Model-free control of microgrids

The model-free control methodology, originally proposed by [1], has been widely successfully applied to many mechanical and electrical processes. The model-free 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 model-free control method to the control of dc/dc converters. The control of inverter-based 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 inverter-based 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 model-free control methodology including its advantages in comparison with classical methodologies. Section III discusses the application of the model-free control to inverters. Some concluding remarks may be found in Section IV.

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 time-varying. The system, which is SISO, may be therefore described by the input-output equation:

• u and y are the input and output variables,

• E, which might be unknown, is assumed to be a sufficiently smooth function of its arguments.

From (1), we define an ultra-local model, which represents (1) over a small time period. Definition 2.1 [1] If u and y are respectively the variables of input and output of a system to be controlled, then this system can be described as the ultra-local model defined by:

where α ∈ R is a non-physical constant parameter, such that F and αu are of the same magnitude, and F contains all structural information of the process.

In all the numerous known examples, it was possible to set n = 1 or 2 [6]. Let us emphasize that one only needs to give an approximate numerical value to α. The gained experience shows that taking n = 2 allows to stabilize switching systems.

Definition 2.2 [1] We close the loop via the intelligent PI controller, or i-PI controller,

where arXiv:1104.0215v2 [cs.SY] 9 Oct 2013 ) ] is an approximation of the output derivative;

• y is the measured output to control and y * is the output reference trajectory;

• ε = y * -y is the tracking error;

• C(ε) is of the form K p ε + K i ε. K p , K i are the usual tuning gains.

Equation ( 3) is called the model-free control law or modelfree law.

The i-PI controller ( 3) is compensating the poorly known term F and controlling the system therefore boils down to the control of an integrator. The tuning of the gains K P and K I becomes therefore straightforward.

Our implementation of ( 3) assumes a sampled-data control context, where the control input is kept constant over the inter-sampling interval and the output derivatives are approximated by finite-differences of the outputs. At the kth sampling instants, we have [2]:

where u k refers to the averaged duty-cycle at the kth sampling instant and T c = 0.1 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 F in ( 2) is re-estimated 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 model-free control in a microgrid environment, the following results present the simulation of a voltage-controlled inverter, a tri-phase 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 duty-cycle values that drive each IGBT.

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 stand-alone mode and grid-connected mode. All the inductors and capacitors described on the schemes have their values respectively close to 1 mH and 10 µF. The dc bus voltage E is equal to 400 V and we take α = 30 in (2).

Consider a single-phase inverter working in stand-alone mode, driven by the duty-cycle u, for which the output voltage v out is controlled (Fig. 1). The load is a resistor R that switches from R ≈ 10 Ω to R ≈ 1000 Ω at t = 0.02 s. Figure 2 presents the output voltage response of the invert

…(Full text truncated)…

This content is AI-processed based on ArXiv data.