Optimized coordinated control of LFC and SMES to enhance frequency stability of a real multisource power system considering high renewable energy penetration
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Abstract
With rapidly growing of Renewable Energy Sources (RESs) in renewable power systems, several disturbances influence on the power systems such as; lack of system inertia that results from replacing the synchronous generators with RESs and frequency/voltage fluctuations that resulting from the intermittent nature of the RESs. Hence, the modern power systems become more susceptible to the system instability than conventional power systems. Therefore, in this study, a new application of Superconducting Magnetic Energy Storage (SMES) (i.e., auxiliary Load Frequency Control (LFC)) has been integrated with the secondary frequency control (i.e., LFC) for frequency stability enhancement of the Egyptian Power System (EPS) due to high RESs penetration. Where, the coordinated control strategy is based on the PI controller that is optimally designed by the Particle Swarm Optimization (PSO) algorithm to minimize the frequency deviations of the EPS. The EPS includes both conventional generation units (i.e., nonreheat, reheat and hydraulic power plants) with inherent nonlinearities, and RESs (i.e., wind and solar energy). System modelling and simulation results are carried out using Matlab/Simulink® software. The simulation results reveal the robustness of the proposed coordinated control strategy to preserve the system stability of the EPS with high penetration of RESs for different contingencies.
Keywords
Renewable energy sources (RESs) Load frequency control (LFC) Egyptian power system (EPS) Superconducting magnetic energy storage (SMES)1 Introduction
Due to the growing demand on utilizing Renewable Energy Sources (RESs) as a future solution for energy shortages, many conventional generation units are being replaced by the RESs that have several impacts on the performance of the renewable power systems such as lack of system inertia. The RESs exchange electrical power with the power systems through power electronic devices (i.e., inverters and converters), which reduce the overall system inertia. Consequently, the inverterbased RESs will cause high frequency/voltage fluctuations compared to the conventional generation units [1]. Moreover, the irregular nature of the RESs and random load deviations can cause severe power generation fluctuations. Therefore, the frequency control becomes more difficult in case of any mismatch between the power generation and the load demand, particularly, with highlevel RESs (e.g., wind and solar energy) penetration into the power systems. Hence, the Load Frequency Control (LFC) is considered one of the most important issues in power systems to maintain the system frequency and the power variations at their standard values. Whereas system frequency depends on active power and the system voltage greatly depends on the reactive power. Therefore, the control of power systems can be classified into two fundamental issues. a) control of the active power along with the frequency, b) control of the reactive power along with the voltage regulation [2].
To overcome the frequency instability problem, numerous control techniques for power system frequency control have been implemented such as fuzzy logic controller [3], artificial neural network (ANN) [4], linear quadratic regulator (LQR) controller [5] and robust controllerbased H_infinte [6]. Although the control strategies [3, 4, 5, 6] gave a good dynamic response, they are a dependency on the designer’s experience and need long computational time. On the other hand, realworld LFC is performed based on ProportionalIntegralDerivative (PID) or PI controllers because of it has many merits such as; lower cost, simple structure, robustness performance and a successful practical controller that can provide excellent control performance regardless of the perturbations and variations in the system parameters [7]. However, these controllers suffer from a complicated process of parameters tuning based on trial and error method. In such a case, the robustness of the system is not guaranteed against further perturbations in the system parameters. Therefore, several optimization algorithms were used to find the optimal parameters of the PI or PID controllers in the LFC loop such as particle swarm optimization (PSO) [8], cuckoo optimization algorithm [9], ant colony algorithm [10], quasioppositional harmony search algorithm (QOHSA) [11] etc.
According to the previous studies, most research has focused on the frequency stability analysis in power systems that are modelled as thermal power plants (i.e., nonreheat and reheat power plants) or/and hydraulic power plants depending on the number of areas. However, most of the existing realistic power systems comprise multisource dynamic generators (e.g., thermal, hydraulic and gas power plants). Therefore, several types of power plants should be added to the LFC problem to achieve a realistic study as reported in this research. Furthermore, most of the studied power systems are linear and have a simple structure, where it mainly depends on the conventional generation units. However, several RESs should be integrated into the power systems to achieve more realistic study for the power systems of today. Therefore, recently, a few research and studies on the integration of several RESs into power systems have been conducted in [12, 13, 14, 15]. However, based on the previous researches, the effects of a high penetration level of the RESs have not been considered for frequency stability analysis. Hence, several types of RESs with high penetration levels should be added in the analysis of the LFC issue for achievement more accurate studies for today’s power systems.
With increasing the utilizing of RESs into the modern power systems, it becomes much important to look at methods and techniques to store this energy. Where, there are several Energy Storage Systems (ESSs) such as Superconducting Magnetic Energy Storage (SMES), electric batteries, fuel cells, and others, which have been considered within the design of the modern power systems [16]. Therefore, the ESSs can be used for storing the excess energy from the RESs, as well as, discharging the stored energy to the grid as needed, depending on demand. Among many ESSs, SMES is most suited for improved frequency stability in power systems, due to its outstanding advantages such as fast response, high efficiency, and long lifetime [17]. Therefore, a few research and studies on SMES applications for power systems have been conducted in [18, 19, 20, 21]. According to the aforementioned references, there is no report for SMES system to analyze the frequency stability for a multisource power system during highlevel RESs penetration and contingencies. With increasing of penetration level of the RESs into the power systems, it will be caused higher frequency deviations and the LFC may be failing to maintain the system frequency. Therefore, from the perspective of the LFC, the SMES can be used as a feedback controller in the aim of supporting the frequency control loops (i.e., primary and secondary frequency controls) for frequency stability enhancement of the modern power system as reported in this research.
Based on the above analysis, this research proposes a coordinated control strategy between the secondary frequency control (i.e., LFC) and SMES unit (i.e., auxiliary LFC) for frequency stability enhancement of the EPS with highlevel RESs penetration. Therefore, the main contribution of this work includes the following aspects. (i) this paper presents a real hybrid power system in Egypt that includes both conventional generation sources (i.e., steam, gas and hydraulic power plants) with inherent nonlinearities, and RESs (i.e., wind and solar energy) for studying the frequency stability analysis of such systems. Where, the conventional generation units in the EPS is decomposed into three dynamic subsystems; nonreheat, reheat and hydraulic power plants. Moreover, the physical constraints of the governors and turbines such as Generation Rate Constraints (GRCs) of power plants and speed governor deadband (GDB) are taken into consideration. (ii) this paper proposes a new application of SMES unit as a feedback controller in the aim of supporting the frequency control loops (i.e., primary and secondary frequency controls) for frequency stability enhancement of the studied power system. Where the dynamic structure of the studied SMES model in the previous researches [2, 18, 20] is too simple and it is preferable to use a more realistic model. Moreover, the inductor current of the studied SMES model slowly returns to its nominal value after a system strike. However, the induction current of the SMES model must be quickly restored to its nominal value after a disturbance in the system so that it can respond to the next load disorder immediately. Therefore, restoring the inductor current to its nominal value can be enhanced by using the inductor current deviation as a negative feedback signal in the model of SMES control loop as reported in this study. (iii) the proposed coordinated control strategy of LFC and SMES unit is based on the PI controller that is optimally designed by the PSO algorithm to minimize the frequency deviations of the EPS. Moreover, the proposed coordinated can improve and maintain the frequency stability of the EPS and mainly when the RESs are highly penetrated at partial load. According to [22], the renewable power systems with the proposed coordinated control strategy will provide better stability and performance for the power systems of today, and for those of the future that is expected to integrate more and more RESs; thus, the proposed strategy will ensure an avoidance of system instability and system collapse.
The rest of this paper is structured as follows: Section 2 presents the system configuration including the EPS modelling and SMES technology modelling. The statespace dynamic modelling of the EPS considering RESs and SMES is described in section 3. Section 4 presents the control strategy and problem formulation. Section 5 describes the PSO algorithm. The simulation results and discussion are provided in section 6. Finally, the conclusion is presented in Section 7.
2 System configuration
2.1 Modelling of the EPS
System parameters of the studied power system
Parameter  Value  Parameter  Value 

D  0.028  R_{2}  2.5 
T_{1}  0.4  R_{3}  1.0 
T_{2}  0.4  H  5.7096 
T_{3}  90  P_{n1}  0.2529 
T_{d}  5  P_{n2}  0.6107 
T_{h}  6  P_{n3}  0.1364 
T_{w}  1.0  R_{1}  2.5 
m  0.5  f  50 
The important inherent nonlinearities requirements and the physical constraints enjoined by the system dynamics of the generation units are taken into consideration to obtain an accurate perception for the EPS. One of the most important constraints of power plants is the rate of generation power change because of the limitation of mechanical movements. The physical system dynamics of power plants is represented by GRC and the maximum/minimum limit of the valve gate (i.e., governor deadband (GDB)). The GRC limits the generation rate of output power, which is given as 20% pu. MW/minute, and 10% pu MW/minute for nonreheat and reheat turbines, respectively. However, the actual GRC of the hydraulic power plant is about 50% pu MW/minute, which is higher than the generation rate corresponding to any practical disturbance and hence it will be neglected [22]. On the other side, the GDB restricts the valve opening/closing. Where the GDB of the nonreheat and reheat power plants equal ±0.05, while the GDB of the hydraulic power plant is ±0.01. In this paper, the RESs have loworder dynamic models, which are considered sufficient for frequency stability analysis as reported in [22, 26]. Therefore, the power variations of RESs; the wind power variation (∆P_{WT}) and the PV solar power variation (∆P_{PV}), and the load power variation (∆P_{L}) are considered as disturbance signals to the EPS.
2.2 Frequency control based on SMES system
RESs such as wind, solar, waves, and tides are rapidly growing into today's power system. Where, the RESs exchange power to the power systems through power electronic devices that cause to reduce the system inertia and increase frequency/voltage fluctuations compared to the conventional generation units. Moreover, the intermittent nature of the RESs due to their outputs are dependent on weather will lead to more negative effects on system stability and the LFC may fail to readjust system frequency. These negative effects can limit high penetration of the RESs. Therefore, to overcome this problem, this paper proposes a new application of SMES system that uses as an auxiliary LFC incorporated with the primary and secondary frequency controls to enhance the frequency stability of the EPS with high RESs penetration.
3 Statespace dynamic modelling
Hence, the complete statespace equations for the EPS considering RESs with the coordinated control strategy can be obtained as in (18).
4 Control strategy and problem formulation
The PID Controller has three terms functionality (i.e., P, I and D controllers) covering treatment to both transient and steadystate responses. However, the PID and P controllers cannot yield sufficient control performance with the consideration of nonlinearities and boiler dynamics [28]. To overcome this problem, the PI controller has been employed for system control. Therefore, the proposed coordinated control strategy is based on the PI controller in the EPS considering highlevel RESs penetration and inherent nonlinearities. The PI controller has been validated to be remarkably effective in the regulating of a wide range of processes [7, 28]. However, the PI controller suffers from a complicated process of parameters tuningbased trial and error method. Therefore, this research uses the PSO algorithm to find the optimum parameters of the PI controller for minimizing the system frequency deviation. Where, the PSO algorithm has many merits such as the ease of use, high convergence rates, minimum storage requirements, and less depending on the set of initial values, implying the robustness compared to other methods (i.e., genetic algorithm, artificial neural networks, fuzzy logic, and ant colony) [29]. Considering these advantages, this paper uses the PSO algorithm to tune the PI controller parameters, obtaining the optimum PI controller parameters with the robustness of operations. In this study, the integral of squarederror (ISE) is used as a fitness function that is
The constants of matrices are:
\( {a}_1=\frac{P_{n1}}{T_1{R}_1} \), \( {a}_2=\frac{P_{n2}}{T_2{R}_2} \), \( {a}_3=\frac{P_{n3}}{T_3{R}_3} \), \( {a}_4=\frac{T_d}{2H} \), \( {b}_1=\frac{2m}{T_h}\frac{m}{T_2} \), b_{2} = a_{3}a_{4}, \( {b}_3=\frac{P_3{T}_d}{T_{3.}} \)
5 Optimal PI controller design based on PSO algorithm
5.1 Overview of particle swarm optimization
These equations are used to calculate the new values of velocity and position of each particle according to its previous values. Learning factors of the optimization technique have significant implications on the algorithm convergence rate. Further information for the PSO can be found in [29, 30, 31, 32, 33].
5.2 Implementation of a PSOPI controller
The control parameters of PSO
Parameter  Value 

Size of Swarm, S  50 
Number of iterations, n  50 
Inertia weight factor, w  0.8 
Acceleration constant 1, C_{1}  0.12 
Acceleration constant 2, C_{2}  2 
6 Simulation results and discussions
In this study, the coordinated control strategy between the secondary frequency control loop (i.e., LFC) and the SMES system (i.e., auxiliary LFC) is proposed for frequency stability enhancement of the EPS mainly when the RESs are highly penetrated. Where, the proposed coordinated control strategy is based on the PI controller, which is optimally designed by the PSO algorithm to obtain the minimum value of the EPS frequency deviations. Moreover, the performance of the proposed coordinated control strategy is compared with both; the optimal LFC with/without SMES system under highlevel RESs penetration and system parameters variations (i.e., system uncertainties). The simulation results of the studied power system are carried out using MATLAB/Simulink® software to validate the effectiveness of the proposed coordinated control strategy. The code of the PSO as an mfile is interfaced with the model of the EPS to execute the optimization process. The EPS frequency stability with the proposed coordinated control strategy is investigated under different operating conditions through the following scenarios:
6.1 System performance evaluation without the RESs
 Scenario 1: in this scenario, the studied power system (i.e., the EPS) is assumed to have the default parameters with 100% of default system inertia as indicated in Table 1. Figure 6 shows the EPS frequency deviations with the studied three control strategies. From Fig. 6, It is clear that the SMES controller can improve the frequency response and gives a better damped than the EPS without SMES. Compared to the EPS with/without the SMES controller, the proposed coordinated control strategybased the optimal PI controller can provide a smooth and secure frequency performance. Therefore, the frequency response of the EPS is improved by using the proposed coordinated control strategybased the optimal PI controller. Fig. 7 shows that the proposed coordinated control strategy success for decreasing the required power from the conventional generation units (i.e., nonreheat, reheat and hydraulic power plants) during the sudden load change at time t = 200 s. Hence, the SMES power is greatly discharged by the proposed control strategy. The performance specifications; maximum overshoot (MOS), maximum undershoot (MUS), and maximum settling time (T_{S}) of the EPS for this scenario have been compared in Table 3.Table 3
The performance specification of the EPS for scenario 1
Scenario 1
With SMESBased optimal PI controller
With SMES
Without SMES
MUS (pu)
1.911 × 10^{−3}
8.401 × 10^{− 3}
1.523 × 10^{− 2}
MOS (pu)
0.0
6.440 × 10^{−5}
1.420 × 10^{− 3}
T_{S} (s)
17.297
26.703
27.421

Scenario 2: in this scenario, the dynamic performance of the EPS with the proposed coordinated control strategy is investigated under system parameters variations (i.e., system uncertainties). The variable parameters are T_{1}, T_{2}, T_{3}, T_{h}, T_{d}, T_{w}, m, R_{1}, R_{2}, R_{3}, H, and D, which are changed by ±50% of their nominal value. Figure 8 shows the frequency deviations of the studied power system with the proposed three control schemes under these conditions. It can be clear from these results the proposed coordinated control strategy can effectively regulate the system frequency and guarantee robust performance against system uncertainties. Furthermore, the settling time has lower values using the proposed control strategy than that by using other control strategies. Hence, the designed PI controller for the proposed coordinated control strategy is a robust controller where it does not need to retuning its parameters to deal with system uncertainties. The transient specification of the EPS like MOS, MUS, and T_{S} is indicated in Table 4. Figure 9 shows that the conventional generation units significantly generated the needed power in cases of with/without SMES controller, while the proposed coordinated control strategy could significantly reduce the needed power from the conventional generation units during the sudden load change at time t = 200 s. Moreover, the SMES power is greatly delivered by the proposed control strategybased the optimal PI controller.
The performance specification of the EPS for scenario 2
Scenario 2  With SMESbased optimal PI controller  With SMES  Without SMES  

MUS (pu)  MOS (pu)  T_{S} (s)  MUS (pu)  MOS (pu)  T_{S} (s)  MUS (pu)  MOS (pu)  T_{S} (s)  
+ 50%  1.857 × 10^{−3}  0.0  15.848  7.548 × 10^{− 3}  6.150 × 10^{−5}  23.424  1.266 × 10^{− 2}  2.209 × 10^{− 3}  26.723 
50%  1.982 × 10^{− 3}  0.0  17.935  9.692 × 10^{− 3}  1.249 × 10^{− 4}  38.820  2.237 × 10^{− 2}  2.042 × 10^{− 3}  41.019 
6.2 System performance evaluation with the RESs

Scenario 3: in this scenario, the EPS considering highlevel RESs penetration as seen in Fig. 3 is assumed to have the default parameters with 100% of default system inertia as indicated in Table 1. Figure 11 shows that the EPS frequency response is affected by the sudden load change and the RESs fluctuations. From Fig. 11, it can be noted that the system response using the proposed coordinated control strategy is faster, has a lower steadystate error and better damped than others control strategies. In addition, the numerical results of the transient specification (i.e., MOS, MUS, and T_{S}) for the three control strategies under these conditions are within acceptable ranges as indicated in Table 5. Hence, there is no need to redesign the designed optimal PI controller. On the other hand, in cases of the EPS with/without SMES controller, the conventional generation units significantly generated the needed power during the sudden load change at time t = 200 s, while the proposed coordinated control strategy could significantly reduce the needed power from the conventional generation units as shown in Fig. 12. Moreover, the SMES power is greatly charged/discharged by the proposed coordinated control strategy from/to the EPS, according to the EPS needing.

Scenario 4: the main target of this scenario is to investigate the performance of the EPS with the proposed coordinated control strategy under variation in system parameters (i.e., system uncertainties). The default system parameters as indicated in Table 1 are changed by ±50% of their nominal values. Figures 13 and 14 show the frequency deviations of the EPS with the three control strategies under these conditions. From these figures, it can be concluded that the proposed coordinated control strategy could address the system uncertainties and frequency deviation is quickly driven to zero. Where the proposed control strategy gives a little transient compared with the other control strategies. Furthermore, the numerical results of the transient specification (i.e., MOS, MUS, and TS) for the three proposed control schemes under variation in system parameters are very close to that of the nominal value of system parameters and within the acceptable ranges of the system frequency, according to the European network of transmission system operators for electricity codes [35], as indicated in Table 6. Although, the PI controller is very sensitive to the system uncertainty and nonlinearity, which may be represented by the main demerit of this controller in some industrial applications [12]. It does not need retuning its parameters when the EPS considering high RESs penetration subjected to system uncertainties. This demonstrates the robustness and superiority of the proposed coordinated control strategybased the optimal PI controller in regulation the system frequency in case of system parameters variations as well as high penetration level of the RESs. Figures 15 and 16 show the responses of the conventional generation sources and SMES power for the EPS under these condition of system uncertainties (i.e., ±50% of system parameters) and highlevel RESs penetration. From these figures, it is obvious that the conventional generation units largely generated the required power when applied a sudden load change at t = 200 s in cases of the EPS with/without SMES, while the proposed coordinated control strategy could largely reduce the required power from the conventional generation units. Thus, the SMES power is fastly discharged by the proposed coordinated control strategy when the connection of load change, while the SMES power is greatly charged by the proposed coordinated control strategy when the connection of solar irradiation and wind power at time t = 0 s, and t = 1000 s, respectively.
The performance specification of the EPS for scenario 3
Scenario 3  With SMESBased optimal PI controller  With SMES  Without SMES 

MUS (pu)  1.933 × 10^{− 3}  8.358 × 10^{− 3}  1.508 × 10^{− 2} 
MOS (pu)  1.908 × 10^{− 3}  8.005 × 10^{− 3}  1.469 × 10^{− 2} 
T_{S} (s)  19.432  26.288  27.001 
The performance specification of the EPS for scenario 4
Scenario 4  With SMESbased optimal PI controller  With SMES  Without SMES  

MUS (pu)  MOS (pu)  T_{S} (s)  MUS (pu)  MOS (pu)  T_{S} (s)  MUS (pu)  MOS (pu)  T_{S} (s)  
+ 50%  1.850 × 10^{− 3}  2.57 × 10^{− 5}  17.869  7.56 × 10^{− 3}  7.36 × 10^{− 3}  24.512  1.269 × 10^{− 2}  1.225 × 10^{− 2}  27.018 
50%  2.015 × 10^{− 3}  2.024 × 10^{− 3}  18.559  9.681 × 10^{− 3}  9.417 × 10^{− 3}  26.142  2.188 × 10^{− 2}  2.104 × 10^{− 2}  27.119 
7 Conclusion
Utilizing Renewable Energy Sources (RESs) is attracting great attention in today's power system to face the challenges of future energy shortages. However, the irregular nature of RESs and random load deviations cause large frequency/voltage fluctuations as well as reducing the system inertia that results from replacing the synchronous generators with RESs. Where these effects resulting from utilizing the RESs can limit their penetration. In order to benefit from a maximum capacity of the RESs, this paper proposes a new application of Superconducting Magnetic Energy Storage (SMES) system based on an optimal PI controller that is optimally designed by the Particle Swarm Optimization (PSO) algorithm to enhance the frequency stability of the Egyptian Power System (EPS) considering high RESs penetration. Furthermore, the proposed SMESbased the optimal PI controller is coordinated with the secondary frequency control loop (i.e., Load Frequency Control (LFC)) for improvement and preservation the frequency stability of the EPS considering high RESs penetration. The conventional generation units in the EPS is decomposed into three dynamic subsystems; nonreheat, reheat and hydraulic power plants considering inherent nonlinearities (i.e., governor deadband and generation rate constraints of the power plants). To prove the effectiveness of the proposed coordinated control strategy, the EPS considering highlevel RESs penetration has been tested using Matlab/SIMULINK® software. The simulations results proved that the proposed coordinated control strategy has achieved an effective performance for maintaining the EPS frequency stability. Hence, the proposed coordinated control strategy between the LFC and SMES system (i.e., auxiliary LFC) using the optimal PI controllerbased the PSO algorithm will ensure an avoidance of power system instability and system collapse owing to highlevel RESs integration.
Notes
Acknowledgements
Not applicable.
Funding
This paper was funded by the Cultural Affairs and Missions Sector of the Egyptian Ministry of Higher Education.
Availability of data and materials
Data sharing not applicable to this article as no datasets were generated or analyzed during the current study.
Authors’ contributions
GM as a corresponding author, contributed significantly to analysis, manuscript preparation and manuscript submission. GS, AAE and YM as supervisors helped to perform the study analysis with constructive discussions, professional advice and revised the manuscript. All authors read and approved the final manuscript.
Competing interests
The authors declare that they have no competing interests.
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