A fast-mppt low-complexity autonomous water pumping scheme for PMSM M. Zigliotto, M. Carraro and A. Costabeber Department of Management and Engineering, University of Padua, Vicenza, Italy Department of Electrical and Electronic Engineering, University of Nottingham, Nottingham, NG7 2RD, UK Keywords: PMSM drives, MPPT tracking, water pumping Abstract This paper proposes an autonomous photovoltaic () water pumping system for rural/remote applications. The system has been designed to minimize complexity and cost while guaranteeing fast maximum power point tracking (MPPT). This feature is essential to provide optimum utilization of solar energy, maximizing the amount of extracted water. Low complexity hardware and control ensure higher reliability and ease of installation and servicing. In the proposed scheme, the string is directly connected with the DC-link of a three-phase VSI, driving a PMSM pump with a standard Field Oriented Control (FOC). To achieve fast MPPT, the controller integrates a Sliding-Mode Ripple-Correlation (SMRC) MPPT algorithm, acting on the pump speed reference. The system is therefore capable of operating without the need for additional power conversion stages dedicated to MPPT. Matlab simulation results confirm the effectiveness of the proposed architecture and control. 1 Introduction Installation of autonomous water pumps has always been a challenge and a key resource in those areas of the globe lacking of AC power distribution networks and/or of water distribution systems. Apart from rural areas or small domestic applications, water pumping is of primary importance in those arid regions where it represents the only alternative to wheeled transportation to provide a minimum water supply to the population even during severe droughts. The use of photovoltaic energy has been the most natural choice to power autonomous pumps since the early nineties [1], for the large availability of solar irradiance in desert areas. The benefits of pumping are not limited to desert areas, but attracted interest also for large farms or ranches [2] where autonomous pumping was seen as a convenient way of reducing the load of the distribution system with benefits both for the utilities and for the customers. In water pumping applications, the intermittent nature of photovoltaic power is a negligible issue, as long as the pumping system is capable of exploiting the source, maximizing the harvested energy and the extracted water, guaranteeing a fast and reliable maximum power pint tracking. One of the main constraints when designing a pumping system is to achieve this goal while maintaining reasonable complexity. A simplified hardware guarantees reduced cost and increased reliability, and a simple controller facilitates the commissioning and tuning of the system. Both these features reduce the need for servicing, optimizing the operating costs. Traditionally, small pumping systems ranging from hundreds of W to few kw are based on DC machines, often with direct coupling with the string [3]. The solution has minimum complexity no power converters are used - but the MPPT cannot be guaranteed, thus reducing the overall efficiency and effectiveness of the system. The design is normally based on matching the pump speed-torque characteristic and the string ones to enable a proper operation in a desired range. Recently, a different architecture has been proposed in [4], which includes an additional DC/DC buck converter as coupling element between the string and the DC pump, enabling the implementation of an MPPT algorithm by directly acting on the duty-cycle. Instead [5] proposes a sixpulse inverter driving a three-phase induction machine pump and implementing the MPPT by acting on the operating frequency of the inverter. The solution in [6] adopts the same architecture proposed in [4], applying and optimizing a Perturb and Observe MPPT algorithm. Finally, [7] presents a conversion system similar to the one proposed in this paper but using an induction machine and an additional DC/DC stage to boost and regulate the DC-link voltage of the induction machine drive. To comply with the constraints on MPPT and system complexity, this paper proposes a new autonomous water pumping system where the power stage is composed by a string directly connected to the DC-link of a three-phase VSI driving a PMSM pump, avoiding any intermediate power conversion stage. The choice of a PMSM pump is due to the fact that it provides higher efficiency and higher power factor compared to DC or induction machines. Despite the minimum hardware, the proposed controller achieves MPPT, by merging together a classic Field Oriented Control and a Sliding Mode Ripple Correlation MPPT technique. The theoretical framework of SMRC MPPT has been developed in [8] as a variant of the well-known ripple-correlation scheme [9-11]. It enables an approximated average modelling of the non-linear controller, facilitating the design and obtaining predictable responses to irradiance steps. The proposed architecture and control have been validated in Matlab Simulink, confirming the capability of operating the pump maximising the utilization of power.
2 Water pumping system architecture Figure 1 shows the proposed autonomous photovoltaic water pumping system. The hardware includes a string directly connected to the DC-link of a three-phase inverter (VSI) linked to the PMSM vertical centrifugal pump. The disadvantage of this solution compared to the one proposed in [7] is that the DC-link voltage varies as the solar irradiance varies and moves the maximum power point (MPP). This is normally acceptable, due to the fact that typically the locus of MPPs spans over a fraction of the open circuit voltage. Therefore, the only practical constraint is that both voltage rating and power rating of the pump have to be matched with the MPP voltage and power of the string. These qualitative considerations will become clearer in the simulations presented in the following section. The control of the PMSM is based on a traditional FOC, with the q current reference defined by the speed loop controller. The main differences with respect to a classic speed control are 1) the speed reference, which is now defined by the external SMRC MPPT loop and 2) the d current reference, which is equal to a small AC perturbation instead of the zero reference, to induce in the DC-link a small voltage ripple required to facilitate the ripple correlation MPPT. 2.1 PMSM pump model The time-domain equations of a PMSM, expressed in the dq rotating reference frame synchronous to the rotor PM, are the following: ddii uu dd = RRii dd + LL dd ωω dd dddd mmmmll qq ii qq ddii uu qq = RRii qq + LL qq + ωω (1) qq dddd mmmmll dd ii dd + ωω mmmm Λ mmmm where uu dd and uu qq are the voltages applied to the dd and qq axes respectively, ii dd and ii qq are the stator currents, RR is the phase stator resistance, LL dd and LL qq are the synchronous inductances, Λ mmmm is the rotor flux linkage generated by the magnets, ωω mmmm = ppωω mm is the electromechanical speed and pp is the number of pole pairs. The electromagnetic torque balance equation completes the description of the system: ττ = 3 2 ppλ mmmmii qq + 3 2 pp LL dd LL qq ii dd ii qq (2) In order to correctly derive the parameters of the equivalent mechanical model of the system, the model of a vertical centrifugal pump is here considered. The mechanical torque balance returns: ddωω ττ = JJ mm mm + BB dddd mm ωω mm + BB PP ωω 2 mm + BB pp0 (3) where JJ mm is the total inertia of motor and pump, BB mm the equivalent viscous friction of the motor and ττ pp = BB PP ωω mm 2 + BB pp0 the load torque of the pump. Equation (3) shows that the equivalent viscous friction of motor and pump can be described as BB mm = ff(ωω mm ) = (BB mm + BB PP ωω mm )ωω mm. The hydraulic power of the pump PP pp [WW] is expressed by the relationship [12-13]: PP pp = ρρρρρρρρ ηη PP (4) where QQ mm3 is the pump flow rate, HH [mm] is the total water h head, ηη PP is the pump overall efficiency, usually provided by the pump manufacture, ρρ kkkk mm2 is the fluid density and gg the gravity. The delivery head HH depends on the flow rate QQ by the relationship [13]: HH = αα 0 ωω mm 2 αα 1 ωω mm QQ αα 2 QQ 2 (5) where αα 0, αα 1 and αα 2 are parameters provided by the pump manufacturer. From (5), it follows that an increase in flow rate QQ causes a decrease in the delivery head HH. The overall i MPP U DC = u ω max ω min i d ω m t p ω m = γ sign dτ, γ < 0 0 u p = 0 if u = U MPP u = Asin( ω + PI ωm AC t) i q + + PI id PI iq u d u q ϑ me i d i q dq dq αβ uvw u α u β array + i u iv i w VSI Figure 1: Control scheme of the proposed photovoltaic water pumping system p s C u u u v u w PMSM ω m PUMP 2
performance of the pump varies with the motor speed since QQ varies directly in relation to the change in speed, as well as the absorbed power (4), which increases as the cube of the speed variation. Water pumping in rural areas is a particular application which normally does not require a settled speed regulation. Nevertheless, centrifugal pumps have a mechanical efficiency curve that has an optimum operating speed where the efficiency is maximum and a limited speed variation would be a desirable feature. As a matter of fact, a speed variation is unavoidable when the power changes, because the power balance must be guaranteed. As a general approach, the optimum speed should correspond to a power equal to an average annual power in the specific geographical area. All these considerations strictly depend on the specific pump and on the installation site, and therefore the following analysis will only include a generic speed variation interval. ωω mm,mmmmmm ωω mm,mmmmmm. 2.2 panel modelling For a desired power rating and nominal voltage of the PMSM driving the pump, the modules have to be arranged in an array with parallel and/or series connection to match the nominal voltage and power. Each module in the array can be modelled considering the voltage-current characteristic equation of a silicon monocrystalline cell [12], given by: uu PPPP +NNccRR SSSS ii PPPP ii PPPP = II SSSS II ss ee ηηvv TT NNcc 1 uu PPPP+NN cc RR SSSS ii PPPP (6) RR PPPP NN cc II SSSS is the photo generated current (or short circuit current), uu PPPP and ii PPPP are voltage and current of the module, NN CC is the number of cells, RR SSSS and RR PPPP are the series and shunt resistance of each cell, ηη is the quality factor and VV TT is the temperature equivalent voltage (VV TT = KKKK where KK = qq 1.38 ee 23 JJ/ KK is the Boltzmann s constant), TT is the temperature in KK and qq is the charge of the electron. The model can be extended to any series or parallel connection of modules to form the required array. 2.3 Automatic attainment of maximum power The primary aim of the system is to ensure the maximum energy extraction from the photovoltaic string. Since the MPP of a string varies with irradiation and temperature, the use of an MPPT algorithm is strictly necessary to ensure the maximum power generation and the maximum volume of pumped water. In parallel/series connection of modules, an additional issue is the partial-shading effect, which generates multiple local maxima in the voltage-current characteristic. This aspect is not investigated in this paper, assuming that partial shading is not likely to occur in rural and arid areas where the number of shading objects is limited. Moreover, the limited power rating of the application requires a small surface, making the system less dependent on partial shading caused by clouds. Recalling the scheme in Figure 1 and according to [8], the MPP block drives the toward the MPP by zeroing the gradient of the power (PP PPPP = uu PPPP ii PPPP = uu DDDD ii PPPP ), according to the non-linear pp uu characteristic curve of the string. The proposed control algorithm can be briefly introduced by considering the ideal pp uu characteristics shown in Figure 2, which depends on the operative voltage and on the solar irradiation through the short circuit current II SSSS. For voltages lower than the MPP, the power derivative with respect to voltage is negative, positive on the other side, and zero in the MPP, i.e.: PP PPPP > 0 iiii uu DDDD < UU MMMMMM PP PPPP < 0 iiii uu DDDD > UU MMMMMM (7) PP PPPP = 0 iiii uu DDDD = UU MMMMMM This is the basic approach followed by ripple correlation techniques available in literature. In general, the information on the gradient (7) is then used to drive a control variable able to change the operative point of the conversion system and move it toward the MPP. In the control scheme proposed here, the MPP operating condition is pursued by changing the control variable represented by the speed loop reference of the PMSM pump. Assume that the pump is operating at a certain speed ωω, corresponding to a average power PP, in Figure 2: pp uu curve of a string MPPT with a DC-link voltage UU DDDD. If the power is suddenly decreased, the power balance between generator () and load (pump) is no longer respected, as the mechanical power remains the same while the source power is reduced. The balance is instantaneously provided by the DC-link capacitor, whose voltage tends to drop: without acting on the speed reference, the link discharges to zero and the pump stops operating. Similarly, increasing the power while keeping the same speed reference causes the opposite effect, with the string charging the DC-link until the power is reduced to the value that balances the mechanical power. The first transient causes the trip of the pumping system, while the second guarantees the operation, but at reduced power. The SMRC MPPT scheme has the duty of guaranteeing that the system moves from these non-mpp equilibriums and tracks the maximum power. As shown in (4) 3
[8], SMRC MPPT needs perturbation acting on the system and the original version in [9] as well as the study in [8] uses the ripple at the switching frequency to perform the task. Nevertheless, this requires a more precise voltage and power ripples sensing and might suffer from non idealities due to string reactive parasitics. According to the minimum complexity design criterion for the pumping system, the choice here has been to inject an additional perturbation at lower frequency ωω AAAA on the DC-link voltage ( voltage). This has been done by injecting a current reference signal ii dd = AA sin(ωω AAAA tt) (or a saw tooth wave at the same injection frequency ff AAAA = 1/(2ππππ AAAA )) into the d-axis of the PMSM FOC control. Torque ripple is minimised by minimising the amplitude AA. The equivalent oscillation in the DC-link can be expressed as: uu PPPP = UU DDDD0 + Δuu = UU DDDD0 + f(sin(2ωω AAAA tt)) (8) Where UU DDDD0 is the average DC-link voltage and Δuu = f(aa sin(2ωω AAAA tt)) is a function f( ) of the disturbance injected in the d-current axis. The behavior of the DC-link voltage across the DC-link capacitor C depends on the active power generated by the panel which supplies the PMSM pump expressed by equation (4). The instantaneous power balance is related to the voltage variation as: dduu PPPP dddd = PP PPPP PP PPPPPPPP uu PPPP CC where PP PPPPPPPP is the power absorbed by the pump. Considering that the d-axis and q-axis mutual terms are deleted by means of a decoupling scheme, the equivalent voltage oscillation on the d-axis can be expressed by: (9) uu dd = UU dd0 + KK RRRR Asin(2ωω AAAA tt + φφ RRRR ) (10) Where φφ RRRR and KK RRRR are the added phase and the equivalent gain of the d-axis PI current control. The corresponding instantaneous power is (after some trigonometric substitutions): PP PPPPPPPP = 3 2 uu ddii dd + uu qq ii qq = 3 2 uu 4 qqii qq + AAKK RRRR cos(φφ RRRR ) AA KK RRRR cos(2ωω AAAA tt + φφ RRRR ) + 2AA UU dd0 sin(2ωω AAAA tt) (11) = PP 0 3 4 AA [KK RRRRcos(2ωω AAAA tt + φφ RRRR ) + 2 UU dd0 sin(2ωω AAAA tt)] where PP 0 = 3 4 2 uu qqii qq + AA KK RRRR cos(φφ RRRR ) is the DC power (assuming negligible the effect of the speed oscillation on the q-axis current reference) and 3 4 AA [KK RRRRcos(2ωω AAAA tt + φφ RRRR ) + 2 UU dd0 sin(2ωω AAAA tt)] is the AC added power perturbation. According to (9), and considering that in steady state the DC power through CC equals zero, the DC-link power perturbation is then at twice the injection frequency in the current d-axis, i P = u i K sτ p 1+ sτ P f 1 ε 1+ sτ LPF ε f u f u sgn( ε f ) Kusτ 1+ sτ Figure 3: MPP sliding controller scheme γ s = udc = U DC0 ω m + u i.e. at ff DDDD = ωω AAAA. Figure 3 recalls the SMRC MPPT controller ππ [8], with the two high pass filters used to extract the AC components uu ff and pp ff = HHHHHH(uu PPPP ii PPPP ) of power and voltage (at the same cut-off frequency ωω HHHHHH = 1 = 2ωω ττ AAAA ) with HHHHHH different high frequency gains KK pp for the power and KK uu for the voltage. The correlation block output (i.e. εε(tt)) is then low pass filtered to eliminate the resulting AC components. In first approximation a first order low pass filter at ωω LLLLLL = 1 ωω HHHHHH 20 returns the filtered correlation function εε ff (tt). ττ LLLLLL = The corresponding reference for the pump speed loop (i.e. the output of the MPP controller) is then: ωω mm tt = γγ ssssssss εε ff (ττ) dddd 0 (12) Where γγ < 0 is the integral gain of the MPP controller. It is worth recalling what happens when the system is in MPP and experience a transient in the power: 1) If the solar irradiation decreases, the pump tends to discharge the link and moves the operating point of the string in the region where εε ff (tt) > 0 PP PPPP > 0. According to (12), the speed reference is then decreased, until the new equilibrium at the new MPP is reached (εε ff (tt) = 0). 2) If the solar irradiation increases, the pump tends to find a new steady state in an operating point of the string in the region where εε ff (tt) < 0 PP PPPP < 0. According to (12), the speed reference is increased, until the new equilibrium at (εε ff (tt) = 0) is reached. The presence of the ripple disturbance intrinsically causes a reduction of the extracted power if compared to the ideal MPPT. Nevertheless, in the specific autonomous application, the reaching of the exact MPPT is not considered critical, and a fast and reliable response to changing weather conditions is considered a priority. The output ramp speed reference is finally limited to the operating pump speed range, equal to ωω mm,mmmmmm ωω mm,mmmmmm. 4
3 Numerical results and discussion In this section, the general analysis proposed so far has been applied to a specific case study of a minimum-size water pumping system with a single module rated for 230W and a pump driven by a PMSM rated for 150W. The proposed SMRC MPPT controller has been verified in Matlab/Simulink environment, according to the panel characteristic reported in Table 1 and the estimated MPP curves of Figure 4 have been derived substituting the parameters of Table 1 in the model (6). The dotted line in figure represents the MPP locus of the panel. The electrical machine is a small PMSM, whose parameters are reported in Table 2. The Simulink scheme implements the same control architecture of Figure 1, including the switching model of the three-phase VSI and dynamic feed forward decoupling action. Saturations and quantization effects of the 10 bit A/D current conversions and encoder resolution (i.e. @ 1024 ppr) in the control chain are included. The goal of the following set of simulations is to evaluate the effect of the proposed control technique, assuming that initially the motor is at standstill and a sequence of solar irradiance steps is applied, emulating a worst case example of sunlight variability. Figure 4 and 5 show that in correspondence of the first solar irradiation step of 160 WW/ mm 2 occurring at t=0, the DC-link voltage is quickly moved from the open circuit voltage of the module toward the MPP point with a consequent speed reference variation of 1000 rrrrrr in the PMSM control loop. Figure 4: (left) Extracted power for II SSSS = 1.44 7.22 AA at steps of 1.44 AA and MPP locus for the panel in Table 1. electrical parameters Maximum power PP PPPP,NN Open circuit nominal voltage VV OOOO Maximum voltage at PP PPPP,NN Short circuit current II SSSS Number series cells NN CC Total series resistance Total shunt resistance Value 230 WW 42.3 VV 34.3 V 7.22 AA 80 0.4Ω 500Ω Figure 5: Consecutive sequence of solar irradiation transient variations and corresponding ii dddd pump currents. Table 1: module nominal parameters @ 1000W/m 2, 25 C Motor and control parameters ph-ph nominal RMS voltage UU NN Polar pairs pp Nominal current II NN Nominal power PP NN Stator inductance LL = LL dd = LL qq Saliency ratio ξ = LL qq /LL dd Motor Inertia JJ mm Viscous Friction BB mm Pump BB PP Symmetric PWM frequency ff ss Injection frequency ff AAAA Injection current amplitude A DC-link capacitance CC Value 50 V 2 3.8 AA 0.15 kw 1.6 mh 1 1.2ee 5 kgm 2 1ee 3 Nms/rad 1ee 5 Nms/rad 16 khz 500 Hz 0.1 A 470 μf Table 2: Control, PMSM and centrifugal pump parameters. Figure 6: Pump speed variation and DC-link voltage UU DDDD response during consecutive irradiation step transients. The control strategy is then evaluated by applying other consecutive solar irradiance steps of different amplitude and direction, while the equivalent pump load is generated by 5
considering the mechanical torque balance in (3), i.e. with a load torque proportional to the square of the mechanical speed. The pump load torque follows the mechanical balance (3), and, as expected, the control reacts to the consecutive solar irradiation transients in Figure 5 by changing the speed reference and discharging the DC-link only in response to a step down in the solar irradiation as already discussed. The d-q current transient variations (the perturbation is injected in d-axis) are also reported. Figure 6 also proves that the DC-link voltage, i.e. the panel voltage obtained with the proposed control scheme (without DC/DC converter) always guarantees the MPP operation, in a good agreement with the MPP voltages locus in Figure 4. Finally, the equivalent power absorbed by the pump (PP PPPPPPPP ) and the one generated by the photovoltaic module are shown in Figure 7. Also the powers match the MPP ones in Figure 4. Figure 7: Power generated by the panel and absorbed by the PMSM centrifugal pump. 4 Conclusions The paper presented an autonomous water pumping architecture and control for rural/remote applications. The development of the proposed system has been driven by the need for minimum complexity hardware able to guarantee the maximum power point tracking with a simplified control scheme and with fast response to solar irradiation transients. In the proposed system, the string is directly connected to the DC-link of a three-phase VSI driving a PMSM coupled with a centrifugal pump. The control scheme is a traditional speed loop with FOC control, modified to enable the implementation of the sliding-mode ripple-correlation MPPT previously proposed in [8]. The behaviour of the system has been tested in Matlab/Simulink environment, showing a satisfactory response to a sequence of solar irradiation transients. Regardless the amplitude and the direction of the transient (step-up, step-down), the controller promptly responds and guarantees the maximum power extraction from the system, optimising the volume of pumped water. 5 References [1] S. Makukatin, "Water from the African sun," Spectrum, IEEE,vol.31, no.10, pp.40,43, Oct. 1994 [2] K. Stokes, J. Bigger, Reliability, Cost, and Performance of -powered Water Pumping Systems: A Survey For Electric Utilities Energy Conversion, IEEE Transactions on, Vol. 8, No. 3, September 1993, pp.506-512 [3] M. Kolhe; J.C. Joshi, D.P. Kothari, "Performance analysis of a directly coupled photovoltaic waterpumping system," Energy Conversion, IEEE Transactions on, vol.19, no.3, pp.613,618, Sept. 2004 [4] M.A. Elgendy, B. Zahawi, D.J. Atkinson, "Comparison of Directly Connected and Constant Voltage Controlled Photovoltaic Pumping Systems," Sustainable Energy, IEEE Transactions on, vol.1, no.3, pp.184,192, Oct. 2010 [5] E. Muljadi, " water pumping with a peak-power tracker using a simple six-step square-wave inverter," Industry Applications, IEEE Transactions on, vol.33, no.3, pp.714,721, May/Jun 1997 [6] M.A. Elgendy, B. Zahawi, D.J. Atkinson, "Assessment of Perturb and Observe MPPT Algorithm Implementation Techniques for Pumping Applications," Sustainable Energy, IEEE Transactions on, vol.3, no.1, pp.21,33, Jan. 2012 [7] J.V. Mapurunga Caracas, G. De Carvalho Farias, L.F. Moreira Teixeira, L.A.de Souza Ribeiro, "Implementation of a High-Efficiency, High-Lifetime, and Low-Cost Converter for an Autonomous Photovoltaic Water Pumping System," Industry Applications, IEEE Transactions on, vol.50, no.1, pp.631,641, Jan.-Feb. 2014 [8] M. Carraro, A. Costabeber, and M. Zigliotto, Convergence analysis and tuning of ripple correlation based MPPT: A sliding mode approach, in Proc. of EPE 13, pp. 1 10, 2013. [9] P. Midya, P. Krein, R. Turnbull, R. Reppa, and J. Kimball, Dynamic maximum power point tracker for photovoltaic applications, in Proc. Of PESC 96, 27th Annual IEEE, vol. 2, Jun 1996, pp. 1710 1716 vol.2. [10] S. Brunton, C. Rowley, S. Kulkarni, and C. Clarkson, Maximum power point tracking for photovoltaic optimization using ripple-based extremum seeking control, Power Electronics, IEEE Transactions on, vol. 25, no. 10, pp. 2531 2540, oct. 2010. [11] R. Leyva, C. Alonso, I. Queinnec, A. Cid-Pastor, D. Lagrange, and L. Martinez-Salamero, Mppt of photovoltaic systems using extremum - seeking control, Aerospace and Electronic Systems, IEEE Transactions on, vol. 42, no. 1, pp. 249 258, jan. 2006. [12] Roger, A, M and Jerry, V, Photovoltaic systems engineering 2nd edition, Taylor & Francis e-library, 2005 [13] A. Saadi, A. Moussi, Optimisation of Back-boost converter by MPPT Techniquewith a Variable Referance Voltage Appliedto Photovoltaic Water Pumping System under Variable Weather condition, Asian Journal of Information Technology, volume 6. 2, pp. 222-229, 2007 6