Maximum power point tracking (MPPT) systems have been developed in the ... maximum available solar array power, converter 2 charges the battery with a ...
A new Maximum Power Point Tracking system
W.J.A. Teulings, J.C. Marpinard
A. Capel
D.O’Sullivan
Laboratoire d’Automatique et d’Analyse des Systkmes CNRS - Toulouse, France
Alcatel-Espace Toulouse, France
European Space Agency ESTEC - Noordwijk, The Netherlands
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In power systems involving a load, a battery and a solar array, a MPPT is a promissing principle to extract the maximum amount Of energy from the solar array and distribute it to the battery and loads. A digital hill-climbing control strategy combined with a bidirectional current mode power cell is presented which allows to get a regulated bus voltage topology, suitable for space applications, by means of two converters. Theory, simulation and breadboard validation are successively detailed.
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current controlled bidirectional regulators has conducted to an efficientand simple power system topology. The paper will end with a breadboard validation of the a promissing power system principle, which will topology for future Low Earth Orbit spacecrafts.
2. DIGITAL HILL-CLIMBING MPPT 1. INTRODIJCTION
The power system in a satellite remains always a sensitive system, as it has to guarantee a correct electrical distribution to the users, in spite of the hostile environment from where it has to extract the necessary energy. The power system consists of a solar array, a battery and the users, interconnected by means of DC/DC-converters or regulators. The electrical energy drawn from the solar array in sunlight is transferred to the users and the energy in excess is stored into the battery for the eclipse operations or when peak power demands occur. The solar array is therefore the key element in a power system, as it constitutes the link between the sunlight energy and the necessary electrical energy. The sizing of this element is an important task for power system designers, as the solar array is characterized by its area and its efficiency expressed in W/m 2 , making it the largest component of the spacecraft. Therefore trading-off its area versus the power needs at mission end of life is a permanent objective calling for challenges between technology of solar cell, solar panels and power conditioning efficiency. The present paper deals with the last aspect of this challenge, and will describe a way to extract the maximum amount of power from a given solar array by forcing it to operate at its maximum power point, with a particular power conditioning topology, called Maximum Power Point Tracking (MPPT). In a first step, the principle of the control algorithm that seeks to optimize continuously the power delivered by the solar array will be described and verified by computer simulations. The main feature of this principle concerns the application of the hill-climbing control strategy in a closed loop system, where signal processing is realized by numerical techniques. Combining this modern control strategy with
0-7803-1243-0/93$03.00 Q 1993 IEEE
Maximum power point tracking (MPPT) systems have been developed in the sixties when the first missions involving spacecrafts operating at variable distances from the sun (0.5 up to 1.5 Astronomic Unit) have been investigated. Several projects have been planned calling for several different power tracking principles with the objectives to use this approach even for Low Earth Orbit applications. 2. I . The evolution of maximum power point tracking
One of the first descriptions of a MPPT-system has been published on 1968, when A.F. Boehringer and J. Hausmann described a “self-adaptive DC-converter for spacecraft powersupply”. It was the beginning of a huge development of the domain. Noteworthy are the contributions of A. Poncin and Y. Robin-Jouan, which appeared during the 70’s. The necessity to isolate the load, the battery and the solar array has led to the triangular concept, shown in fig. 1, which has been employed eversince.
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Fig. 1 : Classical triangular structure
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The converters of this triangular topology transfer electric energy from the solar array to the load, from the battery to the load or also from the solar array to the battery. The converters are controlled by a control algorithm that seeks to optimize continuously the power delivered by the solar array. This implies that a certain voltage ( V M p p ) related to the maximum power point should be imposed to the solar panel terminals. Since this maximum power voltage may vary within a large interval, the algorithm has to track it continuously. The central control-unit of this structure is rather complex, because it has to manage three power-converters simultaneously. During daylight, converter 1 regulates the bus voltage, which is the voltage across the load terminals. As long as the power consumption of the load is below the maximum available solar array power, converter 2 charges the battery with a power value complementary to the maximum solar array power. In order to do this, it has to maintain VMPP at its input terminals. Whenever the load power demand exceeds the maximum solar array capacity, the control-unit immediately commands converter 2 to stop, and commands converter 3 to discharge the battery. The 80’s have produced the digital implementation of the MPPT control-strategy. Schoeman and van Wyk [I] discovered that the maximum power voltage is a fixed percentage (75 YO) of the open-circuit voltage of the solar array. Unfortunately, this only holds for solar arrays in terrestrial applications, as in this case, temperature and light intensity fluctuations are relatively small. In a space-application, the tracking should be maintained in a wide operation-interval. An interesting contribution has been made in 1989 by Snyman and Enslin [2], offering a system-configuration with 2 power-paths between solar array and battery. Solar energy is not only transferred by means of the DC/DC-converter (max. efficiency 90 YO)but as well by means of a capacity in parallel with this converter. The overall efficiency is always superior to that of the individual converter. However, in space-applications, capacities are critical components, that have to be avoided on key positions in the power system, without redundancy.
This approach implies to use a power cell topology which can operate as a buck, for battery charge for instance if the battery voltage VB is always lower than the solar array voltage VSA and as a boost for the discharge of the battery, according to an unique control signal vc, generated by the central control-unit. vsa
U Fig. 2: The bidirectional MPPT topology
2.3. The control strategy
in order to force the solar array to operate at its maximum power point, a closed loop system has to be implemented which will control the bidirectional power cell inserted between the solar array and the battery according to a command signal vc which results from the process of the solar array power measurement and its derivative. In the case where a regulated bus voltage is distributed, the complexity of a direct power measurement may be avoided as it must necessarily be the sum of the power absorbed by the load and the battery. This is true for all situations provided that the converters operate in steady-state. The power absorbed by the load is proportional to its current because the voltage is maintained at the fixed value Vn. The same reasoning holds for the battery. Its voltage varies but can be considered as constant between 2 samples, so that the current passing through it is proportional to the power that it absorbs or delivers.
2.2. The hidirectional topology
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Actually for space-applications, regulated bus voltage and MPPT are possible only with the classical triangular topology [3] displayed on fig. 1. According to this approach, it is impossible for converters 2 and 3 to operate at the same time, as one is dedicated to the charge of the battery (BCR) and the other to its discharge (BDR). The MPPT process has to be applied to both converters as the rationale of this principle is to maximize the charge process and minimize the discharge of the battery during sunlight periods. This fact has led to replace converters 2 and 3 by a single bidirectional one. This bidirectional converter realizes both the battery charge and discharge function, and is responsible for MPP-tracking in both cases. The topology is shown on fig. 2. By reducing the number of converters from 2 to 3, the following two advantages are possible:
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Bdirectional b MC* regulator
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- weight reduction, which is important for space-applica-
Hill climbing Digital algonthm
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- less complex control-unit, because the converter under MPPT-control is always the same one.
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Fig. 3: Principle o f the MPPT control strategy
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This solution is attractive because instead of using a multiplier to calculate the solar array power, two simple operational amplifiers suffice. These two opamps operate at a fixed gain corresponding to the voltage values of the bus and the battery. This principle is presented in fig. 3.
frequency is 40 times lower than the converter switchingfrequency.
2.4. Application of maxinitrnt current control to the MPPT converter
To optimize the solar array power and to maintain a fixed voltage on the bus, an intelligent control-unit is necessary. This control-unit only controls the MPPT converter placed between solar array and battery, whence the possibility of simplification of the control interface. The input information being the solar array power, the unit seeks to maximize this power by means of a so-called hill-climbing algorithm. This hill-climbing algorithm can successfully be applied thanks to the fact that only one maximum exists on the power voltage curve. At its output, is generated the maximum power point voltage vh4pp that has to be applied to the solar array. In fig. 4 are detailed the solar array characteristics for fixed temperature and insolation.
In fig. 5 the whole system is schematically depicted. In steady-state, a limit-cycle oscillation is established around the maximum power point. This oscillation is used by the MPPT sampling, at a fixed frequency. An input-filter reduces the voltage ripple on the solar array, but must remain of modest dimensions in order not to falsify the calculation of the arraypower. Two current controlled converters are used. The MPPT converter is bidirectional and operates both in buck and in boost-mode. The bus-controlling converter only operates in buck-mode, because the energy transfer to the load is irreversible and bus voltage Vo will be always lower than
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Fig. 4: Solar array characteristics for fixed ambient conditions
It can be observed a one-to-one correspondence between array-power and voltage, hence a one-to-one correspondence between array-power and current. The control strategy will consist in driving the bidirectional power cell in the current controlled mode, in such a way that if vc is the control signal resulting from the comparison of the hill-climbing algorithm and VSA, we have [4]:
iB = G.vc
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The solar array used in the simulations has a maximum deliverable power of 1 200 W. The AID and D/A-converters are sized to 8 bit to have an inaccuracy smaller than (fraction). The bidirectional power cell between the solar array and the 2 battery operates in the current control mode (MC ), according to a control signal vCi. In order to compensate the intrinsic instability of such a mode when the duty cycle is larger than an additional sawtooth signal with slope K I is superim60 50 YO, posed to the command vCi.This allows to get the well known control law for corrected MC* systems, which link the maximum inductor current iM to the input-signal VCI such as:
in!= Glvc, - K1 t,
where tc is the conduction time of the power cell. The power cell, with reactive element L I , operates as a buck during battery charge and as a boost during the discharge of the battery. The battery-current iB is controlled by the control signal vel, at a sampling period T according to the control law, valid for change and discharge modes:
(2.1.)
where G is the current mode transconductance and i s the battery-current. Therefore, if Po is the load power operating on the regulated bus Vo with a load current io, the maximum power P ~ p p of the solar array is defined by:
(2.2.) assuming efficient converters in this closed loop system. A digitally implemented hill-climbing algorithm has been chosen for its simplicity of realisation and easy working conditions. The solar array power is obtained by application of analogous electronics. Thereafter it is converted in digital form, and processed by the algorithm. The MPPT sampling-
(2.3.)
(2.4.)
The transition from charge to discharge does not affect the inductor current waveform as charge and discharge are ruled by the same control law. A continuous and smooth transition results. This means that if such a converter/controller unit is connected to a battery, it can control the average batterycurrent, and thereby its power, both in charge and in discharge conditions.
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BUS-VOLTAGE CONTROL
one-to-one correspondence of solar array current and voltage, it results a control of the maximum power voltage. In fact, the principle is based on the observation that it is only needed one degree of freedom (solar array current or voltage) to completely control the solar array power.
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The control strategy involving the digital hill-climbing algorithm associated to a current controlled bidirectional power cell have been submitted to numerical simulations. Several configurations have been tested, and the most representatives are detailed next. They concern the cold-start transient to get the solar array locked on the maximum power point and its recovery after abrupt changes in the solar array characteristics, for instance after a change in the open-circuit voltage Voc.
3. I . Cold-start transient
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On fig. 6 are represented the evolutions of the main parameters of the MPPT process. They imply the solar array parameters VSA and ISA,the average value of the power cell inductor current iL, the bus voltage V,.
HILL-CLIMBING ALGORITHM
Comparator
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Fig. 5: MPPT-system with hill-climbing algorithm
The second converter, located between the solar array and the load, operates also in the current mode for the bus voltage regulation. The delivered current io is as well as for the battery, controlled by a command vc2, with a superimposed saw tooth K2 such as:
where Gz is the transconductanceof the current mode. For each MPPT sampling period, the hill-climbing algorithm gives the new voltage-reference Vnrpp to be appved to the solar array. This reference is translated by the MC' controller into a certain average output-current, drawn from or supplied to the battery. The solar array current is the sum of the current supplied to the M PPT converter and to the busregulating converter. The contribution of the bus-converter is entirely determined by the energy-needs of the users, and cannot be manipulated. The contribution of the MPPT converter on the contrary can be completely adapted to force the solar array supply the maximum power current. Due to the
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In the very beginning, there is a transient response, because the capacities have to be loaded and the controller has to be initialised. After about 0.01 sec. (half-way the screen), the M PPT-voltage is attained. Thereafter, two sudden two loadincreases are applied. The first one still leaves some array-current to be transferred to the battery, but the second one causes the battery-current to be inverted. This can be seen in fig. 6 where it can be noticed "llbuck I " crossing the 0 ampkre line (dashed-line in the middle) after the second load-charge. It is important to note that apart from transient effects, the maximum power voltage VAfPP is maintained at 40 V (VSA, solid line without marker in figure). The bus voltage remains regulated, and only load transients can be observed. The array voltage presents a large transient to reach the V.\/pp voltage and to remain locked at this value even after the load transients. On fig. 7 is shown the V , w P locus during transient.
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Fig. 9: Solar array parameter Voc changes
Fig. 7: Corresponding movement on solar array curve
3.2. Change in open-circuit voltage 4. BREADBOARD VALIDATION
The MPP recovery from any disturbing conditions is an important feature for a space born MPPT. These changes may affect Voc or /sc due to sunlight or temperature conditions. Same parameters are displayed for a VOcchanges from 50.5 to 42 V, which implies a smaller maximum power voltage. Starting from a stable limit-cycle oscillation on the upper curve of fig. 8, the MPPT is displaced toward the lower one. This last curve corresponds to the new solar array characteristic, on which the initial excursion is larger due to transient effects. However, after the establishment of a new stable limit-cycle oscillation, the same small amplitude excursion is noticed.
A breadboard verification has been done with energy-transfer in the SOW-range. The hill-climbing algorithm has been hardware implemented. As already stated, the samplingfrequency is 40 times lower than the converter-frequency, which is 50 kHz. The low MPPT sampling-frequency ( I 250 Hz) has permitted to use low-cost A/D and D/A converters. On fig. I O is shown the behaviour of the circuit in steady-state.
signal
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Fig. 8: Corresponding change of solar array curve
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Fig. IO: MPPT-voltage and search-direction. Time-scale: 1 mddiv
If the electrical parameter transients are considered for the solar array (VSA, /SA), the regulator power cell (IL)and the distributed voltage Vo, these behaviours are displayed on fig, 9. Following the power excursion shown on fig. 8, the solar array current and the battery charge current decrease abruptly, while the solar array voltage presents a smooth change as V n i p p is not really affected. The bus regulated voltage is not affected. The hill-climbing algorithm representation is represented by the signal of the counter output. The square-wave curve represents the search-direction which is either 1 (count up) or -I (count down). Because the new maximum power voltage is lower than the previous one, the search-direction is negative during the transient time (variable DIR in fig. 8). 837
The stair-case curve represents the MPPT-voltage (A), and below is shown the search-direction signal (B). The limitcycle oscillation of the MPPT-voltage has an amplitude of 150 mV which is quite small compared to the maximum solar array voltage (20 V). A time-delay of a nearly half an MPPTperiod exists between the search-direction reference (B) and the resulting MPPT-voltage. This is due to the electrical circuit, that accounts for AID conversion-time. On fig. I 1 is shown the MPPT-voltage occuring with an imposed high voltage excursion amplitude to demonstrate the immunity of the hill-climbing logic circuits to noise. Pulses on fig. 1 I B, represents the signal generated by the comparator (fig. 5 ) ordering a change of the search direction.
5 . CONCL~JSION
Fig 1 I MPPT-voltage and comparator output Time-scale 5 ms/div
The high loop-gain causes an oscillation of larger amplitude than strictly necessary, but is employed to demonstrate that a reversal of search direction can only occur after the detection of a power decrease by the comparator. On fig. 12, the MPPTvoltage is depicted once again, but this time together with the S/H control signal, during a same search-direction process.
A new maximum power point tracker has been described which gathers the features of the digital hill-climbing strategy control and the bidirectional current mode power cell. It results a simplified power conditioning topology which includes the energy source managements (solar array and battery) and a regulated distributed voltage by means of two DC/DC regulators. Transitions from battery charge (quadrant 1) to battery discharge (quadrant 4) mode take place without any discontinuity. The new system realises both maximum power point tracking and uninterrupted power-supply to the load. These performances have been demonstrated with the support of a numerical simulation where the selected digital hill-climbing algorithm has been submitted to abrupt transients resulting from cold-start and solar array parameter changes. A breadboard validation of the principle has confirmed the predicted performances from theory and simulation. N o instability has been noticed in the breadboard behaviour resulting from the mutual influence of two closed loop systems, one controlling the MPPT principle, the second achieving a regulated bus voltage distribution, both loops operating in a sampling mode. The combination of the digital hill-climbing MPPT algorithm, as it was presented, and the bidirectional MC2 power cell control interfacing both energy sources has been verified as a viable topology, conducting to a simple regulated bus topology, which will be promissed to a good future as well for space-applications in Low Earth Orbit missions as for terrestrial developpements for remote stations.
REFERENCES [I]
[2]
Fig 12 MPPT-voltage and S/H control signal Time scale 0 5 ms/dlv
[3]
Clearly it is demonstrated that the new MPPT-voltage ( A ) is only ready a half MPPT-period after the sampling-instant. In the meantime, A/D conversion. calculation and D/A conversion take place.
[4]
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J.J. Schoeman, J.D. van Wyk: "A simplified maximum power controller for terrestrial photovoltaic panel array" IEEE PESC 1982, p.p. 36 1-367. D.B. Snyman, J.H.R. Enslin: "Comhined low-cost, high-efficiency inverter, peak power tracker and regulator for P.V. applications" IEEE PESC 1989, p.p. 67-74. A Poncin. "Advanced power conditioning using a maximum power point tracking system" Spacecraji electric power conditioning seminar Frascati -Italy, 20-24 may 1974. A . Capel. J.-C. Marpinard, M. Valentin and J. Jalade: "Low cost standardised current-control modulator for high-power switching converters" ESA Journal 1984, Vol 8, p.p. 437-446.
