of frequency error multiplied by a bias factor B and tie-line deviation. ACE = BΔF + ΔP tie Single area power system receives combined signal from ADRC output and frequency error. These signals are processed through governor, turbine and generator, and finally turn out LFC outputs frequency and tie power flow deviations.

MODEL OF INTERCONNECTED POWER SYSTEM
The dynamic model of interconnected power system for ADRC-based LFC is shown in Figure 3. There are six areas which are considered as interconnected with each other through tie-lines. Among these six areas, three areas are considered as generation-rich as compared with their load whereas the other three areas are considered as load-rich. The load-rich areas are represented as three disturbance sources, and any change in load is treated as a disturbance. These disturbances are fed back to different generation-rich areas. Since the generators of an area respond coherently during disturbances, they are represented by an equivalent generator. The load disturbances are applied to each power plant block as input. The load change signal can be planned at the load buses by calculating the line power flow at those buses. Hence, this signal will be transmitted to the power plants. Tie-line reactance and the distance between the load-rich area and generation-rich area are the two variables for tie-line synchronizing coefficient (T). The design constraints of the system and ADRC parameters are listed in Appendix A, Tables A.1-A.4.
All generating stations (G 1 , G 2 and G 3 ) are deemed alike in Figure 3. The detail of power plant-1represented by 'A' is illustrated in Figure 4. Non-reheat turbine and reheat turbine are considered in generation-rich and load-rich areas, respectively, along with other equipments. Two quantities are taken as output from each load-rich area, ACE and frequency deviation. Frequency deviation is first integrated and then multiplied by tieline synchronizing coefficient to get the tie-line errors (∆P tie ). The complete demonstration of load-rich area is depicted in Figure 5.
Finally, a complete model of an interconnected power system is ready to compute the effect of ACE, frequency deviation and tie-line flow deviation if there is any load change.

FEEDBACK PATH SELECTION FOR LOAD FREQUENCY CONTROL
A system is said to be feedback if two or more dynamical systems are associated collectively such that each system FIGURE 3 Dynamic model of interconnected power system for ADRC-based LFC persuades the other and their dynamics are thus stalwartly attached. Tracking the fundamental response of a feedback system is difficult because the first system influences the second and the second system influences the first, leading to a circular argument.
In an interconnected power system, there are some generation-rich areas and some load-rich areas. Connection from load-rich area to generation-rich area of an interconnected power system for the purpose of load frequency control is termed as feedback path. Selecting the right feedback path is a difficult task due to complex interconnections among various areas.
In this paper, a comparative study is presented by considering three generation-rich areas and three load-rich areas (3G3L), load change of 0.1 p.u., simultaneous and individual, both, and all possible feedback paths from load-rich areas to generationrich areas.

Feedback path in power system
Loads of different areas may change, remain constant, or may change simultaneously or individually. Study should be done that whether the load change of all load centres should be considered, or individual load change should be considered for selecting the feedback paths. The tie-line synchronizing coefficient (T ij ) represents the distance between two areas (G i to L j ). The value of T ij increases with the decreasing distance between two areas.

Tie-line synchronizing coefficient
The sum of all outflowing line powers, P tie,ij, is equals to the total real power that goes out of a particular control area i, ΔP tie,i , in the lines connecting area i with neighbouring areas, i.e., The simulations are applied to all lines j that terminate in area i. If the line losses are neglected, the individual line power can be written as, where, x ij is the reactance of tie-line connecting areas i and j, V i and V j are the bus voltages of the line. If the phase angles deviate from their normal values 0 i and 0 j by the amounts of Δ i and Δ j , respectively, one gets the incremental power ΔP tie, i j over the line as given by, where, The phase angles are related to the area frequency changes by, From the above equations we get, where, The T ij is called the tie-line power coefficient or synchronizing coefficient (T). It is the ratio of power flow between two connected buses. Therefore, it determines the power deviations between areas of power system.

Individual load change
To investigate the effect of individual load change and feedback to a generation-rich area, a load change of 0.1 p.u. at t = 2 s is applied. How the individual load change can be applied from load-rich area-1 (L 1 ) to generation-rich area-1 (G 1 ) is shown in Figure 6. The output response of the LFC, peak amplitude of ACE, frequency error and tie-line power flow error, are taken from the generator of generation-rich area, and illustrated from Figures 7-9. The LFC responses for only three feedback paths (L 1 G 1 L 2 G 1 L 3 G 1 ) are depicted in these figures. The main target of LFC is to minimize the magnitude of ACE. ACE, frequency error and tie-line error are considered on the basis of highest amplitude. If the peak error magnitude is controlled, the other will be automatically controlled [13]. Hence, the lowest error magnitude is considered for choosing the right feedback path. Table 2 presents the LFC performance for individual load change and feedback to a single generator. For example, with individual load changes in L 1 , L 2 , and L 3 , respectively, and feedback to G 1, feedback path L 1 G 1 obtains the lowest ACE. Similarly, L 3 G 2 and L 1 G 3 obtain the lowest ACE for feedback to area G 2 and G 3 , respectively.
As a comparison has been performed between PID-based LFC and ADRC-based LFC in [21] where ADRC proves to be a capable of replacing the PID with numerous advantages in performing the load frequency control in a power system.

Simultaneous load change
Simulations are carried out to obtain the system response for simultaneous load change in all the load-rich areas. All possible feedback paths from load-rich area to generation-rich area are shown in Figure 10. The scenario of simultaneous load change can be figured as the feedback path L 1 G 1 L 2 G 2 L 3 G 3 in Figure 11. The effects of simultaneous load changes on ACE, frequency error and tie-line error of the power plant-1 are presented in Figures 12-14. A 0.1 p.u. load change is applied simultaneously from L 1 , L 2 and L 3 . Table 3 is completed considering all possible feedback paths. For a comprehensive understanding, the effects of load change on LFC are shown only for three feedback connections (L 1 G 1 L 2 G 2 L 3 G 3 , L 2 G 1 L 1 G 2 L 1 G 3 and L 3 G 1 L 1 G 2 L 1 G 3 ). However, all the figures' values are tabulated in Table 3. It is seen that the minimum ACE belongs to the feedback path L 1 G 1 L 3 G 2 and L 1 G 3 .
It is observed from Tables 2 and 3 that the lowest error magnitude of ACE is obtained from the feedback path L 1 G 1, L 3 G 2, and L 1 G 3 which are also the same as the individual load change feedback L 1 G 1 , L 3 G 2 and L 1 G 3 . From this observation, it can be concluded that the consideration of individual load change is enough for selecting the optimal feedback paths rather than considering the simultaneous load changes of all load centres.

COMPARATIVE ANALYSIS
In this section, the performance of ADRC-based LFC is compared with a PID-based LFC to demonstrate its effectiveness for reducing overshoot magnitude and period that eventually  increase the stability of a power system. A single area power system shown in Figure 5 is taken into account for the comparison purpose. In the control part of the Figure 5, the ADRC controller is replaced by a PID controller. The parameters of the PID controller is tuned after several iterations of trial and error process to obtain better results in response and the parameters are given in Table A.5. To provide a fair comparison, the parameters of PID, ADRC and single area power system are presented in Appendix A. A disturbance of 0.1 p.u. step load change at 0.2 s is applied in the network to determine the performance of the both controllers. The efficacy of the two control systems is depicted in Figure 15, where ACE, frequency deviation and time line power flow deviations are considered as measurements for the performance. It is observed that a remarkable lower error magnitude is obtained from the ADRC-based LFC than PID-based LFC. This is because of the characteristics of disturbance rejection of the ADRC that increases power system reliability and security. The proposed controller reduces the transient magnitude around 57% for ACE, 55% for frequency error and 72% for tie-line error as compared to the PID controller. It also demonstrates a faster recovery response than PID controller. Therefore, it can be concluded that the proposed controller has superior performance over the PID controller.

LIMITATIONS
The designed ADRC can guarantee the fast response of the ACE with small overshoot. However, during the process of simulating ADRC in a power system, the magnitude of the control effort shows a big peak value at the initial stage of the simulation and the time required to settle down the response is long. There is a scope to reduce the peak amplitude of response and quickly settle down the response by improving the ADRC controller as well as ESO. ADRC-based LFC of interconnected power system has been considered with non-reheat and reheat turbine only, but another commonly used turbine named hydraulic turbine has not been considered. Although the stability of the power system has not been analysed in this study, the power system is operating in a stable condition. This can be further investigated systematically using root locus and Nyquist stability analysis. In addition, economic aspects to select the several feedback paths are not considered in this study.

CONCLUSION
This paper develops the ADRC-based LFC for an interconnected power system to select the optimal feedback path for improving system stability and reliability. Feedback control is a powerful approach to obtaining systems in a stable condition and to meet desired performance, despite undergoing major disturbances and model uncertainties. Feedback connections from various load-rich areas to generation-rich areas in an interconnected power system are very important for its stability. Lower error magnitude for any feedback path is considered as evidence for the correct feedback connection between the generationrich area and load-rich area. For selecting the optimal feedback paths of an interconnected power system, only individual load change of all load-rich areas is sufficient rather than considering the simultaneous load change of all load-rich areas. In addition, the study demonstrates that ADRC based controller can reduce transient magnitude around 57% for ACE, 55% for frequency error and 72% for tie-line error as compared to the state of art PID controller.
In the future work, the stability analysis of the power system with the integration of renewable energy sources and hydraulic turbine unit will be conducted to further analyse the LFC of the interconnected power system.