Model-free control of microgrids
MMODEL-FREE CONTROL OF MICROGRIDS
Loïc Michel ∗ , Wim Michiels ∗ and Xavier Boucher †∗ Department of Computer ScienceKU LeuvenCelestijnenlaan 200AB - 3001 HeverleeE-mail: { Loic.Michel, Wim.Michiels } @cs.kuleuven.be † E-mail: [email protected]
ABSTRACT
A new "model-free" control methodology is applied for thefirst time to power systems included in microgrids networks.We evaluate its performances regarding output load and sup-ply variations in different working configuration of the micro-grid. Our approach, which utilizes "intelligent" PI controllers,does not require any converter or microgrid model identifi-cation while ensuring the stability and the robustness of thecontrolled system. Simulations results show that with a sim-ple control structure, the proposed control method is almostinsensitive to fluctuations and large load variations.
Index Terms — Power system analysis computing, Auto-matic control, Power system modeling, Computer simulation,State-space methods
1. INTRODUCTION
The model-free control methodology, originally proposed by[1], has been widely successfully applied to many mechani-cal and electrical processes. The model-free control providesgood performances in disturbances rejection and an efficientrobustness to the process internal changes. A preliminarywork on power electronics [2] presents the successful applica-tion of the model-free control method to the control of dc/dcconverters. The control of inverter-based microgrids has beendeeply studied and some advanced methods have been suc-cessfully developed and tested (e.g. [3] [4] [5]). This paperextends the previous results to the control of inverter-basedmicrogrids in different situations related to islanded and grid-connected modes. In particular, we will show that the pro-posed control method is robust to strong load variations eitherin voltage, current or power control cases.The paper is structured as follows. Section II presents anoverview of the model-free control methodology including itsadvantages in comparison with classical methodologies. Sec-tion III discusses the application of the model-free control toinverters. Some concluding remarks may be found in SectionIV.
2. MODEL-FREE CONTROL: A BRIEF OVERVIEW2.1. General principles
We only assume that the plant behavior is well approximatedin its operational range by a system of ordinary differentialequations, which might be highly nonlinear and time-varying.The system, which is SISO, may be therefore described by theinput-output equation: E ( t, y, ˙ y, . . . , y ( ι ) , u, ˙ u, . . . , u ( κ ) ) = 0 (1) • u and y are the input and output variables, • E , which might be unknown, is assumed to be a suffi-ciently smooth function of its arguments.From (1), we define an ultra-local model, which repre-sents (1) over a small time period. Definition 2.1 [1] If u and y are respectively the variables ofinput and output of a system to be controlled, then this systemcan be described as the ultra-local model defined by: y ( n ) = F + αu (2) where α ∈ R is a non-physical constant parameter, such that F and αu are of the same magnitude, and F contains allstructural information of the process. In all the numerous known examples, it was possible to set n = 1 or [6]. Let us emphasize that one only needs to givean approximate numerical value to α . The gained experienceshows that taking n = 2 allows to stabilize switching systems. [1] We close the loop via the intelligent PIcontroller , or i-PI controller, u = − [ F ] α + y ( n ) ∗ α + C ( ε ) (3) where a r X i v : . [ c s . S Y ] O c t [ F ] is an estimate of F in (2), computed on-line as [ y ( n ) ] − αu , where [ y ( n ) ] is an approximation of theoutput derivative; • y is the measured output to control and y ∗ is the outputreference trajectory; • ε = y ∗ − y is the tracking error; • C ( ε ) is of the form K p ε + K i (cid:82) ε . K p , K i are the usualtuning gains.Equation (3) is called the model-free control law or model-free law. The i-PI controller (3) is compensating the poorly knownterm F and controlling the system therefore boils down to thecontrol of an integrator. The tuning of the gains K P and K I becomes therefore straightforward.Our implementation of (3) assumes a sampled-data con-trol context, where the control input is kept constant over theinter-sampling interval and the output derivatives are approx-imated by finite-differences of the outputs. At the k th sam-pling instants, we have [2]: u k = u k − − αT c { ( y k − − y k − + y k − ) − (cid:0) y ∗ k − − y ∗ k − + y ∗ k − (cid:1)(cid:9) + C ( y ∗ k − − y k − ) (4)where u k refers to the averaged duty-cycle at the k th sam-pling instant and T c = 0 . ms is the switching period. Themain advantage of the proposed control approach is that sud-den changes in the model, e.g. due to load changes, and modeluncertainty can be overcome as F in (2) is re-estimated at ev-ery sampling instant from the output derivatives and inputs.We note that the potential amplification of noise by differenti-ation of the output can be countered by using moving averagefilters, see [7].To illustrate the utilization of the model-free control in amicrogrid environment, the following results present the sim-ulation of a voltage-controlled inverter, a tri-phase controlledinverter and a power controlled inverter under disturbancessuch as e.g. load changes. We compare the results with a PIcontrol that has been tuned using an ITAE criteria in order tooptimize the transient with the initial load [8]. Simulationshave been performed using the averaging method [9] [10] forwhich the controlled inputs in every case correspond to theaveraged duty-cycle values that drive each IGBT.
3. CONTROL OF INVERTER-BASED MICROGRID3.1. Voltage-controlled inverter
We apply in this section the proposed method to the control ofthe output voltage of inverters, which are used in typical con-figurations within microgrid [11] in both stand-alone mode and grid-connected mode. All the inductors and capacitorsdescribed on the schemes have their values respectively closeto 1 mH and 10 µ F. The dc bus voltage E is equal to 400 Vand 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 switchesfrom R ≈
10 Ω to R ≈ at t = 0 . s. Figure 2presents the output voltage response of the inverter accord-ing to the output voltage reference v ∗ out when a classical PIcontroller and an i-PI controller are considered. Fig. 1 . Full bridge inverter with a load. (a) i-PI control(b) PI control
Fig. 2 . Comparison between the PI and i-PI control ( K p =20 , K i = 0 ) for the voltage-controlled inverter. .1.2. Multiple loads 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. 3). Fig. 3 . Full bridge with two loads.The inverter is firstly loaded by a resistor (load "1") andthen a second unknown load (load "2") is added at t = 0 . s. Figure 4 shows the output voltage response of the inverterin open-loop. Figure 5 presents the inverter output voltage v out response with an i-PI controller for different K p and K i parameters. Fig. 4 . Response of the inverter in open-loop (the second load"2" is connected at t = 0 . s). Consider a current-controlled tri-phase inverter working inboth stand-alone mode / grid-connected mode. The currentin each phase is controlled (Fig. 6) by i-PI (each phase has itsown i-PI controller); I L a , I L a , I L a are the controlled cur-rents going through the inductors L a , L a , L a and I ∗ L a , I ∗ L a , I ∗ L a are the corresponding reference currents. Math-ematically we have a multiple input, multiple output system(MIMO) and the local models, each pairing one input and oneoutput, take the form : ˙ y = F ( y , y , y , u , u ) + α u , ... ˙ y = F ( y , y , y , u , u ) + α u , hence the interdependencies between the inputs and outputsthat are not-paired are absorbed in the terms F i . The terms u , (a) K p = 20 , K i = 0 (b) K p = 50 , K i = 100 Fig. 5 . i-PI control of the output voltage. u and u are the averaged duty-cycle that drive the IGBTs ofthe bridge.The load is composed of a tri-phase resistor ( ≈
10 Ω ) anda tri-phase capacitor ( ≈ µ F). Figure 7 presents the voltagesand currents of the inverter in stand-alone mode with a tri-phase load change ( R = 1000 Ω , C = 0 . µ F) at t = 0 . s.Results are similar in the case of unbalanced conditions. Wetake α = α = α = 30, K p = 500 and K i = 300 . Fig. 6 . Tri-phase bridge inverter connected to the grid.A grid disconnection is presented Fig. 8 : a sinusoidalperturbation of 25 % of the grid amplitude at 500 Hz is addedto the grid and the inverter is disconnected from the grid at t = 0 . s. ig. 7 . Stand-alone mode current-controlled inverter withload changes. (a) Inverter alone (without control).(b) i-PI control. Fig. 8 . Perturbated grid and disconnection from the grid.
Controlling the output power of an inverter is important whenconsidering parallelization of inverters and load sharing [12][13].Consider the single-phase full bridge inverter describedFig. 1 working in stand-alone mode; the load is a resistor( R = 100 Ω ). We consider in this section the control of theactive power (cid:104)P(cid:105) at the output of the inverter for which thei-PI controller is configured with α = 30 , K p = 20 and K i =0 . The output active power P is defined by : (cid:104)P(cid:105) = 1 T c (cid:90) tt − T c v out i out d t (5) and its estimator is based on a moving-average filter. This isa direct control and the i-PI controller corrects the amplitudeof the output sinusoidal signal in order to satisfy the powerreference (cid:104)P(cid:105) ∗ . Figure 9 shows the active output estimatedpower (cid:104)P(cid:105) of the inverter controlled by i-PI. A load changeoccurs ( R = 50 Ω ) at t = 0 . s. This strategy can also workin tri-phase systems. Fig. 9 . Power-controlled inverter.
Consider two single-phase inverters connected in parallel andworking in stand-alone mode (Fig. 10). According to thepower sharing methodology [14], the inverter "1" is control-ling the output voltage v out and the inverter "2" is controllingthe current i L Two identical ultra-local models are associatedto these inverters with the same parameters α = 30 , K p = 20 and K i = 100 . Figure 11 shows the output controlled voltage v out of the associated inverters. Fig. 10 . Parallelization of inverters.
4. CONCLUDING REMARKS
We presented the model-free control methodology in an elec-trical network environment. Simulations show encouraging ig. 11 . Output voltage of the parallelized inverters.results and show that the model-free control has the follow-ing features : • robust to strong load / topological load changes (e.g.strong change of the resistor value or addition of a loadthat may increase the order of the whole system); • robust to external perturbations (e.g. grid sinusoidalperturbation); • direct control in abc frame for tri-phase systems andnon-linear control (e.g. power control).A combination of the proposed control strategies allowsto extend the results to the control of multiple sources consid-ering simultaneously voltage, current and power control. Fur-ther work concerns the study of the stability of the model-freecontrol in networked systems, and the optimal input-outputpairing for MIMO systems. Acknowledgements
The article presents results of the project G.0717.11 of theResearch Council Flanders (FWO).
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