A harmony search-based H-infinity control method for islanded microgrid

Journal Pre-proof A harmony search-based H-infinity control method for islanded microgrid Bishoy. E. Sedhom, Magdi. M. El-Saadawi, Mostafa. A. Elhosseini, Mohammed A. Saeed, Elhossaini. E. Abd-Raboh

PII: DOI: Reference:

S0019-0578(19)30468-9 https://doi.org/10.1016/j.isatra.2019.10.014 ISATRA 3387

To appear in:

ISA Transactions

Received date : 28 November 2018 Revised date : 27 October 2019 Accepted date : 28 October 2019 Please cite this article as: B.E. Sedhom, M.M. El-Saadawi, M.A. Elhosseini et al., A harmony search-based H-infinity control method for islanded microgrid. ISA Transactions (2019), doi: https://doi.org/10.1016/j.isatra.2019.10.014. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

© 2019 Published by Elsevier Ltd on behalf of ISA.

Journal Pre-proof

A Harmony Search-based H-Infinity Control Method for Islanded Microgrid

Bishoy. E. Sedhom*1, Magdi. M. El-Saadawi1, Mostafa. A. Elhosseini2, Mohammed A. Saeed, Elhossaini. E. Abd-Raboh1 1

Dept. of Electrical Engineering, Mansoura University, Mansoura, Egypt Dept. of Computers Engineering & Control Systems, Mansoura University, Mansoura, Egypt * [email protected] 00201220570035

Jo

urn a

lP

re-

pro of

2

Journal Pre-proof A Harmony Search-based H-infinity Control Method for Islanded Microgrid Abstract: This paper proposes a harmony search (HS) based H-infinity (H∞) control method to promote the conventional droop control method. The proposed method is used to enhance the performance of the voltage/frequency (V/F), controller. It can regulate both voltage and frequency to their rated values while enhancing autonomous microgrid (MG) power quality. The results gained from the proposed controller were compared with the results achieved by using the model predictive control (MPC) technique to show the applicability of the proposed controller. On top of that, a comparison between different controllers presented in this paper is performed. Keywords: Voltage Control, Microgrid, Power Quality, Harmony Search, H-Infinity, Frequency Control

Jo

urn a

lP

re-

pro of

1. Introduction MGs can be defined as a small-scale electric grid that contains loads, dispersed generations (DGs), energy storage units and control and protection systems [1]. Using MG is more attractive as it improves the system quality, decreases the carbon emission, and reduces the losses in power systems [2]. MG operators face a challenge of the optimal frequency and voltage control under different operating modes. MG operation may be grid-connected or isolated. When MG operates at grid-connected mode, its frequency and voltage are related to the grid frequency and voltage [3]. Control systems are needed to maintain the active and reactive power output from the DGs integrated to MG. However, under isolated mode operation, the MG is disconnected from the distribution network and operates in an islanded mode. Consequently, there will be a change in the MG frequency and voltage away from their rated values and a durable control system is required to regulate the values for frequency and voltage in this mode [4]. In general, the control methods are classified into primary and secondary control methods. The primary control methods are used to restore the MG frequency and voltage to the utility prescribed limitation. Anyhow, these methods cannot restore the MG frequency and voltage to the rated values. Primary control methods include; distributed control, central control, master/slave control, voltage/frequency (V/F) control methods [5], active–reactive power (P/Q) control [6], droop control [7], peer to peer control [6], PI/PID control [8], and sliding mode control [9]. The secondary control methods are used to modify the operation of the primary controllers and hence, keep the MG frequency and voltage at their rated values under any variations in load. These methods include; particle swarm optimization [10], fuzzy logic control [11], artificial neural networks [12], H-infinity [13], model predictive control [14], and linear quadratic regulator [15]. In the existence of external-disturbances and uncertainty parameters, H∞ control method can be used to promote the stability and enhance the system performance. This technique uses the method of linear-matrix inequalities (LMI) to deal with the control problem, as it can be directly utilized to explore feasible and appropriate solutions. It can decrease the impact of system disturbances and uncertainties; it can also enhance the system transient stability the existence of uncertainties [13]. In addition, this control method fosters the power quality of the system, as it can be defined as a repetitive control method involving both inner-voltage and outer-current control loops. It preserves the flexibility of the system in case of switching between different modes of control. It can be applied to solve MIMO models. In the meantime, the effect of disturbances on the controllers can also be mitigated. In addition, the H∞ control method has the ability to mitigate the resonance effect caused by the connection of capacitors for improving the system power factor. Nonetheless, this control method may be considered impractical for large dimensions system and with handling nonlinear constraints [9]. H∞ controller is powerful control technique used to generate an appropriate control signal with effective handling of the system disturbances on the controller outputs [16]., An interior model is utilized to the H∞ control method to achieve a proper repetitive control [17]. H∞ control was applied in the literature for many applications in MG control. In [18], H∞ was utilized for controlling the voltage source inverter (VSI) integrated with MG. It was applied to adjust the system frequency in [19] and to control system voltage in [20]. This technique has been used for robust control of inductance – capacitance – inductance filtered converter-based DGs in MGs [21], control system's power-sharing [22], and to enhance small and large-signal stability [23]. However, authors in [18-23] have utilized the H∞ method to adjust a single parameter such as frequency, voltage, current, power management or power quality. In those papers, the weighting parameters of the H∞ controller were chosen according to the trial and error method. However, this paper applies the H∞ controller to adjust the MG frequency and voltage and to reducing the THD. In addition, the weighted parameters of the H∞ controller are optimally obtained using the HS algorithm. H∞ controller is implemented in this paper to control isolated MG frequency and voltage with an optimally controlled variance in the load. Two weighting parameters (𝜉 and µ) are used to implement the output control signals and to optimally match efficiency and intensity in H∞ closed loop. In this paper, an HS-based optimization algorithm is applied to obtain appropriate values of these weighting. This algorithm is a metaheuristic optimization and based on the simulation of a musical artistic tune [24 ]. It is robust, efficient, easy in implementation and requires fewer mathematical equations [25]. In the last decade, the HS-algorithm has been used to solve a lot of power system problems including automatic generation control [26], dynamic economic dispatch [27], load frequency control [28], unit-commitment and optimal power flow problems [29-30]. On other hand, the algorithm has many applications in MGs including solving the problem of MG scheduling [31], improving operating efficiency of a MG [32], optimal clustering of MGs [33], optimal sizing of hybrid MGs [34], and improving the dynamic response of DG units [35]. HS algorithm has many advantages; simple modeling, easy implementation, less adjustable parameters, and quick convergence. This algorithm can explore the solution region's space in a reasonable time, and it has a memory to optimally choose the similar best harmonies in the population. On another hand, HS is a random search method such as genetic algorithms (GA) and particle swarm optimization (PSO) technique, as it doesn't need any prior domain knowledge. HS varies from these 1

Journal Pre-proof

re-

pro of

strategies as it requires only one search memory to develop, so it has the distinctive computational simplicity feature [36]. Generally, HS is simple to implement, efficient in computation, and it is a high-quality optimization algorithm. In addition, it can deal with complex engineering optimization problems as it has a low number of setting parameters [37]. The system stability analysis is performed by using root locus study, system step response, and singular value decomposition (SVD) to prove the proposed controller effectiveness. A comparison is performed between applying both the proposed H∞ based HS control method MPC method. MPC technique is considered as the most common controller in industrial problems. It has the ability to minimize the tracking error, achieve a fast problem computation, and it is considered an economical control method. In addition, the MPC method has the ability to handle both states and control constraints of the non-minimum phase. MPC is proposed to estimate the dynamic behavior of the system on a specified horizon. Nonetheless, it does not have the ability to cope with the unknown system parameters as it mainly depends on the system model. Moreover, for this method, it is so hard to analyze system performance and the process model cannot be recognized efficiently [8]. Referring to the aforementioned research on MGs, it can be seen that great efforts were done to enhance the performance of MGs. However, the control methods for MGs still missing innovative techniques, which have the ability to optimally control the MG frequency and voltage and enhance its power quality. The performance of the proposed method is verified in this paper by using a complex MG hypothetical system including multi-DGs under several loading conditions including both linear and nonlinear loads. The optimal settings of H∞ weighted parameters will be investigated through a detailed parametric study using the HS algorithm. This paper's key contributions are: - Optimally control the system frequency and voltage while enhancing power quality of an autonomous MG under load variations - Enhancing the droop control method performance by applying the H∞ robust control for adjusting MG frequency and voltage. - Using HS–based H∞ control method to precisely determine the weighting parameters of the proposed controller. - Exploring the stability of the system using root locus, system step response, bode diagram, and SVD. The remainder of the paper is organized as follows; section 2 presents the related work, including the base control method, droop controller, H∞ controller, MPC method, and HS optimization algorithm. Section 3 demonstrates a brief description of the proposed control method, and section 4 presents a case study, results and discussion, and the stability and robustness analysis. The summing-up of this work is presented in section 6. 2. Related work The base control method, droop controller, H∞ controller, MPC technique, and the HS optimization algorithm are discussed. in the following subsections.

Jo

urn a

lP

2.1. Base Control Method The base control method is used to regulate the MG in its autonomous operation condition. In this case, it is required to control MG frequency and voltage within their prescribed values to meet all load requirements. This control method is very important during the transition from off-grid to on-grid modes [3]. The base control method is consisting of two control loops including the voltage/frequency and current control loops. These two control loops are applied to provide the current and voltage reference to the VSI [5]. The complete Simulink diagram of this control method is depicted in Fig.1. The diagram consists of two control loops V/F and current control loops. The direct and quadrature components of the current are adopted through a current cross-coupling compensation control to eliminate the interaction between the two components. The base controller will be applied to control the islanded MG in section 4.

2

Journal Pre-proof VSI Converter

PCC

Lf

DG

L1

R1

Vdc Rf RLC Load

Cf

il abc

PWM

δ

ABC to dq Reference Frame

ild ilq vod voq iod ioq

pro of

dq to ABC

ild

v*id

+ + -

+

PI

vod

ωLf

voq + + +

v*iq

+

i*ld

PI

vo abc

Fref

1 ωinv

θinv

- vod dq

S

ilq

- voq

PI

i*lq

-

PI

Volage/Frequency Control Loop

i*lq

v*od +

ild

ωLf

i*ld

V/F Control Loop

i*ld

-

ilq

Current Control Loop

v*iq

Current Control Loop

v*id

io abc

vo abc

v*oq

i*lq

Fref

×

2π

vo abc

abc

+

Fig. 1. Simulink representation of the base control method

lP

re-

2.2. Droop Control Method MG under its islanded operation can be controlled using the droop control technique. To adjust the MG frequency and voltage, three loops of controllers are applied including power, voltage, and current control loops. These control loops applied to provide the reference active and reactive power and reference current and voltage to the VSI [38]. Besides, an LCL filter is adopted to filter the VSI voltage output to increase the system's power quality [39]. A Simulink model representing the three control loops is explained in Fig. 2. Generally, the characteristic of the frequency droop is used to maintain the system's active power and frequency as the frequency decrease results in an active power output increase of the VSI. Similarly, the characteristic of the voltage droop is used to adjust the system voltage and reactive power output from VSI as the voltage decrease result in an increase in the output reactive power of the VSI. To achieve a convenient power-sharing among the connected DGs, the gains of the droop controller must be optimally obtained [40]. This method will be adopted to control the frequency and voltage of the MG, and the results will be shown in section 4. VSI Converter

Lf

Vdc

Rc

vb abc

io abc

vi abc

Rf RLC Load

δ

v*id

v*iq

il abc vo abc io abc

Cf LCL Filter

PWM

+ + vod

voq + + +

+

PID

ild

v*id v*iq

ilq

Current Control Loop

PID

voq

ω

vod

Voltage Control Loop

i*lq

i*ld

i*ld

+

+ -

+ F

ωLf

i*ld

v*od v*oq

Droop Control Loop

0

Voltage Control Loop

ωLf

ʃ

ild ilq vod voq iod ioq

Current Control Loop

+

δ

ABC to dq Reference Frame

dq to ABC

Jo

DG

PCC

Lc

vo abc

urn a

il abc

iod

ild

ioq

ilq -

ωCf

i*lq

i*lq

+

ωCf

F

+ +

+

PID

P

P&Q Calculation

vo d,q io d,q

Droop Control Loop

+ -

PID

Q

v*od ω v*od

vod voq +

ω*

Q*

- + + V*

+ + P*

Droop Gains

Q P

v*oq

Fig. 2. Simulink representation of the power, voltage and current control loops 3

Journal Pre-proof

pro of

2.3. H-Infinity control method In modern control theory, the H∞ controller is considered as a very powerful control technique. It has the ability to maintain robust multivariable linear systems stability in the existence of system disturbances and uncertainties [17]. The central concept of the H∞ controller is based on the LTI system of the plant P(s), and the schematic block diagram of the linear feedback H∞ controller is presented in Fig. 3. As shown in Fig. 3, the control input is represented as u, the disturbances and other external inputs are represented as w, the measured output is characterized as y, and the controlled output is characterized as z. The C(s) controller must be synthesized with considering input y and output u to achieve system stability and minimize the output performance if disturbance inputs are present. This control method is used to determine the controller C(s) and to synthesize the sub-optimal problems. The standard formulation of the LTI system structure is represented in (1). 𝑥̇ = 𝐴𝑥 + 𝐵1 𝑤 + 𝐵2 𝑢 𝑦 = 𝐶2 𝑥 + 𝐷21 𝑤 + 𝐷22 𝑢 (1)

re-

The feedback closed-loop transfer function in Fig. 3. can be mathematically expressed as: 𝐴 𝐵1 𝐵2 𝑥 𝑥̇ 𝑥 𝑥 𝑃 𝑃12 [ 𝑧 ] = 𝑃(𝑠) [𝑤] = [ 11 ] [𝑤] = [𝐶1 𝐷11 𝐷12 ] [𝑤] (2) 𝑃21 𝑃22 𝑦 𝑢 𝑢 𝐶2 𝐷21 𝐷22 𝑢 The feedback branch function is expressed as; 𝑢 = 𝐶𝑦 (3) Whereas, the closed loop representing the transfer function from w to z is expressed as; 𝑇𝑤𝑧 = 𝑃11 + 𝑃12 𝐶 (𝐼 − 𝑃22 )−1 𝑃21 (4) Where; 𝐼 defines an identity matrix The ∞ - norm from 𝑤 to 𝑧 must be reduced to be less than a pre-determined positive number 𝛾 to achieve the system stability The ∞ - norm can be mathematically expressed as; ‖𝑇𝑤𝑧 (𝑠)‖∞ < 𝛾 (5) The plant P(s) is linearized as follows; 𝐷 𝐷12 𝐶 P(s) = [ 11 ] + [ 1 ] (𝑆𝐼 − 𝐴)−1 [𝐵1 𝐵2 ] (6) 𝐷21 𝐷22 𝐶2 External Input w

lP

Plant P(s)

Control Signal u

H∞ Controller C(s)

External Output z

Measured Variables y

urn a

Fig. 3. Basic of H∞ controller

Jo

2.4. Model predictive control (MPC) method MPC is an integral controller applied to automate the future system response. MPC can be used in the tracking, optimization, management, and assessment of disturbance [41]. To adjust the MG system within the specific time horizon, the inputs to the control system must be selected correctly to reduce the cost variable. The cost-function is realized by considering the current values of the resulting processes and the perturbation model prediction [42]. The independent-variables impact on the dependent-variables is estimated by the MPC method. The performance of the plant system is used to estimate the unmeasured input quantities which are considered as dependent variables. In addition, the power output is independent-variables. Both variables should be used to achieve the optimal solution of the control problem and to reduce the reference tracking errors. The MPC system plant design is shown in Figure 4. In this analysis, the MPC is applied to the four-loop plant design including droop, voltage, current control loops, and control loop for LCL filter and coupling circuit. These control loops are used for providing the reference frequency, voltage, and current to the VSI and in addition, enhancing the MG power quality.

4

Journal Pre-proof

VSI Converter il abc DG

Vdc

Lf

Lc

vo abc

Rc

PCC vo abc

io abc

vi abc Rf

RLC Load

Cf vo abc LCL Filter

PWM

io abc

abc to dq

δ

dq to abc

pro of

δ

State-Space of the Plant Model v* id

v o d,q io d,q

v* iq

v* id

io d,q

MPC Controller

v o d,q

v* iq

ω* V* Q* P*

re-

Fig. 4. MPC method plant model

urn a

lP

2.5. Harmony Search Algorithm HS optimization method is a metaheuristic technique that imitates the cycle of natural music improvising. The musicians use the improvisation process to obtain the best harmony states similar to that of the jazz improvisation. The musicians of the jazz band try to get the proper pitches to obtain perfect harmony [25]. In this method, an aesthetic standard is used to estimate the quality of the improvised harmony. The musician pitches must be adjusted to get better harmony in music. The pitches can be adjusted as they can be chosen under different combinations. The first is that the musician plays any pitch from the memory. The second is that the musician plays one pitch close to that in memory [35]. The third that the musician plays a random pitch from the defined limits [43]. HS algorithm depends on limited number of parameters including harmony memory size (HMS), harmony memory consideration rate (HMCR) that is likely to consider decision variables stored in harmony memory (HM), timeline adjustment rate (PAR) for the likelihood of randomly altering selected HM data, bandwidth of the generation Finally, there are the number of improvisations[ 45] that define the maximum number of iterations. The main steps of the HS algorithm can be defined as follows: Step1: Initialize the HS algorithm optimization parameters Step2: Initialize the HM Step3: Apply the improvisation process to get a new harmony from HM Step4: Calculate the fitness function of each improvisation Step5: Updating the HM Step6: Until achieving the stopping criteria, repeat step3, step4, and step5.

Jo

Proposed H∞ Control Method-Based HS Optimization Algorithm Although no interaction link between the DGs is required for the droop controller, it has its own inconvenience which limits the appropriate operation in MGs. The main disadvantage of this system is the difference in voltage and frequency from the nominal value for the correct power-sharing change in MG. To enhance the response of the droop controller, this paper suggests an innovative approach to enhance the droop controller performance by optimizing the H∞ controller with the HS algorithm. H∞ is used to synthesize controls with efficient quality to ensure stability and minimize the effects of disturbances and uncertainties. The H∞ approach suggests involving a control circuit for the internal voltage and an external control loop for the system. In the presence of uncertainties, the approach is successful in improving transient stability. The impact of disruptions on the control system can be minimized. A schematic diagram for the H∞ method is explained in Fig. 5, where the plant transfer function is defined by P(s) and feedback control is given by C(s). The control method being proposed is used in autonomous mode to enhance the MG voltage/frequency and to enhance the quality of the system. 3.

5

Journal Pre-proof

External Output z

Plant P

{

ωref vref VSI Converter

External Input w

PCC

Lf

il abc

DG

L1

R1

vo abc

i o abc

Vdc Rf RLC Load

Cf

il abc vo abc i o abc ABC to dq Reference Frame

PWM

ʃ

ild ilq vod voq iod ioq dq to ABC

v*id v*iq

Control Signal u

ild

ilq

Current Control Loop

i*ld

voq

vod

Voltage Control Loop

i*lq

e

pro of

δ

δ

ω

Droop Control Loop

v*od

v*oq

0

H∞ Controller C

Q

P

P&Q Calculation

vo d,q io d,q

Measured Variables y

Fig. 5. Structure of a control system using the H∞ method

Jo

urn a

lP

re-

The mathematical equations represent the control loops are handled in the dq reference frame are taken as presented in [46-47]. The complete inverter modeling in state-space equations is presented in (7) and (8). 𝑣𝑖𝑑𝑖 𝜔𝑟𝑒𝑓 𝑣𝑖𝑞𝑖 [𝑥𝑖𝑛𝑣𝑖 ̇ ] = 𝐴𝑖𝑛𝑣𝑖 [𝑥𝑖𝑛𝑣𝑖 ] + 𝐵𝑖𝑛𝑣𝑖1 [ 𝑣 ] + 𝐵𝑖𝑛𝑣𝑖2 [𝑣 ] (7) 𝑟𝑒𝑓 𝑏𝑑𝑖 𝑣𝑏𝑞𝑖 𝑣𝑖𝑑𝑖 𝜔𝑟𝑒𝑓 𝑣 [𝑦𝑖𝑛𝑣𝑖 ] = 𝐶𝑖𝑛𝑣𝑖 [𝑥𝑖𝑛𝑣𝑖 ] + 𝐷𝑖𝑛𝑣𝑖1 [ 𝑣 ] + 𝐷𝑖𝑛𝑣𝑖2 [𝑣 𝑖𝑞𝑖 ] (8) 𝑟𝑒𝑓 𝑏𝑑𝑖 𝑣𝑏𝑞𝑖 Where; 𝑇 𝑥𝑖𝑛𝑣𝑖 = [𝛿𝑖 𝑃𝑖 𝑄𝑖 ∅𝑑𝑖 ∅𝑞𝑖 𝛾𝑑𝑖 𝛾𝑞𝑖 𝑖𝑙𝑑𝑖 𝑖𝑙𝑞𝑖 𝑣𝑜𝑑𝑖 𝑣𝑜𝑞𝑖 𝑖𝑜𝑑𝑖 𝑖𝑜𝑞𝑖 ] ∗ 𝜔𝑟𝑒𝑓 − 𝜔 𝑒1 𝑣𝑟𝑒𝑓 − 𝑣𝑜𝑑 ∗ 𝑒2 𝑣 ∗ − 𝑣𝑜𝑑 𝑒 [𝑦𝑖𝑛𝑣𝑖 ] = 3 = 𝑜𝑑 ∗ 𝑒4 𝑣𝑜𝑞 − 𝑣𝑜𝑞 𝑒5 ∗ 𝑖𝑙𝑑 − 𝑖𝑙𝑑 [𝑒6 ] ∗ [ 𝑖𝑙𝑞 − 𝑖𝑙𝑞 ] Where 𝐴𝑖𝑛𝑣𝑖 , 𝐵𝑖𝑛𝑣𝑖1 , 𝐵𝑖𝑛𝑣𝑖2 , 𝐶𝑖𝑛𝑣𝑖 , 𝐷𝑖𝑛𝑣𝑖1 , and 𝐷𝑖𝑛𝑣𝑖2 is introduced in [48]. 𝑣𝑜d , 𝑣oq , are the direct and quadratic components of the voltage, 𝑖𝑜𝑑 , and 𝑖oq are the direct and quadratic components of the current, 𝛿 is the angular displacement of the frequency, 𝑃𝑖 , 𝑄𝑖 are the fundamental active and reactive power, ω* is the grid angular frequency, 𝜔𝑟𝑒𝑓 and 𝑣𝑟𝑒𝑓 are reference frequency ∗ ∗ and a reference voltage, 𝑣𝑜𝑑 and 𝑣𝑜𝑞 are d-axis and q-axis voltage, ∅𝑑𝑖 and ∅𝑞𝑖 are the state variables defined for PI controllers of the voltage control loop, 𝛾𝑑𝑖 and 𝛾𝑞𝑖 are the state variables defined for PI controllers of the current control loop, and 𝑖𝑙𝑑𝑖 and 𝑖𝑙𝑞𝑖 are the direct and quadrature components of 𝑖𝑙𝑖 . 𝑣𝑏d , 𝑣bq are the dq components of the PCC voltage, and 𝑣𝑖𝑑 , 𝑣𝑖𝑞 are the dq components of the inverter voltage. The inner model M is used as a repeated frequency control system, as explained in Fig. 6(a). It can be represented as a low pass filter with W(s) as shown in (9) [47]. The state-space model of the internal model M is represented in (10). 𝜔𝑐 𝑊(𝑠) = (9) 𝑠+ 𝜔𝑐

Where 𝜔𝑐 is the cut-off frequency of the low pass filter W. 𝐴 𝐵𝑤 −𝜔 𝜔𝑐1 𝑊=[ 𝑤 ] = [ 𝑐1 ] (10) 𝐶𝑤 𝐷𝑤 1 0 To improve the system performance, two extra parameters 𝜉 and µ are utilized to assure system freedom as presented in Fig. 6(b). The realizing of the generalized plant is then obtained as in (11) where C is the controller to be devised.

6

Journal Pre-proof

w

pro of

𝐴𝑖𝑛𝑣𝑖 0 0 𝐵𝑖𝑛𝑣𝑖1 𝐵𝑖𝑛𝑣𝑖2 𝐵𝑤 𝐶𝑖𝑛𝑣𝑖 𝐴𝑤 𝐵𝑤 𝜉 𝐵𝑤 𝐷𝑖𝑛𝑣𝑖1 𝐵𝑤 𝐷𝑖𝑛𝑣𝑖2 𝑃̃ = 𝐷𝑤 𝐶𝑖𝑛𝑣𝑖 𝐶𝑤 𝐷𝑤 𝜉 𝐷𝑤 𝐷𝑖𝑛𝑣𝑖1 𝐷𝑤 𝐷𝑖𝑛𝑣𝑖2 0 0 0 0 𝜇 [ 𝐶𝑖𝑛𝑣𝑖 0 𝜉 𝐷𝑖𝑛𝑣𝑖1 𝐷𝑖𝑛𝑣𝑖2 ] Assuming that ω = 0, the realization of the transfer function from a to b can be found as follows: 𝐴𝑖𝑛𝑣𝑖 + 𝐵𝑖𝑛𝑣𝑖2 𝐷𝑐 𝐶𝑖𝑛𝑣𝑖 𝐵𝑖𝑛𝑣𝑖2 𝐶𝑐 𝐵𝑖𝑛𝑣𝑖2 𝐷𝑐 𝐶𝑤 0 −1 𝐴𝑖𝑛𝑣𝑖 𝐵𝑖𝑛𝑣𝑖2 𝐵𝑐 𝐶𝑖𝑛𝑣𝑖 𝐴𝑐 𝐵𝑐 𝐶𝑤 0 𝑇𝑏𝑎 = (1 − [ ] 𝐶) 𝑊 = [ ] 𝐶𝑖𝑛𝑣𝑖 𝐷𝑖𝑛𝑣𝑖2 0 0 𝐴𝑤 𝐵𝑤 𝐶𝑖𝑛𝑣𝑖 0 𝐶𝑤 0 Where, 𝐴 𝐵𝑐1 𝐵𝑐2 𝐶=[ 𝑐 ] 𝐶𝑐 𝐷𝑐1 𝐷𝑐2 After obtaining the controller C, the system stability can be tested by checking ||Tba||∞.

(11)

(12)

(13)

Generalized Plant

ωref

{v

z

ref

Plant P u

W(s)

ξ

{

+ + e

+ +

Plant P

Internal Model M

y H∞ Controller C

u

e

W

µ

}

re-

H∞ Controller C

Fig. 6(a). Structure of a control system using H∞ repetitive Fig. 6(b). H∞ controller with weighting parameters control Fig. 6. Formulation of the proposed H∞ controller

Jo

urn a

lP

The test and error approaches have been used to extract weighted parameters from most papers that are using the H∞ control method. This paper proposes an insightful way of optimally evaluating the controller weighted parameters. The suggested approach depends on applying the HS optimization algorithm. The HS optimization algorithm intent is to optimally pick the H∞ control method's weighting parameters (𝜉 and µ) for each load variance for improving both the system stability and the MG power efficiency. This paper uses the fitness function of the frequency and voltage signals failure. The elementary pseudo-code describes the HS-algorithm is illustrated in Table 1.

7

Journal Pre-proof TABLE 1. HS Pseudocode

re-

pro of

Initialize the HS parameters HMS, HMCR, PARmin, PARmax, bwmin, bwmax, NI Generate a number of feasible harmonies equal to HMS for HM Calculate the fitness function (Fit) value of each harmony in HM for iteration, i ←1 to max Iteration NI do for j ← 1 to 2 do r1 ← generate random number if r1 < HMCR do Xnew(j) ← randomly pick harmony of HM r2 ← generate random number if PARmin < r2 < PARmax do BW ← bwmin + (bwmax – bwmin) * rand Xnew(j) ← Xnew(j) – rand * BW end else Xnew(j) ← random value from the possible range end end Calculate the fitness function (Fitnew) value of the Xnew(i) Sort HM and get the worst fit if Fitnew < Fitworst do Save the new harmony in HM Remove the worst harmony from the HM end end

Case study The proposed approach is used to evaluate its applicability on a test-system with or without a linear load. This analysis applies to the island-based testing system, the base controller, drop-control and the control techniques suggested and then compares the effects. Finally, the test-system is subject to the MPC testing method and the results achieved are compared to the controller proposed. The test-system contains three DG units and three loads of a suspected MG. The MG is integrated with the main grid via a grid-breaker to swap between both islanded and grid-connected modes. Table 2 gives the parameters of the system under study. The test-system is represented using the Matlab/Simulink environment as explained by Fig. 7. All the results obtained by applying different controllers are measured from Bus 3 including the output voltage, current, and frequency. Bus 3 is the furthest bus from the DGs controllers, so it represents the worst condition. Hence, if the frequency and voltage at that bus are optimally adjusted, it is obvious that the frequency and voltage at other buses (nearer to the DGs controllers) must be adjusted.

Jo

urn a

lP

4.

Fig. 7. Simulink representation of the test system

8

Journal Pre-proof

Components

TABLE 2. Parameters of the test system Parameters Symbols Nominal frequency f

DG system

Quantity 50 Hz

Nominal peak phase voltage

V

540 V

Active power rating

P

130 kW

Reactive power rating

Q

70 kVAR

Inductance

L1

5.42 mH

Capacitance

C

11 μF

Converter LCL filter

L2

0.13 mH

P1, P3

45 kW

Reactive power

Q 1, Q 3

15 kVAR

Active power

P2

40 kW

Reactive power

Q2

25 kVAR

Droop controller coefficients

Frequency droop characteristics

𝑚𝑝

0.001

Voltage droop characteristics

𝑛𝑞

0.0033

PI controller coefficients for voltage controller

Proportional gain

Kpv

10

Integral gain

Kiv

2

PI controller coefficients for current controller

Proportional gain

Kpc

30

Integral gain

Kic

0.5

Load 1, Load 3 Load 2

pro of

Inductance Active power

Jo

urn a

lP

re-

4.1. The base control method This section presents the applying of the base controller to the prescribed MG test system by considering linear and nonlinear loading conditions. 4.1.1. Linear loading condition The system load profile with the linear loading condition is presented in Figs. 8(a) and 8(b). The system voltage, current, and frequency are explained by Fig. 9. The load voltage and current waveforms are analyzed using Fast Fourier transform (FFT) to check the changes in system power quality. The load current THD becomes 3.16 % after the application of the base controller and the THD of the load voltage decreases to 2.74 %.

9

Journal Pre-proof

Load Active Power

Load Reactive Power 50

100

50

1030-

30 30

10

1010

30-

re-

50

10

50- Fig. 8(b) Reactive load power for case 1 0 0.2 0.4 0.6 (linear 0.8 1load) 1.2 1.4 1.6 1.8 2 Time (Seconds) Load Load Reactive Reactive Power Power 50 50

(kVAR) Qload Qload (kVAR)

100

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Time (Seconds)

50100.2 0.4 1.4 1.4 1.6 1.8 2 0 0 0.2 0.4 0.6 0.6 0.8 0.8 1 1 1.21.2 1.6 1.8 (Seconds) TimeTime (Seconds)

2

urn a

lP

Fig. 8(c) Active load power for case 2 Fig. 8(d) Reactive load power for case 2 (Non-linear load) (Non-linear load) Fig. 8. Load curves for the two case studies

Fig. 9(a) Load voltage

Jo

Pload (kW)

0 Fig. 8(a) Active load power for case1 0 0.2 0.4 0.6 0.8load) 1 1.2 1.4 1.6 1.8 2 (linear Time (Seconds) Load Active Power 150

30

pro of

Qload (kVAR)

Pload (kW)

150

Fig. 9(b) Load current

10

Journal Pre-proof

pro of

Fig. 9(c) System frequency Fig. 9. Outputs for base case controller with a linear load

re-

4.1.2. Nonlinear loading condition The nonlinear system load profile was given in Figs. 8(c) and 8(d). Figure 10 shows the system results output (i.e. voltage, current, and frequency) and Fig. 11 presents the voltage and current FFT analysis. From Fig. 11, the load current THD is 8.09% and the load voltage THD is 38%.

urn a

lP

Fig. 10(a) Load voltage

Jo

Fig. 10(b) Load current

Fig. 10(c) System frequency Fig. 10. Outputs for base case controller with non- linear load

4.2. Droop control method This section presents the applying of the droop controller to the prescribed MG test system by considering linear and nonlinear loading conditions.

11

Journal Pre-proof 4.2.1. Linear loading condition The droop controller is verified using the MG test-system loaded in the presence of a linear load given in Figs. 8(a), (b). The system outputs are presented on the left side of Fig. 11. The results show that the load current and voltage THD are 0.93% and 1.93% respectively as shown on the left side of Fig. 12. 4.2.2. Nonlinear loading condition The droop control approach is implemented in three different nonlinear loads connected to buses 1, 2 and 3, as presented in Fig. 7. The active and reactive load profiles of the system were presented in Figs. 8(c), 8(d). the output system results are shown on the left side of Fig. 13. The voltage and current FFT analysis are presented on the left-side of Fig.14. From these figures, the load current and voltage THD are 2.02% and 3.42% respectively.

re-

pro of

4.3. HS optimization algorithm The HS algorithm is practiced to the test-system (presented in Fig.7) using the Matlab environment. The application of the HS algorithm determines the H∞ control method's optimal weighting parameters. Table 3 displays the HS algorithm parameters. Each iteration indicates the fitness value as shown in Fig. 15(a) and each improvisation's fitness value is shown in Figure 15(b). With a linear load, the fitness function is 0.3241, 𝜉 = 22.7542 and µ = 29.1539. While in case of nonlinear load the fitness function value is 0.3717, and 𝜉 = 24.1184 and μ= 26.0040 The HS algorithm is applied to perform an off-line tuning and then the best-found parameter setting of the H∞ controller is used online to control the system. It takes about 1500 Function Evaluations (FEs) for HS to approach optimal settings of the H∞ parameters. In this case study, the simulation time (off-line) for the linear loading case is 109 seconds using CPU with processor Intel (R) Core (TM) i3 and RAM 8 GB. Also, the simulation time (off-line) for the nonlinear loading case is 113 seconds. While the system on-line settling time is 5.32 μs. TABLE 3. Parameters of HS algorithm No Parameters of HS Values 1 HMS 30 2 HMCR 0.9 3 PARmax 0.9 4 PARmin 0.4 5 bwmax 1.0 6 bwmin 0.0001 7 NI 50

urn a

lP

4.4. Applying the proposed control method The employment of the proposed controller to the prescribed MG test system with considering linear and nonlinear loading conditions are outlined below 4.4.1. Linear loading condition The suggested controller is examined for a linear loading condition using the MG test system (shown in Figs. 8(a), (b)). By means of the Matlab hinfsyn algorithm, the controller C is obtained. The two weighting parameters are obtained as 22.7552 and 29.1539 respectively. The right side of Fig. 11 shows the output system results attained by applying the proposed procedure. The load current and voltage THD are obtained from the FFT analysis presented on the right-side of Fig.12 as 0.66% and 1.26% respectively. 4.4.2. Nonlinear loading condition Using Matlab hinfsyn algorithm, the proposed controller is implemented to the MG test-system. As obtained from the optimization algorithm HS, 𝜉, and µ are registered in 24.1184 and 26.0040 respectively. The system load profiles are presented in Figs. 8(c), 8(d). The system output results are presented on the right-hand side of Fig. 13. The load current and voltage THD are obtained from the FFT analysis on the right-side of Fig. 14 as 0.89% and 1.21% respectively.

Jo

4.5. MPC method The MPC method is practiced to the studied MG test-system to validate the soundness of the proposed method. The system output results are shown in Fig. 16. Figure 17 shows the THD study of the voltage and current waveforms. The two loading conditions are used for this process, the effects of the process for the first loading state (without linear loading) are shown in the left-side of the Figs. 16 and 17. Meanwhile, the right-side of the Figs. 16 and 17 show the effects of adding a nonlinear load to the test system. FFT analysis for load voltage and current shows that the THD is 0.82 % and 1.4 % with a linear loading condition. Moreover, for the nonlinear loading condition, the THD of the load current and voltage are 1.08% and 1.4% respectively.

12

Journal Pre-proof Droop Control Method

Proposed Control Method

pro of

Fig. 11(a) Load voltage

re-

Fig. 11(b) Load current

Proposed Control Method

urn a

Droop Control Method

lP

Fig. 11(c) System frequency Fig. 11. Outputs for a case study with linear load

Jo

Fig. 12(a) FFT analysis for load current waveform

Fig. 12(b) FFT analysis for load voltage waveform Fig. 12. FFT analysis of current and voltage waveforms with linear load 13

Journal Pre-proof Droop Control Method

Proposed Control Method

pro of

Fig. 13(a) Load voltage

lP

re-

Fig. 13(b) Load current

Fig. 13(c) System frequency Fig. 13. Outputs for a case study with a non-linear load Proposed Control Method

urn a

Droop Control Method

Jo

Fig. 14(a) FFT analysis for load current waveform

Fig. 14(b) FFT analysis for load voltage waveform Fig. 14. FFT analysis of current and voltage waveforms with a non-linear load 14

Journal Pre-proof

With Non-Linear Load

pro of

With Linear Load

re-

Fig. 15(a) Fitness values at each iteration

Fig. 15(b) Fitness values at each improvisation Fig. 15. Fitness Values of HS Algorithm

lP

4.6. Comparative Analysis A comparative study is carried out between the droop controller, the proposed controller and the MPC controller compared to the base control method. This comparative analysis is made under the two conditions of system loading. Through implementing the base method, the MG frequency and voltage vary in linear loading conditions, as shown in Fig. 9 from their nominal values according to system load variance. Nevertheless, in the case of nonlinear loading condition, the base control cannot change the MG frequency and voltage to their nominal values, as depicted in Fig. 10.

urn a

As shown on the left-side of Figs 11(a) and (c), the droop controller can adjust the MG frequency and voltage to a satisfactory limit under the MG load variation. However, after the system load variation, it failed to restore the rated frequency and voltage values. There are many impacts of applying the nonlinear load to the MG on the system voltage and frequency. Consequently, the droop controller does not have the ability to modify the MG frequency and voltage as presented on the leftside of Figs. 13 (a) and (c), respectively.

Jo

Through implementing the proposed H∞ based HS control method, the MG frequency and voltage are modified and regulated to their normal prescribed values after system load changes for the two loading conditions, as depicted on the rightside of Figs. 11(a) and (c) for linear loading condition and Figs. 13(a) and (c) for nonlinear loading. In the case of linear loading condition, applying the MPC approach to the studied-system shows that the system output results are improved over the droop control method. Nevertheless, the ripples that presented in the waveforms of the MG frequency and voltage are more enormous due to the MPC method than the control method suggested, as depicted in the left and right sides of Figs. 16(a) and (c) respectively for linear and nonlinear loading conditions. Based on the THD of the voltage and current waveforms, a comparison between the control methods is presented in table 4. Compared to the values dedicated by applying the base control method for linear loading condition, the current and voltage waveforms THD of the proposed method are improved by 79.11% and 54.01%, 70.56% and 29.56% for the droop controller, 74.05% and 48.90% for the MPC. The THD also increases 88.99% and 72.37% for the proposed controller in the case of a nonlinear loading condition, 86.65% and 58.57% for the MPC system, and 74.90% and 31.95% for the droop control method. Such results show that the approach suggested increases the voltage THD and current waveforms better than the other methods. Considering maximum frequency deviation (MFD), the controller response time (CRT), an integral of square error (ISE), another comparison held between the controllers for the system frequency and voltage waveforms. The response time shows how quickly after any load change the controller can restore both the device voltage and nominal frequency values. The maximum frequency deviation is the average increase or decrease in the waveform of the system frequency, while the ISE calculates the deviation from their nominal values in system voltage and frequency waveforms. Table 5 shows a comparison based on these indices between the controllers. The results show that the proposed control method has better performance compared to the other controllers in regulating the frequency and voltage of MG. 15

Journal Pre-proof With linear load

With non-linear load

pro of

Fig. 16(a) Load voltage

lP

re-

Fig. 16(b) Load current

Fig. 16(c) System frequency Fig. 16. Outputs for a case study with the MPC method With non-linear load

urn a

With linear load

Jo

Fig. 17(a) FFT analysis for load current waveform

Fig. 17(b) FFT analysis for load voltage waveform Fig. 17. FFT analysis of current and voltage waveforms with MPC method 16

Journal Pre-proof

pro of

TABLE 4. Comparison between various control methods based on THD With Linear Loading Condition Base Control Droop Control Proposed Control MPC Method Method Method Method % % % % % % % value value decrease value decrease value decrease THDI 3.16 0.93 70.56% 0.66 79.11% 0.82 74.05% THDV 2.74 1.93 29.56% 1.26 54.01% 1.40 48.90% With Non-Linear Loading Condition Base Control Droop Control Proposed Control MPC Method Method Method Method % % % % % % % value value decrease value decrease value decrease THDI 8.09 2.03 74.90% 0.89 88.99% 1.08 86.65% THDV 3.38 2.30 31.95% 1.21 72.37% 1.40 58.57%

lP

re-

TABLE 5. Comparison between various control methods based on CRT, MFD, and ISE With Linear Loading Condition MPC Method Base Control Droop Control Proposed Control Method Method Method CRT 0.04 0.029 0.01 0.025 MFD 2.59 2.29 0.45 0.9 ISEV 8823 6591 978.6 2784 ISEF 43.24 15.95 7.789 10.07 With Non-Linear Loading Condition MPC Method Base Control Droop Control Proposed Control Method Method Method CRT 0.052 0.045 0.015 0.029 MFD 24.99 3.55 0.60 1.19 ISEV 9395 6754 1198 3774 ISEF 67.48 46.58 8.285 10.35 In General, the results obtained show that the proposed method has the ability to regulate the MG operation in presence of different loading conditions. Also, the reduction of the THD of current and voltage waveforms leads to enhancing the MG power quality by applying the proposed method. The suggested method of control improves the CRT, reduces the MFD, and improves the system frequency and voltage ISE.

𝑌(𝑠) 𝑋(𝑠)

=

𝐺(𝑠) 1+𝑘 𝐺(𝑠)𝐻(𝑠)

urn a

4.7. Stability analysis The root locus and system step response were obtained to assess the system stability under the implementation of the proposed control approach. The root locus is used under the variation of system parameters to analyze the locus of the roots in the s-plane. The feedback control scheme is presented below in Fig. 18. The feedforward, feedback, and transfer functions of the controller are the G(s), H(s), and k. The root locus approach is applied to study the impact of the gain variations on the position of the closed-loop system poles of [49]. The transfer function of the closed-loop obtained from Fig. 18 is as follows; (14) Y(s)

X(s)

G(s)

+

Jo

-

H(s)

C

Fig. 18. Standard closed-loop system

Fig. 19 (a) is quite revealing in several ways. First, the profile stays in the Left-hand plane (LHP) whatsoever the gain of the controller. Second, further analysis showed that the designer has the freedom to choose appropriate system gain to match transient system response. From the data in Figure 19 (b), it is apparent that the settling time (5.32 μs) and the rise time (2.66 μs) 17

Journal Pre-proof

pro of

are decreased to an acceptable value. These results suggest that the controller can adjust the MG parameters efficiently and very fast.

lP

re-

Fig. 19(a) System root locus

Fig. 19(b) System step response Fig. 19. Stability analysis

Jo

urn a

Furthermore, system stability is analyzed based on singular value decomposition (SVD). The SVD is obtained for the frequency response and to process noise. Considering the process noise the minimum SVD 𝜎𝑚𝑖𝑛 = −130 𝑑𝐵 as depicted in Fig. 20(a) and (b). The most surprising aspect is that the system is less prone to process noise.

Fig. 20(a) SVD frequency response 18

pro of

Journal Pre-proof

Fig. 20(b) SVD frequency response to process noise Fig. 20. System stability singular values decomposition

urn a

lP

re-

The gain margin is the factor that increases the gain before instability takes place, while the phase is constant, i.e., the gain margin is a measure of gain uncertainty tolerance. Similarly, the phase margin definition assumes that the gain margin is kept constant, so the phase margin is a metric of pure phase sensitivity tolerance. According to the open-loop bode plot of the system is shown in Fig. 21 is marginally stable.

Fig. 21. System bode diagram

Jo

4.8. Robustness analysis Since the working circumstances may differ (changes in load and, disturbances), and control systems are typically built using much-simplified models, the control system must be robust to function correctly in these conditions. Mathematically, this implies that not just for one plant, but for a collection of plants, the controller must perform well. Despite model uncertainty, the system's stability must be preserved. To have a robust controller it is required to design a controller that satisfies stability in uncertain conditions. If the system also meets performance specifications such as sensitivity and disturbance rejection, good tracking, steady-state performance, the system is ensured that it has robust performance [50]. There are usually two categories of model uncertainty: structured uncertainty and unstructured uncertainty. If one is unsure about the place of the poles, zeros, or gain of the system, this is an example of structured uncertainty. The system coupling parameters are presumed to be unpredictable and off by 20 % so as to examine the robustness of the proposed controller against structured uncertainty. What is interesting in Fig. 22(a) is that still at the utmost point of uncertainty, the output is adequately accepted (as demonstrated by the percent overshoot, rise and settling times). SVD extends the bode magnitude response to MIMO 19

Journal Pre-proof

pro of

systems and is helpful for robustness analysis. SVD offers a helpful way to quantify multivariable directionality, but in terms of frequency-domain performance and robustness [51], the maximum singular value is also very useful. From the data in figure 22 (b) Fig. 22(c), it is apparent that the control system has robust performance.

urn a

lP

re-

Fig. 22(a) System step response in the presence of uncertainty

Jo

Fig. 22(b) SVD in the presence of uncertainty

Fig. 22(c) Bode diagram in the presence of uncertainty Fig. 22. System robustness analysis in the presence of uncertainty 20

Journal Pre-proof Unstructured uncertainty can be modeled in different ways, like additive and multiplicative uncertainty [50]. Feedback decreases the closed-loop system's sensitivity to uncertainties or differences in components situated in the system's forward route. Rejection of disturbance relates to the reality that feedback can eliminate or decrease the impacts of undesirable disturbances in the feedback loop. Disturbance tracking and rejection require low sensitivity while noise suppression requires small complementary sensitivity. For the specified uncertainty, one can check the stability of the closed-loop using the small-gain theorem; then it is important to understand what is the least uncertainty that will destabilize the scheme. In the event of multiplicative uncertainty, the lowest destabilizing uncertainty is also referred to as a multiplicative stability margin (MSM). 1 𝑀𝑆𝑀 = (15) 𝑀𝑟

Where 𝜔

pro of

𝑀𝑟 = 𝑠𝑢𝑝 ⏟ |𝑇(𝑗𝜔)|

urn a

lP

re-

In addition, the symbol “sup” represents the function’s supremum. The supremum of a function is its maximum value even it is not achieved. Let us compute the MSM for the system. For the MSM, it is required to obtain the complementary sensitivity and find its peak value. The plot is shown in Fig. 23, the peak value is 0.48, resulting in an MSM of 2.083. Thus, unmodelled multiplicative uncertainties with transfer function magnitudes below 2.083, the system will be robustly stable against.

Fig. 23. The frequency response of the complementary sensitivity for determining the MSM 5.

Conclusion

Jo

A proposed control method for regulating frequency/voltage as well as improving the power quality of an autonomous MGs was presented in this paper. The approach depended on enhancing the conventional droop control method by using a robust H∞ controller. To enhance the system stability, the HS optimization technique was applied to accurately determine the weighted parameters of H∞ controller. The proposed controller succeeded in regulating the frequency and voltage to their nominal values after any breach of system loading while enhancing the power quality of the MG. The proposed approach was applied to a testsystem in presence of two loading conditions in the MATLAB/SIMULINK environment. Based on the THD for voltage and current waveforms, CRT, MFD, and the ISE for frequency and voltage waveforms, a comparative analysis between a base controller, droop controller, the proposed H∞ based HS controller, and a proposed MPC controller was performed. The comparison showed that the suggested controller had a more agile response, a reduced MFD, a reduced ISE for frequency and voltage waveforms, and a better power quality. Considering root locus, step response, and SVD, the stability analysis was performed. The settling and the rise times were reduced to minimum values. Besides, a robustness judgment based on step response, SVD, and bode diagram were conducted to prove system robustness against system parameter uncertainties. In addition, the stability of the closed-loop using the small-gain theorem was investigated when the system subjected to multiplicative uncertainty. On top of that, the multiplicative stability margin (MSM) was calculated. Together these results provide important insights: (1) the proposed control system is more stable, (2) effective to change in the frequency and voltage of the system, (3) improve the quality of the system power, and (4) system robustness against system parameter uncertainties

21

Journal Pre-proof Reference

Jo

urn a

lP

re-

pro of

[1] A. Rabiee, M. Sadeghi, J. Aghaeic, A. Heidari, "Optimal Operation of Microgrids Through Simultaneous Scheduling of Electrical Vehicles and Responsive Loads Considering Wind and PV Units Uncertainties", Renewable and Sustainable Energy Reviewers, Vol. 57, 2016. [2] M. Mahmoud, M. Rahman, F. Sunni, "Review of Microgrid Architectures – A System of Systems Perspective", IET Renewable Power Generation, Vol. 9, 2015. [3] B. Sedhom, M. El-Saadawi, A. Hatata, and E. Abd-Raboh, "Review on Control Schemes for Grid Connected and Islanded Microgrid", Journal of Electrical Engineering, Vol. 19, Iss. 3, pp. 557-572, 2019. [4] B. Satish, S. Bhuvaneswari, "Control of Microgrid – A Review", International Conference on Advances in Green Energy (ICAGE), IEEE, Thiruvananthapuram, India, 2014. [5] W. Huang, M. Lu, L. Zhang, "Survey on Microgrid Control Strategies", Energy Procedia, Vol. 12, 2011. [6] S. Monesha, S. Ganesh Kumar, M. Rivera, "Microgrid Energy Management and Control: Technical Review", IEEE International Conference on Automatica (ICA-ACCA), Curico, Chile, 2016. [7] H. Han, et al., "Review of Power Sharing Control Strategies for Islanding Operation of AC Microgrids", IEEE Transactions on Smart Grid, Vol. 7, 2016. [8] M. Mahmoud, N. Alyazidi, M. Abouheaf, "Adaptive Intelligent Techniques for Microgrid Control Systems: A Survey", Electrical Power and Energy Systems, Vol. 90, 2017. [9] P. Monica, M. Kowsalya, "Control Strategies of Parallel Operated Inverters in Renewable Energy Application: A Review", Renewable and Sustainable Energy Reviews, Vol. 65, 2016. [10] W. Saedi, S. Lachowics, D. Habibi, O. Bass, "Voltage and Frequency Regulation-Based DG Unit in an Autonomous Microgrid Operation Using Particle Swarm Optimization", Electrical Power and Energy Systems, Vol. 53, 2013. [11] S. Ahmadi, S. Shokoohi, H. Bevrani, "A Fuzzy Logic-Based Droop Control for Simultaneous Voltage and Frequency Regulation in an AC Microgrid", Electrical Power and Energy Systems, Vol. 64, 2015. [12] N. Chettibi, A, Mellit, A. Pavan, "Adaptive Neural Network-Based Control of a Hybrid AC/DC Microgrid", IEEE Transactions on Smart Grid, Vol. PP, 2016. [13] C. Qing, T. Hornik, "Cascaded Current – Voltage Control to Improve the Power Quality for a Grid-Connected Inverter with a Local Load", IEEE Transaction on Industrial Electronics, Vol. 60, 2013. [14] M. Yu, Y. Wang, Y. Li, "Hierarchical Control of DC Microgrid Based on Model Predictive Controller", 42nd Annual Conference of the IEEE Industrial Electronics Society (IECON), IEEE, Florence, Italy, 2016. [15] P. Devi, R. Santhi, D. Puhpalatha, "Introducing LQR-Fuzzy Technique with Dynamic Demand Response Control Loop to Load Frequency Control Model", IFAC-Paper Online, Vol. 49, 2016. [16] Q. Lam, A. Bratcu, D. Riu, "Robustness Analysis of Primary Frequency H∞ Control in Stand-Alone Microgrids with Storage Units", IFAC Papers Online, Vol. 49, 2016. [17] T. Hornik, Q. Zhong, "H∞ Repetitive Voltage Control of Grid-Connected Inverters with a Frequency Adaptive Mechanism", IET Power Electronics, Vol. 3, 2010. [18] Z. Jankovic, A. Nasiri, L. Wei, "Robust H∞ Controller Design for Microgrid – Tied Inverter Applications", Energy Conversion Congress and Exposition (ECCE), IEEE, Montreal, QC, Canada, 2015. [19] H. Bevrani, M. Feizi, S. Ataee, "Robust Frequency Control in an Islanded Microgrid: H∞ and μ-Synthesis Approaches", IEEE Transaction on Smart Grid, Vol. 7, 2016. [20] A. Kahrobaeian, Y. Mohamed, "Direct Single-Loop μ-Synthesis Voltage Control for Suppression of Multiple Resonances in Microgrids with Power Factor Correction Capacitors", IEEE Transaction on Smart Grid, Vol. 4, 2013. [21] A. Kahrobaeian, Y. Mohamed, "Robust Single-Loop Direct Current Control of LCL-Filtered Converter-Based DG Units in Grid-Connected and Autonomous Microgrid Modes", IEEE Transaction on Power Electronics, Vol. 29, 2014. [22] M. Hossain, H. Pota, M. Mahmud, M. Aldeen, "Robust Control for Power Sharing in Microgrids with Low-Inertia Wind and PV Generators", IEEE Transaction on Sustainable Energy, Vol. 6, 2015. [23] H. Baghaee, M. Mirsalim, G. Gharehpetian, H. Talebi, "A Generalized Descriptor-System Robust H∞ Control of Autonomous Microgrids to Improve Small and Large Signal Stability Considering Communication Delays and Load Nonlinearities", Electrical Power and Energy Systems, Vol. 92, 2017. [24] T. Taj, T. Khan, I. Ijaz, "An Enhanced Harmony Search (ENHS) Algorithm for Solving Optimization Problems", Electrical and Electronic Engineering Conference, St. Petersburg, Russia, IEEE, 2014. [25] M. Cheng, D. Prayogo, Y. Wu, M. Lukito, "A Hybrid Harmony Search Algorithm for Discrete Sizing Optimization of Truss Structure", Automation in Construction, Vol. 69, 2016. [26] C. Shiva, V. Mukherjee, "Comparative Performance Assessment of a Novel Quasi-Oppositional Harmony Search Algorithm and Internal Model Control Method for Automatic Generation Control of Power Systems", IET Generation Transmission & Distribution, Vol. 9, 2015. [27] R. Jha, et al., "Dynamic Economic Dispatch of Micro-Grid using Harmony Search Algorithm", India Conference (INDICON), New Delhi, India, IEEE, 2015. 22

Journal Pre-proof

Jo

urn a

lP

re-

pro of

[28] G. Shankar, V. Mukherjee, "Load Frequency Control of an Autonomous Hybrid Power System by Quasi-Oppositional Harmony Search Algorithm", International Journal of Electrical Power & Energy Systems, Vol. 78, 2016. [29] V. Kamboj, S. Bath, J. Dhillon, "Implementation of Hybrid Harmony/Random Search Algorithm Considering Ensemble and Pitch Violation for Unit Commitment Problem", International Journal of Electrical Power & Energy Systems, Vol. 77, 2016. [30] K. Pandiarajan, C. Babulal, "Fuzzy Harmony Search Algorithm Based Optimal Power Flow for Power System Security Enhancement", International Journal of Electrical Power & Energy Systems, Vol. 78, 2016. [31] J. Zhang, et al., "A Hybrid Harmony Search Algorithm with Differential Evolution for Day-Ahead Scheduling of a Microgrid with Consideration of Power Flow Constraints", Applied Energy, Vol. 183, 2016. [32] K. Kim, S. Rhee, K. Song, K. Lee, "An Efficient Operation of a Micro Grid using Heuristic Optimization Techniques: Harmony Search Algorithm, PSO, and GA", Power and Energy General Meeting, IEEE, San Diego, USA, 2012. [33] M. Abedini, M. Moradi, S. Hosseinian, "Optimal Clustering of MGs Based on Droop Controller for Improving Reliability using a Hybrid of Harmony Search and Genetic Algorithms", ISA Transactions, Vol. 61, 2016. [34] A. Maleki, F. Pourfayaz, "Sizing of Stand-Alone Photovoltaic/Wind/Diesel System with Battery and Fuel Cell Storage Devices by Harmony Search Algorithm", Journal of Energy Storage, Vol. 2, 2015. [35] P. Satapathy, S. Dhar, P. Dash, "Stability Improvement of PV-BESS Diesel Generator-Based Microgrid with a New Modified Harmony Search-Based Hybrid Firefly Algorithm", IET Renewable Power Generation, Vol. 11, 2017. [36] X. Gao, X. Wang, K. Zenger, "Harmony Search Method for Optimal Wind Turbine Electrical Generator Design", Journal of Structural Mechanics, Vol. 49, 2016. [37] X. Wang, X. Gao, K. Zenger, "An Introduction to Harmony Search Optimization Method", Springer, 2015. [38] M. Moradi, M. Eskandari, S. Hosseinian, "Cooperative Control Strategy of Energy Storage Systems and Micro Sources for Stabilizing Microgrids in Different Operation Modes", Electrical Power and Energy Systems, Vol. 78, 2016. [39] A. Bidram, A. Davoudi, F. Lewis, J. Guerrero, "Distributed Cooperative Secondary Control of Microgrids Using Feedback Linearization", IEEE Transactions on Power Systems, Vol. 28, 2013. [40] R. Hamidia, H. Livania, S. Hosseinianb, G. Gharehpetianba, "Distributed Cooperative Control System for Smart Microgrids", Electric Power Systems Research, Vol. 130, 2016. [41] A. Ersdal, D. Fabozzi, L. Imsland, N. Thornhill, "Model Predictive Control for Power System Frequency Control Taking into Account Imbalance Uncertainty", IFAC Proceeding Volumes, 2014, 47, (3), pp. 981-986. [42] R. Urquidez, G. Palomo, O. Elias, L.Trujillo, "Systematic Selection of Tuning Parameters for Efficient Predictive Controllers using a Multiobjective Evolutionary Algorithm", Applied Soft Computing, 2015, 31, pp. 326-338. [43] A. Askarzadeh, A. Rezazadeh, "Parameter Identification for Solar Cell Models using Harmony Search-Based Algorithm", Solar Energy, Vol. 86, 2012. [44] J. Park, S. Kwon, M. Kim, S. Han, "A Cascaded Improved Harmony Search for Line Impedance Estimation in a Radial Power System", IFAC Papers Online, Vol. 50, 2017. [45] A. Ibrahim, H. Hamza, I. Saroit, "Harmony Search Based Algorithm for Dynamic Shortest Path Problem in Mobile AD HOC Networks", Third International Conference on Digital Information and Communication Technology and Its Applications (DICTAP2013), Ostrava, Czech Republic, July 2013. [46] A. Hatata, B. Sedhom, M. El-Saadawi, "A Modified Droop Control Method for Microgrids in Islanded Mode", Nineteenth International Middle East Power Systems Conference (MEPCON), Cairo, Egypt, IEEE, 2017. [47] B. Sedhom, M. El-Saadawi, and E. Abd-Raboh, "Advanced Control Technique for Islanded Microgrid based on H-Infinity Controller", Journal of Electrical Engineering, Vol. 19, Iss. 1, pp. 335-347, 2019. [48] B. Sedhom, A. Hatata, M. El-Saadawi, and E. Abd-Raboh, "Robust Adaptive H-Infinity Based Controller for Islanded Microgrid Supplying Non-Linear and Unbalanced Loads", IET Smart Grid, DOI. 10.1049/iet-stg.2019.0024, 2019. [49] H. Bevrani, "Robust Power System Frequency Control", Springer, Boston, 2014. [50] Stefani, T. Raymond, "Design of feedback control systems", Oxford University Press, Inc., 1993. [51] Skogestad, Sigurd, and I. Postlethwaite, "Multivariable feedback control: analysis and design" Vol. 2. New York: Wiley, 2007.

23

Journal Pre-proof

Highlight -

Optimally control the system voltage and frequency while improving the power quality of an islanded MG under system load variation. Improving the performance of the droop control method by applying

pro of

-

the H∞ robust control to adjust MG voltage and frequency. -

Using HS–based H∞ control method to accurately detect the weighting parameters of the proposed controller.

Investigating the system stability using root locus, system step

urn a

lP

re-

response, and SVD.

Jo

-