Modelfree control of microgrids
Abstract
A new "modelfree" control methodology is applied for the first time to power systems included in microgrids networks. We evaluate its performances regarding output load and supply variations in different working configuration of the microgrid. Our approach, which utilizes "intelligent" PI controllers, does not require any converter or microgrid model identification while ensuring the stability and the robustness of the controlled system. Simulations results show that with a simple control structure, the proposed control method is almost insensitive to fluctuations and large load variations.
Loïc Michel, Wim Michiels and Xavier Boucher
Department of Computer Science
KU Leuven
Celestijnenlaan 200A
B  3001 Heverlee
Email: Loic.Michel, Wim.Michiels@cs.kuleuven.be
Email: xavier.b.eng@gmail.com
Power system analysis computing, Automatic control, Power system modeling, Computer simulation, Statespace methods
1 Introduction
The modelfree control methodology, originally proposed by [1], has been widely successfully applied to many mechanical and electrical processes. The modelfree control provides good performances in disturbances rejection and an efficient robustness to the process internal changes. A preliminary work on power electronics [2] presents the successful application of the modelfree control method to the control of dc/dc converters. The control of inverterbased microgrids has been deeply studied and some advanced methods have been successfully developed and tested (e.g. [3] [4] [5]). This paper extends the previous results to the control of inverterbased microgrids in different situations related to islanded and gridconnected modes. In particular, we will show that the proposed control method is robust to strong load variations either in voltage, current or power control cases.
The paper is structured as follows. Section II presents an overview of the modelfree control methodology including its advantages in comparison with classical methodologies. Section III discusses the application of the modelfree control to inverters. Some concluding remarks may be found in Section IV.
2 Modelfree control: a brief overview
2.1 General principles
We only assume that the plant behavior is well approximated in its operational range by a system of ordinary differential equations, which might be highly nonlinear and timevarying. The system, which is SISO, may be therefore described by the inputoutput equation:
(1) 

and are the input and output variables,

, which might be unknown, is assumed to be a sufficiently smooth function of its arguments.
Definition 2.1
[1] If and are respectively the variables of input and output of a system to be controlled, then this system can be described as the ultralocal model defined by:
(2) 
where is a nonphysical constant parameter, such that and are of the same magnitude, and contains all structural information of the process.
In all the numerous known examples, it was possible to set or [6]. Let us emphasize that one only needs to give an approximate numerical value to . The gained experience shows that taking allows to stabilize switching systems.
2.2 Intelligent PI controllers
Definition 2.2
[1] We close the loop via the intelligent PI controller, or iPI controller,
(3) 
where

is an estimate of in (2), computed online as , where is an approximation of the output derivative;

is the measured output to control and is the output reference trajectory;

is the tracking error;

is of the form . , are the usual tuning gains.
Equation (3) is called the modelfree control law or modelfree law.
The iPI controller (3) is compensating the poorly known term and controlling the system therefore boils down to the control of an integrator. The tuning of the gains and becomes therefore straightforward.
Our implementation of (3) assumes a sampleddata control context, where the control input is kept constant over the intersampling interval and the output derivatives are approximated by finitedifferences of the outputs. At the th sampling instants, we have [2]:
(4) 
where refers to the averaged dutycycle at the th sampling instant and ms is the switching period. The main advantage of the proposed control approach is that sudden changes in the model, e.g. due to load changes, and model uncertainty can be overcome as in (2) is reestimated at every sampling instant from the output derivatives and inputs. We note that the potential amplification of noise by differentiation of the output can be countered by using moving average filters, see [7].
To illustrate the utilization of the modelfree control in a microgrid environment, the following results present the simulation of a voltagecontrolled inverter, a triphase controlled inverter and a power controlled inverter under disturbances such as e.g. load changes. We compare the results with a PI control that has been tuned using an ITAE criteria in order to optimize the transient with the initial load [8]. Simulations have been performed using the averaging method [9] [10] for which the controlled inputs in every case correspond to the averaged dutycycle values that drive each IGBT.
3 Control of inverterbased microgrid
3.1 Voltagecontrolled inverter
We apply in this section the proposed method to the control of the output voltage of inverters, which are used in typical configurations within microgrid [11] in both standalone mode and gridconnected mode. All the inductors and capacitors described on the schemes have their values respectively close to 1 mH and 10 F. The dc bus voltage is equal to 400 V and we take in (2).
3.1.1 Single load
Consider a singlephase inverter working in standalone mode, driven by the dutycycle , for which the output voltage is controlled (Fig. 1). The load is a resistor that switches from to at s. Figure 2 presents the output voltage response of the inverter according to the output voltage reference when a classical PI controller and an iPI controller are considered.
3.1.2 Multiple loads
Consider a singlephase inverter working in standalone mode, driven by the dutycycle , for which the output voltage is controlled (Fig. 3).
The inverter is firstly loaded by a resistor (load "1") and then a second unknown load (load "2") is added at s. Figure 4 shows the output voltage response of the inverter in openloop. Figure 5 presents the inverter output voltage response with an iPI controller for different and parameters.
3.2 Triphase currentcontrolled inverter
Consider a currentcontrolled triphase inverter working in both standalone mode / gridconnected mode. The current in each phase is controlled (Fig. 6) by iPI (each phase has its own iPI controller); are the controlled currents going through the inductors , , and , , are the corresponding reference currents. Mathematically we have a multiple input, multiple output system (MIMO) and the local models, each pairing one input and one output, take the form :
hence the interdependencies between the inputs and outputs that are notpaired are absorbed in the terms . The terms , and are the averaged dutycycle that drive the IGBTs of the bridge.
The load is composed of a triphase resistor () and a triphase capacitor (F). Figure 7 presents the voltages and currents of the inverter in standalone mode with a triphase load change (F) at s. Results are similar in the case of unbalanced conditions. We take = = = 30, and .
A grid disconnection is presented Fig. 8 : a sinusoidal perturbation of 25 of the grid amplitude at 500 Hz is added to the grid and the inverter is disconnected from the grid at s.
3.3 Powercontrolled inverter
Controlling the output power of an inverter is important when considering parallelization of inverters and load sharing [12] [13].
Consider the singlephase full bridge inverter described Fig. 1 working in standalone mode; the load is a resistor (). We consider in this section the control of the active power at the output of the inverter for which the iPI controller is configured with , and . The output active power is defined by :
(5) 
and its estimator is based on a movingaverage filter. This is a direct control and the iPI controller corrects the amplitude of the output sinusoidal signal in order to satisfy the power reference . Figure 9 shows the active output estimated power of the inverter controlled by iPI. A load change occurs () at s. This strategy can also work in triphase systems.
3.4 Parallel inverters
Consider two singlephase inverters connected in parallel and working in standalone mode (Fig. 10). According to the power sharing methodology [14], the inverter "1" is controlling the output voltage and the inverter "2" is controlling the current Two identical ultralocal models are associated to these inverters with the same parameters , and . Figure 11 shows the output controlled voltage of the associated inverters.
4 Concluding remarks
We presented the modelfree control methodology in an electrical network environment. Simulations show encouraging results and show that the modelfree control has the following features :

robust to strong load / topological load changes (e.g. strong change of the resistor value or addition of a load that may increase the order of the whole system);

robust to external perturbations (e.g. grid sinusoidal perturbation);

direct control in frame for triphase systems and nonlinear control (e.g. power control).
A combination of the proposed control strategies allows to extend the results to the control of multiple sources considering simultaneously voltage, current and power control. Further work concerns the study of the stability of the modelfree control in networked systems, and the optimal inputoutput pairing for MIMO systems.
Acknowledgements
The article presents results of the project G.0717.11 of the Research Council Flanders (FWO).
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