Design a novel fractional order controller for smart microgrid using multi-agent concept
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Abstract
A microgrid system deploys various components such as solar, wind, diesel generator, fuel cell, flywheel, aqua electrolyser, ultra-capacitor, and storage batteries etc. A microgrid system operates through a centralized control system that works on the current condition of the sources and loads. The status of renewable and non renewable sources as well as load is obtained through the multi-agent system (MAS) to regulate a controllable source as per the deficit between demand and supply. The message interchange in the MAS is considered to be compatible with a user data gram protocol/internet protocol-based network. The present study implements the application of MAS to control a smart microgrid in a Matlab/simulation environment. The simulation results reveal that the present MAS can provide the persistent transition from microgrid when disturbances occur. This indicates the effectiveness of MAS as a technology for controlling the microgrid process. A fractional order (FO) based controller is employed and its parameters are optimized through gravitational search algorithm. The FO controller demonstrates enhanced performance in contrast to the integer order controller under linear as well as nonlinear operating conditions. Furthermore, the proposed controller additionally exhibits its superiority in terms of robustness against parameter changes and disconnection of various components.
Keywords
Fractional PID controller Microgrid Renewable energy Multi agent system GSA1 Introduction
For the recent hundreds of years, Fossil fuel is the principle source to create power. As we realize that fossil fuel isn’t accessible in plenteous. It gives the trouble flag to create and utilize new sustainable power sources. Energy condition in developing countries is exceptionally crucial and most of the power units are operated by natural gas or other natural resources. Therefore, the natural reserve has tumbled to its impediments and it might keep going for further couple of years. So the age of power from elective sources has turned into the need for world. One of the essential requirements for financial advancement in any country on the planet is the accessibility of reliable power supply system with low carbon impression levels. Microgrid system which utilizes sustainable sources may be a compelling arrangement of this power emergency. Solar and wind energies are considered as the most suitable solution to the present situation. As both are pollution free and available in abundance. Renewable energy sources nowadays play an important role in eco friendly electric power generation systems. Microgrid is a viable solution to incorporate renewable sources into distributed network [1]. Besides controlling of non controllable sources is the challenging assignment. Inferable from the presence of non controllable power sources, there is dependably an issue of demand and supply in a microgrid. The solution for such problem, one is to furnish microgrid with diesel generator/gas alternator/battery/energy component to cross over any barrier between the power created by the sustainable sources and loads [2]. However the working expense and emission level of such system are altogether high contrasted with environmentally friendly power sources. Hence microgrid should employ control schemes to resolve the power quality issues like stability due to the practical varying input energy and load while augmenting the utilization of the sustainable resources. The performance of microgrid is influenced by the controller parameters and indulgence of renewable energy sources. Recently, optimal control of microgrid has become the challenging field in research area. Various optimization search methods like genetic algorithm [3], particle swarm intelligence [4], self-organizing migrating algorithm [5], and electromagnetism algorithm [6] have been used for controller tuning in microgrid to suppress interruption. Intelligent frequency control techniques using fuzzy logic too shows tremendous improvement in system performance against load changes and disturbances [7]. Research based on fractional calculus has been gaining attention due to its flexibility and effective solution to the control design application [8, 9]. Podlubny [10] proposed a fractional controller where the fractional integral and fractional differential terms with controller gain were used. Since then, there is lot of research work has been done on fractional order PIDs (FOPIDs) and employed in numerous domains [11, 12, 13, 14]. Various research papers for tuning of FOPID can be found in the literature such as Ziegler–Nichols-type rules [15, 16], optimal tuning [17], tuning for robustness control [18, 19], auto-tuning [20, 21], and tuning based on reducing the number of parameters [22]. In the same line, various advanced control strategy based on FOPID controllers were proposed. For example, Smith indicators structures [23], internal mode controller [24, 25], hybrid control [26], gain scheduling [27] and many others. Latest surveys in the evolution of FOPIDs can be viewed in [28, 29, 30, 31]. Furthermore, some usages of fractional calculus are also reported in field of Biomedical [32], electro-hydraulic system [33], robotic manipulators [34, 35], Pneumatic position servo system [36], Industrial process [37] and water level control [38]. Incorporation of computational intelligence with fractional calculus has led to considerable attention of many researchers in the field of power system [39].
The fundamental operation of any power system depends upon control design. The control design comprising of hardware and software units is used for communicating system status and control signals. In ordinary electric power system, this is executed by Supervisory Control and Data Acquisition (SCADA) system. In recent time, the controlling and supervision activity of electric power system are done by automated agent system, which is commonly known as a multi-agent system. A MAS is a combination of few agents working together to achieve the objective of the system. The MAS has now turned into a useful tool in creating complex frameworks owing to the properties of autonomy, sociality, reactivity and pro-activity. The MAS is self-governing in the sense that they work without human interventions. The MAS also has social ability as they are associated with different agents by means of some sort of operator communication protocol. The agents see and respond to their conditions. Finally, the MAS are proactive because they can show objective oriented behaviour by taking activities. The exhaustive details of centralized microgrid control operation of multi agent system (MAS) can be found in [40, 41]. A centralized microgrid control system is economical because it reduces the number of individual controller for each energy storage system and hence improves the performance which declines due to complex loop connections. Further, there is no need of tuning each controller separately.
This research work has proposed a centralized fractional order frequency controller based on the concept of MAS. Different components of microgrid interact through user data gram protocol/internet protocol (UDP/IP). The five parameters of FOPID controller, namely proportional gain constant, integral time constant, differentiator time constant, integral order, and differentiator order has been considered for tuning. The proposed controller parameters have been optimized by gravitational search algorithm (GSA). Moreover, GSA has been successfully implemented in many fields like AGC of interconnected power systems [42] and in optimal controlling of DC microgrid [43]. Since it needs just two parameters and has capability to discover global optimum, therefore it gives better outcomes when compared with other nature enlivened algorithms. Inferences from the above points of interest make this research work actualize the GSA for tuning the parameters of controller. The outcomes as far as performance indices, robustness against parametric variations, nonlinearities and disconnection of different components exhibit the viability of FOPID controller when contrasted with standard FOPI/PID/PI controller.
This study is structured as in the subsequent way. Section 2 presents details the components of microgrid model. Section 3 briefly introduces the FO controller Sect. 4 describes the optimization technique. Objective function and simulation results of FOPID controller structure along with FOPI/PID/PI are presented in Sect. 5 followed by conclusion in Sect. 6.
2 Microgrid central controller (MGCC)
IP addresses of different agents of microgrid system
Microgrid component as agent | Sending port address | Receiving port address |
---|---|---|
System agent | 10.64.5.601/40101 | – |
Load agent | 10.64.5.601/40102 | – |
Solar photo voltaic system agent | 10.64.5.601/40103 | – |
Wind turbine generator agent | 10.64.5.601/40104 | – |
Aqua Electrolyser (AE) | 10.64.5.601/40301 | – |
Control unit | ||
Fuel cell (FC) | 10.64.5.601/40401 | – |
Diesel engine generator (DEG) | 10.64.5.601/40501 | 10.64.5.601/40203 |
Flywheel energy storage system (FESS) | 10.64.5.601/40601 | 10.64.5.601/40204 |
Ultra capacitor (UC) | 10.64.5.601/40701 | 10.64.5.601/40205 |
Battery energy storage system (BESS) | 10.64.5.601/40801 | 10.64.5.601/40206 |
Microgrid components with their nominal parameter values [39]
Block name | Nominal values |
---|---|
Wind turbine generator (WTG) | K_{WTG} = 1, T_{WTG} = 1.5 |
Solar photo voltaic system (SPV) | K_{PV} = 1, T_{PV} = 1.8 |
Diesel engine generator (DEG) | K_{DEG} = 1/300, T_{DEG} = 2 |
Battery energy storage system (BESS) | K_{BESS} = −1/300, T_{BESS} = 0.1 |
Flywheel energy storage system (FESS) | K_{FESS} = −0.01, T_{FESS} = 0.1 |
Ultra capacitor (UC) | K_{UC} = −0.7, T_{UC} = 0.9 |
Aqua electrolyser (AE) | K_{AE} = −0.002, T_{AE} = 0.5 |
Fuel cell (FC) | K_{FC} = 0.01, T_{FC} = 4.0 |
2.1 Wind turbine generator
Here all the non linearity is neglected.
2.2 Solar voltaic system
2.3 Ultra capacitor
2.4 Diesel engine power generation system
2.5 Fuel cell
2.6 Aqua electrolyser
It uses K_{n} = 0.6.
2.7 Flywheel energy storage system
2.8 Power and frequency deviation
Here M (inertia constant)/D (damping constant) has been considered to 0.4/0.03 for the proposed study [39].
2.9 Uncontrollable energy sources
To study the impact of stochastic components (wind power, solar power, and load) on proposed micro grid’s performance, following methodologies are adopted.
2.9.1 Modeling of wind speed
The practical wind speed is generated by auto-regressive and moving average (ARMA) time-series model [44].
Here the average wind speed has been considered as 5.5 m/s between 0 and 41 s, 7.5 m/s between 41 and 81 s, and 4.5 m/s between 81 and 120 s.
2.9.2 Modeling of SPV radiation and load
Here considered area of the SPV array is equal to 4084 m^{2} with 10% of conversion efficiency, ϕ(14) is the input radiation on the surface of the SPV cells and T_{a}= 25 °C is the surrounding temperature.
3 Mathematical formulation of fractional order (FO) controller
3.1 Fractional calculus
- 1.Riemann–Liouville definition$$\begin{aligned} D^{\alpha } f\left( t \right) & = \frac{1}{{\varGamma \left( {n - \alpha } \right)}}\frac{{d^{n} }}{{dt^{n} }}\mathop \int \nolimits_{0}^{t} \frac{f\left( \tau \right)}{{(t - \tau )^{\alpha + 1 - n} }} \\ & \alpha \in {\mathbb{R}}^{ + } , n \in {\mathbb{Z}}^{ + } ,n - 1 \le \alpha < n \\ \end{aligned}$$(17)
- 2.Caputo’s definition$$\begin{aligned} D^{\alpha } f\left( t \right) & = \frac{1}{{\varGamma \left( {n - \alpha } \right)}}\mathop \int \nolimits_{0}^{t} \frac{{d^{n } f\left( \tau \right)}}{{(t - \tau )^{\alpha + 1 - n} }} \\ & \alpha \in {\mathbb{R}}^{ + } , n \in {\mathbb{Z}}^{ + } ,n - 1 \le \alpha < n \\ \end{aligned}$$(18)
- 3.Grunwald–Letnikov definitionwhere \(\left( {\begin{array}{*{20}c} \alpha \\ 0 \\ \end{array} } \right) = \frac{{\varGamma \left( {\alpha + 1} \right)}}{{\varGamma \left( {i + 1} \right)\varGamma \left( {\alpha - i + 1} \right)}}\); \(\left( {\begin{array}{*{20}c} \alpha \\ 0 \\ \end{array} } \right)\) = 1 for i = 0,$$D^{\alpha } f\left( t \right) = \mathop {\lim }\nolimits_{h \to 0} \frac{1}{{h^{\alpha } }} \mathop \sum \limits_{i = 0}^{{\left( {\frac{t}{h}} \right)}} \left( { - 1} \right)^{i } \left( {\begin{array}{*{20}c} \alpha \\ i \\ \end{array} } \right)f\left( {t - ih} \right)$$(19)
Here h is step size.
3.2 Fractional order PID controller (FOPID)
This controller has five parameters i.e. three gain constants as K_{P} K_{I}, K_{D} and two fractional operator λ and µ.
4 Outline of gravitational search algorithm (GSA)
5 Simulation result and analysis
5.1 Performance of the controller under linear operating conditions
Controller’s parameter after optimization
Controller structure | Optimized parameters | |||||
---|---|---|---|---|---|---|
J_{min} | K_{p} | K_{I} | K_{D} | λ | μ | |
PI | 3.098 | 0.92 | 0.512 | – | – | – |
PID | 2.5660 | 0.8856 | 0.56 | 0.0678 | 1 | 1 |
FOPI | 2.981 | 0.845 | 0.458 | – | 0.512 | – |
FOPID | 2.4508 | 0.7959 | 0.7937 | 0.0341 | 0.2662 | 0.9919 |
Transient characteristics of PI/FOPI/PID/FOPID controller
Controllers | Overshoot (p.u) | Undershoot (p.u) | Settling time (s) | |||
---|---|---|---|---|---|---|
Δ f | Control signal | Δf | Control signal | Δf | Control signal | |
PI | 0.9567 | 2.11 | − 0.04 | 0 | Not settle down to final set point | Not settle down to final set point |
FOPI | 0.9505 | 2.09 | − 0.02 | 0 | Not settle down to final set point | Not settle down to final set point |
PID | 0.895 | 2.04 | − 0.017 | 0 | 8 | 66 |
FOPID | 0.8567 | 2.01 | − 0.012 | 0 | 5 | 64 |
5.2 Robustness against ultra capacitor parameter variation
Performance Index of controller for parameter variation of ultra capacitor
Condition | Performance (ISE) | |
---|---|---|
FOPID | PID | |
Nominal | 2.4089 | 2.566 |
Increase 30% | 2.3902 | 2.5238 |
Increase 50% | 2.3711 | 2.4931 |
decrease 30% | 2.483 | 2.601 |
decrease 50% | 2.5481 | 2.7612 |
5.3 Robustness against eliminating different components
Robustness against eliminating different components of microgrid
Component open | Performance Index-ISE | |
---|---|---|
PID | FOPID | |
Nominal | 2.4089 | 2.566 |
Diesel | 2.511 | 2.621 |
Battery | 2.421 | 2.575 |
Flywheel | 2.443 | 2.591 |
5.4 Performance of the controller under non-linear operating conditions
5.5 Performance of controller under uncertainty in data transmission using UDP/IP
The ADC are used with sample and hold circuit to get digital data in smart micro grid. As mentioned in [41] if considered sampling time is less than smallest time constant then system output will have same response in both continuous and discrete. Thus this study adopted sampling time equal to 0.1 s which is smallest time constant of components employed in the microgrid (in proposed study flywheel system has smallest time constant).
6 Conclusion
MAS-based centralized control scheme with FOPID controller for islanded microgrid has been investigated in this research work. The GSA has been employed to search the optimized values of parameters of the controllers. It is discovered that the dynamic execution of the microgrid with FOPID controller is superior to PID controller for variation in renewable power generation. The study has been done in terms of deviation in frequency, control signal, robustness against parameter variations of ultra capacitor, robustness against by disconnecting the different components of micro-grid. The system performance has also been observed by including the nonlinearities like GRC in energy storing and generating components. The reliability of the system is substantiated by the fact that only one time controller is tuned under nominal condition. It is also apparent from the results that the multi agent based microgrid control system can fully meet the requirements of supply and demand.
Notes
Compliance with ethical standards
Conflict of interest
On behalf of all authors, the corresponding author states that there is no conflict of interest.
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