1
Modeling, Parameterization and Damping Optimum-based Control System
2
Design for an Airborne Wind Energy Ground Station Power Plant
3
Danijel Pavković†*, Mihael Cipek†,1 , Mario Hrgetić†, Almir Sedić‡ †
4
Faculty of Mechanical Engineering and Naval Architecture, University of Zagreb, Zagreb, Croatia ‡
5 6
INA – Industrija nafte, d.d., Zagreb, Croatia
emails:
[email protected];
[email protected];
[email protected];
[email protected]
7 8
ABSTRACT
9
This paper presents the results of modeling and parameterization of the high-altitude wind energy system
10
ground station power-plant equipped with a generator/motor unit as a primary power source tethered to the
11
airborne module via a winch system, an ultracapacitor energy storage system, and grid inverter connected to the
12
common direct-current link. Consequently, a suitable ground station power plant control strategy is designed,
13
comprising the generator/motor speed control and cable tension control system, direct-current link power flow
14
coordination control, and grid-side inverter control strategy. Control system design is exclusively based on the
15
damping optimum criterion which provides a straightforward way of closed-loop damping tuning. The
16
effectiveness of the proposed ground station control strategy is verified by means of comprehensive computer
17
simulations. These have pointed out to precise coordination of the winch electrical servodrive with the airborne
18
module-related rope force control system and sustained power production during the airborne module ascending
19
phase in the presence of high-altitude wind disturbances, and continuous power delivery to the grid-side inverter,
20
facilitated by the utilization of ultracapacitor energy storage. This indicates rather robust behavior of the overall
21
ground station control system under anticipated external disturbance conditions.
22 23
KEYWORDS
24 25
High-altitude wind energy; ultracapacitor energy storage; grid-tied inverter; power flow control strategy; power source coordination
26 27
1
Corresponding author 1
1
1. INTRODUCTION
2
Even though the possibility of harnessing of the relatively steady high-altitude/high-speed wind power has
3
been continually studied since the early 1980’s (see e.g. [1]), it has become increasingly attractive over the last
4
decade. This is primarily due to inherent limiting factors of ground-based wind-turbine systems related to the
5
size constraints of the turbine blade and the generator, high investment costs, and relatively unpredictable nature
6
of near-surface winds. One of the key advantages of high-altitude wind energy (HAWE) systems over traditional
7
wind turbine-based systems is that the HAWE system power-plant is located at the ground level, so that the
8
winch machine size and power ratings are no longer an issue. Hence, a number of studies have been carried out
9
up to date, concerning many theoretical aspects of high-altitude wind power system modeling and airborne
10
module (ABM) control, and various practical aspects of airborne module vs. ground station interaction and
11
airborne module trajectory optimization.
12
In particular, reference [2] has shown that detailed modeling of airborne module aerodynamic behavior
13
represents the key prerequisite for the development of suitable ABM guidance strategies and flight control
14
trajectory optimization based on nonlinear model predictive control (MPC) approach. The effectiveness of MPC-
15
based trajectory optimization approach has been subsequently verified in [2] by means of detailed computer
16
simulations and experiments based on a scaled-down high-altitude wind energy system prototype. The airborne
17
module, typically being tethered to the ground station via a winch system and a suitable generator/motor unit,
18
interacts with the ground station through tether tension force, which also mandates a detailed analysis of
19
ABM/tether/winch system, as outlined in [3]. To this end, reference [4] has proposed a multi-segment tether
20
model in order to model the spatially-distributed (so called catenary) shape of the rope in a systematic and
21
straightforward manner, which also inherently includes the tether dynamic behavior and compliance effects.
22
Based on such ABM dynamic models, the airborne unit flight-path-related cycle energy production can be
23
analyzed, as shown in [5], and the energy efficiency of the prospective flight trajectories can be calculated, as
24
illustrated in [6]. Naturally, ABM trajectory (flight path) optimization may also be used for the purpose of on-
25
line maximization of net energy gain [7]. In order to gain the theoretical limit of net energy production, off-line
26
optimization of the airborne module trajectory and the energy production can be based on the solving of the non-
27
linear programming (NLP) problem, as shown in [8]. In particular, the dynamic state equations of the airborne
28
module system and its interaction vs. ground station winch system through the compliant tether have been
29
transformed in [8] into a spatially-discretized grid based on polynomial approximations suitable for NLP
30
optimization problem by using the so-called pseudo-spectral collocation method. Finally, ABM trajectory
2
1
profiles may also be used for the assessment and subsequent selection and optimization of ABM monitoring and
2
control hardware based on the overall system performance requirements [9].
3
An interesting avenue of research in this field has been dedicated to investigation of novel airborne unit
4
designs, such as lighter-than-air turbine systems for fixed-altitude power production [10]. These types of fixed-
5
position high-altitude turbine systems may, in turn, feature highly-specialized turbine configurations and turbine
6
blade designs [11]. Different variable-altitude systems that produce upward lift force by using a parasail-based
7
flying wing configuration have also been considered, either in the form of a single unit [12], or a multiple
8
parasail-unit system [13]. In the latter case, multiple units may provide additional control authority, and
9
continuity of resulting tether pulling force. An alternative approach has been considered in [14], based on
10
positive-buoyancy rotating airborne balloons aimed at exploiting the so-called Magnus’ effect between high-
11
altitude winds and airborne unit rotating body. Alternative uses of high-altitude wind energy harvesting systems,
12
such as those for wind-assisted marine propulsion have been investigated in [15], and their power production
13
potential has been investigated with respect to high-altitude parasail vs. ship’s course and speed. Note also that
14
suitable geographical locations need to be identified before high-altitude wind energy systems are fielded, which
15
suggests certain limitations to the breadth of their implementation [16]. Recently, an emphasis has also been
16
given to optimal choice of airborne wind energy system configurations [17], and respective investigations of
17
fluid mechanics principles governing the dynamic behavior of airborne modules, either realized in the form of
18
variable-altitude units (see e.g. [14]), or those implemented at fixed altitudes [11]. In the latter case, the effect of
19
high-altitude winds intensity and direction variability to wind turbine shell orientation have been analyzed [18],
20
with the aim to define guidelines for stable turbine shell design.
21
Continuous power production may be possible in the case of “stationary” airborne wind turbine [10], and,
22
possibly, in the cases of multi-parasail high-altitude wind energy system [13], and specialized carousel-like
23
ground station configurations [2]. However, many other airborne wind energy harvesting concepts are typically
24
characterized by inherently intermittent power production cycle due to the requirement to eventually spool the
25
tether and return the airborne unit to initial altitude (see e.g. [9]). This is especially emphasized when those
26
systems are used as isolated wind energy production units. In order to mitigate the power production
27
intermittence issues, an energy storage system of sufficiently large storage capacity should be included into the
28
ground-station power-plant [19]. The comprehensive power flow analysis presented in [19] has also shown that
29
ultracapacitor (supercapacitor) energy storage systems (ESS), even though characterized by relatively low
30
energy densities, may still be suitable for HAWE systems characterized by relatively narrow ranges of ABM
3
1
altitude changes (i.e. less than 300 m). This is primarily due to ultracapacitors being characterized by relatively
2
long service and cycle life [20], which would be favorable in the case of rather frequent charging/discharging
3
demands (frequent cable winding/unwinding), likely to be encountered over the aforementioned narrow ranges
4
of HAWE system operating altitudes [19]. In particular, if batteries were used under such frequent energy
5
storage charging/discharging operation, it would likely result in frequent battery replacement, which would
6
increase the investment, operation and maintenance costs, as indicated in [19].
7
In the above literature overview, investigation of different ground station topologies and related modeling and
8
control system design have not been considered. Namely, due to the possibly high level of complexity of the
9
ground station topology, comprising several mutually-interacting mechatronic and power electronics subsystems,
10
it would be advantageous to first derive and parameterize suitable power flow / mechatronic system models.
11
These models could then be used as a basis for the selection of suitable control system structures for individual
12
dynamic subsystems, and subsequent design and verification of dedicated control loops. Moreover, the design of
13
superimposed control system for individual control loops coordination also needs to be performed in a precise
14
and straightforward manner, which further emphasizes the requirement for accurate process modeling. Finally, it
15
would be advantageous if the individual control system design would be based on a straightforward controller
16
tuning methodology. In this way, analytical relationships for power flow control strategy parameters can be
17
provided in relation to key parameters of the controlled plant [21], and the design-specific parameters related to
18
the closed-loop damping [22]. A certain level of robustness of closed-loop damping tuning should also be
19
expected in relation to the anticipated range of process model parameter variations (see e.g. discussion in [23]).
20
Taking into account the aforementioned issues, the hypothesis of this work is that by designing a
21
comprehensive multi-level control strategy, precise and coordinated operation of individual ground stations’
22
constituent components can be achieved, thus facilitating uninterrupted and smooth power delivery to the main
23
electrical grid by using a suitably-sized ultracapacitor energy storage system. Moreover, the utilization of the so-
24
called damping optimum criterion [22] in control system design should facilitate a straightforward and analytical
25
way of tuning of individual control loops, thereby also assuring fast and well-damped behavior of individual
26
ground station control systems.
27
The paper is organized as follows. In Section 2, the considered HAWE system is outlined and the constituent
28
components of its ground station are modeled and parameterized. Section 3 presents the ground station control
29
strategy design, wherein each control subsystem has been designed with the aim of fast and well-damped
30
response characteristics based on the damping optimum criterion. Section 4 presents the comprehensive
4
1
simulation results of HAWE ground station system under steady-state conditions and during wind power
2
disturbances. Concluding remarks and possible avenues for future research are given in Section 5.
3 4
2. HIGH-ALTITUDE WIND ENERGY GROUND STATION TOPOLOGY
5
This section presents the results of modeling and parameterization of the individual HAWE ground station
6
subsystems including the motor/generator servo unit, ultracapacitor energy storage system equipped with appropriate
7
power converter and grid-tied inverter connected to the common direct-current link.
8 9
2.1. System overview
10
In a typical high-altitude wind energy system, the airborne module is tethered via a cable (rope) to the ground-
11
level winch system, whose topology is outlined in Fig. 1a. It is then used for power production during the airborne
12
module ascending phase, i.e. until the cable is almost completely unwound from the winch, which mandates
13
periodic cable winding (spooling) with ABM descent. Since ground-level power-plant features a reversible
14
electrical machine (generator/motor) unit, the cable can be easily wound at relatively low power settings (Fig.
15
1b) by reducing the aerodynamic lift vs. drag ratio of the airborne module [14]. An ultracapacitor energy storage
16
system has been included within the ground station. Its primary function is to store electrical energy during the
17
ABM ascending (power production) phase, and to subsequently provide sufficient power for cable winding and
18
electrical grid supply during the airborne module descending phase (Fig. 1b). The ultracapacitor ESS and other
19
ground station subsystems are connected to the common direct-current (DC) link via appropriate power
20
electronics systems (power converters). Their topologies are based on recommendations for wind power systems
21
presented in [25], and those related to energy storage system interfacing circuits given in [26].
5
1 2
Figure 1. Schematic representation of considered HAWE system (a) and illustration of its power flow cycle (b).
3 4
2.2. Modeling of individual subsystems
5
The ground station power-plant mechatronic system is modeled herein, based on the dynamical behavior of the
6
winch servodrive control system, the ultracapacitor energy storage system power flow relationships and the electrical
7
circuit representation of the common DC link and the grid inverter inductive-capacitive-inductive (LCL) filter.
8
2.2.1. Winch electrical drive
9
The structure of the winch motor/generator speed control loop with proportional-integral (PI) speed controller is
10
shown in Fig. 2. PI speed controller is traditionally used in controlled electrical drives [26] and power converter
11
control [27], and it is typically embedded within the servomachine power converter [28]. The electrical
12
servomachine torque limits are dependent on the winch drive operating point (rotational speed g), due to
13
servomachine power converter voltage limitations (see e.g. [26]). In the above model, the load torque at the winch
14
side related to cable pulling force Fr is given by w = FrrW.
6
1
The total winch inertia Jtot referred to the electrical machine shaft in the case of the direct drive (no gearbox) is
2
calculated in the following manner, which is valid under the assumption of negligible rope compliance and rather
3
small rope mass when compared to the mass of the airborne module mABM: J tot J m J w mABM rW2 ,
4
(1)
5
where Jm and Jw in equation (1) are electrical machine and winch moments of inertia, respectively, mABM is the ABM
6
mass and rW is the winch radius.
7 8
Figure 2. Block diagram of motor/generator speed control system.
9 10 11 12 13
2.2.2. Ultracapacitor energy storage system The ultracapacitor-based ESS is typically modeled as a lumped-parameter resistor-capacitor electrical circuit [29], whose current vs. voltage relationship under negligible charge leakage conditions is given by: u uc
Quc 1 iuc R s C uc C uc
iuc dt iuc R s ,
(2)
14
where iuc in equation (2) is ultracapacitor current (iuc < 0 for discharging), uuc is terminal voltage, Cuc and Rs are
15
ultracapacitor capacitance and series resistance, respectively, and Quc is the accumulated electrical charge.
16 17 18 19 20
The ultracapacitor electrical circuit representation in equation (2) can be translated into an equivalent ultracapacitor power flow model by using the following ultracapacitor accumulated energy relationship [29]: Wuc
2 2 Quc 2Qmax , 2Cuc 2Cuc
(3)
where Qmax in equation (3) is the ultracapacitor charge capacity, and = Quc/Qmax is the ultracapacitor state-of-charge. Since ultracapacitor input power Pc is related to the ultracapacitor current iuc = dQuc/dt as follows:
7
2 Pc iuc Rs
1 2
dWuc , dt
(4)
the final nonlinear model relating ultracapacitor input power Pc and state-of-charge reads as follows: 2 2 2 Q max 4 R s C uc Pc Q max d f ( , Pc ) . dt 2 R s C uc
3
(5)
4 5 6 7
2.2.3. Direct-current link power flow model Based on the DC link electrical circuit representation in Fig. 1a, the DC link accumulated energy can be described by the following first-order model: dWdc Pdc,mg PESS PL , dt
8 9 10
(6)
where Pdc,mg, PESS and PL are motor/generator inverter load, energy storage system power flow and grid-tied inverter load, respectively, and Wdc is the accumulated energy of the DC link capacitor related to its voltage udc as follows:
Wdc
11
2 C dc u dc . 2
(7)
12 13
2.2.4. Grid inverter harmonic filter model
14
Three-phase four-quadrant grid inverter in Fig. 1a comprises an LCL harmonic filter for the purpose of suppressing
15
the higher-order current harmonics [30], due to its output voltage u1 being controlled by means of pulse-width
16
modulation (PWM) switching action. In the case of symmetrical grid-side load, the dynamic behavior of the three-
17
phase LCL harmonic filter can be analyzed based on the equivalent single-phase electrical circuit [31], which is
18
shown in Fig. 3a. The corresponding dynamic model can be conveniently represented by the block diagram shown in
19
Fig. 3b.
20 21 22
In the case when the LCL filter capacitive impedance 1/(2fgridC3f) is rather large (i.e. due to relatively small C3f choice), the LCL filter Laplace-domain transfer function can be simplified to a simple first-order lag model [31]: G f (s)
i1 ( s ) 1 , u1 ( s ) u 2 ( s ) R f L f s
(8)
23
where Rf = R1f + R2f and Lf = L1f + L2f in equation (8) represent the overall resistance and inductance of inverter-side
24
and grid-side reactors, which can be conveniently used in the grid inverter control system design.
8
1 2
Figure 3. Single-phase representation of LCL harmonic filter (a) and its block-diagram model (b).
3 4
2.3. Component sizing and parameterization
5
The individual subsystems of the HAWE system ground station power-plant are sized and parameterized based on
6
the HAWE system power production cycle requirements, and the specific considerations related to efficiencies of
7
individual ground station components, and the requirement for continuous grid power delivery.
8 9
2.3.1. Grid inverter power output and energy storage requirement
10
The parameters of HAWE system power cycle specification (Fig. 1b) and average efficiencies of its constituent
11
subsystems used in this work are listed in Table 1. These parameters are used to determine the ESS energy capacity
12
requirements and anticipated grid power delivery under steady-state HAWE power cycle (Table 1). The grid power
13
delivery Pgrid and energy storage requirement Wst are determined based on the procedure presented in [19], and
14
summarized in equations (9) and (10):
Pgrid grid
15
Wst
16
2 2 2 W2 MG FC ES Pm,asc Tasc | Pm,des | Tdes , 2 Tdes Tasc ES
(9)
2 Pgrid Tdes Tasc ) | Pm,des | (Tdes ES 1 . 2 2 2 2 grid ES W MG FC (W MG FC ES Pm,ascTasc | Pm,des | Tdes )
(10)
17
Based on these relationships, the energy storage capacity requirement Wst and anticipated (theoretical) grid power
18
delivery Pgrid are calculated and also listed in Table 1.
19 20
Table 1. Basic data of hypothetical HAWE system.
1 2
Maximum anticipated mechanical power1 at winch during ascending phase Pm,asc
170 kW
Maximum anticipated mechanical power at winch during descending2 phase |Pm,des|
58 kW
Based on maximum mechanical power data for a suitably chosen PMSM servomachine from [28]. Based on analysis presented in [19] 9
Altitude range h
300 m
Ascending vs. descending phase duration Tasc / Tdes 3
60 s / 40 s
Electrical machine + power converter average efficiency g = MGFC 4
0.84
Winch system average efficiency W 5
0.95
Grid inverter average efficiency grid 6
0.96
Energy storage system average efficiency ES 7
0.87
Energy storage minimum capacity requirement Wst
1.32 kWh
Theoretical grid power delivery Pgrid
32 kW
Winch radius rW 8
0.325 m
Total inertia referred to the motor/generator shaft Jtot 9
47 kgm2
1 2
However, the ultracapacitor energy storage capacity needs to be adjusted based on the requirement on the
3
minimum allowable state-of-charge min in order to avoid ultracapacitor system operating in the highly-inefficient
4
low state-of-charge region. Moreover, the storage system capacity should also be oversized with respect to
5
anticipated aging-related 20% capacity loss during the ultracapacitor system lifetime [36]. This is especially likely to
6
occur under highly-variable charging/discharging regimes, such as in electric vehicle applications [37]. Based on
7
equation (3), the following expression is derived for the adjusted ultracapacitor storage capacity [19]: Wst , adj
8
osWst osWst , 2 1 min 1 (1 max ) 2
(11)
9
where max = 1 – min is the maximum depth-of-discharge of the ultracapacitror energy storage system, and os = 1/0.8
10
= 1.25 is the energy storage oversizing factor related to the aforementioned aging-related 20% capacity loss. Based
11
on the above relationship, the adjusted energy storage capacity in the case when operation below 60% of state-of-
12
charge is not desired (min = 0.6) amounts to 2.6 kWh.
13 14
3
Based on analysis presented in [9] Estimated based on efficiency maps presented in [32], and anticipated machine operating points from [28]. 5 Based on winch transmission efficiency from [33] and winch PMSM electrical drive efficiency from [34] 6 Anticipated average efficiency of grid-connected inverters according to analysis presented in [35]. 7 Estimated efficiency of ultracapacitors according to [36] and DC/DC power converter according to [29]. 8 Based on winch speed and rope spooling data from [9]. 9 Based on motor inertia Jm = 4.5 kgm2 [28] and estimated winch inertia Jw = 26.7 kgm2 and ABM mass of 150 kg, as indicated in [9]. 4
10
1
2.3.2. Winch electrical drive rating and power losses assessment
2
A direct-drive permanent-magnet synchronous machine (PMSM) motor/generator with matching inverter is chosen
3
in this study, having in mind the above specifications in Table 1. The rated and maximum torque curves of the
4
motor/generator + inverter system are shown in Fig. 4a (cf. [28]). These curves have been derived by scaling up the
5
available efficiency map of a similar lower-power electrical drive, which has been obtained from the available
6
literature [38]. The results in Fig. 4a indicate that inverter-driven PMSM can be characterized by relatively high
7
efficiencies in high-power operating regimes.
8 9 10
Based on the overall efficiency map g(g, g) the power losses map Ploss(g, g) in Fig. 4b is calculated in the following form, which is more convenient for simulation purposes: Ploss ( g , g ) Pg
1 g ( g , g )
g ( g , g )
gg
1 g ( g , g )
g ( g , g )
,
(12)
11 12
Figure 4. Efficiency map (a) and power losses map (b) of motor/generator and inverter unit according to (12).
13 14
2.3.3. Ultracapacitor energy storage system
15
The ultracapacitor ESS parameterization and sizing is based on the data for commercial modules from [39]. These
16
modules are characterized by 125 V voltage rating, rated capacitance Cmod = 62 F, series resistance Rmod = 15 m,
17
and maximum short-term discharge rate of 1850 A. In order to obtain the adjusted energy storage capacity Wst,adj of
18
2.6 kWh according to equation (11), a total of 20 ultracapacitor modules are required. However, HAWE system DC-
19
link voltage also needs to be matched fairly closely to the operating range of the motor/generator inverter unit DC
20
bus (which typically operates between 460 V and 690 V [28]). For the choice of ultracapacitor idling voltage Uc0 =
21
500 V, and energy capacity of 2.6 kWh, four groups of five parallel-connected ultracapacitor modules need to be
22
stacked in a series connection. In that case, the overall ultracapacitor system capacitance Cuc and series resistance Rs
23
can be calculated as follows: 11
Cuc
1
5 4 C mod 77.5 F , R s Rmod 12 m . 4 5
(13)
2
According to equation (13), the maximum ultracapacitor charge Qmax = CucUc0 = 10.8 Ah is obtained based on
3
ultracapacitor stack idle voltage Uc0 = 500 V and equivalent capacitance Cuc = 77.5 F.
4
Note that fixed efficiency DC of the DC/DC power converter has been included in the above overall energy storage
5
system efficiency ES. However, in real life applications, the DC/DC converter efficiency is modeled by a static
6
curve, which is typically above 0.92 (see [40] and references therein) during high-power charging and discharging.
7
This would result in overall energy storage system efficiency ES 0.87 for the typical case of ultracapacitor system
8
efficiency exceeding 0.95 [41].
9 10
2.3.4. Direct-current link capacitance and grid-side harmonic filter
11
The DC link capacitance Cdc is chosen based on the analysis of requirement of power transmission between the DC
12
link and the grid [40], which is expressed in the following inequality condition related to the magnitude of allowable
13
DC link voltage variations [42]: C dc
14
S grid
grid U dc U dc
,
(14)
15
where Sgrid is the anticipated grid apparent power delivery, grid = 2fgrid is the grid voltage frequency, Udc is DC link
16
average voltage, and Udc is the acceptable magnitude of DC link voltage ripple. By inserting Sgrid = 32 kVA, Udc =
17
690 V, fgrid = 50 Hz, and voltage variation Udc/Udc = 2%, the DC link capacitance needs to satisfy Cdc 11 mF.
18
The LCL filter design can be based on the recommendations in [43], wherein the filter bandwidth and higher-order
19
harmonic suppression ability are taken into account. Based on the procedure presented therein, the final LCL filter
20
parameters are listed in Table 2, along with anticipated resistances R1f and R2f of individual LCL filter reactors.
21 22
Table 2. LCL filter parameters for HAWE system grid inverter.
Parameter
C3f
R3f
L1f
L2f
R1f
R2f
Value
40 F
0.63
3.3 mH
0.33 mH
100 m
10 m
23 24
12
1
3. CONTROL SYSTEM DESIGN
2
This section presents the design of individual control systems aimed at coordinated winch servodrive and tether
3
pulling force control, and DC link power flow control for the purpose of facilitating steady grid inverter power
4
delivery.
5 6
3.1. Damping optimum criterion
7
In order to obtain a well-damped speed control system response, the controller tuning may be carried out according
8
to the damping optimum criterion [22]. This is a practical pole-placement-like analytical method of design of linear
9
continuous-time closed-loop systems, which results in straightforward analytical relationships between the controller
10
parameters and the parameters of the process model. The tuning procedure is based on the following closed-loop
11
characteristic polynomial:
12
Ac ( s ) D2n 1 D3n2 DnTen s n D2Te2 s 2 Te s 1 ,
(15)
13
where Te is the closed-loop equivalent time constant, and D2, D3,..., Dn are the damping optimum characteristic ratios.
14
The damping optimum criterion has been proposed in [22] with the aim to find analytical relations between the
15
coefficients of characteristic polynomial of an arbitrary order, so that the system has an optimal damping which
16
corresponds to the so-called “optimal” damping ratio = 0.71 of the second-order dynamic system. In the damping
17
optimum based-design, the aforementioned requirement can be generalized for the linear system of any order. In the
18
so-called optimal case Di = 0.5 (i = 2 … n), resembling the behavior of a second-order system with damping ratio
19
= 0.71, the closed-loop system has a quasi-aperiodic step response characterized by an overshoot of approximately
20
6% and the approximate rise time (1.8 – 2.1)Te. This choice of characteristic ratios Di may be considered optimal in
21
those applications where small overshoot and related well-damped behavior are critical.
22
In general, the response damping of any closed-loop mode may be adjusted through varying the characteristic ratios
23
D2, D3, … Dn. The damping of dominant closed-loop dynamics (i.e. the dominant closed-loop poles damping ratio) is
24
primarily influenced by the most dominant characteristic ratio D2, whereas the damping of higher-frequency modes
25
is adjusted by means of higher (so-called less dominant) characteristic ratios D3, … Dn. For example, by reducing the
26
characteristic ratio D2 to approximately 0.35 the fastest (boundary) aperiodic step response without overshoot is
27
obtained. On the other hand, if D2 is increased above 0.5 the closed-loop system response damping decreases, and
28
larger step response overshoots are obtained [23].
13
1
Regarding the choice of the closed-loop equivalent time constant Te, a larger Te value generally results in improved
2
control system robustness and reduced noise sensitivity. However, this also results in response slowdown and less
3
efficient disturbance rejection, because Te increase results in narrower closed-loop system bandwidth.
4 5
3.2. Winch electrical drive speed control system
6
Assuming small values of power converter and speed measurement delays in the block diagram representation of
7
the winch servomachine speed control loop in Fig. 2, these delays can be lumped into a single lag term characterized
8
by time constant T = T + Tm. This approximation results in the following form of closed-loop transfer function
9
characteristic polynomial:
10
Ac ( s )
J tot T Tc 3 J tot Tc 2 s s Tc s 1 . K c K c
(16)
11
By equating the coefficients of the closed-loop transfer function denominator (16) with the coefficients of the third-
12
order damping optimum polynomial (n = 3 in equation (15)), and rearranging, the following expressions for the PI
13
speed controller parameters are obtained:
14
Tc Te
T J tot , K c , D2 D3 D2 Te
(17)
15
wherein by setting D2 = D3 = 0.5 (“optimal” tuning case) a fast and well-damped speed control loop response is
16
obtained with respect to external disturbance (cable force Fr = wrW) variations.
17 18
3.3. Winch drive superimposed control and rope tightening control
19
The superimposed motor/generator control strategy, shown in Fig. 5, coordinates the winch electrical servosystem
20
and ABM-based rope force control subsystems by commanding appropriate references to the winch speed control
21
loop and the ABM lift/drag control system (see e.g. [4]). The coordination strategy needs to determine the ABM
22
mode of operation based on the open-loop reconstruction of the unwound rope length. The unwinding (un-spooling)
23
is initiated when the estimated unwound rope length lˆr is below the lower threshold lmin. In that case, the winch
24
control system is commanded by the positive speed reference (wR = vasc/rW; vasc = 5 m/s), thus initiating the ABM
25
ascending phase. On the other hand, when the estimated unwound rope length exceeds the upper threshold lmax, a
26
negative (downward motion) speed reference is commanded (wR = vdes/rW < 0; vdes = –7.5 m/s). The generated winch
27
drive speed reference R0 is fed through a first-order low-pass filter, in order to facilitate relatively smooth winch
28
drive reversing, thus preventing likely excitation of rope vibration modes and undesired winch stresses. The 14
1
coordination strategy may also forward its commands to the ABM flight control strategy, alongside the pulling force
2
target FR, which may be used to enhance the power production when additional energy is required for energy storage
3
system recharging (e.g. due to DC link power requirement PdcR + PL in Fig. 5).
4
5 6
Figure 5. Block diagram of superimposed winch coordination strategy.
7 8
In order to properly facilitate the winch winding/unwinding, it is necessary to determine if rope tension is sufficient
9
to avoid the possible entanglement associated with rope slackening. Simple threshold logic is used within the
10
coordination strategy in Fig. 5, where the non-zero winch speed reference is commanded only if the estimated rope
11
force Fˆr is larger than a predefined positive threshold Fthr. The rope force estimator is based on the winch inertia
12
dynamic model (Fig. 2), implemented within the so-called Luenberger observer (see e.g. [44]). This is done by
13
modeling the rope force as a-priori unknown and slowly-varying disturbance (dFr/dt 0), and by extending the
14
overall multi-variable model with correction terms based on the winch speed tracking error [45]:
15
16
ˆ g
1 J tot
(rW Fr g ) K e ( g ˆ g ) ,
(18)
ˆ Fr K eF ( g ˆ g ) ,
(19)
17
where ˆ g and Fˆr are estimated winch speed and rope force, respectively, and parameters Ke and KeF in equations
18
(18) and (19) are the so-called estimation error correction gains.
19 20
The Luenberger estimator design based on the damping optimum criterion, considers the following estimator characteristic polynomial, obtained by combining equations (16) and (17):
15
1 2 3 4
Ac ( s )
J tot J K s 2 tot e s 1 , rW K eF rW K eF
(20)
which is, in turn, equated to the damping optimum characteristic polynomial (n = 2) in equation (15). After some manipulation and rearranging, the final expressions for estimator correction gains read as follows: K e
J tot 1 , K eF . D2 o Teo D2oTeo2 rW
(21)
5 6
3.4. Direct-current link and ultracapacitor energy storage system power flow control
7
Figure 6 shows the block diagram of combined control of DC link and ultracapacitor ESS, which is aimed at
8
maintaining the DC link accumulated energy Wdc (i.e. DC link voltage udc) according to equations (6) and (7) within
9
narrow limits in order to minimize the voltage stresses to the common DC link capacitor bank [46]. The DC link
10
control system is based on the DC link PI feedback controller commanding appropriate charging/discharging
11
command to the energy storage system. The ultracapacitor ESS control system includes a proportional (P) controller
12
of ultracapacitor state-of-charge and which is combined with the superimposed charging/discharging demand from
13
the DC link control loop which command appropriate charging/discharging power commands to the ultracapacitor
14
DC/DC power converter (see e.g. [40]).
15
Since the DC link process model resembles in the structural sense the process model found in speed-controlled
16
electrical servo-drives and is characterized by second-order integral-lag process dynamics, PI controller can be
17
used instead of the more sophisticated controllers, such as the PID controller (see e.g discussion in [23]). In
18
particular, utilization of derivative action within PID controller might increase the closed-loop noise sensitivity,
19
which may play an emphasized role when power converter control applications are considered.
20
In the DC link PI controller design, the parasitic lag Tu represents the ultracapacitor ESS response lag. Based on
21
the block diagram representation in Fig. 6 (and assuming no interaction from the ultracapacitor state-of-charge
22
controller, P = 0), application of the damping optimum tuning procedure (see Subsection 3.1) results in the
23
following expressions for the DC link PI controller parameters:
24
TIdc Tedc
Tu 1 , K Rdc . D2 dc D3dc D2 dc Tedc
(22)
25
Indeed, these expressions resemble the result of winch servomachine speed controller design (cf. equations (16) and
26
(17)). Again, by setting the characteristic ratios to D2dc = D3dc = 0.5 a fast and well-damped DC link control loop
27
behavior is obtained with respect to external disturbance (Pdc,mg and PL).
16
1 2
Figure 6. Block diagram of DC link and ultracapacitor ESS control system.
3 4
The ultracapacitor ESS control system commands appropriate charging/discharging power commands to the
5
ultracapacitor DC/DC power converter (see e.g. [40]) by means of a proportional (P) controller of ultracapacitor
6
state-of-charge and a superimposed charging/discharging demand from the DC link control system. The state-of-
7
charge feedback controller is enabled (ENchg flag is ON) when generator/motor unit produces power (ABM
8
ascending phase, Pdc,mg > 0). During ABM descending phase (Pdc,mg < 0), the feedback controller is disabled, and only
9
the superimposed command (demanding discharging) is active. However, if the ultracapacitor becomes fully-charged
10
( = R), further charging is disabled, and the excess power (discharging command P < 0) is re-routed towards the
11
grid inverter (by means of simple switching logic also shown in Fig. 6).
12 13 14
For the purpose of ultracapacitor state-of-charge controller design, the nonlinear ultracapacitor model in equation (5) is linearized in the vicinity of the anticipated operating point (0, Pc0) as follows:
f ( 0 , Pc 0 ) f ( 0 , Pc 0 ) Pc b K p Pc , Pc
(23)
15
where = –0 and Pb = Pc – Pc0 correspond to perturbation variables in the linearized model (Fig. 6), with model
16
parameters (damping parameter b and gain Kp) given as follows:
17
b
18
1 1 2 Rs Cuc 2 Rs Cuc
Kp
1 4R C 2 P 1 s2 uc2 c 0 0 Qmax
Cuc 2 Qmax 02 Qmax 4 Rs Cuc2 Pc 0
17
.
,
(24)
(25)
1
Taking into account that the ultracapacitor capacitance Cuc parameter in equations (24) and (25) is typically rather
2
large, the damping parameter b should take on fairly small values in comparison (b 0). Based on the block diagram
3
in Fig. 6 with b 0, the state-of-charge closed-loop transfer function is given by:
4 5 6 7 8
Gc ( s)
( s) 1 . R ( s) 1 ( K K p ) 1 s ( K K p ) 1Tu s 2
(26)
By applying the damping optimum methodology to closed-loop equation (26), the following expressions for the closed-loop equivalent time constant Teu and controller gain K are obtained: Teu
Tu 1 , K , Teu K p D2,uc
(27)
with D2,uc = 0.35 chosen to obtain closed-loop response without overshoot, as elaborated in [40].
9 10
3.5. Grid-tied inverter control system
11
Grid-tied inverter power delivery can be controlled within the grid-synchronized control framework in the rotating
12
direct-quadrature (d-q) coordinate frame which facilitates decoupled active and reactive power control [47], as shown
13
in Fig. 7a. In the aforementioned cascade control scheme, the superimposed PI controllers of grid active and reactive
14
power delivery command the current references idR and iqR to inner current control loops. These inner control loops
15
correspond to the direct (d) and quadrature/orthogonal (q) current components id and iq, calculated from harmonic
16
phase currents ia, ib and ic by using the direct Park transform [27]:
17
18
i id 2 cos( ) cos( 2 / 3) cos( 4 / 3) a i i b , q 3 sin( ) sin( 2 / 3) sin( 4 / 3) i c
(28)
where = grid dt is the phase angle of the grid voltage harmonic waveform at grid frequency grid = 2fgrid.
19
The currents id and iq are controlled by respective fast PI controllers, as shown in Fig. 7b, which are typically
20
embedded within the inverter control unit. The current control system also needs to include compensation of d-q axis
21
cross-coupling terms ud and uq based on the available grid frequency grid and current measurements (feed-
22
forward d-q axis decoupling). The current controller outputs, i.e. the voltage references udR and uqR, are then used to
23
calculate the inverter phase voltage references uaR, ubR, and ucR by means of inverse Park transform:
24
cos( ) sin( ) u aR u cos( 2 / 3) sin( 2 / 3) u dR . bR u u cR cos( 4 / 3) sin( 4 / 3) qR
(29)
25
In order to facilitate the calculation of direct and quadrature quantities in the d-q rotating reference frame, and to
26
establish the direct and inverse Park transforms in (28) and (29), it is necessary to synchronize the inverter with
18
1
respect to the grid voltage. For that purpose, a synchronous reference frame phase-locked-loop (SRF-PLL) algorithm
2
[48] is considered in Fig. 7a. The inverter is synchronized herein with respect to the direct component ud through
3
estimation of grid voltage phase angle and frequency grid. A dedicated PI-type PLL algorithm is used for that
4
purpose, which controls the quadrature component of the rotating-frame grid voltage (uq) to zero [49].
5
Grid-tied inverter power flow control system design is also based on the damping optimum tuning procedure,
6
which starts with the definition of the closed-loop characteristic polynomials for the active and reactive power
7
control loops:
8
Ac , P ( s ) 1
9
Ac ,Q ( s ) 1
2 3U fm K RP 3K RPU fm 3U fm K RQ 2 3K RQU fm
TIP s TIQ s
2Tei TIP 2 s , 3K RPU fm 2Tei TIQ 3K RQU fm
s2 ,
(30)
(31)
10
where Ufm is the phase voltage magnitude in d-q frame under synchronized conditions (i.e. ud = Ufm and uq = 0), and
11
Tei is the equivalent lag of the “fast” inner current control loop (Fig. 7a).
12 13 14
15 16
By applying the damping optimum approach to closed-loop characteristic polynomials (30) and (31), the following analytical expressions for PI controller parameters are obtained: D T TIP TIQ Tec 1 2c ec , Tei K RP K RQ
2 3U fm
(32)
Tei 1 , D2 c Tec
(33)
with Tec and D2c in equations (32) and (33) subject to feasibility condition Tei > D2cTec.
17
As indicated by block diagram in Fig. 7b, the current controller design should be the same for the direct and
18
quadrature current control loops due to their symmetrical structures. Moreover, the largest open-loop time constant
19
(i.e. the LCL filter time constant Tf = Lf/Rf herein) is typically cancelled out by the PI controller zero in the current
20
control loop design (see [26]), thus resulting in a straightforward choice for the PI controller integral time constant:
21 22 23
Tci
Lf Rf
Lf1 Lf 2 Rf1 Rf 2
.
(34)
Due to aforementioned zero-pole canceling, the current control system closed-loop transfer function now reads: 1
Gc ,iq ( s ) Gc,id ( s ) 1
R f Tci K ci
T T s ci i s 2 K ci
.
(35)
24
By equating the denominator of the transfer function model (35) with the second-order damping-optimum
25
characteristic polynomial (n = 2 in equation (15)), the following expressions are obtained for current controller
26
proportional gain Kci and closed-loop equivalent time constant (closed-loop equivalent lag) Tei: 19
T Ti , K ci ci R f , D 2i Tei
1
Tei
2
where Rf is the equivalent series resistance of the LCL filter (see Subsection 3.1).
(36)
3
4 5
Figure 7. Block diagram of superimposed grid-tied inverter power flow control system and grid synchronization
6
system (a) and inner current control system (b).
7 8 9
Finally, the damping optimum methodology is also applied in the design of PLL-based grid synchronization loop, wherein the uq “feedback” signal is obtained by using Park transform [27]: u q U fm cos(ˆ ) ,
10
11
which is linearized in the vicinity of the steady-state solution ˆ ˆ as follows: u q U fm sin(ˆ) U fm ˆ .
12 13 14
(37)
(38)
Application of the damping optimum criterion to the PLL system, linearized according to equations (37) and (38), and characterized by the following closed-loop transfer function characteristic polynomial: Apll ( s )
15
T pll T p U fm K pll
s3
T pll U fm K pll
s 2 T pll s 1 .
(39)
16
The characteristic polynomial in equation (39) takes on a similar form as in the case of winch servomachine speed
17
control loop, which results in the following expressions for PLL PI control algorithm integral time constant Tpll and
18
proportional gain Kpll:
19
T pll Te, pll
Tp D2 pll D3 pll
, K pll
20 21 20
1 . D2 pll Te, pllU fm
(40)
1
4. SIMULATION RESULTS
2
The ground station and grid inverter control system dynamic models, incorporating the above presented control
3
system sub-models, has been implemented within the Matlab/SimulinkTM simulation software environment. The
4
respective simulation models implemented in SimulinkTM graphical user interface are given in the Apendix in order
5
to illustrate the complexity and mutual interconnections of the individual sub-models of the power flow strategy
6
and grid inverter control system (Fig. A1). The dynamic equations within the simulation model are solved by using
7
the variable-step Dormand-Prince integration method, with relative and absolute tolerances of 10-3 and 10-6,
8
respectively, which should result in favorable model accuracy. The parameters of individual controllers and rope
9
force observer are listed in Table A1 in Appendix.
10
The proposed high-level coordination strategy including the winch servodrive and ABM/rope tension control
11
system and power flow control system has been first tested for the cases of steady power production characterized by
12
constant wind strength and sudden wind disturbance (wind power drop), as illustrated in Fig. 8. In both of these
13
scenarios, the ground station operation starts with rope unwinding until maximum unwound length is achieved,
14
which is followed by periodic winding and unwinding between the minimum and maximum unwound rope lengths
15
(Fig. 8d). Assuming effective ABM vs. rope force control, as outlined in [4], the rope tension force Fr profile (Fig.
16
8a) needs to be countered by the winch servodrive torque (g) under the closed-loop winch drive speed control (see
17
Figs. 8b and 8c). In the case of steady-state power production (blue traces in Fig. 8), winch drive alternates between
18
rather high and relatively low torque values. On the other hand, when wind disturbance (wind strength drop) is
19
simulated by means of rope pulling force reduction, servodrive adjusts the related torque values under the closed-
20
loop speed control, which maintains the predefined altitude rate of change given in Table 1, and discussed in
21
Subsection 3.3.
21
1 2
Figure 8. Results of winch servodrive and AMB coordination control strategy verification for the case of ABM
3
ascending from ground level and subject to high-altitude wind disturbance effect: rope force (a),
4
generator/motor unit torque (b), generator/motor unit speed (c), and rope length (d).
5 6
Figure 9 shows an initial detail of the rope unwound length and tension force responses for the simulation scenario
7
in Fig. 8, which illustrates the performance of the rope force estimator and related winch unwinding enabling logic.
8
These results show that the proposed rope force estimator (tuned with Teo = 50 ms herein) is characterized by a
9
relatively fast and well-damped response, and is able to track the rope force profile (Fig. 9b) resulting from the winch
10
drive vs. ABM coordination. Based on the estimated force, winch unwinding is enabled only after the rope is
11
sufficiently taut (Fig. 9a); otherwise, the winch is kept at standstill to allow the rope tension to build up until the
12
predefined threshold (Fthr = 3 kN) is exceeded (Fig. 9b).
13
14 15
Figure 9. Details of winch system responses at beginning of rope unwinding: rope unwound length (a), and actual
16
and estimated rope force traces (b).
17 18
Figure 10 shows the power flow control system responses related to the winch servodrive vs. rope tension control
19
system responses in Fig. 8, for the case of constant grid active power target PR,grid = 15 kW. In particular, during the
20
power production phases, the winch motor/generator unit DC-link output power Pdc,mg effectively covers for the power 22
1
requirement PESS of the ultracapacitor ESS and grid inverter DC link load PL. On the other hand, during ABM descent
2
phase, the energy storage system discharge operation covers for the power consumption of the motor/generator unit
3
required for rope winding under low tension conditions, while also supplying the steady grid-side inverter active
4
power delivery (Figs. 10a – 10c). These DC link power flow profiles are reflected in the ESS state-of-charge, which is
5
initially charged from partially discharged state ( = 30%) to near 100% state-of-charge during the initial ABM ascent
6
to maximum altitude (ESS pre-charging under closed-loop control). Since state-of-charge target R is reached during
7
this phase of operation, the excess power needs to be re-routed towards the grid inverter, thus briefly increasing the
8
overall grid power delivery. Since periodic ESS charging and discharging is mandated by the HAWE system operating
9
cycle, the ESS state-of-charge varies in this scenario between 80% and 100% during HAWE system cyclic operation
10
(Fig. 10d). Moreover, during the wind disturbance event, the motor/generator unit power production is notably
11
decreased, which is reflected in reduced ESS charging (and discharging) power (Figs. 10b and 10e), thus ultimately
12
leading to state-of-charge drift towards lower values (Fig. 10d). After the power production increase, the ultracapacitor
13
ESS state-of-charge is steadily increased (i.e. being recharged by additional power from motor/generator) so that it
14
eventually establishes the steady-state charging/discharging cycle between 80% and 100% state-of-charge. DC link
15
accumulated energy under considered highly-varying power profiles is shown in Fig. 10f. The results indicate that the
16
proposed DC link controller is able to maintain the DC link energy level (i.e. voltage) within narrow bounds (-2% and
17
+4% of the target value WdcR = 6.25 kJ herein).
18
The power flow control strategy has also been validated for the case of quasi stochastic wind disturbance and
19
varying grid inverter power delivery, with the main simulation results presented in Fig. 11. In this particular
20
scenario, the speed-controlled winch electrical servodrive maintains the required winch speed profile (Fig. 11a),
21
but the effect of highly-varying wind disturbance manifests itself in large-magnitude quasi-stochastic
22
perturbations in rope force-related winch torque (Fig. 11b). The resulting variability of the winch
23
generator/motor unit power (Fig. 11c) and the varying power demand from the grid inverter (Fig. 11e) needs to
24
be covered by the ultracapacitor ESS (Fig. 11d). In this scenario, characterized by lower average power
25
production, the ultracapacitor ESS state-of-charge also takes on lower values compared to the case of no wind
26
disturbance (cf. Figs. 10d and 11d).
27
Figure 12 shows the responses of grid inverter control strategy shown in Fig. 7 for the case of constant active
28
power command PR,grid = 15 kW with reactive power command kept at zero QR,grid = 0. The active and reactive
29
power responses in Fig. 12a and corresponding direct and quadrature current and voltage responses in Figs. 12b and
30
12c are characterized by fast and well-damped dominant transient behavior, which is characteristic for damping
23
1
optimum tuning method, albeit with some high-frequency transients due to finite time required for the convergence
2
of grid frequency grid estimate based on PLL algorithm (Fig. 12d), which is also characterized by well-damped
3
response shape. Ultimately, the above results facilitate high control performance of individual phase harmonic
4
currents and corresponding phase voltage references (Figs. 12e and 12f), wherein steady-state phase currents are
5
characterized by zero DC bias (offset) and negligible distortion from the target sinusoidal (harmonic) waveforms.
6
7 8
Figure 10. DC link power flow responses without and with stepwise wind disturbance (drop in wind strength): DC
9
link power from generator/motor unit (a), ultracapacitor ESS power profile (b), grid inverter load (c), ESS state-of-
10
charge (d), ESS current (e) and DC link energy (f).
24
1 2
Figure 11. Winch drive and power flow control strategy with quasi-stochastic wind disturbance: generator/motor unit
3
speed (a), generator/motor unit torque (b), DC link power flow from generator/motor and ESS (c), ESS state-of-
4
charge (b), grid inverter load (c), ESS state-of-charge (d), grid inverter load (e) and DC link energy (f).
5 6
Figure 12. Grid inverter responses under power/current cascade control and grid synchronization: active and reactive
7
power (a), d-q frame currents (b), d-q frame voltages (c), grid frequency and its estimate (d), phase currents (e) and
8
phase voltage references (f). 25
1
5. CONCLUSION
2
The paper has presented the modeling, parameterization and control system design for the high-altitude wind
3
energy system ground station power-plant equipped with an ultracapacitor energy storage system. The control strategy
4
has been aimed at coordinating the individual power sources connected to the common direct-current link, in particular
5
the winch motor/generator servodrive, an ultracapacitor energy storage system, and grid-side inverter.
6
The control strategy has included the low-level winch motor/generator unit speed control system equipped with a
7
PI speed controller, and the superimposed control level intended for coordination between the winch servodrive and
8
the cable tension control via airborne module lift force. The upper-level winch control system has been based on a
9
Luenberger observer of rope tension force and relatively simple switching logic. The DC power flow control has
10
been based on a DC link accumulated energy PI controller commanding appropriate upper-level
11
charging/discharging command to the ultracapacitor ESS equipped with a simple proportional-type state-of-charge
12
controller. Finally, the grid-tied inverter has been equipped with active and reactive power flow control system
13
established in the grid-synchronous d-q reference frame, and synchronized to the grid by means of a dedicated phase-
14
locked-loop algorithm. The tuning of aforementioned feedback controllers, Luenberger estimator, and the phase-
15
locked-loop synchronization algorithm has been based on the damping optimum criterion, yielding straightforward
16
analytical relationships for controller and observer parameters, and assuring their well-damped closed-loop behavior.
17
The effectiveness of the proposed ground station control system has been verified by means of comprehensive
18
computer simulations for two characteristic HAWE system operating scenarios, corresponding to steady power
19
production and the case of sudden high-altitude wind disturbance emulated through reduced cable pulling force
20
magnitude. The results have shown that: (i) the winch servodrive can be effectively coordinated with cable tension
21
system so that cable unwinding has been enabled only when the cable has been sufficiently taut; (ii) the DC link control
22
system effectively distributes the power flow between the motor/generator unit, ultracapacitor ESS and grid inverter,
23
while keeping the DC link energy within narrow bounds; and (iii) the grid inverter control system can provide smooth
24
delivery of active and reactive power to the grid. Finally, the control system performance has also shown robustness
25
with respect to quasi-stochastic wind disturbance, wherein energy for maintained grid power delivery has been supplied
26
by the ultracapacitor energy storage system.
27
Future work may be directed towards further refinement of the proposed control strategy, such as coordination
28
between the motor/generator unit, ultracapacitor ESS and grid inverter. These measures may include the variable rope
29
spooling and un-spooling speeds in order to accommodate the complex trajectories made by the airborne module, and
26
1
varying active and reactive power demands from the grid inverter and their coordination with the ABM power
2
production cycle and energy storage system.
3 4
Acknowledgement
5
It is gratefully acknowledged that this work has been supported by the European Commission through the “High
6
Altitude Wind Energy” FP7 project, grant No. 256714. It is also acknowledged that the presented research has been
7
conducted in part within the activities of the Center of Research Excellence for Data Science and Cooperative Systems
8
supported by the Ministry of Science and Education of the Republic of Croatia. Authors would also like to express
9
their appreciation of the efforts of the journal Editor and anonymous reviewers whose comments and suggestions
10
have helped to improve the quality of the presented subject matter.
11 12
NOMENCLATURE Abbreviations:
Parameters:
ABM
airborne module
C3f
LCL filter capacitance [F]
DC
direct current
Cdc
DC link capacitance [F]
ESS
energy storage system
Cuc
ultracapacitor ESS capacitance [F]
HAWE high-altitude wind energy
Di
damping optimum characteristic ratios (i = 2…n)
LCL
inductive-capacitive-inductive
fgrid
grid voltage frequency [Hz]
PI
proportional-integral
Jtot
total inertia at winch side [kgm2]
PLL
phase-locked loop
Jw, Jm
winch and generator inertia [kgm2]
PMSM permanent-magnet synchronous machine
Kc
PI speed controller proportional gain
PWM
pulse-width modulation
Kci
current controller proportional gain
SRF
synchronous reference frame
Ke, KeF Luenberger observer correction gains
d-q
direct-quadrature
Kpll
PLL proportional gain
Dynamic variables:
KRdc
DC link PI controller proportional gain
^
estimated value
KRP,KRQ grid inverter power controller proportional gains
Ac(s)
closed-loop characteristic polynomial
K
state-of-charge controller proportional gain
Fr, FR
rope pulling force and rope force reference [N]
L1f, L2f
LCL filter reactor inductances [H]
ia, ib, ic
instantaneous phase currents [A]
Ldc
storage system inductances [H]
iuc
ultracapacitor current [A]
mABM
airborne module mass [kg]
iESS
storage system current [A]
Qmax
ultracapacitor charge capacity [As]
i1, i2, if
LCL filter current components [A]
rW
winch radius [m]
id, iq,
direct and quadrature current components
R3f
LCL filter capacitive branch resistance []
lr
unwound rope length [m]
R1f, R2f
LCL filter reactor Ohmic resistances []
Pc
ultracapacitor power [W]
Rs
ultracapacitor ESS series resistance []
27
Pdc,mg
motor/generator power [W]
Tasc, Tdes duration of ABM ascending and descending [s]
PdcR
DC link power reference [W]
Tc
PI speed controller integral time constant [s]
PESS
energy storage system power [W]
Tci
current controller integral time constant [s]
Pgrid
grid inverter active power [W]
Te
damping optimum equivalent time constant [s]
Pg
generator/motor mechanical power [W]
TIdc
DC link PI controller integral time constant [s]
Ploss
power losses map [W]
TIP,TIQ
grid inverter power controller time constants [s]
PL
grid inverter load [W]
Wst,
ESS energy storage requirement [J], [kWh]
Pm,asc
power at winch during ABM ascending [W]
Wst,adj
ultracapacitor energy storage capacity [J], [kWh]
|Pm,des|
power at winch during ABM descending [W]
h
ABM altitude range [m]
Qgrid
grid inverter active power [VAr]
W
winch system mechanical efficiency
Sgrid
grid inverter apparent power [VA]
MG
generator/motor efficiency
s
-1
Laplace operator [s ]
FC
generator/motor power converter efficiency
u1, u2
LCL filter input and output voltage [V]
ESS
energy storage system efficiency
ua,ub,uc instantaneous phase voltages [V]
grid
grid inverter efficiency
udc, Udc instantaneous and average DC link voltage [V]
g
generator/motor and power converter efficiency
ud, uq
os
energy storage over-sizing factor
closed-loop damping ratio
direct and quadrature voltage components [V]
ud,uq d-q axis cross-coupling terms [V] uuc
ultracapacitor terminal voltage [V]
g, w
generator and winch angular velocity [rad/s]
Uc0
ultracapacitor stack idle voltage [V]
R,
generator angular velocity reference [rad/s]
grid,
grid voltage frequency [rad/s]
vasc, vdes ABM ascending and descending speed [m/s] Wdc, Wuc DC link and ultracapacitor energy [J], [kWh]
g, w
generator and winch torque [Nm]
ultracapacitor state-of-charge
grid voltage phase angle [rad]
1 2
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1
Appendix: Simulation model and key parameters
2 3
Figure A1. Ground station power flow control system model (a), and grid inverter control system (b)
4
implemented in Matlab/SimulinkTM software environment. 33
1
Table A1. Parameters of individual controllers and rope force observer.
Speed controller proportional gain Kc = 2332.2
Power controller proportional gain KRP = –KRQ = 5.36·10-4
Speed controller integral time constant Tc = 40 ms
Power controller integral time constant TIR = TIQ = 0.64 ms
Luenberger observer correction gain Ke = 40
Current controller proportional gain Kci = 1.65
Luenberger observer correction gain KeF = 1.15·105
Current controller integral time constant Tci = 33 ms
DC link controller proportional gain KRdc = 66.67
SRF PLL controller proportional gain Kpll = -1.607
DC link controller integral time constant TIdc = 30 ms
SRF PLL controller integral time constant Tpll = 4 ms
State-of-charge controller gain K = 4.5·105 2
34
