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Load Frequency Control for Multi Area Smart Grid based on Advanced Control Techniques
Alexandria Engineering Journal (2018) xxx, xxx–xxx
H O S T E D BY
Alexandria University
Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com
ORIGINAL ARTICLE
Load Frequency Control for Multi Area Smart Grid based on Advanced Control Techniques Mohamed M. Ismail *, Ahmed F. Bendary Faculty of Engineering, Helwan University, Egypt Received 27 June 2018; revised 19 October 2018; accepted 1 November 2018
KEYWORDS LFC; PI; FOPID; Fuzzy; MPC; Multi area power system
Abstract One of the main interested subjects in electric power systems is the integration of electric vehicles to the existing power network as well as the influence of this integration with the other types of renewable sources connected to the multi area power system networks. Load Frequency Control (LFC) are used to regulate and control the output frequency signal of the electric generated power within an area in response to changes in system loads and power in tie line changed with other area. This paper presents a new design of various types of load frequency PI controllers based on different types of Artificial Intelligent (AI) optimization techniques such as Fuzzy logic, FOPID tuned by fuzzy and Model Predictive Control (MPC) for a four area power system. The performance of the controller under study shows an enhancement in the frequency deviation signal as well as the peak overshoot and Settling time for the frequency output signal. The performance of the proposed scheme is validated using MATLAB/SIMULINK tools. Ó 2018 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction LFC is considered as a one of the main important aspects in power system network as it considered as a direct representation for the primary constraint achievement in power system as well as a view for the change either in demand or generation side. The disturbance in load demand side in a certain area affects the frequency stability in the other areas so it is essential in the electric power networks to design such a load frequency controller to maintain the network stability [1]. Many researchers have been work to overcome the load freqency problems specially after increase the concept of multi * Corresponding author. E-mail address: [email protected] (M.M. Ismail). Peer review under responsibility of Faculty of Engineering, Alexandria University.
area networks as several number of utilities are connected with each other through the tie lines which carries the power exchanged between them and the loss in stability appear in a certain area due to the influence of disturbance in the anther area [2], so it is necessary to design such a load frequency controller to enhance and maintain the frequency stability. Many techniques has been carried on the design of LFC either; using the conventional PI controller which lead to bad results shown in large overshoots and dynamic performance due to the continuous variation of the operating point of power system [3,4] or using the AI optimization techniques like Fuzzy logic, Particle Swarm Optimization (PSO), Genetic Algorithm (GA) as it used in determining and tuning of the PID controller parameters which enhance directly the system outputs. These control techniques are based on smooth computing for LFC parameters which guarantee not only the system frequency but also zero elimination Steady state error.
https://doi.org/10.1016/j.aej.2018.11.004 1110-0168 Ó 2018 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: M.M. Ismail, A.F. Bendary, Load Frequency Control for Multi Area Smart Grid based on Advanced Control Techniques, Alexandria Eng. J. (2018), https://doi.org/10.1016/j.aej.2018.11.004
2 The research field in multi area power system was carried out in previous articles [5], shows the enhancement of using fuzzy logic for PI controller in dynamic performance when compared with the conventional PI controller, while [6] Presents the implementation of both fuzzy logic and Particle Swarm for optimization of PID controller gains used in five area LFC [7]. Presents the implementation of ANN and fuzzy logic for enhancement the performance of PID used in four area such that area 1 and area 2 consists of thermal reheat power plant and the area 3 and area 4 consists if hydro power plant. Reference no [8] Presents the tuning of PID controller used in LFC in four area networks using fire fly algorithm [9]. The LFC was presented with the penetration of wind generation in hydro power plant integrated with a thermal power plant in supplying a load [10]. Gives a wide view for different control techniques and different power resources used as well as the values of overshoots and settling time for different operating conditions [11–15]. Presents a frequency control scheme for an isolated power system consists of hydro power plant, diesel generator, photo voltaic and fuel cell and the enhancement in the dynamic system performance using different techniques. Ziegler and Nichols were proposed PID controller tuning methods in 1942 and have been widely utilized either in the original form or in modified forms. Different types of PID controller tuning methods were discussed in [16–18]. Ziegler and Nichols method is considered as a base case for comparison the settling times, overshoots and maximum deviation [19–22]. In the past few years MPC are used in power system applications as a powerful tool and shows great improvement in the stability performance, Model predictive control (MPC) is considered as a one of the most recent promising control algorithms that utilize an explicit process model to predict the future response of plant [23– 29]. The PID controller was commonly used in electrical power system applications [20,21], while the Fraction Order PID is now widely used as an alternative for the PID based on AI optimization techniques, in order to achieve the optimum design of controller through taking into account five different design specifications instead of three parameters which adds more flexibility to controller design and real world processes become more accurately controlled [30]. The applications of using fuzzy logic fot load frequency control was indicated in [30–35]. FOPID controller are now widely used for different applications instead of the conventional PID controller as in [36,37]. This work is considered as a development in the work done in [3] but with the modifying of the four area system to be interconnected with renewable resources as wind turbine and photo voltaic system as well as the designed controller is designed to be based on FOPID and MPC. The effect of electric vehicle charging and discharging is also considered in the proposed model. The comparison is done in this article through specified methods of tuning. The conventional PID controller may give better response using another adaptation technique. But we are succeeding to improve the frequency deviation response of 4 area using FOPID and MPC.
M.M. Ismail, A.F. Bendary either PI controller tuned by Ziegler-Nicholas or AI optimization techniques like fuzzy logic, FOPID tuned by fuzzy or MPC. The four-area system as shown in Fig. 1 consists of a steam reheat turbine connected with the renewable resources as mentioned above and each single area system are connected via tie line, the established system is providing reliability through the interconnections and the generation compensation fail in case of any generation loss in any area by supplying from anther area. The four-area model is integrated with a renewable source such as wind turbine and PV module in addition to electric vehicle as shown in Fig. 2. Different types of controller as mentioned above is implemented to obtain high performance in dynamic stability. Due to the nonlinearity of the power system component used in the modelling of power system network, the conventional controller has been developed to overcome these problems. In four area modelling, the controller is based primary on proportional integral controller as the integer gain include the advantage of both reaching to the fast-transient recovery and low overshoot. In recent years there has been growing interest in EVs. The introduction and widespread use of EVs could potentially lead to significant impacts on power systems, a method to model EV charging load was developed and the impact of vehicle charging load on the load demand of a local distribution network was analyzed. However, it was assumed that all the EVs had the same battery type and the characteristics of different EV classes were not taken into consideration. The transfer function that describe the effect of charging and discharging of EV is shown in Figs. 3a and 3b. The variation in the load torque effect is also studied as an extra disturbance to the frequency control of the proposed system. MATLAB/Simulink tools is used for modelling the fourarea power system including the effect of renewable sources and electrical vehicles as shown in Figs. 3a–3d, this simulated system is connected with the designed controller and the system controller has been subjected to different operating conditions in order to validate the efficiency of controller response performance. The disturbance in this model is the effect of PV and wind fluctuation output as indicated in Figs. 3c and 3d. 3. Control techniques 3.1. LFC based on Ziegler-Nicholas Ziegler and Nichols were proposed PID controller tuning methods in 1942 and have been widely utilized either in the
Area 3
2. System modelling The main objective of this paper is to design a modified LFC implemented for a four area power system network based on
Area 2
Area 1
Fig. 1
Area 4
Four Area System Interconnection.
Please cite this article in press as: M.M. Ismail, A.F. Bendary, Load Frequency Control for Multi Area Smart Grid based on Advanced Control Techniques, Alexandria Eng. J. (2018), https://doi.org/10.1016/j.aej.2018.11.004
Load frequency control for multi area smart grid
Fig. 2
3
Four Area System Connected to Renewable sources.
original form or in modified forms. The comparison with Ziegler and Nichols method is usually used as a basic and simplest method that can be used. Ziegler and Nichols method not need deep knowledge of the system and can be used in this case by applying step input to the system and the slope of output response can be used to determine the parameters of PID controller. Fig. 3a
Transfer function of EV.
Fig. 3b
Effect of EV on the frequency deviation.
Please cite this article in press as: M.M. Ismail, A.F. Bendary, Load Frequency Control for Multi Area Smart Grid based on Advanced Control Techniques, Alexandria Eng. J. (2018), https://doi.org/10.1016/j.aej.2018.11.004
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M.M. Ismail, A.F. Bendary
Fig. 3c
Simulated Four Area System Integrated with Renewable Energy Sources and Electrical Vehicle.
3.2. LFC based on model predictive control In the past few years MPC are used in power system applications as a powerful tool and shows great improvement in the stability performance, Model predictive control (MPC) is considered as a one of the most recent promising control algorithms that utilize an explicit process model to predict the future response of plant [23–27]. The main objective of the MPC is to linearize the complex nonlinear system as well as tuning the system parameters to reach the desired output val-
ues as it is designed to achieve optimization. Fig. 4 shows the block diagram of the MPC. Model Predictive Control (MPC) is one of the most rising control techniques in industry for the last two decades, was widely used in academia and application to control FCC. It is an advanced optimum control strategy solved over a finite horizon of time. The control strategy is that at kth instant, a sequence of control actions u(k); u(k + 1); : : : ; u(k + M) are calculated for M samples, where M is the control horizon. This controller output trajectory is calculated based on mini-
Please cite this article in press as: M.M. Ismail, A.F. Bendary, Load Frequency Control for Multi Area Smart Grid based on Advanced Control Techniques, Alexandria Eng. J. (2018), https://doi.org/10.1016/j.aej.2018.11.004
Load frequency control for multi area smart grid
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Fig. 3d Effect of electric vehicles and renewable energy resources on power system.
mizing the error between the actual plant output and the predicted outputs using plant model ^y(k); ^y(k + 1); :::; ^y(k + 1) for a finite time horizon N, called prediction horizon. These predicted outputs work as a reference for the plant to follow. Only the first calculated value of control action trajectory is applied to the plant. Then the controller starts this process again to calculate new control action trajectory based on the new set of inputs/outputs values are available, to find the optimum values for the manipulated variables. The control horizon M and prediction horizon N are used as tuning parameters for the controller; where M can be extend to N-1 samples. Both have a significant effect on controller behavior beside inputs/outputs weights. The MPC strategy relies on objective function (or cost function). The objective function is an equation attempt to minimize the error between the desired and actual plant output trajectory, while valuing the constraints over output and input changes. Various types of objective functions are available leading to different types of MPC algorithms. The most common objective function is the quadratic type function, which is the minimization of squares of error and control trajectories. It can be formulated as minN
N X
fukþjjk gj¼0 j¼0
jj^ ykþjjk rkþjjk jj2Qy þ jjDukþjjk jj2Su
ð1Þ
where y vector represents the prediction of plant output(s) through identified plant model with length N, r is the reference trajectory with the same length of y, and u represents the
Fig. 4
change in manipulated input(s) with length M, N is prediction horizon. Also, there are two weighting factors that are used to control the contribution of outputs and inputs in minimization calculation, Qy is the weighting factor for output(s), and Su is weight of changes in manipulated input. The controller calculates the minimum of objective function to obtain optimum control action, this is done every time sample. From the above formulation, we can understand the criticality of dynamic model of the plant being controlled; which is used to predict the unit output. The successful implementation of prior identification process is the key to obtain the accurate plant model. Constraints One of key advantages of MPC is ability to take constraints into account implicitly in control algorithm. These constraints can be applied on both inputs and outputs. So over input can be written like: umin ui umax, i = 0,1,. . .,n 1, Also we can apply constraints on rate of change of input like Dumin Dui Dumax, i = 0,1,. . .,n 1 For output constraints will be ymin yi ymax, i = 0,1,. . .,n Where yk + 1 can be written like ymin Cxk+i ymax, i = 0,1,. . ., n Constraints can also be classified according to how much it can be relaxed or violated. This achieved in MPC through weighting factors that manipulates the strength of limits or boundaries on objective function calculation, or what is called slack variables. Simply it can be put into two types. Hard Constraints: named hard constraints because they can’t be violated; they must be satisfied. Hard constraints represent the process boundaries like equipment physical limits that if violated may affect the safety of equipment and plant. Also, product quality limits can’t be violated because this will cause ‘‘out of specifications product” which will impact plant economic aspects. Soft Constraints: are constraints can be violated if necessary to achieve feasible optimization. This is achieved by what is called ‘‘constraints relaxation”. Even of their direct effect on closed loop stability; and they may turn the system to instability. Neglecting constraints in design of MPC controller probably cause poor closed loop response, and lead to instability. This work uses the quadratic programming format.
Model Predictive Control (MPC) Concept.
Please cite this article in press as: M.M. Ismail, A.F. Bendary, Load Frequency Control for Multi Area Smart Grid based on Advanced Control Techniques, Alexandria Eng. J. (2018), https://doi.org/10.1016/j.aej.2018.11.004
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M.M. Ismail, A.F. Bendary
3.3. LFC based PID controller tuned by fuzzy logic Fuzzy logic is considered as a one of the most widely used optimization techniques, many papers presents the developing in this technique through its implementation in power system networks. The fuzzy logic controller is integrated with the PI controller in order to enhance the plant output [30–35]. In this paper the controller design are based on the error and the change in error as an inputs to the self tuning and the optimum gains will be the output as shown in Fig. 5. The controller design used the error and change of error as inputs to the self tuning, and the gains (KP1, KI1, KD1) as outputs. The FLC is adding to the conventional PID controller to adjust the parameters of the PID controller on-line according to the change of the signals error and change of the error.
Fig. 5
Fig. 6
Fig. 7
The controller proposed also contain a scaling gains inputs (Ke, KDe) to satisfy the operational ranges (the universe of discourse) making them more general. Now the control action of the PID controller after self tuning can be describing as: Z deðtÞ UPID ¼ KP2 eðtÞ þ KI2 edt þ Kd2 ð2Þ dt where KP2, KI2, and KD2 are the new gains of PID controller and are equals to: KP2 ¼ KP1 KP; KI2 ¼ KI1 KI; and KD2 ¼ KD1 KD
ð3Þ
where KP1, KI1, and KD1 are the gains outputs of fuzzy control that are varying online with the output of the system under
Proposed Fuzzy Self Tuning.
Memberships Function of Inputs (e).
Memberships Function of Inputs (De).
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Load frequency control for multi area smart grid
Fig. 8
Table 1 e/de NB N Z P PB
Table 2 e/de NB N Z P PB
Table 3 e/de NB N Z P PB
7
Memberships Functions of Outputs.
Rule bases for determining the gain Kp1. N PB P Z P PB
Z PB P P P PB
P PB P P PB PB
Fig. 9 Closed loop control system with a fractional order controller.
Rule bases for determining the gain KI1. N Z P P P PB
Z Z P Z P PB
P Z P P P PB
Rule bases for determining the gain KD1. N S P PB PB PB
Z Z PB PB PB PB
P P PB PB PB PB
control. And KP, KI, and KD are the initial values of the conventional PID. The triangular input and output member ship functions of the fuzzy self-tuning are shown in the Figs. 6–8. A sample of fuzzy logic rules are shown in Tables 1–3
and differentiation are respectively k and u (both positive real numbers, not necessarily integers) and if k = 1 and u = 1, the integer order PID controller return to three parameters as the conventional PID type. In this article, the fractional order PID controller generalizes the integer order PID controller and expands it from point to plane. This expansion adds more flexibility to controller design and real world processes more accurately controlled [36]. The general transfer function of FOPID is as following: Gc ¼
UðsÞ 1 ¼ kp þ kI k þ kD sl ; ðk; l > 0Þ EðsÞ s
ð4Þ
In this paper the modification done for tuning the FOPID by using fuzzy logic controller that give enhancement in the system performance. The proposed new technique is shown in Figs. 10 and 11. For the fuzzy FOPID, we are using the same fuzzy logic described before used with the conventional PID with adding FOI with the term of Ki fuzzy output and FOD with the term of Kd fuzzy output. The transfer function of FOI will be GcðsÞ ¼ skik , while the transfer function of FOD will be: GcðsÞ ¼ kdsl 3.5. Genetic algorithm (GA)
3.4. LFC based on fractional order PID The Fraction Order PID is now widely used as an alternative for the PID based on AI optimization techniques, in order to achieve the optimum design of controller through taking into account five different design specifications instead of three parameters as indicated in Fig. 9 in order to take the advantage of fraction order parameter k and u. The orders of integration
Genetic Algorithms (GA.s) are a stochastic global search method that mimics the process of natural evolution. It is one of the methods used for optimization. The parameters (k and l) are adopted using genetic algorithm (GA) such that the gains Kp, Ki and Kd are constant and selected using ZN method [36]. The convergence criterion of a genetic algorithm is a user-specified conditions for example the maximum
Please cite this article in press as: M.M. Ismail, A.F. Bendary, Load Frequency Control for Multi Area Smart Grid based on Advanced Control Techniques, Alexandria Eng. J. (2018), https://doi.org/10.1016/j.aej.2018.11.004
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M.M. Ismail, A.F. Bendary
+ Ki FUZZY LIKE PID
Fig. 10
Kd
FOI
PLANT
+
+
FOD
Fuzzy FOPID construction.
Fuzzy FOPID construction in MATLAB Simulink.
Fig. 11
Table 4
output
Kp
Reference
Values of controller parameters in different studied cases.
Parameters
P
I
D
k
l
ZN Fuzzy Logic FOPID based on GA (FOI) FOPID based on GA (FOD)
16.34 27.943 0 0
6.7 0.76223 0.76223 0
2.1 0.535 0 0.535
0 0 0.453 0
0 0 0 0.8391
number of generations or when the string fitness value exceeds a certain threshold. In this paper, we are defining the parameters to be used in the GA optimization as followings: system overshoot = max(yout) 1, alpha = 13; beta = 6, The fitness
function (to be minimized) is defined as: F = (de2/dt) * beta + system overshoot*alpha, the no of variables is two (k and l), the population type is double vector, population size is 30, the initial range of variable is [0.01–1] For the reproduc-
Please cite this article in press as: M.M. Ismail, A.F. Bendary, Load Frequency Control for Multi Area Smart Grid based on Advanced Control Techniques, Alexandria Eng. J. (2018), https://doi.org/10.1016/j.aej.2018.11.004
Load frequency control for multi area smart grid
9
tion, the elite count is 2 and the crossover friction is 0.8, the mutation function is Gaussian, the crossover function is scattered, the stopping rules is the no of generation is 100, and the stall time limit is 200 sec. In this article, the comparison is obtained between three different methods. The constraints are the values of the controller gains are (0 < Kp < 1000), (0 < Ki < 50), (0 < Kd < 50), (0 < k < 1) and (0 < l < 1). 4. Simulation results The simulation is done using MATLAB simulation. The values of PID and FOPID parameters after adaptation are indicated in Table 4.
In this section the results of the proposed system prepared by Matlab/Similink tools for the freqency deviation of the Predescribed four area power system network are presented using different types of controllers. Figs. 12–15 compare the frequency deviation for the first, second, third and fourth area versus time respectively in case of using PI controller tunned by ZN, MPC, fuzzy logic and FOPID tuned by fuzzy. Fig. 12 show the frequency deviation of the smart grid for the first area, it can found that the MPC give the best performance with minimum over shoot, while the FOPID tuned using fuzzy logic and GA is better than the conventional PID controller tuned by fuzzy logic and the ZN tuning method is the worst case. The same performance can be found in Figs. 13–15 which are related to the second, third and fourth area respectively.
0.04 based on PI tuned by ZN based on MPC based on fuzzy logic based on FOPID tuned by fuzzy
Frequency Deviation (HZ)
0.03 0.02 0.01 0 -0.01 -0.02 -0.03 -0.04
0
5
10
15
20
25
time (sec)
Fig. 12
Frequency Deviation for area 1.
0.04 based on PI tuned by ZN based on MPC
0.03
based on fuzzy logic based on FOPID tuned by fuzzy
Frequency Deviation (HZ)
0.02 0.01
0 -0.01 -0.02 -0.03
-0.04 0
5
10
15
20
25
time (sec)
Fig. 13
Frequency Deviation for area 2.
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M.M. Ismail, A.F. Bendary 0.06 based on PI tuned by ZN based on MPC based on fuzzy logic based on FOPID tuned by fuzzy
Frequency Deviation (HZ)
0.04
0.02
0
-0.02
-0.04
-0.06
0
5
10
15
20
25
time (sec)
Fig. 14
Frequency Deviation for area 3.
0.04 based on PI tuned by ZN based on MPC based on fuzzy logic based on FOPID tuned by fuzzy
Frequency Deviation (HZ)
0.03 0.02 0.01 0 -0.01 -0.02 -0.03 -0.04
0
5
10
15
20
25
time (sec)
Fig. 15
Frequency Deviation for area 4.
Table 5 Performance of Different Tuning Algorithms for PI Controller for first area power system.
Table 6 Performance of Different Tuning Algorithms for PI Controller for second area power system.
Controller Type PI tunned by ZN PI based on MPC PI based on fuzzy logic PI based on FOPID tuned by fuzzy
Controller Type PI tunned by ZN PI based on MPC PI based on fuzzy logic PI based on FOPID tuned by fuzzy
Peak Overshoot 0.035 0.011 0.0095 0.0045
Table 5 compare the Performance of Different Tuning Algorithms for PI Controller and presents the values of settling time and peak overshoots for various type of used con-
Peak Overshoot 0.04 0.011 0.02 0.003
troller for the first controller, Tables 6–8 presents the optimal controller parameters for area 2, 3 and 4 respectively for various type of used controller.
Please cite this article in press as: M.M. Ismail, A.F. Bendary, Load Frequency Control for Multi Area Smart Grid based on Advanced Control Techniques, Alexandria Eng. J. (2018), https://doi.org/10.1016/j.aej.2018.11.004
Load frequency control for multi area smart grid Table 7 Performance of Different Tuning Algorithms for PI Controller for third area power system. Controller Type PI tunned by ZN PI based on MPC PI based on fuzzy logic PI based on FOPID tuned by fuzzy
Peak Overshoot 0.05 0.03 0.01 0.009
11
[7]
[8]
[9]
[10]
Table 8 Performance of Different Tuning Algorithms for PI Controller for fourth area power system. Controller Type PI tunned by ZN PI based on MPC PI based on fuzzy logic PI based on FOPID tuned by fuzzy
Peak Overshoot 0.035 0.025 0.025 0.0029
[11]
[12]
[13]
5. Conclusion Load Frequency Control (LFC) are used to regulate and control the output frequency signal of the electric generated power within an area in response to changes in system loads. This article discuss the effect of renewable sources and electric vehicles on the load frequency deviation. This paper presents new techniques for tuning the PI controllers based on different types of Artificial Intellegent (AI) optimization techniques such as Fuzzy logic, FOPID tuned by fuzzy and Model Predictive Control (MPC) for a four area interconnected power system. The performance of the controller under study is tested and validated using MATLAB/SIMULINK tools. The simulation results proof that the new techniques is succeeded to improve the controller performance by reducing the percentage overshoot. FOPID controller tuned by fuzzy, gives the best performance for the proposed model that was tested. References [1] A. Salami, S. Jadid, N. Ramezani, The Effect of load frequency controller on load pickup during restoration, in: 1st International Power and Energy Conference, PECON 2006, 2006, pp. 225–228. [2] D.K. Sambariya, V. Nath, Load frequency control using fuzzy logic based controller for multi-area power system, Brit. J. Math. Comput. Sci. (2016) 1–19. [3] Mohamed M. Ismail, M.A. Moustafa Hassan, Artificial intelligence based load frequency controllers for different multi areas power, Int. J. Control Autom. Syst. 1 (1) (2012). [4] V. Nath, D.K. Sambariya, Application of NARMA L2 controller for load frequency control of multi-area power system, in: IEEE Proceeding of 10th International Conference on Intelligent Systems and Control (ISCO 2016), vol. 2, 2016, pp. 352–358. [5] Emre Ozkop, Ismail H. Altas, Adel M. Sharaf, Load frequency control in four area power systems using fuzzy logic PI controller, in: 16th National Power Systems Conference, 15th– 17th December, 2010. [6] Sukhwinder Singh Dhillona, Jagdeep Singh Latherb, Sanjay Marwahac, Multi area load frequency control using particle swarm optimization and fuzzy rules, in: 3rd International
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12 [26] F. Xu, B. Huang, E.C. Tamayo, Assessment of economic performance of model predictive control through variance/constraint tuning, in: Proc IFAC ADCHEM, Gramado, Brazil, 2006, pp. 899–904. [27] J.M. Maciejowski, Predictive Control: With Constraints, Pearson Education, 2002. [28] S.J. Qin, T.A. Badgwell, A survey of industrial model predictive control technology, Control Eng. Pract. 11 (7) (2003) 733–764. [29] A.A. Tyagunov, High-Performance Model Predictive Control for Process Industry PhD, Technische Universiteit Eindhoven, Rusland, 2004. [30] S.P. Ghoshal, Multi-area frequency and tie-line power flow control with fuzzy logic based integral gain scheduling, J.-EL 84 (2003) -. [31] H.D. Mathur, H.V. Manjunath, Frequency stabilization using fuzzy logic based controller for multi-area power system, South Pacific J. Nat. Sci. (2007) 22–30. [32] Y.H. Song, A.T. Johns, Applications of fuzzy logic in power systems: part 1 general introduction to fuzzy logic, Power Eng. J. (1997) 219–222.
M.M. Ismail, A.F. Bendary [33] Y.H. Song, A.T. Johns, Applications of fuzzy logic in power systems: part 2 comparison and integration with expert systems, neural networks and genetic algorithms, Power Eng. J. (1998) 185–190. [34] Y.H. Song, A.T. Johns, Applications of fuzzy logic in power systems: part 3 example applications, Power Eng. J. (1999) 97– 103. [35] Mohamed M. Ismail, Ahmed F. Bendary, Protection of DFIG wind turbine using fuzzy logic control, Alexandria Eng. J. 55 (2) (2016) 941–949. [36] Mohamed M. Ismail, Ahmed F. Bendary, Abdelghany M. Abdelghany, A hybrid fuzzy logic FOPID position controller for DC motor driving tracking systems system, Ind. J. Electric Eng. Comput. Sci. 5 (2). [37] K.P.S. Rana, V. Kumar, N. Mittra, N. Pramanik, ‘‘ Implementation of fractional order integrator/differentiator on field programmable gate array, Alexandria Eng. J. 55 (2016) 1766–1774.
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H O S T E D BY
Alexandria University
Alexandria Engineering Journal www.elsevier.com/locate/aej www.sciencedirect.com
ORIGINAL ARTICLE
Load Frequency Control for Multi Area Smart Grid based on Advanced Control Techniques Mohamed M. Ismail *, Ahmed F. Bendary Faculty of Engineering, Helwan University, Egypt Received 27 June 2018; revised 19 October 2018; accepted 1 November 2018
KEYWORDS LFC; PI; FOPID; Fuzzy; MPC; Multi area power system
Abstract One of the main interested subjects in electric power systems is the integration of electric vehicles to the existing power network as well as the influence of this integration with the other types of renewable sources connected to the multi area power system networks. Load Frequency Control (LFC) are used to regulate and control the output frequency signal of the electric generated power within an area in response to changes in system loads and power in tie line changed with other area. This paper presents a new design of various types of load frequency PI controllers based on different types of Artificial Intelligent (AI) optimization techniques such as Fuzzy logic, FOPID tuned by fuzzy and Model Predictive Control (MPC) for a four area power system. The performance of the controller under study shows an enhancement in the frequency deviation signal as well as the peak overshoot and Settling time for the frequency output signal. The performance of the proposed scheme is validated using MATLAB/SIMULINK tools. Ó 2018 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
1. Introduction LFC is considered as a one of the main important aspects in power system network as it considered as a direct representation for the primary constraint achievement in power system as well as a view for the change either in demand or generation side. The disturbance in load demand side in a certain area affects the frequency stability in the other areas so it is essential in the electric power networks to design such a load frequency controller to maintain the network stability [1]. Many researchers have been work to overcome the load freqency problems specially after increase the concept of multi * Corresponding author. E-mail address: [email protected] (M.M. Ismail). Peer review under responsibility of Faculty of Engineering, Alexandria University.
area networks as several number of utilities are connected with each other through the tie lines which carries the power exchanged between them and the loss in stability appear in a certain area due to the influence of disturbance in the anther area [2], so it is necessary to design such a load frequency controller to enhance and maintain the frequency stability. Many techniques has been carried on the design of LFC either; using the conventional PI controller which lead to bad results shown in large overshoots and dynamic performance due to the continuous variation of the operating point of power system [3,4] or using the AI optimization techniques like Fuzzy logic, Particle Swarm Optimization (PSO), Genetic Algorithm (GA) as it used in determining and tuning of the PID controller parameters which enhance directly the system outputs. These control techniques are based on smooth computing for LFC parameters which guarantee not only the system frequency but also zero elimination Steady state error.
https://doi.org/10.1016/j.aej.2018.11.004 1110-0168 Ó 2018 Faculty of Engineering, Alexandria University. Production and hosting by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). Please cite this article in press as: M.M. Ismail, A.F. Bendary, Load Frequency Control for Multi Area Smart Grid based on Advanced Control Techniques, Alexandria Eng. J. (2018), https://doi.org/10.1016/j.aej.2018.11.004
2 The research field in multi area power system was carried out in previous articles [5], shows the enhancement of using fuzzy logic for PI controller in dynamic performance when compared with the conventional PI controller, while [6] Presents the implementation of both fuzzy logic and Particle Swarm for optimization of PID controller gains used in five area LFC [7]. Presents the implementation of ANN and fuzzy logic for enhancement the performance of PID used in four area such that area 1 and area 2 consists of thermal reheat power plant and the area 3 and area 4 consists if hydro power plant. Reference no [8] Presents the tuning of PID controller used in LFC in four area networks using fire fly algorithm [9]. The LFC was presented with the penetration of wind generation in hydro power plant integrated with a thermal power plant in supplying a load [10]. Gives a wide view for different control techniques and different power resources used as well as the values of overshoots and settling time for different operating conditions [11–15]. Presents a frequency control scheme for an isolated power system consists of hydro power plant, diesel generator, photo voltaic and fuel cell and the enhancement in the dynamic system performance using different techniques. Ziegler and Nichols were proposed PID controller tuning methods in 1942 and have been widely utilized either in the original form or in modified forms. Different types of PID controller tuning methods were discussed in [16–18]. Ziegler and Nichols method is considered as a base case for comparison the settling times, overshoots and maximum deviation [19–22]. In the past few years MPC are used in power system applications as a powerful tool and shows great improvement in the stability performance, Model predictive control (MPC) is considered as a one of the most recent promising control algorithms that utilize an explicit process model to predict the future response of plant [23– 29]. The PID controller was commonly used in electrical power system applications [20,21], while the Fraction Order PID is now widely used as an alternative for the PID based on AI optimization techniques, in order to achieve the optimum design of controller through taking into account five different design specifications instead of three parameters which adds more flexibility to controller design and real world processes become more accurately controlled [30]. The applications of using fuzzy logic fot load frequency control was indicated in [30–35]. FOPID controller are now widely used for different applications instead of the conventional PID controller as in [36,37]. This work is considered as a development in the work done in [3] but with the modifying of the four area system to be interconnected with renewable resources as wind turbine and photo voltaic system as well as the designed controller is designed to be based on FOPID and MPC. The effect of electric vehicle charging and discharging is also considered in the proposed model. The comparison is done in this article through specified methods of tuning. The conventional PID controller may give better response using another adaptation technique. But we are succeeding to improve the frequency deviation response of 4 area using FOPID and MPC.
M.M. Ismail, A.F. Bendary either PI controller tuned by Ziegler-Nicholas or AI optimization techniques like fuzzy logic, FOPID tuned by fuzzy or MPC. The four-area system as shown in Fig. 1 consists of a steam reheat turbine connected with the renewable resources as mentioned above and each single area system are connected via tie line, the established system is providing reliability through the interconnections and the generation compensation fail in case of any generation loss in any area by supplying from anther area. The four-area model is integrated with a renewable source such as wind turbine and PV module in addition to electric vehicle as shown in Fig. 2. Different types of controller as mentioned above is implemented to obtain high performance in dynamic stability. Due to the nonlinearity of the power system component used in the modelling of power system network, the conventional controller has been developed to overcome these problems. In four area modelling, the controller is based primary on proportional integral controller as the integer gain include the advantage of both reaching to the fast-transient recovery and low overshoot. In recent years there has been growing interest in EVs. The introduction and widespread use of EVs could potentially lead to significant impacts on power systems, a method to model EV charging load was developed and the impact of vehicle charging load on the load demand of a local distribution network was analyzed. However, it was assumed that all the EVs had the same battery type and the characteristics of different EV classes were not taken into consideration. The transfer function that describe the effect of charging and discharging of EV is shown in Figs. 3a and 3b. The variation in the load torque effect is also studied as an extra disturbance to the frequency control of the proposed system. MATLAB/Simulink tools is used for modelling the fourarea power system including the effect of renewable sources and electrical vehicles as shown in Figs. 3a–3d, this simulated system is connected with the designed controller and the system controller has been subjected to different operating conditions in order to validate the efficiency of controller response performance. The disturbance in this model is the effect of PV and wind fluctuation output as indicated in Figs. 3c and 3d. 3. Control techniques 3.1. LFC based on Ziegler-Nicholas Ziegler and Nichols were proposed PID controller tuning methods in 1942 and have been widely utilized either in the
Area 3
2. System modelling The main objective of this paper is to design a modified LFC implemented for a four area power system network based on
Area 2
Area 1
Fig. 1
Area 4
Four Area System Interconnection.
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Load frequency control for multi area smart grid
Fig. 2
3
Four Area System Connected to Renewable sources.
original form or in modified forms. The comparison with Ziegler and Nichols method is usually used as a basic and simplest method that can be used. Ziegler and Nichols method not need deep knowledge of the system and can be used in this case by applying step input to the system and the slope of output response can be used to determine the parameters of PID controller. Fig. 3a
Transfer function of EV.
Fig. 3b
Effect of EV on the frequency deviation.
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M.M. Ismail, A.F. Bendary
Fig. 3c
Simulated Four Area System Integrated with Renewable Energy Sources and Electrical Vehicle.
3.2. LFC based on model predictive control In the past few years MPC are used in power system applications as a powerful tool and shows great improvement in the stability performance, Model predictive control (MPC) is considered as a one of the most recent promising control algorithms that utilize an explicit process model to predict the future response of plant [23–27]. The main objective of the MPC is to linearize the complex nonlinear system as well as tuning the system parameters to reach the desired output val-
ues as it is designed to achieve optimization. Fig. 4 shows the block diagram of the MPC. Model Predictive Control (MPC) is one of the most rising control techniques in industry for the last two decades, was widely used in academia and application to control FCC. It is an advanced optimum control strategy solved over a finite horizon of time. The control strategy is that at kth instant, a sequence of control actions u(k); u(k + 1); : : : ; u(k + M) are calculated for M samples, where M is the control horizon. This controller output trajectory is calculated based on mini-
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Load frequency control for multi area smart grid
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Fig. 3d Effect of electric vehicles and renewable energy resources on power system.
mizing the error between the actual plant output and the predicted outputs using plant model ^y(k); ^y(k + 1); :::; ^y(k + 1) for a finite time horizon N, called prediction horizon. These predicted outputs work as a reference for the plant to follow. Only the first calculated value of control action trajectory is applied to the plant. Then the controller starts this process again to calculate new control action trajectory based on the new set of inputs/outputs values are available, to find the optimum values for the manipulated variables. The control horizon M and prediction horizon N are used as tuning parameters for the controller; where M can be extend to N-1 samples. Both have a significant effect on controller behavior beside inputs/outputs weights. The MPC strategy relies on objective function (or cost function). The objective function is an equation attempt to minimize the error between the desired and actual plant output trajectory, while valuing the constraints over output and input changes. Various types of objective functions are available leading to different types of MPC algorithms. The most common objective function is the quadratic type function, which is the minimization of squares of error and control trajectories. It can be formulated as minN
N X
fukþjjk gj¼0 j¼0
jj^ ykþjjk rkþjjk jj2Qy þ jjDukþjjk jj2Su
ð1Þ
where y vector represents the prediction of plant output(s) through identified plant model with length N, r is the reference trajectory with the same length of y, and u represents the
Fig. 4
change in manipulated input(s) with length M, N is prediction horizon. Also, there are two weighting factors that are used to control the contribution of outputs and inputs in minimization calculation, Qy is the weighting factor for output(s), and Su is weight of changes in manipulated input. The controller calculates the minimum of objective function to obtain optimum control action, this is done every time sample. From the above formulation, we can understand the criticality of dynamic model of the plant being controlled; which is used to predict the unit output. The successful implementation of prior identification process is the key to obtain the accurate plant model. Constraints One of key advantages of MPC is ability to take constraints into account implicitly in control algorithm. These constraints can be applied on both inputs and outputs. So over input can be written like: umin ui umax, i = 0,1,. . .,n 1, Also we can apply constraints on rate of change of input like Dumin Dui Dumax, i = 0,1,. . .,n 1 For output constraints will be ymin yi ymax, i = 0,1,. . .,n Where yk + 1 can be written like ymin Cxk+i ymax, i = 0,1,. . ., n Constraints can also be classified according to how much it can be relaxed or violated. This achieved in MPC through weighting factors that manipulates the strength of limits or boundaries on objective function calculation, or what is called slack variables. Simply it can be put into two types. Hard Constraints: named hard constraints because they can’t be violated; they must be satisfied. Hard constraints represent the process boundaries like equipment physical limits that if violated may affect the safety of equipment and plant. Also, product quality limits can’t be violated because this will cause ‘‘out of specifications product” which will impact plant economic aspects. Soft Constraints: are constraints can be violated if necessary to achieve feasible optimization. This is achieved by what is called ‘‘constraints relaxation”. Even of their direct effect on closed loop stability; and they may turn the system to instability. Neglecting constraints in design of MPC controller probably cause poor closed loop response, and lead to instability. This work uses the quadratic programming format.
Model Predictive Control (MPC) Concept.
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M.M. Ismail, A.F. Bendary
3.3. LFC based PID controller tuned by fuzzy logic Fuzzy logic is considered as a one of the most widely used optimization techniques, many papers presents the developing in this technique through its implementation in power system networks. The fuzzy logic controller is integrated with the PI controller in order to enhance the plant output [30–35]. In this paper the controller design are based on the error and the change in error as an inputs to the self tuning and the optimum gains will be the output as shown in Fig. 5. The controller design used the error and change of error as inputs to the self tuning, and the gains (KP1, KI1, KD1) as outputs. The FLC is adding to the conventional PID controller to adjust the parameters of the PID controller on-line according to the change of the signals error and change of the error.
Fig. 5
Fig. 6
Fig. 7
The controller proposed also contain a scaling gains inputs (Ke, KDe) to satisfy the operational ranges (the universe of discourse) making them more general. Now the control action of the PID controller after self tuning can be describing as: Z deðtÞ UPID ¼ KP2 eðtÞ þ KI2 edt þ Kd2 ð2Þ dt where KP2, KI2, and KD2 are the new gains of PID controller and are equals to: KP2 ¼ KP1 KP; KI2 ¼ KI1 KI; and KD2 ¼ KD1 KD
ð3Þ
where KP1, KI1, and KD1 are the gains outputs of fuzzy control that are varying online with the output of the system under
Proposed Fuzzy Self Tuning.
Memberships Function of Inputs (e).
Memberships Function of Inputs (De).
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Load frequency control for multi area smart grid
Fig. 8
Table 1 e/de NB N Z P PB
Table 2 e/de NB N Z P PB
Table 3 e/de NB N Z P PB
7
Memberships Functions of Outputs.
Rule bases for determining the gain Kp1. N PB P Z P PB
Z PB P P P PB
P PB P P PB PB
Fig. 9 Closed loop control system with a fractional order controller.
Rule bases for determining the gain KI1. N Z P P P PB
Z Z P Z P PB
P Z P P P PB
Rule bases for determining the gain KD1. N S P PB PB PB
Z Z PB PB PB PB
P P PB PB PB PB
control. And KP, KI, and KD are the initial values of the conventional PID. The triangular input and output member ship functions of the fuzzy self-tuning are shown in the Figs. 6–8. A sample of fuzzy logic rules are shown in Tables 1–3
and differentiation are respectively k and u (both positive real numbers, not necessarily integers) and if k = 1 and u = 1, the integer order PID controller return to three parameters as the conventional PID type. In this article, the fractional order PID controller generalizes the integer order PID controller and expands it from point to plane. This expansion adds more flexibility to controller design and real world processes more accurately controlled [36]. The general transfer function of FOPID is as following: Gc ¼
UðsÞ 1 ¼ kp þ kI k þ kD sl ; ðk; l > 0Þ EðsÞ s
ð4Þ
In this paper the modification done for tuning the FOPID by using fuzzy logic controller that give enhancement in the system performance. The proposed new technique is shown in Figs. 10 and 11. For the fuzzy FOPID, we are using the same fuzzy logic described before used with the conventional PID with adding FOI with the term of Ki fuzzy output and FOD with the term of Kd fuzzy output. The transfer function of FOI will be GcðsÞ ¼ skik , while the transfer function of FOD will be: GcðsÞ ¼ kdsl 3.5. Genetic algorithm (GA)
3.4. LFC based on fractional order PID The Fraction Order PID is now widely used as an alternative for the PID based on AI optimization techniques, in order to achieve the optimum design of controller through taking into account five different design specifications instead of three parameters as indicated in Fig. 9 in order to take the advantage of fraction order parameter k and u. The orders of integration
Genetic Algorithms (GA.s) are a stochastic global search method that mimics the process of natural evolution. It is one of the methods used for optimization. The parameters (k and l) are adopted using genetic algorithm (GA) such that the gains Kp, Ki and Kd are constant and selected using ZN method [36]. The convergence criterion of a genetic algorithm is a user-specified conditions for example the maximum
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M.M. Ismail, A.F. Bendary
+ Ki FUZZY LIKE PID
Fig. 10
Kd
FOI
PLANT
+
+
FOD
Fuzzy FOPID construction.
Fuzzy FOPID construction in MATLAB Simulink.
Fig. 11
Table 4
output
Kp
Reference
Values of controller parameters in different studied cases.
Parameters
P
I
D
k
l
ZN Fuzzy Logic FOPID based on GA (FOI) FOPID based on GA (FOD)
16.34 27.943 0 0
6.7 0.76223 0.76223 0
2.1 0.535 0 0.535
0 0 0.453 0
0 0 0 0.8391
number of generations or when the string fitness value exceeds a certain threshold. In this paper, we are defining the parameters to be used in the GA optimization as followings: system overshoot = max(yout) 1, alpha = 13; beta = 6, The fitness
function (to be minimized) is defined as: F = (de2/dt) * beta + system overshoot*alpha, the no of variables is two (k and l), the population type is double vector, population size is 30, the initial range of variable is [0.01–1] For the reproduc-
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Load frequency control for multi area smart grid
9
tion, the elite count is 2 and the crossover friction is 0.8, the mutation function is Gaussian, the crossover function is scattered, the stopping rules is the no of generation is 100, and the stall time limit is 200 sec. In this article, the comparison is obtained between three different methods. The constraints are the values of the controller gains are (0 < Kp < 1000), (0 < Ki < 50), (0 < Kd < 50), (0 < k < 1) and (0 < l < 1). 4. Simulation results The simulation is done using MATLAB simulation. The values of PID and FOPID parameters after adaptation are indicated in Table 4.
In this section the results of the proposed system prepared by Matlab/Similink tools for the freqency deviation of the Predescribed four area power system network are presented using different types of controllers. Figs. 12–15 compare the frequency deviation for the first, second, third and fourth area versus time respectively in case of using PI controller tunned by ZN, MPC, fuzzy logic and FOPID tuned by fuzzy. Fig. 12 show the frequency deviation of the smart grid for the first area, it can found that the MPC give the best performance with minimum over shoot, while the FOPID tuned using fuzzy logic and GA is better than the conventional PID controller tuned by fuzzy logic and the ZN tuning method is the worst case. The same performance can be found in Figs. 13–15 which are related to the second, third and fourth area respectively.
0.04 based on PI tuned by ZN based on MPC based on fuzzy logic based on FOPID tuned by fuzzy
Frequency Deviation (HZ)
0.03 0.02 0.01 0 -0.01 -0.02 -0.03 -0.04
0
5
10
15
20
25
time (sec)
Fig. 12
Frequency Deviation for area 1.
0.04 based on PI tuned by ZN based on MPC
0.03
based on fuzzy logic based on FOPID tuned by fuzzy
Frequency Deviation (HZ)
0.02 0.01
0 -0.01 -0.02 -0.03
-0.04 0
5
10
15
20
25
time (sec)
Fig. 13
Frequency Deviation for area 2.
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M.M. Ismail, A.F. Bendary 0.06 based on PI tuned by ZN based on MPC based on fuzzy logic based on FOPID tuned by fuzzy
Frequency Deviation (HZ)
0.04
0.02
0
-0.02
-0.04
-0.06
0
5
10
15
20
25
time (sec)
Fig. 14
Frequency Deviation for area 3.
0.04 based on PI tuned by ZN based on MPC based on fuzzy logic based on FOPID tuned by fuzzy
Frequency Deviation (HZ)
0.03 0.02 0.01 0 -0.01 -0.02 -0.03 -0.04
0
5
10
15
20
25
time (sec)
Fig. 15
Frequency Deviation for area 4.
Table 5 Performance of Different Tuning Algorithms for PI Controller for first area power system.
Table 6 Performance of Different Tuning Algorithms for PI Controller for second area power system.
Controller Type PI tunned by ZN PI based on MPC PI based on fuzzy logic PI based on FOPID tuned by fuzzy
Controller Type PI tunned by ZN PI based on MPC PI based on fuzzy logic PI based on FOPID tuned by fuzzy
Peak Overshoot 0.035 0.011 0.0095 0.0045
Table 5 compare the Performance of Different Tuning Algorithms for PI Controller and presents the values of settling time and peak overshoots for various type of used con-
Peak Overshoot 0.04 0.011 0.02 0.003
troller for the first controller, Tables 6–8 presents the optimal controller parameters for area 2, 3 and 4 respectively for various type of used controller.
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Load frequency control for multi area smart grid Table 7 Performance of Different Tuning Algorithms for PI Controller for third area power system. Controller Type PI tunned by ZN PI based on MPC PI based on fuzzy logic PI based on FOPID tuned by fuzzy
Peak Overshoot 0.05 0.03 0.01 0.009
11
[7]
[8]
[9]
[10]
Table 8 Performance of Different Tuning Algorithms for PI Controller for fourth area power system. Controller Type PI tunned by ZN PI based on MPC PI based on fuzzy logic PI based on FOPID tuned by fuzzy
Peak Overshoot 0.035 0.025 0.025 0.0029
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5. Conclusion Load Frequency Control (LFC) are used to regulate and control the output frequency signal of the electric generated power within an area in response to changes in system loads. This article discuss the effect of renewable sources and electric vehicles on the load frequency deviation. This paper presents new techniques for tuning the PI controllers based on different types of Artificial Intellegent (AI) optimization techniques such as Fuzzy logic, FOPID tuned by fuzzy and Model Predictive Control (MPC) for a four area interconnected power system. The performance of the controller under study is tested and validated using MATLAB/SIMULINK tools. The simulation results proof that the new techniques is succeeded to improve the controller performance by reducing the percentage overshoot. FOPID controller tuned by fuzzy, gives the best performance for the proposed model that was tested. References [1] A. Salami, S. Jadid, N. Ramezani, The Effect of load frequency controller on load pickup during restoration, in: 1st International Power and Energy Conference, PECON 2006, 2006, pp. 225–228. [2] D.K. Sambariya, V. Nath, Load frequency control using fuzzy logic based controller for multi-area power system, Brit. J. Math. Comput. Sci. (2016) 1–19. [3] Mohamed M. Ismail, M.A. Moustafa Hassan, Artificial intelligence based load frequency controllers for different multi areas power, Int. J. Control Autom. Syst. 1 (1) (2012). [4] V. Nath, D.K. Sambariya, Application of NARMA L2 controller for load frequency control of multi-area power system, in: IEEE Proceeding of 10th International Conference on Intelligent Systems and Control (ISCO 2016), vol. 2, 2016, pp. 352–358. [5] Emre Ozkop, Ismail H. Altas, Adel M. Sharaf, Load frequency control in four area power systems using fuzzy logic PI controller, in: 16th National Power Systems Conference, 15th– 17th December, 2010. [6] Sukhwinder Singh Dhillona, Jagdeep Singh Latherb, Sanjay Marwahac, Multi area load frequency control using particle swarm optimization and fuzzy rules, in: 3rd International
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Please cite this article in press as: M.M. Ismail, A.F. Bendary, Load Frequency Control for Multi Area Smart Grid based on Advanced Control Techniques, Alexandria Eng. J. (2018), https://doi.org/10.1016/j.aej.2018.11.004