A Voltage and Frequency Control Strategy for Stand-Alone Full Converter Wind Energy Conversion Systems

Transcription

1 energies Article A Voltage an Frequency Control Strategy for Stan-Alone Full Converter Win Energy Conversion Systems Anrés Peña Asensio * ID, Santiago Arnaltes Gómez ID, Jose Luis Roriguez-Ameneo, Manuel García Plaza, Joaquín Eloy-García Carrasco ID an Jaime Manuel Alonso-Martínez e las Morenas Electrical Engineering Department, Carlos III University of Mari, Av. e la Universia 30, Leganés, Mari, Spain; arnalte@ing.uc3m.es (S.A.G.); ameneo@ing.uc3m.es (J.L.R.-A.); manuelgarciaplaza@gmail.com (M.G.P.); jeloygar@ing.uc3m.es (J.E.-G.C.); jalonsom@ing.uc3m.es (J.M.A.-M..l.M.) * Corresponence: anpenaa@ing.uc3m.es Receive: 26 January 2018; Accepte: 20 February 2018; Publishe: 25 February 2018 Abstract: This paper aresses the esign an analysis of a voltage an frequency control (VFC) strategy for full converter (FC)-base win energy conversion systems (WECSs) an its applicability for the supply of an isolate loa. When supplying an isolate loa, the role of the back-to-back converters in the FC must change with respect to a gri-connecte application. Voltage an frequency are establishe by the FC line sie converter (LSC), while the generator sie converter (GSC) is responsible for maintaining constant voltage in the DC link. Thus, the roles of the converters in the WECS are inverte. Uner such control strategies, the LSC will automatically supply the loa power an hence, in orer to maintain a stable operation of the WECS, the win turbine (WT) power must also be controlle in a loa-following strategy. The propose VFC is fully moelle an a stability analysis is performe. Then, the operation of the WECS uner the propose VFC is simulate an teste on a real-time test bench, emonstrating the performance of the VFC for the isolate operation of the WECS. Keywors: win energy; frequency regulation; permanent magnet synchronous generators (PMSGs); full converter (FC); voltage-source converter; isolate operation 1. Introuction Among renewable energies, win energy conversion systems (WECSs) are some of the most relevant, with more than 432 GW installe by 2015 [1]. Research an integration of win turbines (WTs) an voltage-source converters (VSCs) have increase the possibilities for application of win energy an improve its controllability [2]. Control an operation of WECSs have been wiely stuie in the literature. Mainly, these stuies have focuse on gri-connecte operations, [3 5], lately incluing gri-supporting functions such as frequency support [6,7]. The system propose in the paper iffers from the classical application of WECSs in that it is not esigne to extract the available win power but to supply the power emane by the loa. In such situations, the propose control system ensures that the WECS can supply the eman without the nee for aitional power sources. One of the first stuies concerning the supply of an isolate loa from a WECS was carrie out by [8] employing a oubly-fe inuction generator (DFIG). Further stuies on this topic, when the generator is connecte to an unbalance system, have been publishe by the same research group [9,10]. While in these stuies an inirect flux control was propose, in [11] a irect flux control is employe. Energies 2018, 11, 474; oi: /en

2 Energies 2018, 11, of 19 DFIGs have also been successfully inclue in more complex microgri systems through the use of roop control systems [12]. However, there has been little research about full converter (FC)-base WECSs, where the role of the power converters changes significantly compare to DFIGs [13]. Moreover, since stanalone applications usually require low to meium power WECSs, FC solutions using permanent magnet synchronous generators (PMSGs) an squirrel-cage inuction generators (SCIGs) seem more suitable than DFIGs [14,15]. FC stan-alone control systems are propose in [16 20]. In [16], the GSC is controlle using a maximum power point tracking (MPPT) strategy, while the line sie converter (LSC) controls the DC voltage. Power balance is achieve by a ump resistor connecte at the DC bus. In [17] an [18] the voltage control is performe in an open loop an there is no control of the inverter current. Moreover, in these stuies the effect of win variation on the loa balancing is not analyse. A similar stuy is presente in [19] but employing a current-source converter. This scheme is analyse in [20] for suen unbalance operating conitions when feeing three isolate single phase loas. Most stuies relate to isolate operation have focuse primarily on the generator control through laboratory testing using a primary mover capable of supplying power whenever it is emane by the isolate loa. However, in a real stanalone operation of a WECS, a key concern is how to balance generation an loa. To face this problem several authors have suggeste the integration of more than a source [21 25] in the so-calle hybri systems, where energy storage systems (ESSs) an iesel generators play a significant role in power balancing. In [21] a FC system is connecte in parallel to a battery ESS with little insight in the voltage an frequency control (VFC). The WECS is commane to follow a MPPT strategy an the ESS performs the power balance. In [22] the iesel generator is replace by a photovoltaic (PV) system. A small battery ESS an a ump loa are use to balance power. In [23] the isolate system is fe through a fixe spee WT an a battery ESS. In this paper, a ifferent approach is presente. The roles of the converters in the WECS are inverte from usual FC applications so the WECS LSC controls AC voltage an frequency while the generator sie converter (GSC) is responsible for maintaining constant voltage in the DC link. Also, instea of using a ummy loa or an aitional power source, as in hybri systems, power balance is achieve by the spee regulation of the WT through pitch angle control. On top of that, a VFC is propose, base on the orientation of the output voltage vector along a synchronous axis rotating at the reference frequency. The ability of the VFC to maintain the stator voltage oriente towar the synchronous reference axis means that constant voltage an frequency are obtaine, which in turn means that the emane active an reactive powers are supplie by the FC. In orer to implement such principles, a new approach is propose in this paper where the variations in the LSC filter capacitor voltage will provie the information neee for balancing active an reactive power in the isolate system. The LSC currents are also controlle to avoi large excursions an protect the converter against overcurrents [26]. In Section 2, ynamic moels of the ifferent elements are presente. Using these moels, in Section 3 the propose control strategies are explaine. The propose system ynamics an stability are analyse in Section 4. Simulation results, using both the state-space moel an a etaile switching moel in PSIM are presente an iscusse in Section 5 to emonstrate the capabilities an contributions of the propose control scheme. Experimental results on a real-time test bench have also been obtaine for further emonstration of the control operation. 2. System Moel To properly unerstan the system behaviour, mathematical moels of the ifferent components of the system are presente. A scheme of the system is presente in Figure 1 which inclues the WT, the PMSG, the back-to-back converter, an the isolate loa.

3 Energies 2018, 11, of 19 Figure 1. Complete system scheme. PMSG: permanent magnet synchronous generator; LSC: line sie converter; GSC: generator sie converter. The system moel is ivie in three subsections. First, in the WT moel, the relationship between the blae pitch angle β an the WT power an rotational spee will be illustrate. Then, the PMSG moel will serve as a basis for the GSC control, responsible for maintaining constant DC link voltage espite variations in the generator voltage an frequency. Finally, the front-en converter is moelle in the state space. This moel will be use later in Section 3 to erive the VFC Win Turbine Moel The aeroynamic moel is base on the power characteristics of the WT. The mechanical power of the turbine is given by the equation P m = 1 2 ρav3 C p (λ, β), (1) where ρ is the air ensity, A is the WT rotor area, v is the win velocity, an C p is the power coefficient of the WT, which is a function of the tip spee ratio, λ, an the blae pitch angle, β. A generic equation was use to moel the function C p (λ, β). This equation is base on the turbine characteristics of [27]. The relationship between the power coefficient an the tip spee ratio for various pitch angles can be seen in Figure 2a. This figure shows how β affects C p an therefore the WT power, meaning that β can be use for controlling the WT power. In most of the literature relate to WECSs, this relation is employe to limit the power extracte at high win spees. However, as will be shown in Section 3.1, in this work this relation is use to achieve the power balance by a loa following strategy. From the C p (λ, β) relationship at constant β, Figure 2b shows the WT power characteristics (WT power vs. WT rotational spee Ω), for ifferent win spees. More importantly, this figure also shows the maximum power loci, which are obtaine when the WT is operate with the maximum power coefficient, C p = 0.48, at λ = 8.1 an β = 0. As it will be shown in Section 3.3, the maximum power curve is particularly relevant because it efines the steay-state stability limit of the WT. If the emane power is increase beyon this curve, the subsequent reuction in the rotational spee will lea to a further reuction of the WT power, making the system unstable. This curve will be use in the control strategy of the LSC to limit the maximum active power that the WECS can supply to guarantee a stable operation.

4 Energies 2018, 11, of 19 Figure 2. Graphical representation of win turbine (WT) equations: (a) C p versus λ for ifferent β values; (b) WT power (p m ) for ifferent win spees an maximum power loci (curve BC) PMSG Moel The electrical behavior of a PMSG can be expresse in a stationary reference frame as u s = ψ t ejɛ R s is L s t i s, (2) where subscript s stans for stator, u s an is are the stator voltage an current, respectively, ψ are the stator total magnetic flux linkage, ɛ is the angular position of the rotor, an R s an L s the stator resistance an inuctance, respectively. Since the PMSG ynamics are significantly faster than the WT ones, a steay-state moel can be use for illustrating their interaction. From Equation (2) the steay state moel of the PMSG can be obtaine as U s = jω r ψ R s Is jωl s Is, (3) where ω r is the electrical angular spee, relate to the rotational spee through the pole pair numbers p n as ω r = p n Ω. This expression shows that the stator voltage is a function of the WT spee. Thus, by keeping constant Ω through pitch control, as explaine in Section 3.1, the electromagnetic force, emf, an voltage (jω r ψ) will be constant as well. The stator voltage will vary with the power eman ue to the current-epenent terms of Equation (3).

5 Energies 2018, 11, of 19 In orer to implement the previous strategy on a ynamic control system, a transformation to a q rotating frame oriente to the rotor is use. The orientation to the rotor results in steay-state constant values for the control variables. Applying this transformation to Equation (2) leas to u s = R s i s L s t i s + ω r L s i sq, (4) u sq = ω r ψ R s i sq L s t i sq ω r L s i s. (5) For a balance three-phase system, the output power can be calculate as P s = 2 3 R( u s,q i s,q ) (6) where the asterisk inicates the complex conjugate. Using Equations (4) (6) the output power can also be expresse as P s = 2 3 (ω rψi sq R s is,q 2 ) (7) The term relate to the stator resistance can be interprete as power losses an thus the electromagnetic torque is erive as T em = P em Ω = P p n em ω = 2 r 3 (ψp ni sq ) (8) Equation (8) shows that torque can be controlle by means of the q-component of the stator current i sq. In a gri-connecte FC, i sq is regulate to control the rotational spee of the WT an in this way control the WT power. However, in the off-gri application power is impose by the loa an i sq will be use to balance the power at the DC bus. This means that this current component will be obtaine by the DC voltage controller to maintain constant DC voltage, which in turns means that the generator supplies the power that is emane by LSC to supply the loa. This is further evelope in Section VSC Inverter Moel The AC-sie of a VSC can be represente by a three-phase AC voltage source connecte to the system through a interfacing reactor, moelle by its inuctance L an resistance R [28 30] as seen in Figure 3. Figure 3. Scheme of the voltage-source converter (VSC) station. The ynamics of the DC link have been moelle by a controlle current source i DC in parallel with the DC bus capacitor C DC. This is useful to stuy the effects of the VFC on the DC-link, consiering the voltage control performe by the GSC that will be explaine in Section 3.2. Using pulse-with moulation (PWM), the relation between DC an AC voltages can be expresse as where m k is the moulating signal corresponing to phase k [29]. u mk = m k U DC 2, (9)

6 Energies 2018, 11, of 19 At the AC sie, the total capacitance connecte is represente by C. This inclues the high frequency filter, which is consiere purely capacitive at the funamental frequency [31], an other capacitor banks connecte at the point of common coupling (PCC). The VSC terminal voltage u m an the capacitor bank voltage u g are relate by the equation: u gk = u mk Ri k L t i k, (10) where i k is the converter current an subscript k stans for the system phase (k = a, b, c). The phase currents an voltages an the moulating signals can be expresse in a rotating q reference frame as i = i + ji q, ig = i g + ji gq, u g = u g + ju gq, u m = u m + ju mq an m = m + jm q, respectively. Therefore, Equation (10) can be expresse in a synchronous q reference frame, rotating at constant frequency ω 0, as u g = u m R i L t i jω 0 L i, (11) As will be explaine in Section 3.3, the voltage vector of the capacitor bank, u g, will be oriente to this reference frame by controlling the current, i, by means of the internal voltage of the converter um. On the other han, at the capacitor bank, the voltage equations per phase are i k i gk = C t u gk, (12) where i gk is the phase k current emane by the loa. By applying the Park transformation, the above equation can be expresse in a q reference frame as i ig = C t u g + jω 0 C u g (13) The loa is moelle as a constant power source that emans active power P L an a reactive power Q L. This introuces a non-linear relation between the controlle voltage u g an the emane current ig. This relation can be expresse in a q reference frame as i g = P Lu g + Q L u gq u 2 g +, (14) u2 g i gq = P Lu gq Q L u g u 2 g +. (15) u2 g Finally, the ynamics on the DC-link capacitor consiering the relationship between the VSC DC an AC variables is expresse as C DC t U DC = I DC 1 U DC 3 2 R( u m i ), (16) where the last term is the erive from the active AC power, neglecting the VSC losses.

7 Energies 2018, 11, of 19 The complete system ynamic equations can be obtaine by separating the real an imaginary parts of Equations (11) an (13). Moreover, these equations plus Equation (16) can be expresse per unit as c ω 0 t u g,pu = i,pu + cu gq,pu i g,pu, (17) c ω 0 t u gq,pu = i q,pu cu g,pu i gq,pu, (18) c DC ω 0 l ω 0 t i,pu = m u DC,pu u g,pu ri,pu + li q,pu, (19) l ω 0 t i q,pu = m q u DC,pu u gq,pu ri q,pu + li q,pu, (20) t u DC,pu = i DC,pu m i,pu m q i q,pu. (21) Base values for per unit transformation have been selecte consiering the ratings of the PMSG use for the real-time implementation. They are presente in Table 1. Table 1. Base values for per unit transformations. Label Value Units Description U b V AC base voltage U c,b 2U b - DC base voltage S b 3000 VA Base power f b 50 Hz Base frequency Ω WT 375 rpm Base rotational spee In the rest of the paper, variables in per unit are shown in lower case an the subinex pu is omitte. In conclusion, the system has five state variables, u g, u gq, i, i q an u DC, two external inputs, p L an q L, an three controlle inputs, m, m q an i DC. The stability of the system will be analyse in Section Control The control system is ivie into WT, GSC, an LSC control. The propose control scheme must be able to maintain constant voltage an frequency at the generator terminals espite a variable win energy source while elivering the emane amount of active an reactive power Win Turbine Power Control In orer to ensure a stable operation, the power emane by the loa must be equal to the power elivere by the WT. To achieve this, the WT power is controlle through pitch control. For a given win velocity, WT operation is only possible below a efine stability limit, as shown in Figure 2b. By regulating rotational spee in isolate operation, pitch control allows for the supply a specific loa in a wier range of win velocities or alternatively to eliver a wier range of power values for a specific win velocity. The generator power being fixe by the electrical loa power, the mechanical equation of the WT Ω t = 1 J (T WT T em ), (22) shows that if the turbine power is higher than the loa power, the rotational spee will increase, or ecrease in the opposite case.

8 Energies 2018, 11, of 19 Therefore, power balance can be achieve by means of a spee control loop: only when the turbine power equals the loa power is the rotational spee maintaine constant. This spee control loop is shown in Figure 4a. Figure 4. Control schemes of: (a) WT Rotational spee (b) GSC (c) VFC. The spee control loop will ensure that the maximum rotational spee of the WT is not exceee by acting on the pitch control system. The blae pitch angle is ajuste, thus reucing or increasing the turbine power until it matches the loa power. Note that this control system is similar to the one use in gri-connecte WECS for limiting power when the win velocity is higher than rate. The only ifference is that here maximum rotational spee can be achieve at any win velocity. Moreover, instantaneous power variations will be supplie by the WT storage of kinetic energy since the pitch actuation is normally limite between 5 /s an 10 /s [32] Generator Sie Converter Control The GSC will be responsible for maintaining the DC-link voltage constant espite the WT spee an torque variations. This is achieve by the regulation of the active power rawn from the PMSG using the stator current q-component, which is relate to active power as seen in Equation (8). The control scheme is epicte in Figure 4b. On the other han, there are several criteria for selecting the stator -component current [3]. In this paper, maximum torque per ampere (i = 0) is employe. This control loop is inclue in the VSC moel of Section 2.3 through the controlle current source i DC as i DC = k pdc (u DC u DC) + k idc x DC, (23) where k pdc an k idc are the DC voltage controller proportional an integral gains, respectively. The ynamics of the internal current control loops are not consiere since their banwith are one

9 Energies 2018, 11, of 19 orer of magnitue higher than the DC voltage control loop an thus they can be neglecte in the VSC moel. x DC is the DC voltage error state, given by 3.3. Voltage an Frequency Control 1 ω 0 t x DC = u DC u DC, (24) The VFC objective is to maintain constant voltage an frequency on the system. It is base on the orientation of the output voltage vector along a synchronous reference axis ( axis). The rotational spee of the synchronous reference axis is the reference frequency of the system ω 0. If the control can maintain the voltage vector orientate along the synchronous reference axis, the frequency is kept constant. A linear approximation can be mae between the magnitue an angle of the voltage an its an q components, respectively. Consiering that u g = u g cos(δ), (25) u gq = u g sin(δ), (26) where δ is the angle between u g an the axis, the following can be euce for small variations of δ aroun 0: u g = u g, (27) u gq = (δ). (28) Also, in steay state, if voltage an frequency are kept constant, then the LSC will supply the active an reactive power emane by the loa. Moreover, consiering Equations (17) an (18), the control of magnitue (u g ) an angle (u gq ) are relate to the control of the active (i ) an reactive (i q ) current, respectively, with a certain coupling between axes. With such principles, the control system is quite simple. There are two control channels, the first one to obtain constant voltage, an the secon one to obtain u gq = 0 (Figure 4c), which in turns means that the voltage vector is kept orientate to the reference axis. The reference -axis orientation is obtaine by integration of the esire frequency ω 0. Note that a phase-locke loop (PLL) is not neee, because the whole control is oriente to a synchronous axis obtaine irectly from integration of the esire angular frequency an therefore the angular position is not subjecte to any measurement noise or gri isturbance. A ynamic saturation for i re f is also inclue. This saturation ensures that the WT never excees its stability limit as explaine in Section 2.1. When the available win power is not enough to supply the loa, the voltage magnitue will rop. In this case, balance must be achieve through loa regulation or loa sheing. Note that with the propose VFC, the loa sheing mechanism woul be base on voltage eviation instea of classical frequency eviation. As state in the introuction, this coul be of application in systems where the loa can be controlle such as battery chargers or electrical pumps. To complete the state-space moel escribe in Section 2.3, the ynamics of the VFC are inclue. In the current controllers, the moulating signals m an m q can be expresse as m = k pc (i re f i ) + k ic x c li q, (29) m q = k pc (i re q f i q ) + k ic x cq + li, (30)

10 Energies 2018, 11, of 19 where k pc an k ic are the current controller proportional an integral gains, respectively, an the compensating cross terms have been ae. x c an x cq are the -q current error states, given by 1 ω 0 t x c = i re f i, (31) 1 ω 0 t x cq = i re q f i q. (32) Similarly, the voltage controller input is the voltage error, while the output is the current reference, given by i re f i re q f = k pv (u re f g u g) + k iv x v + cu gq, (33) = k pv (u re f gq u gq ) + k iv x vq cu g, (34) where k pv an k pv are the voltage controller proportional an integral gains, respectively, an the compensating cross terms have been ae. As in the current controller, x v an x v are the -q voltage error states, given by: 1 ω 0 t x v = u re f g u g, (35) 1 ω 0 t x vq = u re gq f u gq. (36) Consiering the set of non-linear ynamic equations given in Equations (17) (21), (24), (31), (32), (35) an (36), the state-space representation of the system can be obtaine through the Jacobian matrix as where x = A x + B u, (37) t y = C x + D u, (38) x = [u g, u gq, x v, x vq, i, i q, x c, x cq, u DC, x DC ], (39) u = [p L, q L, u re f g, ure gq f, u re f DC ], (40) y = [u g, u gq ]. (41) an A, B, C an D contain only linear time-invariant coefficients. 4. Stability Analysis In orer to assess the ynamics an stability of the overall system, the eigenvalue an sensibility analysis are performe in the following paragraphs. For such purpose, the influence of the system parameters on the loci of ominant eigenvalues is stuie consiering the base-case scenario given in Table 2. Since the system is non-linear, the operation point, or quiescent point, also affects the stability of the system. The base-case operating point values are given in Table 3. For this base case, the eigenvalues are compute an presente in Table 4. The frequency an amping ratio are also given, as well as the ominant states accoring to their participation factors [33].

11 Energies 2018, 11, of 19 Table 2. Base case system parameters in p.u. Label Value Description l 0.1 AC filter inuctance r AC filter resistance c 0.1 AC capacitance c DC 0.35 DC capacitance k pc 2 AC current proportional gain k ic AC current integral gain k pv 2.5 AC voltage proportional gain k iv AC voltage integral gain k pdc 3 DC voltage proportional gain k idc DC voltage integral gain Table 3. Base case operating point in p.u. Label Value Description u g 0 1 AC voltage vector amplitue δ 0 0 AC voltage vector eviation p L0 0.5 Active power eman q L0 0 Reactive power eman u DC0 1 DC voltage amplitue Table 4. Base-case eigenvalue analysis. λ i Eigenvalues [ra/s] Frequency [Hz] Damping Ratio [p.u.] Dominant States ± i u gq, i q ± i u g, i u DC x c, x cq x DC x v, x vq All the eigenvalues have a negative real part an thus the system is stable. One of the system more relevant parameter is the total capacitance connecte at the PCC. Figure 5a shows the system eigenvalue map, together with the associate states, for a variation in c from the base case of 0.1 to 0.3. It can be conclue that a higher capacitance amps voltage variations an reuces the frequency of the associate eigenvalues. Consequently, a very small capacitance coul compromise the system stability. Note that the propose VFC is base on the regulation of the filter capacitance voltage, an thus it represents a relevant parameter for the propose control system operation. Due to the non-linearities of the loa an the VSC moels, the system is epenent on the active an reactive power eman. Figure 5b shows the eigenvalues evolution for a variation of p L from 0.1 to 1 p.u. It can be note how the eigenvalues associate with u g, an thus with voltage amplitue, move towars the imaginary axis. This means they ten to become more ominant an less ampe. The opposite happens with the eigenvalues associate with u gq, an thus with voltage frequency. This stability analysis shows the propose system robustness against variations in both the operating point an internal parameters.

12 Energies 2018, 11, of 19 Figure 5. Moel sensitivity to: (a) Point of common coupling (PCC) capacitance variation (b) Active loa variation. Variations of q L prouce a similar effect but without influence on the eigenvalues relate to DC voltage. Note that power variations coul make the system unstable if the control gains are not selecte correctly. The complete moel time-omain step response has been represente in Figure 6. This figure shows the response to a 0.5 p.u. step in the emane active power an to a 1 p.u. step in the emane an reactive power. This figure emonstrates the capability of the propose VFC to maintain constant voltage an frequency uner such stiff changes. Also, it shows the active power mainly affects the voltage magnitue (-voltage component) while reactive power mainly affects frequency (q-voltage component), because of the ecouple control strategy. Figure 6. State-space moel step response.

13 Energies 2018, 11, of Results an Discussion In this section, the etaile switching moel simulations an real-time results are presente to emonstrate the capability of the propose control operation as well as to valiate the evelope ynamic moels. These etaile simulations were evelope using MATLAB/Simulink (R2013b, The MathWorks, Inc., Natick, MA, USA) in co-simulation with PSIM (version 9.0, Powersim, Inc., Rockville, MD, USA). Simulink was use to implement the control algorithms, whereas PSIM was use for simulating the power system elements. Using this structure, the implementation of the moels represente in Figures 1 4 is fairly straightforwar. The moel has been iscretize accoring to the simulation parameters given in Table 5. Other parameters, such as control proportional an integral gains, are the same as in the base case presente in Tables 2 an 3. Table 5. Simulation parameters. WT: win turbine. Label Value Units Description Ts, cont s Control sampling time Ts, power s Power circuit sampling time D WT 4 m WT iameter H WT 3 s WT time constant ρ kg m 3 Air ensity In orer to obtain a further emonstration of the capabilities of the propose control, the system was teste on the real-time test bench of Figure 7. The WT was emulate base on the harware-in-the-loop scheme evelope in [34]. A more etaile explanation is given in the Appenix. The loa coul not be emulate as a constant power source, instea a resistor an a reactance were use. Figure 7. Test bench use for real-time experiments. PWM: pulse-with moulation. Response to both win an loa variations was stuie. In Section 5.1 a loa step at a constant win spee is performe, an the effect on both the WT an the VSC is represente. In Section 5.2, on the other han, a variable win spee is applie uner constant loa Loa Step Response Despite loa variations, the VSC control system must be able to maintain constant voltage an frequency. Also, the pitch control must ensure steay-state power balance between the WECS an the loa to ensure a stable operation. Simulation results are shown in Figure 8a an real-time results in Figure 8b.

14 Energies 2018, 11, of 19 Figure 8. Loa step response in: (a) A simulation (b) A real-time system. For the simulation, both active an reactive power variations are inclue. A 0.5 p.u. to 1 p.u. an active loa step is applie at t = 0.5 s, while a 0 p.u. to 1 p.u. reactive power step is applie at t = 1 s. The q components of the voltage only suffer small eviations at the changes, espite the loa variation an therefore voltage an frequency are maintaine constant after the transience. Frequency is influence by both active an reactive power variations ue to the coupling between axes. However, in contrast with most power systems, reactive power variations have a more significant influence. Zooms of the AC voltages an currents uring loa transitions are also inclue.

15 Energies 2018, 11, of 19 To obtain a stable operation, the power emane by the loa must equal the power extracte from the WT. For this purpose, the pitch angle must be ecrease in orer to increment power extraction. Note that pitch angle variations are consierably slower than the converter actuation. The ifference between the loa an WT power uring this transience is rawn from the WT kinetic energy, proucing a transience in the rotational spee, closing in this way the instantaneous power balance. Reactive power eman is supplie by the VSC an thus has no influence on the WT power control. Active an reactive power variations were also applie to the real-time system. It can be seen how these results valiate the ones obtaine in simulation an thus the same conclusions can be euce Win Variation Response To stuy the system response to win variations, the win profile of Figure 9 has been use. The profile consists of a turbulent variation aroun 12 m/s. Loa is kept constant, so the WECS power must be constant espite the win velocity variations. Only real-time results are shown to avoi a reunancy of information. Figure 9. Real-time system response to win variations. To balance the system, the objective of the pitch angle control is to maintain a constant WT spee. Figure 9 shows that pitch angle follows win velocity variations, increasing pitch angle if win velocity increases or ecreasing pitch angle if win velocity ecreases, in orer to maintain constant rotational spee. Nevertheless, as the pitch actuator has a low banwith, there are some variations on the rotational spee an the WT power (p m ). This rotational spee variation precisely balances the WT power an output power of the WECS, as commente before. 6. Conclusions This paper has presente the esign an implementation of a VFC strategy for WECSs an its application for supplying an isolate loa.

16 Energies 2018, 11, of 19 The ecouple control of the capacitor -q voltage allows us to achieve a balance between emane an generate active an reactive power, respectively, while maintaining constant voltage an frequency. Frequency control is achieve through the orientation of the voltage vector along an axis rotating at the reference frequency, avoiing the use of a PLL for frequency measurement. The roles of the converters of the FC system are inverte. The WECS LSC controls AC voltage an frequency, while the GSC is responsible for maintaining constant voltage in the DC link. Therefore, power is fixe by the loa eman instea of the WECS. Moreover, another contribution of the propose control scheme is that the VFC uses an inner current control loop for controlling voltage, which allows for the regulation of the current an therefore avois converter overloa. The use of the propose VFC allows the LSC active power to precisely match the loa eman. In contrast with other works, which focuse on the integration of the WT with aitional systems, in the presente work power balance is achieve by the spee regulation of the WT through pitch angle control an thus no aitional power sources, ump resistors, or ESSs are require for the system operation. Power balance is achieve by the spee regulation of the WT through pitch angle control an thus no aitional power sources, ump resistors, or ESSs are require for the system operation. Active power unbalance situations provoke voltage amplitue variations, instea of frequency variations as is the case in power systems with synchronous generators. Therefore, a loa regulation or loa sheing mechanism can be use to achieve power balance base on the voltage rop when win power is not enough to supply the loa. Nevertheless, once the power balance is restore, ue to loa regulation or win spee rise, the algorithm operation is resume automatically thanks to the inclue i limitation, which avois win-up situations an ynamic instabilities. The propose control scheme has been completely moelle an valiate by simulation an real-time implementation, emonstrating its capability to maintain constant voltage an frequency espite loa an win spee variations. Acknowlegments: This work has been supporte by the Autonomous Community of Mari uner the PRICAM project (S2013-ICE-2933). Author Contributions: The authors contribute equally to this work. Conflicts of Interest: The authors eclare no conflicts of interest. Abbreviations The following abbreviations are use in this manuscript: Acronyms VFC FC WECS LSC GSC WT DFIG PMSG SCIG ESS MPPT PWM PCC PLL Voltage an frequency control Full converter Win energy conversion system Line sie converter Generator sie converter Win turbine Doubly-fe inuction generator Permanent magnet synchronous generator Squirrel-cage inuction generator Energy storage system Maximum power point tracking Pulse-with moulation Point of common coupling Phase-locke loop

17 Energies 2018, 11, of 19 Nomenclature ψ β Ω ω f u i m c l r A v λ kp ki Ts pn PMSG magnetic flux linkage WT pitch angle WT rotational spee Electrical frequency in p.u. Electrical frequency in Hz Voltage Current VSC moulating control signal VSC filter capacitance in p.u. VSC filter inuctance in p.u. VSC filter resistance in p.u. WT rotor area Win velocity WT tip spee ratio PI controller proportional gain PI controller integral gain Sampling time PMSG pole pairs number Subinex s r g DC 0 Referre to the PMSG stator Referre to the PMSG rotor Referre to the gri or point of common coupling Referre to the VSC DC link Referre to initial state values Appenix A This appenix escribes in more etail the WT emulation system use for the real-time implementation. WT emulation is base on a DC electrical rive that applies the emulate WT torque to the mechanical axis of the PMSG. The emulation system uses both harware an software elements. Harware inclues: SIMOREG 6RA23s regulator (Figure A1a), to regulate e DC motor. DAQmx USB-6009 moel DAC (Digital to Analog Converter), from National Instruments (Figure A1a), to provie the analogue torque reference. 1GG5 SIEMENS DC motor (Figure A1c) Bornay INCLIN 3000 PMSG (Figure A1). The igital reference is generate from a LabVIEW (version 2014, National Instruments, Mari, Spain) program (Figure A1b), running on a PC with a sample time of 100 ms, which is consiere sufficient to simulate the WT ynamics. Figure A1. WT Emulator equipment. HMI: Human-Machine Interface.

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