Frequency control parameters
Due to the environmental concerns, there is an increasing interest in using renewable energy sources (RESs) for power generation. MGs would provide a suitable infrastructure for integrating RESs to the grid at distribution level. MGs can operate in grid-connected or islanded mode. However, in islanded mode, they would encounter challenges in frequency and voltage control. These problems would be exacerbated in MGs with a high share of power-electronically interfaced DERs; due to the low inertia of the grid. In fact, in low inertia MGs, power imbalances resultin rapid changes in frequency that might endanger the stability of the system . To address these stability concerns, some methods have been proposed to increase the inertia of MGs. In Refs. [2,3], using synchronous condensers have been proposed for this purpose. In addition to contributing to the inertia of the gird, synchronous condensers wouldparticipate inreactivepower control.Inverter-based DERs would also emulate the inertial response of synchronous generators by injecting a power proportional to frequency derivative to the grid.
In dissertation Ref. , a control method has been proposed for converters to emulate the behavior of synchronous generators. Virtual inertia has been implemented in Ref.  to increase the contribution of distributed generators to oscillation damping. To emulate the inertial behavior of synchronous generators, inverter-based DERs require a temporary source of energy similar to the kinetic energy ofthe rotor of synchronous generators.
InRef.,the energy stored in the rotor of doubly fed induction generator (DFIG) based wind turbines and also the ultracapacitor (UC) installed at the dclink of converters are used as energy sources for inertia emulation. In Ref. , HVDC transmission line is controlled to contribute to the inertia of the grid. HVDC links would transfer the inertial power generated by wind farms to the main grid, transfer inertial power from one area of power system to another area or use the energy stored in the DC link to emulate the inertial response. UC is proposed in Ref.  to emulate the inertial response of synchronous generators in an isolated power system. Although some studies have been carried out on contribution of inverter-based DERs to the inertia of MGs, to the best of authors’ knowledge, a systematic method for determining the proper value for inertia constant in islanded MGs has not yet been proposed.
In addition to inertia constant, load frequency controllers and frequency droop coefficient of power sources would affect the frequency response of the grid. Fine-tuning the load frequency controllers would reduce the maximum frequency deviation and also bring back the frequency to the nominal value faster. Different methods have been proposed for load frequency control (LFC) in power systems.
In Ref. 
the performance of model predictive controller for LFC in Nordic power system was investigated. Many researchers have focused on tuning the traditional proportional integral(PI)/proportional integral derivative (PID) controllers using evolutionary algorithms.InRef. bacterialforaging optimization algorithm has been implemented to tune the load frequency controllers of an MG with generation rate constraint (GRC). In Ref.  a hierarchical approach based on fuzzy logic has been proposed to improve the quality of frequency control.
Electrical vehicles have been implemented in Ref.  for frequency control. In Ref. , fractional order PID controllers have been proposed for LFC in a multi-area power system. An adaptive set-point modulation technique has been implemented in Ref.to enhance the performance of PIloadfrequency controllers.
To improve theperformance of frequency controllers in a three-area thermal power system, in Ref.  governors’ frequency droop coefficient (R) have been optimized together with the load frequency controllers’ parameters. Since the grid inertia constant(H),frequency droop coefficient of DERs and parameters of load frequency controllers all affectthe frequency response of MGs, in this paper,tuning these parameters has been suggested to improve the frequency stability of MGs. Based on different criteria that should be met to have a proper frequency response in MGs, a systematic method is proposed for tuning allthe parameters, including R, H and the controllers parameters, simultaneously.
The main goal oftuning these parameters is to improve the frequency stability of MG. However, this goal should be achieved with the minimum cost. Hence, tuning these parameters has been modeled as a multi-objective optimization problem which considers both stability and economic aspects. Considering the fact that usualmulti-objective optimization algorithms, like non-dominated sorting genetic algorithm II (NSGA-II), would not show a good performance in solving optimization problems with more than three objectives , a recently developed many-objective knee point driven evolutionary algorithm (KnEA) is implemented for solving this problem. Finally, to select one of the Pareto optimal solutions obtained by KnEA as the final solution, a strategy based on the minimum sum ofthe normalized objectives is suggested. Also, a method for determining the characteristics of the ultracapacitor required for emulating the determined inertia is proposed. The rest of this paper is organized as follows: in Section 2, the required equipment for increasing the inertia constant of the MG is studied. In Section 3, the process of tuning the parameters of MG for improving its frequency response is explained. The studied MG is introduced in Section 4. Then, in Section 5, by simulation studies carried out in Matlab/Simulink, the effectiveness of the proposed method is investigated.
Objective functions and problem formulation The typical behavior of frequency of an MG after a power deficit is shown in Fig. 1. As can be seen in this figure, frequency undershoot (fnadir ), frequency overshoot (fmax) and the time after which frequency deviation from the nominal value returns to the desired region (tst) are important characteristics of frequency response that should be minimized.
These goals would be achieved by determining the proper values of R and H together with the parameters of PID load frequency controllers (KP , KI and KD). It is important to tune these parameters such that the goals are achieved with the minimum cost. In the following, the objective functions that should be optimized for fine tuning the parameters of an MG are discussed. The purpose of the frequency control in MG, in case of a power imbalance, is to minimize the maximum frequency deviation while bringing the frequency back to the desirable region as soon as possible.
It is also important to have a zero steady state frequency deviation. The first goal would be achieved by minimizing Obj1 and Obj2 which are defined as a function of frequency undershoot and overshoot in Fig. 1, respectively. Obj1 = fn − fnadir (7) Obj2 = fmax − fn (8) where fn is the nominal frequency. The second goal would be achieved by considering the settling time, denoted by tst in Fig. 1, as the third objective: Obj3 = tst (9) where tst is the time after which the frequency deviation will remain smaller than 2% of the maximum deviation for the studied disturbance.
Although (9) minimizes the settling time, it cannot guarantee the zero steady state frequency error; i.e. the frequency might have low amplitude oscillations around the nominal value. Zero steady state frequency deviation is achieved by minimizing the integral of time multiplied by absolute error (ITAE): Obj4 = t sim 0 t × |f (t)|dt (10) where t is time and f(t) is deviation of the frequency from the nominal value (f(t) = f(t) − fn) and tsim is the simulation time. This objective function also would result in a reduction in frequency oscillations. Furthermore, it would affect the settling time. However, since some other conflicting factors such as the maximum frequency deviation are considered in Eq. (10), to minimize the settling time, it is necessary to consider Eq. (9) as one of the objective functions.
 F.M. Uriarte, C. Smith, S.V. Broekhoven, R.E. Hebner, Microgrid ramp rates and
the inertial stability margin, IEEE Trans. Power Syst. 30 (November (6)) (2015)
 N. Mendis, K.M. Muttaqi, S. Perera, Management of battery-supercapacitor
hybrid energy storage and synchronous condenser for isolated operation of
PMSG based variable-speed wind turbine generating systems, IEEE Trans.
Smart Grid 5 (March (2)) (2014) 944–953.
 Nahid-Al-Masood, R. Yan, T.K. Saha, N. Modi, Frequency response and its
enhancement using synchronous condensers in presence of high wind
penetration, in: IEEE Power & Energy Society General Meeting, Denver, CO,
2015, pp. 1–5.
 S. D’Arco, Jon Are Suul, O.B. Fosso, A Virtual Synchronous Machine
implementation for distributed control of power converters in Smart Grids,
Electr. Power Syst. Res. 122 (May) (2015) 180–197.
 T. Shintai, Y. Miura, T. Ise, Oscillation damping of a distributed generator
using a virtual synchronous generator, IEEE Trans. Power Deliv. 29 (April (2))
 M.F.M. Arani, E.F. El-Saadany, Implementing virtual inertia in DFIG-based
wind power generation, IEEE Trans. Power Syst. 28 (May (2)) (2013)
 E. Rakhshani, D. Remon, A. Mir Cantarellas, P. Rodriguez, Analysis of
derivative control based virtual inertia in multi-area high-voltage direct
current interconnected power systems, IET Gener. Transm. Distrib. 10 (May
(6)) (2016) 1458–1469.
 L. Sigrist, I. Egido, E. Lobato Miguélez, L. Rouco, Sizing and controller setting of
ultracapacitors for frequency stability enhancement of small isolated power
systems, IEEE Trans. Power Syst. 30 (July (4)) (2015) 2130–2138.
 A.M. Ersdal, L. Imsland, K. Uhlen, Model predictive load-frequency control,
IEEE Trans. Power Syst. 31 (January (1)) (2016) 777–785.
 S. Mishra, G. Mallesham, A.N. Jha, Design of controller and communication for
frequency regulation of a smart microgrid, IET Renew. Power Gener. 6 (July
(4)) (2012) 248–258.
 Z.A. Obaid, L.M. Cipcigan, Ma. T. Muhssin, Fuzzy hierarchical approach-based
optimal frequency control in the Great Britain power system, Electr. Power
Syst. Res. 141 (December) (2016) 529–537.
 M.H. Khooban, T. Niknam, F. Blaabjerg, T.v Dragicevi ˇ c, ´ A new load frequency
control strategy for micro-grids with considering electrical vehicles, Electr.
Power Syst. Res. 143 (February) (2017) 585–598.
 S.A. Taher, M. Hajiakbari Fini, S. Falahati Aliabadi, Fractional order PID
controller design for LFC in electric power systems using imperialist
competitive algorithm, Ain Shams Eng. J. 5 (March (1)) (2014) 121–135.
 A. Ketabi, M. Hajiakbari Fini, An adaptive set-point modulation technique to
enhance the performance of load frequency controllers in a multi-area power
system, J. Electr. Syst. Inf. Technol. 2 (December (3)) (2015) 391–405.
 J. Nanda, S. Mishra, L.C. Saikia, Maiden application of bacterial foraging based
optimization technique in multiarea automatic generation control, IEEE
Trans. Power Syst. 24 (May (2)) (2009) 602–609.
 X. Zhang, Y. Tian, Y. Jin, A knee point driven evolutionary algorithm for
many-objective optimization, IEEE Trans. Evol. Comput. 19 (December (6))
 J. Morren, J. Pierik, S.W.H. de Haan, Inertial response of variable speed wind
turbines, Electr. Power Syst. Res. 76 (July (11)) (2006) 980–987.
 Y. Brunet, Energy Storage, Wiley, Hoboken, NJ, USA, 2011.
 X. Zhang, Y. Tian, R. Cheng, Y. Jin, An efficient approach to nondominated
sorting for evolutionary multiobjective optimization, IEEE Trans. Evol.
Comput. 19 (April (2)) (2015) 201–213.
 S.A. Pourmousavi, M.H. Nehrir, Real-time central demand response for
primary frequency regulation in microgrids, IEEE Trans. Smart Grid 3
(December (4)) (2012) 1988–1996.
 A. Ketabi, M. Hajiakbari Fini, An underfrequency load shedding scheme for
hybrid and multiarea power systems, IEEE Trans. Smart Grid 6 (January (1))
 I. Pan, S. Das, Kriging based surrogate modeling for fractional order control of
microgrids, IEEE Trans. Smart Grid 6 (January (1)) (2015) 36–44.
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