31st European Photovoltaic Solar Energy Conference and Exhibition
MODELING AND SIMULATION OF LARGE PV PUMPING SYSTEMS
J. Muñoz(*), J.M. Carrillo, F. Martínez-Moreno, Martínez-Moreno, L.M. Carrasco, L. Narvarte. Grupo de Sistemas Fotovoltaicos. Instituto de Energía Solar – Universidad Politécnica de Madrid (IES-UPM) (1) Address: ETS Ingeniería y Diseño Industrial (ETSIDI). Ronda de Valencia, 3. 28012 Madrid (Spain) E-mail: javier@ies-d E-mail:
[email protected] ef.upm.es Orcid ID: orcid.org/0000-0002-9301-9215
ABSTRACT: This paper describes the modelling of components for large PV pumping systems, which have been implemented in an online and free-software simulator of PV systems called SISIFO, which is publicly available at www.sisifo.info.. Among other features, this software tool allows the prediction of water pumped as function of PV www.sisifo.info size and type and the analysis of system performance. Keywords: PV System, PV Pumping, Water-Pumping, Software, Modelling, Simulation.
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INTRODUCTION
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The reduction of cost for PV modules caused by the massive installation of grid-connected systems has increased the economic competitiveness of conventional decentralised PV applications. In particular, there is a renewed interest in water PV pumping systems, which are the object of this paper, and PV-diesel hybrid systems, which are discussed in a concurrent paper of this conference [1]. Large PV water pumps, in the range of hundreds of kW, are emerging as commercial products for water irrigation applications and, even in industrialised countries, they may compete or complement the connection connection to the electricity grid. For example, in Spain, despite the hybridization of grid and PV pumps is not allowed by the present regulatory framework, some regional agriculture associations are studying the possibility of integrating large stand-alone PV pumps in their current irrigation systems. These irrigation systems are usually composed by several centrifugal pumps of several hundreds of kW with an aggregated capacity in the MW range, and associations are decided to supply one of more of these pumps with PV, which would reduce the contractual power required from the electricity grid at noon when kWh prices, besides, are relatively high. To assess this integration and analysing technical as well economic aspects, it is necessary to predict the volume of water pumped by the PV system, typically, for a yearly period. This paper describes the modelling of components for large PV pumping systems, which have been implemented in an online and free-software simulator of PV systems called SISIFO, which is publicly available at www.sisifo.info.. www.sisifo.info This simulation tool allows the prediction for water pumping as function function of PV size and type and the analysis of system performance. Finally, a simulation example of a real 20kW PV pumping demonstrator installed in the Irrigator Community of Alto Vinalopó, Alicante (Spain), is presented. This demonstrator includes a North-South horizontal tracker which improves the efficiency of the PV pumping system in terms of m 3 of pumped water per kWh of the incident irradiance. The presentation of this paper has been organised with the following structure. Section 2 describes the modeling of the system components and Section 3 presents the simulation simulation example. example.
MODELING OF THE WATER PUMPING PV SYSTEM
The configuration of the simulated water pumping PV system is displayed in figure 1, which is composed of a PV generator, a variable-frequency inverter and an AC centrifugal pump.
PV generator
Frequency AC centrifugal converter pump
Figure 1: Configuration of a water pumping PV system.
The detailed modeling of the PV generator and the inverter is beyond the scope of this paper, but it is described elsewhere by the authors [2][3]. It is just worth mentioning that SISIFO allows the simulation of three static and six sun-tracking PV generators. For example, static ground-mounted or building-integrated PV generators in roofs or façades, and conventional one-axis horizontal or two-axes sun-trackers. Sun-trackers generate more energy at higher equipment cost and some of them, e.g., one-axis horizontal solar trackers, may be cost-effective cost-effective in particular energy scenarios at present PV modules prices. We focus here only on the modelling of the system curve (pipeline characteristic) and the AC centrifugal pump, which is composed by an AC motor and a mechanical centrifugal pump. Figure 2 shows the scheme of the AC pump including some of the power terminology defined below in this paper. P1
PH
P2
AC motor
Centrifugal pump
Figure 2: Scheme of an AC centrifugal pump.
2.1 AC motor model The AC motor is characterized by its rated output mechanical power ( P2 ,NOM ), or rated shaft power, and its power conversion conversion efficiency, efficiency, M , which is calculated as: M
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P 2 P 1
p2 p2
(k m 0 k m1 p2 k m 2 p22 )
(1)
31st European Photovoltaic Solar Energy Conference and Exhibition
Where p2=P2/P2 ,NOM being P2 the output mechanical power of the motor and P1 the electric input power of the motor. Parameters k m0, k m1 and k m2 are fitted from the motor efficiency curve, which is normally provided by the manufacturer.
The operating point on pump curve may be calculated either graphically or numerically. Obviously, the second method is used in simulations, but let us first describe the graphic method, which will be useful to illustrate the problem. Graphically, the operating point is in the intersection of pump curve (Equation 2) and system curve (Equation 4). Figure 4 shows an example, where the operating point at rated speed ( 1= NOM ) would be the point A.
2.2 Centrifugal pump model The characteristics of the pumps are normally provided by the manufacturers at a constant, nominal or rated, speed. Figure 3 shows an example of the variation of typical pump parameters as a function of the volumetric water flow, Q, which is usually expressed in [l/s] or [m3/h]. The parameters displayed in Figure 3 are: Head. The curve H-Q of the pump is usually H called the "pump curve". P1 Electric input power. P2 Shaft power. P Pump efficiency. It is defined as the ratio PH/P2, where PH is the hydraulic power, which is equal to PH=k·H·Q. The constant k depends on the dimensions of H and Q. MP Motor-pump efficiency ( MP = M P ). It is defined as the ratio PH/P1.
H Pump curve
1
2
Q2 Q1
NOM
1 Q
Figure 4: Graphical example for determining the operation point of the pump with variable speed.
However, the operation point is not constant because the speed of the pump varies according to the PV power, which itself depends on solar radiation. The variation of the pump speed modifies the pump curve and the operating point. Figure 4 shows the new curve and new operating point B at a lower speed ( 2< 1). As the system curve does not change, the operating point is always in this curve. Hence, the calculation of the operating point requires the determination of pump curves as a function of pump speed. The solution is obtained using the well know affinity laws for pumps, which, assuming that the impeller diameter and water density remain constant, state that:
P1
P2 Q (Flow)
Figure 3: Typical pump characteristics at constant speed provided by manufacturers.
Q1 Q2
For simulation purposes, some of these characteristics are fitted with second order polynomials [4]. For example, H-Q and P 2-Q curves may be written, at rated speed, as:
1 2
1 H 2 2 H 1
2
(2)
P 2(Q ) k P 0 k P 1Q k P 2 Q 2
(3)
(5)
1 P 2 2 2 P 21
H (Q ) k B 0 k B1Q k B 2 Q 2
3
In the previous equation, Q is the volumetric water flow, H is the head and P2 is the shaft power. Subscripts 1 and 2 indicate two different operating points, which are in a parabola that passes through the origin. The equation of this “affinity” parabola is obtained by solving simultaneously the first two affinity equations:
In order to determine the operating point of the pump is necessary to know the relationship between H and Q for the hydraulic components (pipeline, valves, etc.), which is usually so-called the "system curve". The system curve has been modelled with the following equation:
H S (Q ) k S 0 k S 2 Q
System curve
H 2
MP
2
A B
P
Power
C
H 1
Head
Efficiency
Affinity parabola
2
Q 1 1 H 2 2 Q2 H 1
(4)
Q1 Q2
H 1 H 2
Where H S is the system head, and k S0 and k S2 are constants that represent, respectively, static head and friction losses.
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2
2
or (6)
31st European Photovoltaic Solar Energy Conference and Exhibition
For example, in Figure 4, points C and B are in the same affinity parabola. It can be observed that the point C is not in the system curve (because the static head is different from zero) and it can not be an operating point. Nevertheless, it is required as intermediate calculation in the numerical procedure described below. Finally, it is worth pointing out that affinity laws assume that pump efficiency remains constant for points 1 and 2, i.e., that P1= P2. The final goal of the pump modelling is obtaining the relationship between the output water flow, Q, and input shaft power, P2. For this purpose the following numerical procedure is applied: 1. Assume an initial flow equal to Q2. 2. Calculate the corresponding head on system curve, H 2=H S (Q2 ) (point B(Q2 ,H 2 )). 3. Determine the affinity parabola (Equation 6) that passes through point B. 4. Calculate the intersection of the affinity parabola and pump curve (Equation 2), to obtain the point C(Q1 ,H 1 ). 5. Determine the hydraulic power at point C , PH 1=k·H 1·Q1. 6. Determine the shaft power at point C , P2 (Q1 ). 7. Calculate pump efficiency at point C , η P1=P H1 /P2(Q1 ), which is equal to the efficiency at point B, η P2= η P1. 8. Calculate the hydraulic power at point B, PH 2. 9. Finally, determine the shaft power at point B as P22=PH 2 / η P2. Varying Q2, a set of discrete points for P22 are obtained, which allow determining the relationship between flow and shaft power. For simulation purposes, these points are fitted with a third degree polynomial:
Q ( P 2) k Q 0
k Q1 P 2 k Q 2 P 2 2
k Q 3 P 2 3
Figure 6: North-South horizontal one-axis PV tracker installed in the Irrigator Community of Alto Vinalopó, Alicante (Spain).
(a)
(7)
The previous equation has the typical shape displayed in Figure 5, where the parameter P2 MIN is the minimum required shaft power for water pumping.
(b)
Q
(c)
P 2 MIN
P 2
Figure 5: Typical shape of the relationship between flow, Q, and shaft power, P2. The parameter P2 MIN is the required minimum power for water pumping.
d
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SIMULATION EXAMPLE This section presents a simulation example of a real 20kWp PV pumping demonstrator installed in the Irrigator Community of Alto Vinalopó, Alicante (Spain), which pumps water from a borehole whose static head is 250m. This demonstrator includes a North-South horizontal one-axis tracker (see Figure 6) which improves the efficiency of the PV pumping system in terms of m 3 of pumped water per kWh of the incident irradiance.
Figure 7: Characteristics of the AC centrifugal pump.
The characteristics of the centrifugal pump are displayed in Figure 7. Points marked with circles have been obtained from manufacturer information and solid lines are the simulation models. Figure7-a shows the pump curve at the rated speed (2900rpm) together with the system curve. Figure 7-b represents the motor efficiency as a function of the shaft power, which reaches
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31st European Photovoltaic Solar Energy Conference and Exhibition
a maximum around 80%. Figure 7-c displays the mechanical shaft power as a function of the flow at rated speed. And, finally, Figure 7-d shows the calculated curve using the above described numerical procedure, but here as a function of the input electric power, P1. Figure 8 displays the yearly Sankey diagram for the system, where energy losses are indicated as a percentage of the reference yield. In AC, the final yield reaches 2049 kWh/kWp, of which 1158 kWh/kWp are converted into useful hydraulic energy. In terms of water pumping, they are equivalent to 1637m 3/kWp or 32740m3 per year. The performance ratio, PR, is defined here as the ratio of useful hydraulic energy to the reference yield and is equal to 46%. This efficiency may be substantially improved in larger systems, where the pump and motor efficiencies are higher. The initial investment cost of the demonstrator is 2,4€/Wp which, assuming a system lifetime of 20 years, translates into a pumping cost equal to 7.3c€/m 3. Obviously, this cost should decrease for larger systems and by economies of scale, and should be increased with additional costs (capital, operation and maintenance, etc.). Anyway, the final cost could be economically attractive taking into account that, at present, the irrigator community where this demonstrator has been installed spends 12.8c€/m3 (see Table I).
Table I: Yearly grid-connection costs from a representative borehole provided by the Irrigator Community of Alto Vinalopó. Item
Value
Operation time Water pumping Electricity consumption Total electricity cost Per unit costs
2,613h per year 738,679m 3 958,939kWh 94,247€ 9.8 c€/kWh 12.8c€/m 3
14 12 10 ] h /
3
8
m [ w o 6 l F
4 2 0 -10
-5
0 True solar time [hours]
5
10
Figure 5: Daily variation of water flow during the characteristic days of the year.
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CONCLUSIONS This paper has presented the modelling of large PV pumping systems, which has been implemented in SISIFO, an online and free-software simulator of PV systems that is publicly available at www.sisifo.info. Besides, a simulation example of real case study is described, which illustrates some of the capacities of this simulation tool. ACKNOWLEDGEMENT This work has been possible thanks to the funding of the FP7 European Programme (Energy) in the project PhotoVoltaic Cost reduction, Reliability, Operational performance, Prediction and Simulation (PVCROPS), Project reference 308468. (www.pvcrops.eu). REFERENCES [1]
[2]
Figure 8: Yearly Sankey diagram for the simulated PV system. Energy losses are indicated as percentage of the reference yield.
[3]
Finally, it is worth mentioning that SISIFO also allows a detailed analysis of system performance. For example, the user may access to the time series of any simulated variable (powers, losses, water flow, pump speed, etc.). For example, Figure 9 shows the daily variation of water flow during the characteristic days of the year.
[4]
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J. Muñoz, JM Carrillo. Modeling and sizing of large PV-diesel hybrid systems without energy storage. EU PVSEC 2015, Hamburg. Muñoz, J., Marroyo, L., Collares-Pereira, M., Tyutyuyndzhiev, N., Conlon, M., Elmoussaoui, A., and Wilkin, B. An Open-Source Simulation Tool of Grid-Connected PV Systems. 28th European Photovoltaic Solar Energy Conference and Exhibition, 2013, 3882–87. doi:10.4229/28thEUPVSEC2013-5BV.4.18. J. Muñoz et al. SISIFO: An online simulator of PV systems. Technical Reference Manual v1.0. Available at: www.sisifo.info Suehrcke, H., J. Appelbaum, and B. Breshef. Modelling a Permanent Magnet DC Motor/centrifugal Pump Assembly in a Photovoltaic Energy System. Solar Energy. Vol. 59, no. 1–3, 1997: 37–42. doi:10.1016/S0038-092X(96)00117-X.
