THREE DEGREE OF FREEDOM FRACTIONAL CASCADE CONTROLLER

Abstract

The present invention discloses a Three Degree of Freedom Fractional Order Proportional Integral Derivative Filter controller (100a) cascaded with One plus Tilted Derivative controller (100b) for constituting a 3DOFFOPIDN-(1+TD) controller (100) for achieving automatic generation control in a smart grid system. The 3DOFFOPIDN-(1+TD) controller (100) utilizes three degrees of freedom to stabilize frequency and tie-line power fluctuations, when load disturbances and renewable energy source fluctuations occurs in the smart grid system. The three degree of freedom employs three independent feedback loops that satisfies high disturbance rejection ability and achieves set-point tracking and closed loop stability.

Specification

Description:FIELD OF THE INVENTION:
[0001] The present invention relates to a three degree of freedom fractional cascade controller for automatic generation control (AGC) in the smart grid system and a method for the AGC by implementing a quasi-opposition-based arithmetic optimization algorithm (QOAOA) method.

BACKGROUND OF THE INVENTION:
[0002] Smart grid is an electrical power distribution infrastructure which provides communication between utility providers (for instance electricity providers) and customers. Needless to say, smart grid systems deploy plethora of transformers, turbines, power transmission lines, generators, etc. for power distribution. Such conventional smart grid system suffers from one or more technical challenges which hamper the overall system.

[0003] Because of the abrupt variation in loading conditions, there exists a discrepancy between turbine mechanical power and generator electrical power, which leads to a significant disruption in system characteristics such as area frequency and tie-line power flow. Automatic generation control (AGC) is essential for regulating system output power and maintaining both frequency and tie-line power at their pre-set levels, especially when the system faces sudden load changes. However, efficient control scheme is necessary to accomplish reliable load frequency control operation. The AGC is started with conventional P (Proportional), PI (Proportional-Integral), PD (Proportional-Derivative) and PID (Proportional-Integral-Derivative) controller. In all the aforesaid controllers, a signal area controller error (ACE) is provided as input. The dynamic performance of the system and disturbance rejection characteristics is observed to be poor with all these aforesaid conventional controllers.

[0004] Renewable energy sources (RES) are integrated with the conventional smart grid system. However, high renewable energy penetration on the smart grid may lead to supply and demand mismatches, voltage fluctuations, and instability of the network. It, therefore, becomes essential to eliminate the intermittency of RES backup in the energy storage for enhancing of the overall smart grid performance and system dependability.

[0005] On the other hand, there are many state-of-the-art optimization algorithms for a controller to fine-tune the control parameters for bringing regulated output. Such controllers may be exploited in the conventional smart grid system for alleviating above mentioned deficiencies. However, the aforesaid algorithms suffer from local optimal trapping and poor computing efficiency.

[0006] The patent literature US5105138A describes a two degree of freedom PID controller which includes a set-point filter for performing a derivative operation on a process disturbance signal in accordance with a set-point value and a control value of a controlled system, to reduce the disturbance signal.

[0007] The patent literature US10843586B2 describes electric vehicles performing V2G regulation. Such system includes an aggregator that communicates with the electric vehicles according to a dispatch strategy to switch charging with electric power from the electric grid.

[0008] The non-patent literature by Singh et al. titled "Review on Soft Computing-Based Controllers for Frequency Regulation of Diverse Traditional, Hybrid, and Future Power Systems" discusses the use of soft computing-based controllers for frequency regulation in power systems.

[0009] The non-patent literature by Ansari et al. titled "Flow direction optimizer tuned robust FOPID-(1+TD) cascade controller for oscillation mitigation in multi-area renewable integrated hybrid power system with hybrid electrical energy storage" discusses about Flow Direction Algorithm (FDA) for load frequency control and FDA-tuned FOPID-(1+TD) cascade control strategy for a two-area system.

[0010] The non-patent literature by Choudhary et al. titled "FOPTID+1 controller with capacitive energy storage for AGC performance enrichment of multi-source electric power systems" discusses about global neighbourhood algorithm-optimized FOPTID+1 controller for a multi-source one and two-area multi-source power systems.

[0011] The non-patent literature by Xie et al. titled "CPSOGSA Optimization Algorithm Driven Cascaded 3DOF-FOPID-FOPI Controller for Load Frequency Control of DFIG-Containing Interconnected Power System" discusses about a cascaded fractional-order controller for an interconnected power system along with a particle swarm optimization and gravitational search algorithm under the chaotic map optimization technique.

[0012] The non-patent literature by Ranjan et al. titled "Improved frequency regulation in smart grid system integrating renewable sources and hybrid energy storage system" discusses about a quasi-opposition arithmetic optimization algorithm optimized fractional order proportional integral derivative with filter controller cascaded one plus tilted derivative controller to mitigate frequency and tie-line power variations in a multi-area restructured smart-grid system.

[0013] The non-patent literature by Ranjan et al. titled "Effect of Electric Vehicles and Renewable Sources on Frequency Regulation in Hybrid Power System Using QOAOA Optimized Type-2 Fuzzy Fractional Controller" discusses about a cascade combination of interval type-2 fuzzy and fractional order proportional-integral-derivative controllers along with a quasi-opposition arithmetic optimization algorithm for fine-tuning the controller's parameter.

[0014] The non-patent literature by Ranjan et al. titled "QOAOA based optimal controller for frequency regulation in smart grid system incorporating renewable sources and hybrid energy storage system" discusses about a quasi-opposition arithmetic optimization algorithm optimized cascade fractional order proportional integral derivative with filter controller with one plus tilted derivative controller to mitigate frequency and tie-line power variations in a multi-area restructured smart-grid system.

[0015] The non-patent literature by Ranjan et al. titled "A Cascade Fractional Type-II Fuzzy Control Approach for Enhancing Frequency Stability in a Smart Grid System with Diverse Energy Resources" discusses about a quasi-opposition arithmetic optimization algorithm optimized cascade interval type-II fuzzy proportional-integral-derivative fractional order PI controller for a two-area restructure smart grid system.

[0016] The non-patent literature by Ranjan et al. titled "Design and Analysis of Novel QOAOA Optimized Type-2 Fuzzy FOPIDN Controller for AGC of multiarea power system" discusses about an interval-type-2 fuzzy fractional-order proportional-integral-derivative with filter controller and a quasi-opposition arithmetic-optimization-algorithm for fine-tuning the controller's parameter.

[0017] Therefore, there is a need to design a novel controller that curbs irregularities, exhibits high disturbance rejection and enhanced stability (especially closed-loop stability) in the conventional smart grid system and where optimum set point can be achieved for yielding the desired output in the conventional smart grid system.

OBJECTS OF THE INVENTION:
[0018] It is the object of the present invention to provide a controller for satisfying high disturbance rejection ability and achieving set-point tracking and closed loop stability in a smart grid system.

[0019] Yet another object of the present invention is to implement three degree of freedom via three independent feedback loops to stabilize frequency and tie-line power fluctuations, when load disturbances and renewable energy source fluctuations occurs in the smart grid system.

[0020] Yet another object of the present invention is to compute optimal control, tuning and/or scaling parameters for the controller.

SUMMARY OF THE INVENTION:
[0021] According to an aspect, the present invention discloses a three degree of freedom fractional order proportional integral derivative filter controller cascaded with one plus tilted derivative controller (3DOFFOPIDN-(1+TD)) for a smart grid system. The 3DOFFOPIDN controller is configured for receiving inputs from three independent feedback loops, wherein the inputs are real-time reference input signal R(s) and real-time tie-bar power feedback signal Y(s) provided by a plurality of sensors and an external noise signal D(s). The 3DOFFOPIDN controller comprises of a first combiner configured for combining a weighted R(s) with an output from a third combiner. The weighted R(s) signal is obtained by combining R(s) with a gain, WP of a proportional controller. Further, the 3DOFFOPIDN controller comprises of a second combiner configured for combining R(s) with an output from a fourth combiner. The third combiner is configured for combining Y(s) with a weighted D(s) signal. The weighted D(s) signal is obtained by combining D(s) with a weight, Gff. The fourth combiner is configured for combining another weighted D(s) signal with the output of the second combiner. The other weighted D(s) signal is obtained by combining D(s) with a gain, WD of a derivative controller. A first summing device is configured for summing the outputs from the first combiner combined with proportional gain kp, the second combiner combined with integral gain ki and the fourth combiner combined with differential gain kd for producing a first control signal, U1(s) of the 3DOFFOPIDN controller. Further, the 1+TD controller is configured for receiving the first control signal, U1(s) and comprises a tilted-integral-derivative controller and a second summing device. The tilted-integral-derivative controller combines the first control signal, U1(s) with a tilted gain, kt of a tilted controller having a tilt parameter, c and a derivative gain, kd of a derivative controller. A second summing device is configured for summing the first control signal, U1(s) with the output of the tilted-derivative controller for producing a control signal, U(s). The control signal, U(s) is a signal for providing an automatic generation control in the smart grid system. Further, the present 3DOFFOPIDN-(1+TD) controller suppresses disturbance and noise and enhances the closed loop stability of the smart grid system.

[0022] According to an aspect, the derivative controller of the 1+TD controller is cascaded with a feedback loop. The feedback loop comprises of a derivative filter with coefficient, Nf in a feed forward path and a first order integrator in a feedback path.

[0023] According to an aspect, the derivative controller of the 3DOFFOPIDN controller is cascaded with a feedback loop. The feedback loop comprises of a derivative filter with coefficient, N1 in a feed forward path and a first order integrator in a feedback path.

[0024] Yet according to an another aspect, the control signal configured to provide an automatic generation control in the smart grid system has a closed-loop transfer function defined by:
U(s) = (1 + (Kt/s1/c) + ((Nf*KD*s)/(s+Nf)))*U1(s)
wherein Nf represents derivative filter coefficient, Kt and KD represents tilted and derivative gain respectively, c is a tilted angle and wherein U1(s) is given by:
U1(s) = (Wp*kp + (ki/sb) + (WD*kd*N1*s/(s+N1)))*R(s) - (kp + (ki/sb) + ((kd* N1*s)/(s+N1)))*Y(s) - (Gff*kp + Gff*(ki/sb) + Gff*kd*N1*s/(s+N1))*D(s)
wherein WP and WD represents set-points of proportional and derivative controllers respectively, Gff represents weight value to normalize D(s), kp, ki and kd represents proportional-integral-derivative controller gain respectively, b represents fractional coefficient of integral gain and N1 represents derivative filter coefficient.

[0025] Yet according to an another aspect, the present invention discloses a modified Quasi Opposition-based Arithmetic Optimization Algorithm (QOAOA) which includes a Quasi-Opposition Based Learning (QOBL) to derive the control parameters of the present 3DOFFOPIDN-(1+TD) controller.

BRIEF DESCRIPTION OF THE DRAWINGS:
[0026] Figure 1 illustrates a block diagram of the 3DOFFOPIDN-(1+TD) controller of the present invention.

[0027] Figure 2 illustrates a flow chart depicting a method of modified QOAOA algorithm for the 3DOFFOPIDN-(1+TD) controller of the present invention.

[0028] Figure 3 depicts a schematic diagram of a modified Kundur's two area system for real-time testing of the 3DOFFOPIDN-(1+TD) controller.

[0029] Figure 4 illustrates a dynamic response in terms of (a) change in frequency of area-1 (b) change in frequency of area-2 (c) change in tie-line power exchange of the various conventional controllers (like PI, PIDN, 1+TD, FOPIDN-(1+TD), 2DOFFOPIDN-(1+TD)) and the present 3DOFFOPIDN-(1+TD) controller for step load perturbation.

[0030] Figure 5 illustrates a relative dynamic response of various conventional controllers (like PI, PIDN, 1+TD, FOPIDN-(1+TD), 2DOFFOPIDN-(1+TD)) and the present 3DOFFOPIDN-(1+TD) controller for random load perturbation.

[0031] Figure 6 illustrates a schematic diagram of a modified IEEE-39 bus system for real-time testing of the present 3DOFFOPIDN-(1+TD) controller.

[0032] Figure 7 illustrates a dynamic response of the modified IEEE-39 bus system in terms of deviation in (a) frequency of area-1 (b) frequency of area-2 (c) frequency of area-3 (d) tie-line power exchange between areas 1 & 2 of the present 3DOFFOPIDN-(1+TD) controller with respect to without controller.

[0033] Figure 8 illustrates waveform of (a) Solar Power Output (b) Wind Power Output (c) Random load pattern (d) Charging and discharging of Electric Vehicles when 3DOFFOPIDN-(1+TD) controller are deployed in modified IEEE-39 bus system.

[0034] Figure 9 depicts an illustration showing a Hardware-In-the-Loop (HIL) test for testing the present 3DOFFOPIDN-(1+TD) controller in real-time.

[0035] Figure 10 illustrates a response for frequency deviation in Area-1, Area-2 and Area-3 and tie-line power error in Area-1 and Area-2 of the modified IEEE-39 bus test system while testing the present 3DOFFOPIDN-(1+TD) controller in real-time using OPAL-RT Hardware.

[0036] Figure 11 illustrates response for solar power output, wind power output, thermal power output and random load in Area-1, Area-2 and Area-3 of the modified IEEE-39 bus test system while testing the present 3DOFFOPIDN-(1+TD) controller in real-time.

DETAILED DESCRIPTION OF THE INVENTION:
[0037] The present invention discloses a Three Degree of Freedom Fractional Order Proportional Integral Derivative Filter controller cascaded with One plus Tilted Derivative (3DOFFOPIDN-(1+TD)) controller for an automatic generation control (AGC) in the smart grid system. The 3DOFFOPIDN-(1+TD) controller of the present invention addresses the difficulties of AGC design in the smart grids with nonlinearities. The 3DOFFOPIDN-(1+TD) controller of the present invention utilizes three degrees of freedom to stabilize frequency and tie-line power fluctuations, when load disturbances and renewable energy source fluctuations occurs in the smart grid system. The three degree of freedom (3DOF) employs three independent feedback loops that satisfies high disturbance rejection ability and achieves set-point tracking and closed loop stability.

[0038] The present invention achieves 3DOF over conventional two-degree of freedom (2DOF) controllers. Traditional 2DOF controllers deploy two individual loops for controlling action which brings less closed-loop stability as well as the output response and disturbance response are handled individually. By adding an extra feedback loop, the present 3DOF controller may be incorporated with additional tuning parameters, providing more control over the system's response. This allows for better placement of poles and zeros in the system's transfer function, which can increase stability margins. The extra feedback loop also allows the system to be more robust to model uncertainties and parameter variations, which are often factors that challenge stability.

[0039] Further, the load disturbance has no impact on the controlling action which further brings poor regulation in the conventional control systems. On the contrary, 3DOF considers the change in load demand (or load disturbance) as input for the controlling action and deploys an extra independent feedback loop for curbing disturbances and enhancing closed-loop stability.

[0040] As mentioned above, the degree of freedom in a control system is defined as the number of control variables that can be adjusted independently. The purpose of the present 3DOFFOPIDN-(1+TD) controller is to reject high disturbances, considering the dynamic response as well as close loop stability.

[0041] Further, the cascade combination of fractional order controller and tilted ordered controllers is preferred in the present invention over traditional controllers as the cascaded controller enhances disturbance rejection, accurately manipulates energy or mass, rejects load disturbance, compensates for uncertainties (or non-linearity), and tracks set-points. Set points are the desired value/ target that the system or process is intended to reach and maintain with the help of the present controller. Such set-point, for instance, may be achieving desired frequency, power, etc.

[0042] According to an embodiment, the present invention discloses a three degree of freedom fractional order proportional integral derivative filter controller cascaded with one plus tilted derivative controller (3DOFFOPIDN-(1+TD)) for a smart grid system. The 3DOFFOPIDN controller is configured for receiving inputs from three independent feedback loops, wherein the inputs are real-time reference input signal R(s) and real-time tie-bar power feedback signal Y(s) provided by a plurality of sensors and an external noise signal D(s). The 3DOFFOPIDN controller comprises of a first combiner configured for combining a weighted R(s) with an output from a third combiner. The weighted R(s) signal is obtained by combining R(s) with a gain, WP of a proportional controller. Further, the 3DOFFOPIDN controller comprises of a second combiner configured for combining R(s) with an output from a fourth combiner. The third combiner is configured for combining Y(s) with a weighted D(s) signal. The weighted D(s) signal is obtained by combining D(s) with a weight, Gff. The fourth combiner is configured for combining another weighted D(s) signal with the output of the second combiner. The other weighted D(s) signal is obtained by combining D(s) with a gain, WD of a derivative controller. A first summing device is configured for summing the outputs from the first combiner combined with proportional gain kp, the second combiner combined with integral gain ki and the fourth combiner combined with differential gain kd for producing a first control signal, U1(s) of the 3DOFFOPIDN controller. Further, the 1+TD controller is configured for receiving the first control signal, U1(s) and comprises a tilted- integral-derivative controller and a second summing device. The tilted-integral-derivative controller combines the first control signal, U1(s) with a tilted gain, kt of a tilted controller having a tilt parameter, c and a derivative gain, kd of a derivative controller. A second summing device is configured for summing the first control signal, U1(s) with the output of the tilted-derivative controller for producing a control signal, U(s). The control signal, U(s) is a signal for providing an automatic generation control in the smart grid system. Further, the present 3DOFFOPIDN-(1+TD) controller suppresses disturbance and noise and enhances the closed loop stability of the smart grid system.

[0043] According to an embodiment, the derivative controller of the 1+TD controller is cascaded with a feedback loop. The feedback loop comprises of a derivative filter with coefficient, Nf in a feed forward path and a first order integrator in a feedback path.

[0044] According to an embodiment, the derivative controller of the 3DOFFOPIDN controller is cascaded with a feedback loop. The feedback loop comprises of a derivative filter with coefficient, N1 in a feed forward path and a first order integrator in a feedback path.

[0045] Yet according to an another embodiment, the control signal configured to provide an automatic generation control in the smart grid system has a closed-loop transfer function defined by:
U(s) = (1 + (Kt/s1/c) + ((Nf*KD*s)/(s+Nf)))*U1(s)
wherein Nf represents derivative filter coefficient, Kt and KD represents tilted and derivative gain respectively, c is a tilted angle and wherein U1(s) is given by:
U1(s) = (Wp*kp + (ki/sb) + (WD*kd*N1*s/(s+N1)))*R(s) - (kp + (ki/sb) + ((kd* N1*s)/(s+N1)))*Y(s) - (Gff*kp + Gff*(ki/sb) + Gff*kd*N1*s/(s+N1))*D(s)
wherein WP and WD represents set-points of proportional and derivative controllers respectively, Gff represents weight value to normalize D(s), kp, ki and kd represents proportional-integral-derivative controller gain respectively, b represents fractional coefficient of integral gain and N1 represents derivative filter coefficient.

[0046] Yet according to an another embodiment, the present invention discloses a modified Quasi Opposition-based Arithmetic Optimization Algorithm (QOAOA) which includes a Quasi-Opposition Based Learning (QOBL) to derive the control parameters of the present 3DOFFOPIDN-(1+TD) controller.

[0047] The present invention may be envisaged by referring to figures appended at the end of the specification. The figures show various embodiments of the present invention, including the preferred embodiment. However, the figures are not intended to restrict the scope of the invention. Any variations in the drawings therein may fall within the scope of the present invention.

[0048] Figure 1 illustrates a block diagram of 3DOFFOPIDN-(1+TD) controller (100) according to the present invention. The 3DOFFOPIDN-(1+TD) controller (100) comprises of a 3DOFFOPIDN controller (100a) connected in cascade with a (1+TD) controller (100b).

[0049] The 3DOFFOPIDN controller (100a) comprises of a first combiner (102), a second combiner (104), a third combiner (106) and a fourth combiner (108) along with a first summing device (110) and a second summing device (112) along with a plurality of controllers such as a proportional controller with a proportional gain (kp), an integral controller with an integral gain (ki), and a derivative controller with a derivative gain (kd) and derivative filter having coefficient, N1. Further, the 3DOFFOPIDN controller (100a) also comprises an integrator of first order (shown with Laplace Transform block of 1/s) and bth order (shown with Laplace Transform block of 1/sb).

[0050] The summing devices (110, 112, 114) are adapted to add two or more signals whereas the combiners (102, 104, 106, 108) are adapted to add and/or subtract two or more signals as per the sign convention designated on the aforesaid combiners.

[0051] The inputs from three independent feedback loops are provided to the 3DOFFOPIDN controller (100a). The aforesaid inputs are R(s) which represents a reference input, Y(s) which represents a tie-bar power feedback signal, and D(s) which represents an external noise signal. The reference input, R(s) may be the real-time signal carrying fluctuation from the renewable energy source, load demand from sources (like state load dispatch centres), etc. which is provided to the 3DOFFOPIDN-(1+TD) controller (100). Further, the tie-bar power feedback signal, Y(s) may be the signal outputted from sensors (not shown in Figure 1 for the sake of simplicity) which provides input signals to the 3DOFFOPIDN-(1+TD) (100) for regulating the output frequency and tie-line power of interconnected power systems. Such aforesaid sensors for collecting real-time signals may be frequency sensors, load sensors, tie-line power sensors and the like.

[0052] The first combiner (102) is configured to combine weighted R(s) signal with an output from the third combiner (106). The weighted R(s) signal is the reference input R(s) multiplied with the weight (or gain) of a proportional controller, Wp. The second combiner (104) is configured to combine R(s) with an output from the fourth combiner (108). The third combiner (106) is configured to combine Y(s) with a weighted D(s) signal. The weighted D(s) signal is the external noise signal, D(s) multiplied with the weight (or weight factor) Gff. The fourth combiner (108) is configured to combine another weighted D(s) signal with the output of the second combiner (104). The other weighted D(s) signal is the external noise signal, D(s) multiplied with the weight (or gain) of a derivative controller, WD.

[0053] The output from the first combiner (102) is further subjected to a proportional controller with a proportional gain, kp. The output from the second combiner (104) is further subjected to an integral controller with an integral gain, ki followed with a bth order integrator (shown with Laplace Transform block of 1/sb). The output from the fourth combiner (108) is further subjected to a derivative controller with derivative gain, kd followed with a feedback loop. The feedback loop comprises of a derivative filter with a derivative gain coefficient, N1 in the forward path and an integrator of first order in the feedback path.

[0054] The outputs from the proportional controller (kp), integrator controller (ki) and derivative controller (kd) are summed or combined by a first summing device (110) to generate an intermediate control signal, U1(s).

[0055] The transfer function of the intermediate control signal, U1(s) is given by:
U1(s) = (Wp*kp + (ki/sb) + (WD*kd*N1*s/(s+N1)))*R(s) - (kp + (ki/sb) + ((kd* N1*s)/(s+N1)))*Y(s) - (Gff*kp + Gff*(ki/sb) + Gff*kd*N1*s/(s+N1))*D(s) (1)

wherein WP and WD represents set-points of proportional and derivative controllers respectively, Gff represents weight value to normalize D(s), kp, ki and kd represents proportional-integral-derivative controller gain respectively, b represents fractional coefficient of integral gain and N1 represents derivative filter coefficient.

[0056] The output from the first summing device (110), U1(s) is fed to a third summing device (114). Further, the output from the first summing device (110), U1(s) is also fed to a tilted-integral-derivative controller which comprises of a tilted controller and a derivative controller. The tilted controller has a tilt gain Kt connected in cascade with an integrator of cth order (shown with Laplace Transform block of 1/sc). Further, the derivative controller has a derivative gain KD connected in cascade with a feedback loop. The feedback loop comprises of a derivative filter with a derivative gain coefficient, Nf in the forward path and an integrator of first order in the feedback path. The output from the first summing device (110), U1(s) and output from the tilted-integral-derivative controller are summed or combined by the third summing device (114) to obtain a final control signal, U(s).

[0057] The transfer function of the final control signal, U (s) is given by:
U(s) = (1 + (Kt/s1/c) + ((Nf*KD*s)/(s+Nf)))*U1(s) (2)
wherein Nf represents derivative filter coefficient, Kt and KD represents tilted and derivative gain respectively and c is a tilted angle.

[0058] The transfer function may be determined by any computing, controlling and/or processing devices such as processors, controllers, etc. by accessing the control parameters as mentioned in the subsequent paragraphs. The transfer function may also be determined by the computing, controlling and/or processing devices by analysing the input-output data or the input-output relationship for the present controller to determine a mathematical model (or the transfer function).

[0059] The components of the 3DOFFOPIDN-(1+TD) controller (100) like (proportional controller, integrator, derivative with filter, fractional controller, tilted controller, etc.) work together to provide enhanced control performance, robustness, and stability, while handling nonlinearities and uncertainties of the power system and providing a faster response and improved accuracy in regulating the frequency and tie-line power of the interconnected power systems.

[0060] The control signal generated by the 3DOFFOPIDN-(1+TD) controller, U(s) is utilized for required AGC operation and for achieving closed loop control. Alternatively, the control signal, U(s) may also be supplied to a plant for achieving aforesaid operation and closed loop control.

[0061] The values of control parameters like kp, kd, ki, b, Kt, KD, c, N1, Nf, WD, Gff and WP lies in the range of kp,min≤ kp≤ kp,max; ki,min≤ ki≤ ki,max; kd,min≤ kd≤ kd,max; b,min≤b ≤ b,max; Kt,min≤ Kt≤ Kt,max; KD,min≤ KD≤ KD,max; c,min≤ c ≤ c,max; N1,min≤ N1≤ N1,max; Nf,min≤ Nf≤ Nf,max.; WD,min≤WD≤ WD,max, Gff,min≤ Gff ≤ Gff,max and WP,min≤ WP≤WP,max. Such control parameters may be construed as the settings/ values that define how the present controller operates to achieve and maintain the set-point.

[0062] Preferably, the values of the control parameters like kp, kd, ki, b, Kt, KD, c, N1, Nf, WD, Gff and WP lies in the range of -1≤ kp≤ 2; -1≤ ki≤ 2; -1≤ kd≤2; 0≤ b≤ 2; -1≤ Kt≤ 2; -1≤ KD≤ 2; 0≤c≤2; 0≤ N1≤400; 0≤ Nf≤ 400; 0≤WD≤2; 0≤Gff ≤2 and 0≤ WP≤ 2 for enhancing the reliability of the system and for obtaining better parameter optimization.

[0063] For better transient response and stability, proper tuning and optimization process of proposed controller is needed. During the optimization process, different kinds of gains are evaluated in different ranges by which the controller acquires optimum values, and subsequently an improved response is achieved. By proper selection of range of control parameters, transient response and closed loop stability may be improved.

[0064] In an alternate embodiment, though inputs from three independent feedback loops are provided to the present 3DOFFOPIDN-(1+TD) controller (for the sake of brevity), it may also be appreciated that inputs from more than three independent feedback loops (or more extra feedback loops) may also be provided to the present controller for exhibiting increased closed-loop stability and reduced external disturbances through the closed-loop response.

[0065] Figure 2 illustrates a flow chart depicting a modified QOAOA algorithm for computing optimal control parameters for the 3DOFFOPIDN-(1+TD) controller of the present invention.

[0066] Conventional metaheuristic techniques Arithmetic-Optimization Algorithm (AOA) rely on random initialization of parameters and proceeds in search of optimal solution which deviates from the optimal or best solution. Despite the fact that meta-heuristic optimization works quite well among some common techniques, there is a chance of getting stuck at the regional optimum result. To avoid such problem and improve the convergence speed, the popularly known AOA algorithm is further enhanced in the present invention.

[0067] A quasi opposition based learning (QOBL) technique is integrated to the AOA algorithm in modified QOAOA algorithm to provide enhanced control performance, robustness and stability while handling nonlinearities and uncertainties of the power system and providing a faster response and improved accuracy in regulating the frequency and tie-line power of the interconnected power systems. Alternatively, the modified QOAOA is devised to tune the scaling factor of the present 3DOFFOPIDN-(1+TD) controller. The modified QOAOA optimization technique provides high computation speed and global optimal solution.

[0068] The QOAOA algorithm involves generation of opposite as well as quasi-opposite values of initial population as contrast to only opposite values in case of mere opposition based learning. Such values are integrated to filter out the solutions, moving away from the optimal solution at the initial stage. Thereby, the computation speed and chances of not being stuck in the local optimal stage are improved. The various steps involved in QOBL are depicted in the flowchart of Figure 2 and explained as follows:

[0069] Step 1: The AOA and QOAOA parameters are initialized. The AOA and QOAOA parameters are parameters like α and μ. α is a sensitive parameter and defines the exploitation accuracy over the iterations, which is fixed equal to 5. µ is a control parameter to adjust the search process, which is fixed equal to 0.5.

[0070] Step 2: Candidate solution(s) are initialized. Generally, the candidate solutions are generated randomly for beginning the optimization process and the best candidate solution in each iteration is considered as the best-obtained solution or nearly the optimum solution.

[0071] Step 3: Quasi-opposite solution(s) are generated.

[0072] Step 4: A determination is made whether C_iter is lesser or greater than M_iter, where C_iter denotes the current iteration, which is between 1 and the maximum number of iterations, M_iter.

[0073] Step 5: If C_iter is lesser than M_iter, then the method proceeds to compute fitness values of 2n solution from which best n solution is determined else returns the best n solution. The fitness value is computed from the fitness function (FITSE) as provided in equation 8.

[0074] Step 6: The best n solutions are determined.

[0075] Step 7: The Math Optimizer Accelerated (MOA) and Math Optimizer Probability (MOP) parameters are updated.

[0076] The MOA and MOP function is a crucial parameter for controlling the search mode (Exploration and Exploitation) selection in AOA. By incorporating hyperbolic tangent fluctuation into the variation trend of MOA, the exploration ability of the modified QOAOA algorithm is enhanced.

[0077] Step 8: The method continues to Step 8 where p1 is compared with the MOA parameter. If p1 is greater than MOA parameter, then the value for p2 is checked else the value for p3 is checked.

[0078] Step 9: If p2 is greater than 0.5, then division operation is implemented on the parameters. Else, multiplication operation is implemented on the parameters if p2 is less than 0.5.

[0079] Step 10: If p3 is greater than 0.5, then subtraction operation is implemented on the parameters. Else, addition operation is implemented on the parameters if p3 is less than 0.5.

[0080] Step 11: The value of variable is incremented i.e., C_Iter = C_Iter +1 and the control moves back to step 4 for reiterating the steps 5 to 10 for determining the optimal (or best solution) for the control parameter(s) for the 3DOFFOPIDN-(1+TD) controller of the present invention.

[0081] Step 12: If C_iter is greater than M_iter, then the method proceeds to compute the fitness values of 2n solution without executing steps 5-10.

[0082] Step 13: The best n solutions are then returned or determined.

Generation of opposite-point:
[0083] If X(X1, X2, X3……..Xn) is a point in n-dimensional exploration-space such as X belongs to R (Real) domain. Then, the search space center for X is given by:
Mj = (Ubj + Lbj) / 2 (3)

[0084] The production of the opposing point, Xo is given by:
Xoj = [Ubj + Lbj - Xj]1*n, where j is any natural number from 1 to n (4)

Generation of Quasi-opposite point:
[0085] The quasi-opposite point Xqo for n-dimensional search is given by:
Xqoj = rand (Mj, Xoj), where j is any natural number from 1 to n (5)

Updating of Xj:
[0086] By concatenating opposite and quasi-opposition values into a single vector, the search space is updated.
Xj = [Xoj ; Xqoj]1x2n (6)

[0087] The pseudo-logic for computing the quasi-opposition points is as follows:
Mj = (Ubj + Lbj) / 2
If (Xoj< Mj)
Xqoj = Mj + (Xoj - Mj)*p1 % p1 belongs to [0, 1]
Else
Xqoj = Xoj + (Mj - Xoj)*p1
End if-else loop

[0088] The modified QOAOA algorithm may be executed by an external hardware connected externally to the 3DOFFOPIDN-(1+TD) controller for computing the optimal control, tuning and/or scaling parameters. The external hardware may be a processor such as a dedicated control optimization module or central processing unit (not shown in the figures). In an alternate embodiment, the modified QOAOA algorithm may also be executed by a unit of the present 3DOFFOPIDN-(1+TD) controller for computing the optimal control, tuning and/or scaling parameters.

[0089] The present 3DOFFPIDN-(1+TD) controller continuously updates its control parameters based on feedback as the control system operates in real time. Thus, the present 3DOFFPIDN-(1+TD) controller may be self-adaptive in nature allowing it to perform well under varying conditions. The feedback may be based on the observed performance, deviations from set points, and/or noise levels.

[0090] The present 3DOF controller utilizes the output of the algorithm (i.e., the optimized parameter) to perform its control functions.

Implementation of the present 3DOFFOPIDN-(1+TD) controller on various test systems for AGC performance analysis:

[0091] The AGC performance analysis of the 3DOFFOPIDN-(1+TD) controller of the present invention is verified in MATLAB platform by deploying on the modified Kundur's two area system and on the modified IEEE-39 bus test systems.

[0092] The same AGC performance analysis is also verified for compatibility in the real-time scenario. For such analysis, real-time load, solar PV, and wind data are considered in modified IEEE 39 bus test system. The proposed system is sampled at a rate of 100 microseconds during the real-time study. Real-time analysis was conducted on OPAL-RT's OP4510 platform to verify the viability and efficacy of the present controller. It is observed that the present controller is effective for load frequency control (LFC) mechanism.

Implementation of the present 3DOFFOPIDN-(1+TD) controller on modified Kundur's two area system:
[0093] To estimate the effectiveness of the present controller, a comparative analysis was conducted using Mathwork's Matlab and Simulink Toolbox Release 2021b software for the AGC mechanism of a modified Kundur's two-area power system. The rating of each area is considered as 2000 MW. The schematic diagram of the system is as shown in Figure 3. An area control error (ACE) is derived from the system as function of change in tie-line power and the frequency.
ACEi = βi Δfi + Ʃ ΔPtie,ij from limit j=1 to N, where j is not equal to i (7)

[0094] Where i represents the area number, Δf represents the frequency deviation within area i and ΔPtie,ij represents the difference in tie-line power between area i and area j. The ACE is provided as the reference-signal R(s) to the present controller whereas change in frequency mixed with noise signal is supplied as second input to the present controller (combined D(s) + Y(s) signal).

[0095] The generation rate constraint (GRC) and governor dead band (GDB) were set to 3% per minute and 0.0006 pu, respectively and non-linearities were incorporated to enhance the practicality and realism of the present controller. The controller gain settings were limited to a range of -1 to 2 for integer gains (kp, ki, kd, kt, and KD), 0-2 for FO integrator (a) and tilt parameter (b), and 0-400 for the derivative filter (N1 and Nf). In order to compare the present controller with other conventional controllers, the coefficients of each controller are adjusted using the QOAOA techniques. One of the initial steps is to determine the objective function. The integral time of the squared error (ITSE) is utilized in the present study to evaluate controller performance and is expressed as a constrained optimization problem (fitness function) as follows:

FITSE = ∫ ((sum of squares of Δf1, Δf2 and ΔPtie, 12)*t) from limit 0 to tsim over time (8)

[0096] The QOAOA method is utilized to optimize the PI, PIDN, FOPIDN, 1+TD, FOPIDN-(1+TD), 2DOFFOPIDN-(1+TD) and present cascade 3DOFFOPIDN-(1+TD) controllers for optimal tuning.

[0097] The response of the system is analyzed when subjected to step-load perturbations of 1% or 0.01pu. Such change in demand is considered to be known to the user and given as third input to the controller. The control signal generated from the controller is given to the generation system to mitigate the mismatch between load and supply. Figure 4 depicts the system's dynamic behavior as determined by the various controllers i.e., PI, PIDN, 1+TD, FOPIDN-(1+TD), 2DOFFOPIDN-(1+TD) and present 3DOFFOPIDN-(1+TD) controller for step load perturbation. From the frequency response curve PI, PIDN and (1+TD) have oscillatory response, which is not acceptable. In comparison to PI, PIDN and (1+TD) controllers, the FOPIDN-(1+TD), 2DOFFOPIDN-(1+TD) controller's response seems to be consistent but shows increased undershoot and settling time when compared to the present 3DOFFOPIDN-(1+TD) controller. Table 1 illustrates that the present 3DOFFOPIDN-(1+TD) controller surpasses the aforesaid controllers which are measured by transient and steady-state dynamics. Table 2 shows the optimal tuned value of controller parameters obtained using QOAOA for different controllers. The improvement in performance of present 3DOFFOPIDN-(1+TD) controller indicated by maximum variation in frequency (Δf1, Δf2) and power change on the tie-lines (ΔPtie,12) over 2DOFFOPIDN-(1+TD) controller is (80.26%,81.85%) and 33.97% respectively.

Table 1: Comparative of the dynamic performance of various controllers for step load
Maximum Deviation Δf1 Δf2 ΔPtie12
3DOFFOPIDN-(1+TD) -0.0091 -0.0051 -0.0044
2DOFFOPIDN-(1+TD) -0.04612 -0.0281 -0.00677
FOPIDN-(1+TD) -0.09812 -0.0432 -0.0114
1+TD -0.1791 -0.1132 -0.0265
PIDN -0.1812 -0.1161 -0.0269
PI -0.3449 -0.3649 -0.0674
% improvement of suggested controller w.r.t FOPIDN-(1+TD) 90.72 88.194 61.40
% improvement of suggested controller w.r.t 2DOFFOPIDN-(1+TD) 80.26 81.85 33.97

Table 2: Best gain parameters of different controllers acquired by modified QOAOA for step load
Controllers Gains Area 1 Area 2
3DOFFOPIDN-(1+TD) kp 1.9298 1.9896
ki 1.9298 1.9896
kd 1.999 0.1043
Kt 1.973 -0.3902
KD 0.664 -0.9793
b 0.3306 0.0026
c 1.4127 1.9346
N1 384.83 197.91
Nf 384.83 8.712
Wp 0.001 0.0258
WD 0.1922 1.978
Gff 1.998 1.9792
PI kp -0.0951 1.998
ki 0.5318 -0.1310
1+TD Kt 1.987 1.994
KD 1.946 1.894
c 1.212 2.538
Nf 389.32 268.39
PIDN kp 1.9566 1.996
ki 1.994 0.0637
kd 1.956 1.838
N1 163.84 178.21
FOPIDN-(1+TD) kp 1.994 1.998
ki 1.984 0.3896
kd 0.200 -0.0230
Kt 1.989 -0.0217
KD 1.994 1.560
b 0.907 0.404
c 1.984 1.993
N1 400 186
Nf 382.57 400
2DOFFOPIDN-(1+TD) kp -0.1454 0.2813
ki -0.1231 0.0295
kd -0.2385 0.44773
Kt 1.9679 0.0062
KD -0.2609 0.00345
b 1.00 0.0787
c 1.9659 1.0553
N1 198.43 193.369
Nf 249.34 198.43
K1 1.9772 0.0218
K2 1.9375 0.1643

[0098] The same system under test was subjected to a random load variation as depicted in Figure 5 (c) and verified the behaviour of the system with all considered controllers. Figure 5 depicts the system's dynamic behaviour as determined by the various state-of-the art controllers i.e., PI, PIDN, 1+TD, FOPIDN-(1+TD), 2DOFFOPIDN-(1+TD) and present 3DOFFOPIDN-(1+TD) controller for random load perturbation. The frequency response curve depicted in Figure 5 demonstrates that the present 3DOFFOPIDN-(1+TD) controller surpasses the performance of the other tested control methods for the investigated system.

[0099] Table 3 illustrates that the present 3DOFFOPIDN-(1+TD) controller surpasses the above-mentioned controller measured by transient and steady-state dynamics. For unsystematic load, the improvement in performance of present 3DOFFOPIDN-(1+TD) controller indicated by maximum variation in frequency (Δf1, Δf2) over conventional 2DOFFOPIDN-(1+TD) controller is (10.7, 18.73%).

Table 3: Comparative of the dynamic performance of various controllers for random load
Maximum Deviation (10-3) Δf1 Δf2
3DOFFOPIDN-(1+TD) -0.0240 -0.0412
2DOFFOPIDN-(1+TD) -0.0269 -0.0507
FOPIDN-(1+TD) -0.0491 -0.0598
1+TD -0.0521 -0.0625
PIDN -0.0583 -0.9479
PI -0.1428 -0.109
% improvement of suggested controller w.r.t FOPIDN-(1+TD) 51.12 31.12
% improvement of suggested controller w.r.t
2DOFFOPIDN-(1+TD) 10.7 18.73

Implementation of the present 3DOFFOPIDN-(1+TD) controller on modified IEEE 39 bus system:
[0100] The present controller is verified for real-time changes in load demand and the intermittent nature of renewable energy sources using data collected from BSES Rajdhani Power Limited (BRPL), Delhi.

[0101] The modified IEEE-39 bus system is used as a benchmark model and as a test system for investigating the performance of the present controller. The modified IEEE-39 bus system typically includes generators, loads, transformers, and other components like renewable energy sources that represent a realistic power system.

[0102] The modified IEEE-39 bus system is divided into three control areas as shown in the Figure 6. The dynamic response of the system with and without controller's regulation, illustrated in Figure 7 shows the compatibility of invention for IEEE 39 bus test systems. Plug-in Electric Vehicles (PEV) is connected in each area of IEEE 39 bus system to reduce the undesirable transient conditions on load frequency and power-sharing. PEV absorbs excess electricity and discharge it back into the grid as needed, making them useful in supporting the grid with significant RES integration. Figure 8 shows the renewable energy source generation output, random load and charging and discharging of electric vehicles when the present controller is deployed in the modified IEEE-39 bus system.

[0103] The same performance analysis for the present controller system was verified for compatibility in real time scenario. For such analysis, real-time load, solar PV, and wind data are considered in modified IEEE 39 bus test system. The present system is sampled at a rate of 100 microseconds during the real-time study. Real-time analysis was done utilising the OPAL-RT OP4510 platform to verify the viability and efficacy of the present controller. Figure 9 depicts the systematic procedure for carrying out Hardware-In-the-Loop (HIL) tests using OPAL-RT's OP4510 platform. Utilizing a HIL simulator is crucial to ensure the accuracy and robustness of the present controller within the real-world context of the investigated system. For analysis purpose, the system along with the present controller is designed in RT-lab and simulated using OPAL-RT's OP4510 platform. The real-time dynamic response of the investigated system (Modified IEEE 39 bus) is presented in Figure 10 and the generated power in Figure 11 when the present controller is deployed. The dynamic results obtained using OPAL-RT's OP4510 platform confirms the suitability of the suggested control strategy for the investigated system.

[0104] The present 3DOFFOPIDN-(1+TD) controller provides several technical benefits which are not provided by the conventional methods of AGC. Said technical benefits are enlisted below:

[0105] Extra independent loops assure increased closed-loop stability of the controller and reduced external disturbances through the closed-loop response.

[0106] The present controller employs cascade combination of fractional order controller and tilted ordered controllers to enhance disturbance rejection, accurately manipulate energy or mass, reject load disturbance, compensate for uncertainties, and track set-points.

[0107] The present controller adds resiliency to the electric power or smart grid system and makes it better prepared to address emergencies such as severe storms, earthquakes, large solar flares, and terrorist attacks.

[0108] The present controller provides enhanced control performance, robustness, and stability, while handling nonlinearities and uncertainties of the power system and providing a faster response and improved accuracy in regulating the frequency and tie-line power of the interconnected power systems.
, Claims:
1. A three degree of freedom fractional order proportional integral derivative filter controller cascaded with one plus tilted derivative controller (3DOFFOPIDN-(1+TD)) (100) for a smart grid system, the 3DOFFOPIDN-(1+TD) controller (100) comprising:
a 3DOFFOPIDN controller (100a) configured for receiving inputs from three independent feedback loops, wherein the inputs are real-time reference input signal R(s) and real-time tie-bar power feedback signal Y(s) provided by a plurality of sensors and an external noise signal D(s), the 3DOFFOPIDN controller (100a) comprising:
a first combiner (102) configured for combining a weighted R(s) signal with an output from a third combiner (106), wherein the weighted R(s) signal is obtained by combining R(s) with a gain, WP of a proportional controller,
a second combiner (104) configured for combining R(s) with an output from a fourth combiner (108),
the third combiner (106) configured for combining Y(s) with a weighted D(s) signal, wherein the weighted D(s) signal is obtained by combining D(s) with a weight, Gff;
the fourth combiner (108) configured for combining another weighted D(s) signal with the output of the second combiner (104), wherein the another weighted D(s) signal is obtained by combining D(s) with a gain, WD of a derivative controller, and
a first summing device (110) configured for summing the outputs from the first combiner (102) combined with proportional gain kp, the second combiner (104) combined with integral gain ki and the fourth combiner (108) combined with differential gain kd for producing a first control signal, U1(s) of the 3DOFFOPIDN controller, and a 1+TD controller (100b) configured for receiving the first control signal, U1(s), the 1+TD controller (100b) comprising:
a tilted-integral-derivative controller, wherein the first control signal, U1(s) is combined with a tilted gain, kt of a tilted controller having a tilt parameter, c and a derivative gain, kd of a derivative controller, and
a second summing device (114) configured for summing the first control signal, U1(s) with the output of the tilted-integral-derivative controller for producing a control signal, U(s), and
wherein the control signal, U(s) is a signal for providing an automatic generation control in the smart grid system, and
wherein the 3DOFFOPIDN-(1+TD) controller (100) suppresses disturbance and noise and enhances the closed loop stability of the smart grid system.

2. The 3DOFFOPIDN-(1+TD) controller (100) as claimed in claim 1, wherein the derivative controller of the 1+TD controller (100b) is cascaded with a feedback loop.

3 The 3DOFFOPIDN-(1+TD) controller (100) as claimed in claim 2, wherein the feedback loop comprises of a derivative filter with coefficient, Nf in a feed forward path and a first order integrator in a feedback path.

4. The 3DOFFOPIDN-(1+TD) controller (100) as claimed in claim 1, wherein the derivative controller of the 3DOFFOPIDN controller (100a) is cascaded with a feedback loop.

5. The 3DOFFOPIDN-(1+TD) controller (100) as claimed in claim 4, wherein the feedback loop comprises of a derivative filter with coefficient, N1 in a feed forward path and a first order integrator in a feedback path.

6. The 3DOFFOPIDN-(1+TD) controller (100) as claimed in claim 1, wherein the plurality of sensors comprises of frequency sensors, load sensors and tie-line power sensors.

7. The 3DOFFOPIDN-(1+TD) controller (100) as claimed in claim 1, wherein a modified Quasi Opposition-based Arithmetic Optimization Algorithm (QOAOA) is implemented to derive the control parameters of the 3DOFFOPIDN-(1+TD) controller (100).

8. The 3DOFFOPIDN-(1+TD) controller (100) as claimed in claim 7, wherein a Quasi-Opposition Based Learning (QOBL) is integrated into the modified QOAOA for deriving the control parameters of the 3DOFFOPIDN-(1+TD) controller (100).

9. The 3DOFFOPIDN-(1+TD) controller (100) as claimed in claim 1, wherein the control signal configured to provide an automatic generation control in the smart grid system has a closed-loop transfer function determined by a processor and is defined by:
U(s) = (1 + (Kt/s1/c) + ((Nf*KD*s)/(s+Nf)))*U1(s)
wherein Nf represents derivative filter coefficient, Kt and KD represents tilted and derivative gain respectively, c is a tilted angle and wherein U1(s) is given by:
U1(s) = (Wp*kp + (ki/sb) + (WD*kd*N1*s/(s+N1)))*R(s) - (kp + (ki/sb) + ((kd* N1*s)/(s+N1)))*Y(s) - (Gff*kp + Gff*(ki/sb) + Gff*kd*N1*s/(s+N1))*D(s)
wherein WP and WD represents set-points of proportional and derivative controllers respectively, Gff represents weight value to normalize D(s), kp, ki and kd represents proportional-integral-derivative controller gain respectively, b represents fractional coefficient of integral gain and N1 represents derivative filter coefficient.

10. The 3DOFFOPIDN-(1+TD) controller (100) as claimed in claim 1, wherein values of control parameters like kp, kd, ki, b, Kt, KD, c, N1, Nf, WD, Gff and WP lies in the range of kpmin≤ kp≤ kpmax, kimin≤ ki≤ kimax, kdmin≤kd≤ kdmax, bmin≤b≤ bmax, Ktmin≤Kt≤Ktmax, KDmin≤KD≤KDmax, cmin≤c≤cmax, N1min≤N1≤N1max, Nfmin≤Nf≤ Nfmax, WDmin≤WD≤WDmax, Gffmin≤ Gff ≤ Gffmax and WPmin≤ WP≤WPmax.

11. The 3DOFFOPIDN-(1+TD) controller (100) as claimed in claim 10, wherein the values of the control parameters like kp, kd, ki, b, Kt, KD, c, N1, Nf, WD, Gff and WP lies in the range of -1≤ kp ≤ 2, -1≤ ki ≤ 2, -1≤ kd ≤2, 0≤ b≤ 2, -1≤ Kt≤ 2, -1≤ KD≤ 2, 0≤c≤2, 0≤ N1≤400, 0≤ Nf≤ 400, 0≤WD≤2, 0≤Gff≤2 and 0≤ WP≤ 2.

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