 Original research
 Open Access
 Published:
Robust frequency control in a renewable penetrated power system: an adaptive fractional orderfuzzy approach
Protection and Control of Modern Power Systems volume 4, Article number: 16 (2019)
Abstract
Purpose
Load frequency control (LFC) in today’s modern power system is getting complex, due to intermittency in the output power of renewable energy sources along with substantial changes in the system parameters and loads. To address this problem, this paper proposes an adaptive fractional order (FO)fuzzyPID controller for LFC of a renewable penetrated power system.
Design/methodology/approach
To examine the performance of the proposed adaptive FOfuzzyPID controller, four different types of controllers that includes optimal proportionalintegralderivative (PID) controller, optimal fractional order (FO)PID controller, optimal fuzzy PID controller, optimal FOfuzzy PID controller are compared with the proposed approach. The dynamic response of the system relies upon the parameters of these controllers, which are optimized by using teachinglearning based optimization (TLBO) algorithm. The simulations are carried out using MATLAB/SIMULINK software.
Findings
The simulation outcomes reveal the supremacy of the proposed approach in dynamic performance improvement (in terms of settling time, overshoot and error reduction) over other controllers in the literature under different scenarios.
Originality/value
In this paper, an adaptive FOfuzzyPID controller is proposed for LFC of a renewable penetrated power system. The main contribution of this work is, a maiden application has been made to tune all the possible parameters of fuzzy controller and FOPID controller simultaneously to handle the uncertainties caused by renewable sources, load and parametric variations.
Introduction
In today’s modern power systems, the increased electrical energy demand from conventional power sources is becoming expensive and also environmentally hazardous, especially for remote locations and islands. To address these issues, renewable energy sources (RES) would be an attractive alternative solution to meet energy requirements. These RES are clean, but are volatile in nature [1] and this volatility of RES introduces new technical challenges with respect to secure operation of the grid, particularly in frequency control [2]. In order to ensure frequency stability, vastscale energy storage systems (ESSs) have become a vital part in a RES penetrated interconnected power system [3, 4]. Among all ESSs, plugin hybrid electric vehicles (PHEVs) form an excellent option for frequency stability studies due to its inherent distributed availability, fastacting capability and a slow discharge rate while in the idle condition [5, 6]. Moreover, the PHEVs could be utilized by consumers to meet their travel needs, in view of their lowcost charging, reduced CO_{2} emissions and fossil fuel usages.
During the last decade, the PHEVs are being considered by several authors for their proposed load frequency control (LFC) studies with various controllers [7,8,9,10,11,12,13,14,15,16,17,18,19]. In [7] authors suggested a conventional PI/PID controller, in [8] an adaptive control method, in [9] authors proposed a robust PI controller, in [10] a coefficient diagram method, in [11] a generalized model predictive controller (MPC), in [12] with H_{∞} controller, etc. In [13,14,15,16,17] the authors proposed various optimization techniques for secondary LFC with PHEVs. In [13] with a PSO optimized PID controller, in [14] with an imperialistic competitive algorithm (ICA), in [15] with flower pollination algorithm (FPA), in [16] with the whale optimization algorithm, in [17] with the sinecosine algorithm (SCA), etc. In [15,16,17], the authors added the fractionalorder feature to PID controllers to enhance the system frequency deviation response with RES and PHEVs. In [18, 19], the authors proposed various fuzzy PID controllers. In [18] authors suggested traditional fuzzy PID controller, in [19] the authors proposed FOFuzzyPID controller.
All the abovediscussed strategies are applied on linear power systems and have not considered the possible nonlinearities like boiler dynamics, governor deadband, turbine reheat mechanism, and generator rate constraint (GRC) simultaneously in the conventional power sources. The communication delays in EVs have also not been considered. In addition to the abovementioned nonlinearities, the intermittent nature of RES along with reduced system inertia changes the system operating conditions extensively [20]. In order to handle all the abovesaid difficulties, the power system urges an intelligent and efficient controller. From the literature, fractionalorder (FO) and fuzzy logic controllers (FLC) are proven as efficient controllers to address the non linearities in the system. However, it is also noticed that the FO controllers are model dependent and provide better performance only when the exact mathematical model is available. The aforementioned drawback of FO controllers can be overcome by employing FLC. However, their performance highly depends on the optimal selection of membership functions (MFs) and rule base [21]. In order to overcome the specified problems, this paper proposes a novel adaptive FOfuzzyPID controller for frequency control of the power system by inheriting the merits of both FL and FO controllers. In this proposed controller, the parameters of FLC (MFs scaling factors and rule base weights) and FOPID controller are tuned in online using TLBO algorithm. This algorithm is selected because, unlike other algorithms, it is free from algorithmspecific parameters [22]. The superiority of the proposed controller in terms of dynamic performance over the other controllers (PID/FOPID/FuzzyPID/optimized FOFuzzyPID) in the literature is presented in the Section 5.
The key features of this paper are listed below:

1)
An adaptive model free nonlinear controller is proposed by integrating the fuzzy logic and fractional order PID controller features to the LFC problem of RES penetrated power system by considering all nonlinearities.

2)
The FLC performance depends on its MFs scaling factors and rule base weights. A parameterfree optimization (TLBO algorithm) is used for optimal tuning of scaling factors, rule base weights and FOPID controller parameters.

3)
To assess the performance of the proposed controller, an aggregated model of PHEVs with communication delay is also considered in the LFC study

4)
Finally, the robustness of the proposed controller is proven by considering various scenarios with parametric uncertainties in single controller framework.
Modelling of twoarea power system
Figure 1 illustrates a mathematical model of IEE Japan East 107bus30machine power system, which is modelled as a twoarea interconnected power system. This test system consists of conventional power sources (CPS), RES and PHEV aggregator. There are two types of CPS in each area which are thermal and hydro generators with an aggregated speed control mechanism. LFC signals (U_{c1}, U_{c2}) are inputted to the governor of each unit. Each turbine output deviation is inputted to the generatorload model and the system frequency deviations (Δf_{1}, Δf_{2}) are outputted. In area1, CPS and PHEV aggregator are responsible for generationload balance, in area2, CPS are only responsible for the generationload balance. These two areas are interconnected with an AC tieline with a maximum allowable capacity of 500 MW.
In the interconnected power systems, the difference between schedule and actual generation is defined as area control error (ACE) [23]:
where,
Where β_{1,} β_{2} denotes the frequency bias factor of area 1 & area 2; Δf_{1}, Δf_{2} denotes the frequency deviation in area 1 & area 2; T_{12} denotes the synchronizing power coefficient; ΔP_{tie,12} denotes the tieline power deviation; U_{c1}, U_{c2} denotes the control signal from controller; ΔP_{PHEV} denotes the change in output power from EV aggregator; ΔP_{RES} denotes the change in output power from renewable sources; ΔP_{L1}, ΔP_{L2} denotes change in a load of area 1 & area 2; ΔP_{t1}, ΔP_{t2} denotes change in the output power of thermal units in area 1 & area 2; ΔP_{h1}, ΔP_{h2} denotes the change in output power of hydro units in area 1 & area 2; M_{1}, M_{2} denotes the equivalent inertia constant of area 1 & area 2; D_{1}, D_{2} denotes the load damping coefficient of area 1 & area 2; ACE_{1,} ACE_{2} denotes the area control error of area1 & area 2.
Finally, the control signal fed to the governors of each area (U_{ci}) can be expressed as:
Where K_{p}, K_{I}, K_{D} denotes gains of the PID controller and λ, μ denotes the fractional parameters of integrator and differentiator.
The objective of the controller is to minimize the frequency and tieline power deviations to schedule values by minimizing the ACE.
Thermal and hydro generator models
Figure 2ac shows the mathematical models of the thermal generator, boiler dynamics and hydro generator with all possible nonlinearities. This model include all appropriates for LFC studies, i.e. speed governor mechanism, boiler dynamics, reheatturbine system, and generatorload model, etc. [23, 24].
Thermal and hydro generators are responsible for loadgeneration balance in the system by supplying the deficient power to load depending on RES and PHEV aggregator output power. As shown in Fig. 2a & c, the governors of thermal and hydro units adjust their respective valve positions (ΔX and ΔY) according to the control signal (U_{c}) in order to meet the load changes. Where ΔP_{t} and ΔP_{h} indicates the corresponding changes in thermal and hydro generator powers with respect to the load changes.
PHEVs
In renewablerich power systems, the volatility in the RES output power along with load changes leads to large excursions in the system frequency. The governors of the hydro and thermal units are not adequate to mitigate the frequency fluctuations due to their sluggish response [20]. So this conventional sources need an additional energy source with immediate response to discharge or store the energy. The quick reaction of PHEVs makes it a significant alternative [25].
Figure 3 depicts the mathematical model of PHEV aggregator. The output power of PHEV for discharging or charging is selected based on the control signal (U_{c1}) from the controller. In the present work, the U_{c1} is determined by using the adaptive fractionalorder fuzzy PID controller. A bidirectional vehicletogrid (V2G) power control PHEV is chosen for this study. In Fig. 3, the EV aggregator model consists of PFC, LFC and battery charger. e^{−sT} denotes the time delay in the system due to communication delays between LFC control centre and EV aggregator. T_{EV, i} denotes the battery time constant; R_{AG} denotes the speed regulation constant of the EV aggregator. K_{EV, i} denotes the individual EV’s participation factor in the frequency control. The EVs participate in LFC only when they are in charging mode or in idle mode. The participation factor (K_{EV, i}) of each EV depends on their respective battery SOC level. Figure 4a & b shows the K_{EV, i} vs. Battery stateofcharge (soc) of discharge mode and idle mode. If the EVs are disconnected from aggregator, K_{EV, i} = 0. Detailed information regarding the aggregated PHEV model and participation factors is available in [25]. Δ P_{PHEV} represents the change in output power of PHEV aggregator. The maximum upward (\( {\varDelta P}_{AG}^{max} \)) and downward power (\( {\varDelta P}_{AG}^{min} \)) from the PHEV aggregator can be expressed as:
Where N_{EV} represents the number of electric vehicles participating in frequency control. If \( \Delta {P}_{PHEV}>\Delta {P}_{AG}^{max} \) then \( \Delta {P}_{PHEV}=\Delta {P}_{AG}^{max} \) and If \( \Delta {P}_{PHEV}<\Delta {P}_{AG}^{min} \) then \( \Delta {P}_{PHEV}=\Delta {P}_{AG}^{min} \).
Overview of fractional order (FO)& fuzzy logic controllers
FOPID controller
Fractional analytics is a standout amongst the essential branches of calculus in which the order of the integral and differential can take a noninteger value. Since a recent couple of decades, the fractional calculus has been applied successfully in numerous fields of engineering. The detailed analysis regarding fractional calculus is available in [26]. The FOPID controller can be expressed as:
Where K_{P}, K_{I,} and K_{D} denotes the gains of the proportional, integral and derivative controllers. λ & μ denotes the order of integrator and differentiator. In this FOPID controller, a total of five variables need to be optimized, three parameters K_{P}, K_{I,} and K_{D} (same as PID) and two fractional parameters λ, μ. These controllers can exhibits better dynamic performance over an integer order PID controllers (IOPID) due to its additional two degrees of freedom in tuning the two additional noninteger knobs (i.e. λ & μ) [27]. In Eq. (5), if (λ, μ) = (0,0) then it becomes the proportional controller; if (λ, μ) = (1,0) then it becomes PI controller; if (λ, μ) = (0,1) then it becomes PD controller; if (λ, μ) = (1,1) then it becomes PID controller. Figure 5a illustrates the various IOPID controllers in the λμ plane. Figure 5b shows the realization of FOPID controller from the integer order PID controller which expands it from the entire λμ plane [19, 27].
FOfuzzyPID controller
Figure 6a illustrates the structure of the FOFuzzyPID controller. The inputs of the controller are ACE, ACE* and output is U_{f}. Fuzzy logic approach can be divided into three modules viz. fuzzifier, inference engine and the defuzzifier. The fuzzifier assigns the MF ranges to the input and output variables. Figure 6b depicts the MF ranges corresponding to the inputs and output variables which are arranged as Negative Large (NL), Negative Medium (NM), Zero (ZE), Positive Medium (PM) and Positive Large (PL) having centroids at − 1,0.5,0,0.5,1 respectively. The MFs map the crisp values into fuzzy variables. The triangular MFs are chosen for this work due to its simplicity and adaptability in the tuning process [28].
The second module is the inference engine which comprises the rule base and database. Decision making is an inference control action from the rule base which is shown in Table 1.
The third module is the defuzzification, which converts the sum of fuzzy singleton outputs into an equivalent crisp value which is the output of FLC. The defuzzified output of FLC can be expressed as:
As shown in Section 4, the FOFuzzyPID controller has superior performance when compared to FOPID and conventional PID controllers. The crucial factor about the FLC is, its performance highly depends on its parameters (i.e. MFs and rule base). Without precise information about the system, the selection of parameters would not be appropriate. Hence, the designed FLC may not provide optimal performance over a wide range of operating conditions. To addresses the above problem, this paper proposes an adaptive FOFLCPID controller, in which MFs scaling factors and rule base weights are tuned in online according to operating conditions along with FOPID parameters.
Proposed method (adaptive FOFLCPID controller)
In literature, there exist several approaches to tune the MFs scaling factors and rule base of a fuzzy logic controller for various engineering problems [29,30,31]. Several authors proposed FOPID controllers as a solution to some engineering problems including LFC. However, no attempt has been made to combine both the techniques and inherit the merits of each technique by ignoring individual limitations in the process of resolving modern power system stability issues. Based on the requirements and complexities in frequency control of renewable penetrated power system, this paper proposes a novel adaptive FOFLCPID controller for an interconnected power system. Figure 7 depicts the block diagram of online tuning mechanism of the proposed controller. It can be observed that based on the ACE (which resembles the actual operating conditions of the system and feedback to the controller) and desired set point, the parameters of the proposed controller are tuned in online according to actual operating conditions. The specific goal of ACE minimization through the proposed controller is attained by executing the following steps in online:

1)
Tuning of fuzzy parameters (MFs scaling factors and rule weights)

2)
Tuning of FOPID controller.
In order to perform this task, a TLBO algorithm has been employed. The reason for selecting TLBO is, most of the metaheuristic techniques like GA, PSO, GWO, and BHO, etc. highly depends on their own algorithmspecific parameters. Inappropriate choice of these parameters may lead the solution towards divergence. To overcome this problem, an algorithmspecific parameter free optimization technique (TLBO) is used in this paper. TLBO algorithm was introduced in 2012 by Dr.R.V.Rao, inspired from the teachinglearning process. This technique mimics the teachinglearning process in a classroom. It describes two phases of learning

a)
Through teacher is known as teacher phase

b)
Through the interaction of learners with other learners is known as the learner phase.
Teacher phase
In teacher phase, he tries to improve class mean result from a_{1} to any other value a_{2} depending on his capability called teaching factor (TF). At any iteration i, let us consider ‘n’ number of subjects (design variables), ‘p’ no of learners (population size (k = 1,2p)). M_{n, i} represents the total population mean of ‘n^{th}’ variable in ‘i^{th}’ iteration. The best of the population (X_{total − kbest, i})considering all subjects together will be the best learner. According to this algorithm, the best learner is considered as the teacher. The mean_difference of each variable with respect to the teacher can be expressed as:
Where X_{n,kbest,i} is the best learner who is considered as the teacher; rand = random number between [0–1]; T_{F} is a teaching factor which can be expressed as:
T_{F} = 1 indicates no increase in the knowledge level of learner in a particular subject ‘n’. T_{F} = 2 indicates the complete transfer of knowledge.
Where, \( {X}_{n,k,i}^{\prime } \) is the updated knowledge of each learner after teaching phase.
Learners phase
The second phase in this algorithm is the learner phase. In this phase, learners improve their knowledge by interacting among themselves. Select two learners in the population A & B randomly such that \( {X}_{tota{l}_A,i}^{\prime}\ne {X}_{tota{l}_B,i}^{\prime } \). Equation (10) describes how the learners transfer their knowledge between each other. Where \( {X}_{tota{l}_A,i}^{\prime } \) is the total fitness value of the learner in all subjects.
\( {X}_{n,A,i}^{\prime \prime } \) denotes updated knowledge of A^{th} learner after learning phase.
The summarized steps for tuning the parameters of adaptive FOFLCPID controller with TLBO are given as follows:
Step 1: Initialize the population using X_{n} = lb + rand ∗ (ub − lb)
Where,
Step 2: Calculate the fitness of each learner (population) using the following fitness function
Where, t_{sim} = total simulation time (t_{sim} = 200 seconds); t = time at which absolute sum of error samples are collected (t = 1,2,3200 s)
Step 3: The best fitness one in the population is considered as the teacher. Calculate the mean of learners (population) in each subject (variable). Calculate mean_difference & T_{F} using following Eqs. (7) & (8).
Step 4: Update each learner’s knowledge with the help of the teacher’s knowledge using the Eq. (9).
Step 5: Each learner improves his/her knowledge by interacting with other learners according to Eq. (10).
Step 6: If the termination criteria is met (terminate either the tolerance value of ITAE reaches below 0.001 or the iteration count reaches 50), then display the optimal parameters of FLC and FOPID controller, else return to step 2.
Figure 8 depicts the flow chart for the tuning process of proposed controller with TLBO algorithm.
Results and discussions
The adequacy of the proposed controller in frequency control under various scenarios is tested on the IEE Japan East 107bus30 machine power system. This system is recognized as a standard test system to assess the new control strategies with RES penetration. This test system is programmed and simulated in MATLAB 2015a environment. The parameters of the test system are listed in Appendix (A.1). The performance of the adaptive FOFLCPID controller is compared with other controllers in literature i.e., FOFLCPID, FuzzyPID, FOPID, and TLBO PID under various test scenarios. It is well known that the system response relies upon the parameters of these controllers, all the parameters are optimized by using TLBO algorithm.
Scenario 1
The objective of this scenario is to show the superiority of the proposed controller in improving the settling time and overshoots when compared with the other techniques available in the literature. To perform this task, three cases are considered in area 1 alone as an isolated area with EVs.
Case 1
In this case, a step change of 0.01 p.u.in load and wind power is applied at t = 10 & 100 s as a disturbance to the LFC in area 1. The frequency deviation response of various controllers are depicted in Fig. 9a.
Case 2
In this case, a step change of 0.1 p.u.in wind power is applied at t = 5 s as a disturbance to the LFC in area 1. This case is to demonstrate the dynamic performance of the system with the proposed controller, with & without PHEVs in frequency regulation. Figure 9b depicts the frequency deviation response of the system.
Case 3
In this case, a multistep load deviation is applied as a disturbance to the LFC in area1. Figure 9c shows the multistep load deviations. The frequency deviation response of various controllers is depicted in Fig. 9d.
From the Fig. 9a, b & d, it is observed that the dynamic performance is improved and the proposed LFC control scheme can eliminate the effect of load disturbance significantly when compared to other controllers. The dynamic performance of various controllers in cases 1 & 3 in terms of settling time and overshoot are listed in Table 2. The dynamic performance of the proposed controller with and without EVs (case 2) is listed in Table 3.
Scenario 2
The objective of this scenario is to show the robustness of the proposed controller against parametric uncertainties in the system as well as PHEV aggregator. The percentage changes in the parameters of the system and PHEV aggregator are displayed in Table 4.
In this scenario, a step change of 0.05 p.u.in load is applied as a disturbance to the LFC in area 1 along with parametric uncertainties as mentioned in Table 4. The frequency deviation response of area 1, area 2 and tieline power deviations with various controllers are shown in Fig. 10ac. The dynamic performance of various controllers for scenario 2 is listed in Table 5.
From the scenario 2, it is clear that the proposed adaptive FOFuzzyPID controller improves the dynamic response of the system significantly over other methods. Moreover, the simulation results reveal that the proposed approach is more robust to parametric uncertainties over other controllers. On the other hand, the TLBOPID, FOTLBOPID and fuzzy PID controllers have large overshoots and more settling time under the circumstances as mentioned in scenario2.
Scenario 3
In this scenario, it is assumed that there are load changes and wind power changes in area 1 and solar power changes in area 2. The wind power data is extracted from GAMESA company WTG data sheet [32], solar power data from [33]. Figure 11ac illustrates the load, wind power and solar power changes in area 1 and area 2 respectively. Figure 11d & e represents the frequency deviation response in area 1 and area 2. Figure 11f depicts the tieline power flow deviations between area1 and area 2.
Figure 11df reveal that the proposed controller has minimized the frequency and tieline power deviations effectively with a lesser magnitude of the error and overshoots with respect to other controllers. The ITAE (error value) performance criteria of various controllers for scenario 3 is listed in Table 6. The optimized gains of various controllers are given in Table 7. The rule weights of the proposed controller are listed in Table 8. Figure 12 shows the convergence characteristics of the various controllers for scenario 3.
Scenario 4
Finally, to explore the robustness of the proposed controller at the next level, the PHEV aggregator is disconnected from the grid at t = 100 s in scenario 4. For analysis purpose, only a single area (i.e., area 1 as an isolated area) is considered. The same load along with wind and solar power disturbances are considered simultaneously in area1 as shown in Fig. 11ac.
Figure 13 illustrates the simulation results for this scenario. It also shows that the proposed controller improves the frequency response of the system in comparison to other controllers in the literature, especially where the overshoots are concerned. Certainly, from Fig. 13, despite parametric uncertainties and EV aggregator disconnection, the proposed controller shows its supremacy over the other four controllers. As it can be noticed, the TLBOPID, FOTLBOPID, and FuzzyPID controllers unable to provide acceptable performance in scenario 4. FOFuzzyPID controller and proposed adaptive FOFuzzyPID controller have provided an agreeable performance in this scenario. In this duo, the proposed controller shows its superiority in error and overshoot reduction in comparison with FOFuzzyPID controller.
Conclusion
In this work, a novel adaptive FOFLCPID controller is proposed for frequency control of an interconnected power system with RES penetration. In order to improve the robustness against RES intermittencies and load disturbances, the proposed controller is designed at two levels, i.e., Fuzzy and FOPID control levels. Since the FLC’s performance depends on its MFs and rule base, both are tuned by using TLBO algorithm along with FOPID parameters. This proposed approach improves the performance of the LFC with low computation burden and complexity. Moreover, the proposed controller was found adaptive enough to handle the uncertainty in the loads, RES power output and system parameters. The simulation results from the four scenarios validate that the proposed controller is able to minimize the frequency deviations significantly over the TLBOPID, FOTLBOPID, fuzzy PID, FOFLCPID controllers.
Availability of data and materials
Data sharing not applicable to this article as no data were generated or analyzed during the study.
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Acknowledgments
Authors would like to thank the National Institute of Technology Warangal (NITW) for providing the necessary research facilities.
Funding
Not applicable.
Author information
Affiliations
Contributions
AA analyzed and interpreted the modeling and simulation of the test system and controller. SN provided the idea and other technical guidance required for completion of the work. He also prepared the final draft of the manuscript. Both authors have read and approved the final manuscript.
Authors’ information
Anil Annamraju was born in Nellore, India. He received his B.Tech degree in Electrical and Electronics Engineering from Jawaharlal Nehru Technological University, Kakinada, India, in 2010 and M.Tech degree in Power systems from University of Calicut, India, in 2013. Currently, He is working as research scholar in the Electrical Engineering department, National Institute of Technology, Warangal, India. His research interests include Microgrid technologies, Power system stability, operation and Control with Intelligent Techniques.
Srikanth Nandiraju received his B.Tech degree in Electrical and Electronics Engineering from Osmania University, Hyderabad, India, in 1988 and M.Tech degree in Power systems from REC, Warangal, India, in 1998. He received his Ph.D. degree from National Institute of Technology, Warangal, India, in 2006. Since 1989, he is working as faculty in various positions. Currently, he is working as associate professor in the Electrical Engineering department, National Institute of Technology, Warangal, India. He is a member of IEEE and Institute of Engineers (India). He published over 40 research papers in journals and conferences. His research interests include power system stability, operation and control, application of intelligent techniques to Microgrid problems, Real time control of power system, HVDC and FACTS.
Corresponding author
Correspondence to Anil Annamraju.
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Appendix
Appendix
IEEJapanEast107bus data
Thermal generator data
Hydro generator data
PHEV data
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Annamraju, A., Nandiraju, S. Robust frequency control in a renewable penetrated power system: an adaptive fractional orderfuzzy approach. Prot Control Mod Power Syst 4, 16 (2019). https://doi.org/10.1186/s4160101901308
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Keywords
 Adaptive fractional orderfuzzyPID controller
 Renewable energy sources
 Load frequency control
 TLBO algorithm