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Thermal control to maximize photovoltaic powered reverse osmosis desalination systems productivity
Desalination 314 (2013) 10–19
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Desalination journal homepage: www.elsevier.com/locate/desal
Thermal control to maximize photovoltaic powered reverse osmosis desalination systems productivity Leah C. Kelley ⁎, Steven Dubowsky Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
H I G H L I G H T S ► ► ► ►
In the presented PV/RO system, the PV panels are cooled by the RO feed water, which warms as a result. Cooling the PV panels permits the addition of concentrating mirrors. PV panel and RO water temperatures are controlled to increase clean water produced. A 59% increase in water production is achieved experimentally.
a r t i c l e
i n f o
Article history: Received 25 May 2012 Received in revised form 26 November 2012 Accepted 27 November 2012 Available online 27 January 2013 Keywords: Solar power Reverse osmosis Control Thermal Concentrating mirrors
a b s t r a c t Photovoltaic-powered reverse osmosis (PV/RO) is a practical method for desalinating water, especially for many small, remote, off-grid communities. It is shown here that thermal control can increase its productivity, making it more economically attractive. A solar panel produces more power at lower cell temperatures and an RO unit produces more fresh water for a given power with increasing water temperature. These complementary behaviors are exploited by cooling the solar panel using the RO feed water, which warms the water. Cooling the solar panel also permits the use of concentrating mirrors, which further increases system production. The control must also prevent overheating of the panel and the RO unit, and to balance the pressures in the system. Here, a controller is designed to meet these objectives. The effectiveness of controller design is verified in simulation and experiment. © 2012 Elsevier B.V. All rights reserved.
1. Introduction 1.1. Motivation Supplying the world's population with fresh, clean water is a major challenge. The demand for fresh water for drinking, household, irrigation and industrial use has depleted available surface water sources in many regions. Many of these water-stressed regions are near coasts or have brackish ground water sources. For small, remote, off-grid communities in such areas, solar powered (PV) reverse osmosis (RO) desalination is a practical method of providing fresh water [1]. Fig. 1 shows a concept for such a system. Solar thermal processes, such as flash desalination, are better for large population centers [2]. Reverse osmosis (RO) is an energy-intensive process, requiring approximately 4 kW h of energy to desalinate one cubic meter of water [2]. Conventional small-scale, off-grid RO systems are powered by diesel generators. Diesel fuel is expensive and often its supply lines are fragile. Many of water-stressed regions, such as the Middle East, ⁎ Corresponding author. Tel.: +1 617 253 5095; fax: +1 617 258 9346. E-mail address: [email protected] (L.C. Kelley). 0011-9164/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.desal.2012.11.036
North Africa, the Mediterranean, and the Southwestern United States, receive high levels of annual solar radiation, making solar powered reverse osmosis (PV/RO) a competitive alternative to diesel-powered RO systems, as shown in dark gray in Fig. 2 [1,4]. The figure also shows that if the efficiency of such systems can be increased by 25%, PVRO becomes economically feasible for small communities throughout much of the world, providing motivation for enhancing system performance.
1.2. Background and literature The efficiency of a PV/RO system can be increased by improving individual components, such as reverse osmosis membranes and solar panels [1,5]. Here the focus is on improving system performance through control. Control for both conventional and solar powered RO systems has been studied. Techniques such as PID, Fuzzy Logic, Dynamic Matrix Programming, Fault Tolerant and Model Predictive Control have been applied to conventionally-powered RO systems [5–8]. Techniques applied to PV/RO systems include maximum point power tracking algorithms that increase the efficiency of PV panels [9,10].
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Fig. 1. A basic concept PV/RO system [3].
Temperature control of PV/RO feed water to increase system performance has been suggested [11,12], but active control methods to insure that the system operates within the constraints on its elements have yet to be developed. Simple heuristic control of the temperatures in a PV/RO system that splits control into two parts to control temperature and pressure separately is not able to most effectively control both critical variables simultaneously [3]. Here, a thermal controller is developed based on a coupled thermal/pressure model of the system that ensures that the system pressure and temperature limits are not exceeded. Its effectiveness is demonstrated both experimentally and in simulation. 1.3. Approach A thermal control system is developed in which the RO feed water cools the solar panel by flowing through a panel-mounted heat exchanger. The RO feed water is simultaneously warmed. Cooling the solar panel permits the addition of concentrating mirrors to increase the electrical power produced by the solar panels without
overheating them. Hence the fresh water produced is increased. An analytical model of the dynamic thermal processes in the PV/RO system is developed. A linear decoupled controller is designed and evaluated using a full nonlinear simulation of the system dynamics. It is also validated using an experimental PV/RO system.
1.4. Major results and summary The controller developed here manages the temperatures and pressures of the solar panel and RO feed water subject to physical constraints imposed by the heat exchanger and PV/RO system and ensures appropriate pressure balance within the system. In simulation, a 50% increase in water production is achieved when concentrating mirrors are used. Without thermal control, solar concentrators would overheat and degrade the PV panels, greatly reducing their efficiency. A 57% increase in water production is demonstrated experimentally on a small-scale PV/RO system, using concentrating mirrors and the combined temperature/pressure control.
Fig. 2. Areas of economical feasibility for PVRO systems [1].
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2. PV/RO fundamentals A basic photovoltaic-powered reverse osmosis (PV/RO) system is shown in Fig. 1. A solar panel produces electric power for the RO's motor/pump that pressurizes saline source water to a pressure higher than its osmotic pressure that enters a reverse osmosis unit. The unit contains a membrane that is permeable to water, but not salt. Some fraction of the pressurized water flows across the membrane and exits as fresh water. The remaining water exits the RO unit as high pressure brine. An energy recovery device, such as a turbine or pressure exchanger, captures some of its energy, which is added to the solar panel power to drive the RO system. This configuration does not use batteries for energy storage, since they are expensive, have relatively short lives and introduce energy conversion losses. However, systems without batteries must be designed to accommodate daily and seasonal fluctuations in solar radiation and input water salinity. A discussion of such control is beyond the scope of this paper. The solar panels and RO membranes have complementary thermal characteristics. Fig. 3 shows the temperature dependency of the electrical power produced by a solar panel for different levels of solar radiation, based on the two-diode model [13]. For a given level of solar radiation, a solar panel will produce less electrical power as its temperature increases. Therefore, cooling the solar panel will increase its electrical power output. Fig. 4 shows the temperature dependency of fresh water flow rate produced by an RO membrane. For a given applied pressure, the fresh water production increases with increasing temperature. Therefore, warming the incoming feed water will increase the desalinated water produced. The osmotic pressure of saline water also increases with temperature. This suggests that the water production should decrease with temperature. However, the specific energy required to desalinate warmer water decreases with temperature since the increase in membrane permeability dominates the increase in osmotic pressure [14]. The feed water temperature must be limited to prevent membrane degradation. Typically this maximum water temperature is 45 °C [15,16]. These complementary thermal characteristics can be exploited by the system concept shown in Fig. 5. Here, the RO feed water flows through a heat exchanger mounted on the backside of a solar panel, cooling it, while the RO feed water is warmed simultaneously. The cooled solar panel produces more electrical power than a warmer panel, allowing the pump to produce a higher pressure. The fresh water production increases due to both the increase in applied pressure and the increase in RO membrane permeability. Also,
Fig. 4. Effect of temperature on specific energy required for desalination as a function of pressure. Water quality increases with increasing pressure. Figure by A. Bilton, used with permission. [17].
concentrating mirrors can be added to the cooled solar panel to further increase the electrical power produced. This in turn increases the RO pressure without overheating the PV panels. 3. The thermal control problem The temperatures of the solar panel and RO feed water cannot be independently regulated for the simple uncontrolled system shown in Fig. 5. The solar panel will be cooled and the RO water warmed; however, the temperature of the solar panel and RO feed water are dependent on the feed water flow rate. On a warm, sunny day, it is possible for the panel and/or the RO to overheat. Further, since the flow through the panel is restricted by the heat exchanger flow resistance, under high solar radiation conditions the RO pump may demand enough water to pull a negative (vacuum) pressure at its inlet. This can cause problems, such as pump cavitation and excess mechanical stress to the heat exchanger [17]. Fig. 6 shows the design of a controllable thermal subsystem that can control the temperatures of the RO feed water and solar panel and the pressure at the RO pump inlet. This control subsystem consists of a small circulating pump and two proportionally positional valves. Valve U1 is located in a line connecting the feed water source and RO unit, bypassing the heat exchanger. This proportional valve is called the bypass control valve, or bypass valve. Valve U2 is located in a discharge line connecting the heat exchanger to the feed water source. This valve is called the discharge control valve, or discharge valve. The control problem is a multiple input, multiple output problem. To increase the amount of fresh water produced in a day, the control objectives are: minimize the PV panel temperature TPV and maximize the RO feed water temperature TRO, subject to the constraints on temperature and RO inlet pressure PRO shown below: minimizeðT PV Þ; T PV b80∘ C
ð1Þ
T RO b45∘ C
ð2Þ
maximizeðT RO Þ; P RO ≥0:
ð3Þ
4. System model
Fig. 3. Solar panel electrical power temperature dependence. Figure by A. Bilton, based on [13], used with permission.
A complete dynamic thermal/pressure/flow model of the PV/RO system shown in Fig. 6 is developed here for the controller design and validation simulations. The model is linearized and used for the control system design. In this analysis, temperature gradients along
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Fig. 5. A concept of a PV/RO system with uncontrolled thermal exploitation and concentrating mirrors.
the solar panel and heat exchanger surfaces are neglected. It is assumed that there is perfect mixing of the water within the heat exchanger, and the water exiting the heat exchanger is at the same temperature as the water in the heat exchanger. The mixing junction is also assumed to have a common water temperature and heat capacity. Temperatures and pressures are in units of (°C) and (bar), respectively. The pressures are measured with respect to the atmospheric pressure, commonly called gauge pressure. Conservation of energy applied to the water in the heat exchanger yields: C1
dT H ¼ Q wtr þ ρwtr cp;wtr qPV ðT C −T H Þ dt
− − − − − −
Qwtr and RO feed water flow rate qRO are dependent on the incident solar radiation and ambient conditions, as presented in [17]. For control purposes they are treated as disturbances. Conservation of energy applied to the mixing junction in Fig. 6 yields:
ð4Þ C2
where − C1 is the thermal capacitance of the water in the heat exchanger (J/°C) − TH is the temperature of the heat exchanger water,
t is time (seconds), ρwtr is the density of water (kg/L), cp,wtr is the specific heat of water (J/kg/°C), qPV is the water flow rate through the heat exchanger (L/s), TC is the input water temperature, and Qwtr is the net heat transferred from the solar panel to the water (W).
dT RO ¼ ρwtr cp;wtr ½qPV T H þ q1 T C −q2 T RO −qRO T RO dt
ð5Þ
where − C2 is the thermal capacitance of the water in the mixing junction (J/°C),
Fig. 6. A controllable thermal subsystem for a PV/RO system.
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− TRO is the temperature of the RO feed water, assumed to be the same temperature of the water in the mixing junction, − q1 is the water flow rate through the bypass valve (Valve 1) (L/s), − q2 is the water flow rate through the bleed-off valve (Valve 2) (L/s), and − qRO is the RO feed water flow rate (L/s). The water flow rates in Eqs. (4) and (5) depend on the pressure differences between the heat exchanger inlet and RO pump inlet, the fluid resistance of the heat exchanger (for qPV), and the positions of Valves 1 (U1) and 2 (U2) for q1 and q2, respectively. The feed water source and the water discharge are assumed to be at zero gauge pressure. The feed water flow rate qRO depends on the amount of electrical power supplied to the RO pump. By assuming a linear relationship between pressure and flow, and by considering the heat transferred to the water in the heat exchanger Qwtr and the RO feed water flow rate qRO as system disturbances that are functions of incident solar radiation, system Eqs. (4) and (5) are rewritten: dT C 1 H ¼ Q wtr þ ρw cp;w ðP H −P RO ÞU PV ðT C −T H Þ dt
where the constants are defined: a1 ¼
ρw cp;w U PV T C −T H C1
ð12Þ
a2 ¼
ρw cp;w U PV P H −P RO C1
ð13Þ
k1 ¼
ρwtr cp;wtr T RO C2
ð14Þ
a3 ¼
ρw cp;w T þU T U PV T H þ U 1 c 2 RO C2
ð15Þ
a4 ¼
ρw cp;w U PV P H −P RO C2
ð16Þ
a5 ¼
ρw cp;w P RO U 2 þ q RO C2
ð17Þ
ð6Þ
Req ¼ dT C 2 RO ¼ ρw cp;w ½ðP H −P RO ÞT H U PV þ ðP H −P RO ÞT C U 1 −P RO T RO U 2 −qRO T RO dt ð7Þ
where − PH is the pressure at the heat exchanger inlet, (the outlet of the circulating pump) assumed to be positive, − PRO is the pressure at the intake to the RO pump, also assumed positive, − UPV is the fluid flow resistance of the heat exchanger (L/s/bar), − U1 is the fluid flow resistance of Valve 1 (L/s/bar), and − U2 is the fluid flow resistance of Valve 2 (L/s/bar).
1 : U PV þ U 1
Eqs. (9)–(11) represent the uncontrolled system response. Assuming that actuating the control valves yields small, linear changes in the flow resistances u1 and u2, the system response can be written in state space form with two states, tH and tRO, and three outputs of interest, pRO, tRO and tH. The perturbations in heat flux and RO feed flow rate, δQwtr and δqRO, are functions of the solar radiation and RO unit properties, and are treated here as disturbances. The two control inputs are u1 and u2. The state and output equations are:
t_ H t_ RO ¼
The pressure at the RO pump inlet can also be written as a function of heat exchanger pressure and fluid resistances P RO ≈
P H ðU PV þ U 1 Þ−qRO : U PV þ U 1
ð8Þ
Eqs. (6)–(8) describe the thermal, flow and pressure behaviors of the system and are nonlinear. These equations can be linearized by assuming small perturbations about a steady state operating point. To linearize the model, it is assumed that the PV/RO system is operating at a point with feed water flow rate q RO and incoming , both functions of solar radiaheat to the heat exchanger water Q wtr tion, and that the incoming water temperature TC and circulating pump pressure PH are constant. Under these conditions, Valves 1 and 2 are set to positions with fluid resistances Ū1 and Ū2, respectively, which will result in steady state pressure P RO and temperatures T H and T RO . A cloud obscuring the sun causes perturbations in RO water flow rate δqRO and incoming heat δQwtr. Using a Taylor series expansion and discarding the higher-order terms, Eqs. (6)–(8) are rewritten in perturbation coordinates tH, tRO and pRO as: dt H δQ wtr ¼ þ a1 pRO −a2 t H dt C1
ð10Þ
pRO ¼ −Req δqRO
ð11Þ
−a2 a4 b1 þ b2
. 1 0 tH δQ wtr c2 0k2 þ C1 −a5 t RO δqRO u1 0 u2 b3
1 0 1 3 0 0 0 0 −Req pRO δQ wtr 4 t RO 5 ¼ @ 0 1 A t H þ @ 0 0 A t RO δqRO 1 0 0 0 tH 0 1 c1 0 u þ @ 0 0A 1 u2 0 0
ð19Þ
ð20Þ
where c1 ¼ Req P in −P out
ð21Þ
c2 ¼ −a1 c1 Req
ð22Þ
b1 ¼ −a3 c1
ð23Þ
k2 ¼ −k1 −a3 c1 Req
ð24Þ
ρw cp;w T C P in −P RO −a3 c1 C2
b3 ¼ − dt RO ¼ −k1 δqRO −a3 pRO þ a4 t H −a5 t RO dt
2
b2 ¼ ð9Þ
ð18Þ
ρw cp;w P RO T C : C2
ð25Þ
ð26Þ
As discussed, valve resistances u1 and u2 will change with valve positions and are controllable. This open loop system is passive, and is inherently stable.
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Fig. 7. Block diagram for thermal control.
5. Controller design The control problem described above is multiple input multiple output with two control inputs and three system outputs of interest, one of which (PRO) is not a system state. State feedback alone will not guarantee that the pressure constraint in Eq. (3) will be met, because the objective of limiting the PV panel temperature, Eq. (1), competes with the pressure constraint, Eq. (3), due to pressure limits on the heat exchanger. From the system physics, it can be seen that the pressure constraint can be met by a decoupled control law, where u1 is determined by the error between the desired and measured RO inlet pressure epRO and u2 determined by the error between the desired and measured RO water temperature, etRO , shown in the block diagram in Fig. 7. The errors are defined as
From the state-space model in Eqs. (19)–(20), the open loop transfer function from error epRO to perturbation in RO pressure pRO in the Laplace domain can be written with the PI controller as pRO ðsÞ K 1 ðs þ α 1 Þc1 ðs þ a2 Þðs þ a5 Þ ¼ ePRO ðsÞ sðs þ a2 Þðs þ a5 Þ where − K1 is the open loop gain and − α1 is the ratio between the proportional and integral gains. Similarly, the open loop transfer function relating the error eT RO to the perturbation in RO water temperature tRO is
ePRO ¼ P set −P RO;M
ð27Þ
t RO ðsÞ K 2 ðs þ α 2 Þb3 ðs þ a2 Þ ¼ eT RO ðsÞ sðs þ a2 Þðs þ a5 Þ
eT RO ¼ T RO;M −T set
ð28Þ
where
ð30Þ
− K2 is the open loop gain and − α2 is the ratio between the proportional and integral gains.
where − − − −
ð29Þ
Pset- is the commanded RO pump inlet pressure, PRO,M is the measured RO pump inlet pressure, TRO,M is the measured RO water temperature, and Tset is the commanded RO water temperature.
Proportional integral (PI) control is used to command the thermal subsystem to its desired operating point, which is at the constraint boundaries (see Fig. 7). Maximum fresh water production will occur at the highest allowable water temperature TRO, here limited to 40 °C to allow for some overshoot. The maximum water flow rate through the heat exchanger, and hence maximum heat transfer from the PV panel to the water, will occur when the RO inlet pressure is 0, but at 0 gauge pressure water will not flow through the discharge valve (Valve 2 in Fig. 6). Thus, the commanded RO pressure Pset is 0.068 bar (1 psi) to allow for flow through the discharge valve and still maintain sufficient flow of cooling water through the heat exchanger.
Although commanded to a desired operating point, some steadystate error may exist. For example, if the incoming water temperature is very low, the water exiting the heat exchanger may not reach 40 °C, but the PV panel will be cooled and the RO water warmed as much as possible for the given conditions. The PI controllers are designed for specific operating conditions using linear methods. However, since the operating conditions and system disturbances vary widely over time, the controller performance is evaluated in simulation. 6. Controller performance simulation The performance of a small-scale PV/RO system using the thermal controller was simulated for a step in solar radiation and for a day with varying solar radiation and air temperatures. The full nonlinear model of the system was used to represent performance of the
Table 1 Simulation input parameters.
Step response Full day
Duration
Solar radiation I (W/m2)
Ambient air temperature Tair (°C)
Source water temperature Twtr (°C)
1500 s 4 AM to 8 PM
1500 Solar profile based on [18] for Cambridge, MA
38 Data for Nov 9th for Cambridge, MA, from [19]
38 20
Table 2 Simulation initial conditions and commands.
Step response Full day
Initial PV panel temperature TPV (°C)
Initial heat exchanger pressure PH (bar)
Initial RO inlet pressure PRO (bar)
Commanded pressure PRO,c (bar)
Commanded temperature TRO,c (°C)
60 11 (Sunrise)
0.4137 0.4137
0.068 0
0.068 0.068
40 40
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Fig. 8. Controlled system response for a step in solar radiation.
system. The system contains one 230-W solar panel with a heat exchanger, concentrating mirrors that reflect 50% additional sunlight onto the panel, and an RO unit with a nominal daily production of 300–600 L of fresh water per day, depending on location [17]. The nominal steady state operating point used for controller design assumed that the incident solar radiation on the solar panel was 1500 W/m 2, the ambient air temperature was 38 °C, and the incoming water temperature was 38 °C. Under these conditions, the water temperature exiting the heat exchanger will be hotter than 40 °C, and the RO pump will require more water than can be supplied through the heat exchanger, and so both valves need to be actuated.
Based on stability analysis, the controller gains K1 and K2 are both set to 1, and α1 and α2 are set to 0.1. Simulations were implemented in MATLAB Simulink. Tables 1 and 2 summarize the simulation inputs and initial conditions, respectively. The step response of the simulated system is shown in Fig. 8. Fig. 8a shows the simulated temperatures of the solar panel TPV and the water entering the RO unit TRO. The solar panel is cooled to 58 °C under these conditions. The RO water temperature does not quite reach 40 °C, its commanded value, because the water exiting the heat exchanger qPV mixes with water flowing through the bypass valve q1. The flow rates are shown in Fig. 8c. Water flows through the
Fig. 9. Temperature responses for a full-day simulation.
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Fig. 10. Simulated flow rates with thermal control for full-day operation.
Fig. 12. Experimental and simulated results with and without thermal control.
bypass valve in response to the initial pressure drop at the RO pump inlet PRO, shown in Fig. 8b. Some steady state error in RO water temperature is acceptable, provided that the water temperature does not exceed the maximum allowable RO water temperature of 45 °C. Fig. 8b shows that the controller compensates for the initial pressure drop and that at steady state the pressure stabilizes at 0.03 bar. This is below its commanded pressure of 0.068 bar (1 psi). The linearization of Eq. (8) does not account for the coupling between the feed water flow rate and the control input to Valve 1. Eq. (8) was used directly in simulation, and so the coupling accounts for the steady state error. As with RO temperature, some steady state error in RO inlet pressure PRO is also acceptable, provided that it does not drop below its minimum allowable pressure of 0 bar. Fig. 8c shows the simulated flow rates. As the water demanded by the RO unit qRO increases, the water flow through the heat exchanger qPV quickly reaches its maximum allowable value. As the RO pressure PRO shown in Fig. 8b drops, the controller opens Valve 1 and water flows through the heat exchanger bypass q1 into the RO unit. As the temperature of the heat exchanger water (not shown) increases past 40 °C, Valve 2 opens, discharging some of the hot water q2. This forces more water through Valve 1 to meet the RO pressure demand. At steady state, the flow to the RO unit qRO is the sum of the flows through the heat exchanger qPV and Valve 1 q1, minus the flow through Valve 2 q2. The controller successfully manages both the pressure and temperature of the RO feed water at the RO pump inlet. Fig. 9 shows the simulated temperature responses for a full day's operation. The uncontrolled and controlled responses are shown in Fig. 9a and b, respectively. In Fig. 9a, the solar panel TPV gets too hot during the middle of the day, and the RO water TRO does not experience any heating. This case is unrealistic because the effect of concentrating
mirrors on solar panel temperature is included in the simulation without any solar panel cooling, hence the panel overheats. In Fig. 9b, the solar panel temperature TPV is kept much lower by the cooling water (temperature not shown). The RO water TRO is not substantially warmed. In this case the heat transferred from the hot solar panel to the water in the heat exchanger cannot raise the water temperature to its commanded value of 40 °C. Also, since the controller is managing the RO inlet water pressure PRO as well as temperature, some of the cool bypass water q1 mixes with the warmed water exiting the heat exchanger qPV (see Fig. 10), reducing RO water temperature. Fig. 10 shows the flow rates with thermal control for the full-day simulation. Just before 7 AM, the PV/RO system and its controller are turned on. All of the water demanded by the RO unit qRO flows through the heat exchanger qPV until just after 7 AM. This is shown by the overlapping curves for qRO and qPV. Just after 7 AM, the RO water demand causes the pressure at the RO inlet to drop, so the controller opens Valve 1. This is shown by the rapid rise in the flow q1. The RO water flow qRO is the sum of the water flow through the heat exchanger qPV and bypass q1. Since the water temperature never exceeds the commanded temperature of 40 °C, the controller does not open Valve 2 and so the flow through it q2 is 0. 7. Experimental validation The controller design was validated on an experimental PV/RO system in Cambridge, MA (see Fig. 11). The system is capable of producing 300–450 L of fresh water from sea water per day using only solar energy, and was developed to validate physical models and to test control algorithms. It uses one 230-W Sun Power Corporation solar panel with a rated conversion efficiency of 18%, mounted on a
Fig. 11. MIT experimental PVRO system showing the RO unit, left, and solar panel with concentrating mirrors attached, right.
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Fig. 13. Source and RO water temperatures from experiments with and without thermal control.
single axis tracker that is manually adjusted for different seasons. A simple maximum power point tracking algorithm is used to obtain maximum electrical power from the solar panel. A custom, computercontrolled, variable DC to DC converter is used to step down the solar panel voltage to power two positive displacement pumps, which operate in parallel. The pumps increase the pressure of the feed water from atmospheric and pump it into a dual-piston pressure exchanger that uses the energy from the high pressure brine exiting the RO pressure vessel to further increase the feed water pressure. The high pressure feed water flows into a fiberglass pressure vessel containing the RO membrane, where it is desalinated. The recovery ratio of fresh water produced to feed water is a fixed 9%. The system is fully instrumented with pressure, flow, salinity, temperature, current and voltage sensors. Embedded microcontrollers acquire sensor data and use them to control the DC to DC converter and tracker motor. Data logging is performed by a remote computer wirelessly connected to the microcontrollers. A stainless steel heat exchanger unit is mounted to the underside of the solar panel. The unit has a maximum inlet pressure of 0.41 bar (6 psi). A small 17-W circulator pump is used to circulate cooling water through the heat exchanger, through a proportional control valve bypassing the heat exchanger, and through a proportional valve bypassing the RO unit. Flat-plate solar concentrating mirrors (see Fig. 11) are mounted on the solar panel. Experiments with and without concentrated solar power can be performed. The mirrors are aluminum plate covered with reflective mirror film, and provide approximately 50% additional sunlight to the solar panel. The thermal PI controllers for the proportional valves were implemented on the embedded microcontrollers. A baseline experiment without thermal control, concentrating mirrors, solar panel cooling or RO feed water heating was also performed for a seasonal comparison. Fig. 12 shows typical experimental and simulated results for fresh water produced over an hour period in November, adjusted for the difference in experimental starting times. The experimental and simulated results agree well, although the experimental case with no thermal controller or concentrating mirrors produced less fresh water than the simulation predicts due to clouds. The simulation assumes clear-sky conditions. For the controlled case, the simulation predicts a 50% increase in fresh water production with the thermal controller. Experimentally, a 59% increase in fresh water production is achieved, which is due in part to passing clouds reducing the solar radiation received by the solar panel during the baseline experiment. These results compare favorably with other results presented in [3,17], where a 57% increase in water production was achieved experimentally with concentrating mirrors, solar panel cooling and RO feed water warming. It is not feasible to present a
case where thermal concentrating is used without control or cooling, since the PV panels will overheat. Fig. 13 shows the source and RO feed water temperatures recorded during experiments. When the heat exchanger is used, a 4 °C temperature difference between the source water and the heated RO feed water is achieved. It is apparent that during the course of operation, the source water does heat a little while sitting in its storage tank. The source water temperatures recorded at the heat exchanger inlet are much higher than the source water temperature during the baseline experiment since the brine and fresh water streams are both directed into a source water tank and the water is re-circulated during experiments. In Fig. 13, “Control, concentrating mirrors” refers to actively regulated RO inlet pressure, while “No control, concentrating mirrors” refers to passive regulation of the RO inlet pressure through an open bypass line. In both cases, the PV panel is cooled, and the pressure at the RO inlet is regulated to prevent cavitation. The active control system results in a slightly higher RO water temperature, although not enough to show an increase in permeate production. This result is expected, since during November operation the temperature at the heat exchanger outlet never exceeds 40 °C and so the blow-off valve never opens. Mineral scaling is a common problem in RO desalination. It is known that the solubility of certain minerals, including calcium carbonate, calcium sulfate and magnesium hydroxide, decreases with temperature. However, precipitation of scaling minerals is not expected to be problematic here, because the water temperature is limited by both the allowable RO membrane temperature and maximum solar panel temperature, and the water temperature difference between the heat exchanger inlet and outlet is small (4 °C). For typical seawater in this temperature range, scaling minerals such as calcium carbonate have negative Stiff & Davies Solubility Indices and are not likely to precipitate. This experimental validation focuses on thermal control for seawater PV/RO systems. Thermal control can also be applied to brackish water PV/RO systems, and can be validated with appropriate changes to the current experimental unit, such as replacement of a seawater membrane with a brackish membrane, and the use of a different energy recovery device. 8. Conclusions The daily water production of a PV/RO system can be substantially increased by exploiting the complementary thermal characteristics of PV panels and the RO membranes by cooling the solar panels using the RO feed water, warming it in the process. Cooling the solar panels and warming the RO feed water increase the electrical production of the solar panel and the flow rate of fresh water across the RO membrane, respectively. Further increases in electrical energy production are achievable with the addition of concentrating mirrors, which is only possible by cooling the solar panel. Active control of the solar panel and RO feed water temperatures is needed to maximize fresh water production while meeting physical system constraints. Classical methods are used to design a suitable controller, which is validated in simulation and in experiments. The controller presented here successfully manages temperatures while meeting system constraints, and achieves a 59% increase in water production experimentally. This is well above the target goal of a 25% increase in system efficiency. By actively controlling the temperatures of the PV panels and RO feed water, and by using concentrating mirrors, PV/RO can be made economically feasible for remote communities in much of the world. Acknowledgments The authors would like to thank the King Fahd University of Petroleum and Minerals in Dhahran, Saudi Arabia, for funding the research reported in this paper through the Center for Clean Water and Clean
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Energy at MIT and KFUPM under Project Number R6-DMN-08. Also Amy Bilton and Li Meng are acknowledged for their contributions to the experimental studies.
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[1] A.M. Bilton, R. Wiesman, A.F.M. Arif, S.M. Zubair, S. Dubowsky, On the feasibility of community-scale photovoltaic-powered reverse osmosis desalination systems for remote locations, Renew. Energy 36 (2011) 3246–3256. [2] E. Tzen, R. Morris, Renewable energy sources for desalination, Sol. Energy 75 (2003) 375–379. [3] L. Kelley, A.M. Bilton, S. Dubowsky, Enhancing the performance of photovoltaic powered reverse osmosis desalination systems by active thermal management, in: ASME 2011 International Mechanical Engineering Congress and Exposition, ASME, Denver, Colorado, 2011. [4] NASA, NASA Surface meteorology and Solar Energy: Global/Regional Data, National Aeronautics and Space Administration, Atmospheric Science and Data Center, 2009. (Available bhttp://eosweb.larc.nasa.gov/sse> Accessed 14 July 2009). [5] M.A. Ali, A. Ajbar, E. Ali, K. Alhumaizi, Robust model-based control of a tubular reverse-osmosis desalination unit, Desalination 255 (2010) 129–136. [6] I. Alatiqi, H. Ettouney, H. El-Dessouky, Process control in water desalination industry: an overview, Desalination 126 (1999) 15–32. [7] A. Gambier, N. Blumlein, E. Badreddin, Real-time fault tolerant control of a reverse osmosis desalination plant based on a hybrid system approach, in: American Control Conference, 2009. ACC '09, 2009, pp. 1598–1603. [8] A. Abbas, Model predictive control of a reverse osmosis desalination unit, Desalination 194 (2006) 268–280. [9] P.C.M. de Carvalho, R.S.T. Pontes, D.S. Oliveira Jr., D.B. Riffel, R.G.V. de Oliveira, S.B. Mesquita, Control method of a photovoltaic powered reverse osmosis plant
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without batteries based on maximum power point tracking, in: Transmission and Distribution Conference and Exposition: Latin America, 2004 IEEE/PES, 2004, pp. 137–142. M. Thomson, Reverse-Osmosis Desalination of Seawater Powered by Photovoltaics Without Batteries, PhD Thesis, Loughborough University, Leicestershire, UK, 2003. S.F. Cheah, Photovoltaic reverse osmosis desalination system, in: Report No. 104, ITN Energy Systems, Inc., Littleton, CO, 2004. D. Maydan, Systems and Methods for Simultaneously Generating Energy and Treating Water, U.S Patent Application No. 2011/0011802A1, 2011. S.R. Wenham, M.A. Green, M.E. Watt, R. Corkish, Applied Photovoltaics, Earthscan, London, 2007. S.P. Agashichev, K.N. Lootahb, Influence of temperature and permeate recovery on energy consumption of a reverse osmosis system, Desalination 154 (2003) 253–266. Applied Membranes, AMI® membranes 2.5″ seawater FRP wrapped thin film elements, Datasheet, Applied Membranes, Inc., Vista, CA, 2004. FILMTEC Tape-Wrapped 2540 Elements for Commercial Applications, Dow Chemical Corporation, 2010. (Available http://www.dow.com. Accessed 10 December 2010). L.C. Kelley, The Design and Control of a Thermal Management System for a Photovoltaic Reverse Osmosis System, SM Thesis, Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, 2011. C. Rigollier, O. Bauer, L. Wald, On the clear sky model of the ESRA – European Solar Radiation Atlas – with respect to the Heliosat method, Sol. Energy 68 (2000) 33–48. Weather Underground, Inc., History for Cambridge, MA, Weather Underground, Inc., November 9 2011. (bhttp://www.wunderground.com> Accessed 20 November 2011).
Contents lists available at SciVerse ScienceDirect
Desalination journal homepage: www.elsevier.com/locate/desal
Thermal control to maximize photovoltaic powered reverse osmosis desalination systems productivity Leah C. Kelley ⁎, Steven Dubowsky Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
H I G H L I G H T S ► ► ► ►
In the presented PV/RO system, the PV panels are cooled by the RO feed water, which warms as a result. Cooling the PV panels permits the addition of concentrating mirrors. PV panel and RO water temperatures are controlled to increase clean water produced. A 59% increase in water production is achieved experimentally.
a r t i c l e
i n f o
Article history: Received 25 May 2012 Received in revised form 26 November 2012 Accepted 27 November 2012 Available online 27 January 2013 Keywords: Solar power Reverse osmosis Control Thermal Concentrating mirrors
a b s t r a c t Photovoltaic-powered reverse osmosis (PV/RO) is a practical method for desalinating water, especially for many small, remote, off-grid communities. It is shown here that thermal control can increase its productivity, making it more economically attractive. A solar panel produces more power at lower cell temperatures and an RO unit produces more fresh water for a given power with increasing water temperature. These complementary behaviors are exploited by cooling the solar panel using the RO feed water, which warms the water. Cooling the solar panel also permits the use of concentrating mirrors, which further increases system production. The control must also prevent overheating of the panel and the RO unit, and to balance the pressures in the system. Here, a controller is designed to meet these objectives. The effectiveness of controller design is verified in simulation and experiment. © 2012 Elsevier B.V. All rights reserved.
1. Introduction 1.1. Motivation Supplying the world's population with fresh, clean water is a major challenge. The demand for fresh water for drinking, household, irrigation and industrial use has depleted available surface water sources in many regions. Many of these water-stressed regions are near coasts or have brackish ground water sources. For small, remote, off-grid communities in such areas, solar powered (PV) reverse osmosis (RO) desalination is a practical method of providing fresh water [1]. Fig. 1 shows a concept for such a system. Solar thermal processes, such as flash desalination, are better for large population centers [2]. Reverse osmosis (RO) is an energy-intensive process, requiring approximately 4 kW h of energy to desalinate one cubic meter of water [2]. Conventional small-scale, off-grid RO systems are powered by diesel generators. Diesel fuel is expensive and often its supply lines are fragile. Many of water-stressed regions, such as the Middle East, ⁎ Corresponding author. Tel.: +1 617 253 5095; fax: +1 617 258 9346. E-mail address: [email protected] (L.C. Kelley). 0011-9164/$ – see front matter © 2012 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.desal.2012.11.036
North Africa, the Mediterranean, and the Southwestern United States, receive high levels of annual solar radiation, making solar powered reverse osmosis (PV/RO) a competitive alternative to diesel-powered RO systems, as shown in dark gray in Fig. 2 [1,4]. The figure also shows that if the efficiency of such systems can be increased by 25%, PVRO becomes economically feasible for small communities throughout much of the world, providing motivation for enhancing system performance.
1.2. Background and literature The efficiency of a PV/RO system can be increased by improving individual components, such as reverse osmosis membranes and solar panels [1,5]. Here the focus is on improving system performance through control. Control for both conventional and solar powered RO systems has been studied. Techniques such as PID, Fuzzy Logic, Dynamic Matrix Programming, Fault Tolerant and Model Predictive Control have been applied to conventionally-powered RO systems [5–8]. Techniques applied to PV/RO systems include maximum point power tracking algorithms that increase the efficiency of PV panels [9,10].
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Fig. 1. A basic concept PV/RO system [3].
Temperature control of PV/RO feed water to increase system performance has been suggested [11,12], but active control methods to insure that the system operates within the constraints on its elements have yet to be developed. Simple heuristic control of the temperatures in a PV/RO system that splits control into two parts to control temperature and pressure separately is not able to most effectively control both critical variables simultaneously [3]. Here, a thermal controller is developed based on a coupled thermal/pressure model of the system that ensures that the system pressure and temperature limits are not exceeded. Its effectiveness is demonstrated both experimentally and in simulation. 1.3. Approach A thermal control system is developed in which the RO feed water cools the solar panel by flowing through a panel-mounted heat exchanger. The RO feed water is simultaneously warmed. Cooling the solar panel permits the addition of concentrating mirrors to increase the electrical power produced by the solar panels without
overheating them. Hence the fresh water produced is increased. An analytical model of the dynamic thermal processes in the PV/RO system is developed. A linear decoupled controller is designed and evaluated using a full nonlinear simulation of the system dynamics. It is also validated using an experimental PV/RO system.
1.4. Major results and summary The controller developed here manages the temperatures and pressures of the solar panel and RO feed water subject to physical constraints imposed by the heat exchanger and PV/RO system and ensures appropriate pressure balance within the system. In simulation, a 50% increase in water production is achieved when concentrating mirrors are used. Without thermal control, solar concentrators would overheat and degrade the PV panels, greatly reducing their efficiency. A 57% increase in water production is demonstrated experimentally on a small-scale PV/RO system, using concentrating mirrors and the combined temperature/pressure control.
Fig. 2. Areas of economical feasibility for PVRO systems [1].
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2. PV/RO fundamentals A basic photovoltaic-powered reverse osmosis (PV/RO) system is shown in Fig. 1. A solar panel produces electric power for the RO's motor/pump that pressurizes saline source water to a pressure higher than its osmotic pressure that enters a reverse osmosis unit. The unit contains a membrane that is permeable to water, but not salt. Some fraction of the pressurized water flows across the membrane and exits as fresh water. The remaining water exits the RO unit as high pressure brine. An energy recovery device, such as a turbine or pressure exchanger, captures some of its energy, which is added to the solar panel power to drive the RO system. This configuration does not use batteries for energy storage, since they are expensive, have relatively short lives and introduce energy conversion losses. However, systems without batteries must be designed to accommodate daily and seasonal fluctuations in solar radiation and input water salinity. A discussion of such control is beyond the scope of this paper. The solar panels and RO membranes have complementary thermal characteristics. Fig. 3 shows the temperature dependency of the electrical power produced by a solar panel for different levels of solar radiation, based on the two-diode model [13]. For a given level of solar radiation, a solar panel will produce less electrical power as its temperature increases. Therefore, cooling the solar panel will increase its electrical power output. Fig. 4 shows the temperature dependency of fresh water flow rate produced by an RO membrane. For a given applied pressure, the fresh water production increases with increasing temperature. Therefore, warming the incoming feed water will increase the desalinated water produced. The osmotic pressure of saline water also increases with temperature. This suggests that the water production should decrease with temperature. However, the specific energy required to desalinate warmer water decreases with temperature since the increase in membrane permeability dominates the increase in osmotic pressure [14]. The feed water temperature must be limited to prevent membrane degradation. Typically this maximum water temperature is 45 °C [15,16]. These complementary thermal characteristics can be exploited by the system concept shown in Fig. 5. Here, the RO feed water flows through a heat exchanger mounted on the backside of a solar panel, cooling it, while the RO feed water is warmed simultaneously. The cooled solar panel produces more electrical power than a warmer panel, allowing the pump to produce a higher pressure. The fresh water production increases due to both the increase in applied pressure and the increase in RO membrane permeability. Also,
Fig. 4. Effect of temperature on specific energy required for desalination as a function of pressure. Water quality increases with increasing pressure. Figure by A. Bilton, used with permission. [17].
concentrating mirrors can be added to the cooled solar panel to further increase the electrical power produced. This in turn increases the RO pressure without overheating the PV panels. 3. The thermal control problem The temperatures of the solar panel and RO feed water cannot be independently regulated for the simple uncontrolled system shown in Fig. 5. The solar panel will be cooled and the RO water warmed; however, the temperature of the solar panel and RO feed water are dependent on the feed water flow rate. On a warm, sunny day, it is possible for the panel and/or the RO to overheat. Further, since the flow through the panel is restricted by the heat exchanger flow resistance, under high solar radiation conditions the RO pump may demand enough water to pull a negative (vacuum) pressure at its inlet. This can cause problems, such as pump cavitation and excess mechanical stress to the heat exchanger [17]. Fig. 6 shows the design of a controllable thermal subsystem that can control the temperatures of the RO feed water and solar panel and the pressure at the RO pump inlet. This control subsystem consists of a small circulating pump and two proportionally positional valves. Valve U1 is located in a line connecting the feed water source and RO unit, bypassing the heat exchanger. This proportional valve is called the bypass control valve, or bypass valve. Valve U2 is located in a discharge line connecting the heat exchanger to the feed water source. This valve is called the discharge control valve, or discharge valve. The control problem is a multiple input, multiple output problem. To increase the amount of fresh water produced in a day, the control objectives are: minimize the PV panel temperature TPV and maximize the RO feed water temperature TRO, subject to the constraints on temperature and RO inlet pressure PRO shown below: minimizeðT PV Þ; T PV b80∘ C
ð1Þ
T RO b45∘ C
ð2Þ
maximizeðT RO Þ; P RO ≥0:
ð3Þ
4. System model
Fig. 3. Solar panel electrical power temperature dependence. Figure by A. Bilton, based on [13], used with permission.
A complete dynamic thermal/pressure/flow model of the PV/RO system shown in Fig. 6 is developed here for the controller design and validation simulations. The model is linearized and used for the control system design. In this analysis, temperature gradients along
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Fig. 5. A concept of a PV/RO system with uncontrolled thermal exploitation and concentrating mirrors.
the solar panel and heat exchanger surfaces are neglected. It is assumed that there is perfect mixing of the water within the heat exchanger, and the water exiting the heat exchanger is at the same temperature as the water in the heat exchanger. The mixing junction is also assumed to have a common water temperature and heat capacity. Temperatures and pressures are in units of (°C) and (bar), respectively. The pressures are measured with respect to the atmospheric pressure, commonly called gauge pressure. Conservation of energy applied to the water in the heat exchanger yields: C1
dT H ¼ Q wtr þ ρwtr cp;wtr qPV ðT C −T H Þ dt
− − − − − −
Qwtr and RO feed water flow rate qRO are dependent on the incident solar radiation and ambient conditions, as presented in [17]. For control purposes they are treated as disturbances. Conservation of energy applied to the mixing junction in Fig. 6 yields:
ð4Þ C2
where − C1 is the thermal capacitance of the water in the heat exchanger (J/°C) − TH is the temperature of the heat exchanger water,
t is time (seconds), ρwtr is the density of water (kg/L), cp,wtr is the specific heat of water (J/kg/°C), qPV is the water flow rate through the heat exchanger (L/s), TC is the input water temperature, and Qwtr is the net heat transferred from the solar panel to the water (W).
dT RO ¼ ρwtr cp;wtr ½qPV T H þ q1 T C −q2 T RO −qRO T RO dt
ð5Þ
where − C2 is the thermal capacitance of the water in the mixing junction (J/°C),
Fig. 6. A controllable thermal subsystem for a PV/RO system.
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− TRO is the temperature of the RO feed water, assumed to be the same temperature of the water in the mixing junction, − q1 is the water flow rate through the bypass valve (Valve 1) (L/s), − q2 is the water flow rate through the bleed-off valve (Valve 2) (L/s), and − qRO is the RO feed water flow rate (L/s). The water flow rates in Eqs. (4) and (5) depend on the pressure differences between the heat exchanger inlet and RO pump inlet, the fluid resistance of the heat exchanger (for qPV), and the positions of Valves 1 (U1) and 2 (U2) for q1 and q2, respectively. The feed water source and the water discharge are assumed to be at zero gauge pressure. The feed water flow rate qRO depends on the amount of electrical power supplied to the RO pump. By assuming a linear relationship between pressure and flow, and by considering the heat transferred to the water in the heat exchanger Qwtr and the RO feed water flow rate qRO as system disturbances that are functions of incident solar radiation, system Eqs. (4) and (5) are rewritten: dT C 1 H ¼ Q wtr þ ρw cp;w ðP H −P RO ÞU PV ðT C −T H Þ dt
where the constants are defined: a1 ¼
ρw cp;w U PV T C −T H C1
ð12Þ
a2 ¼
ρw cp;w U PV P H −P RO C1
ð13Þ
k1 ¼
ρwtr cp;wtr T RO C2
ð14Þ
a3 ¼
ρw cp;w T þU T U PV T H þ U 1 c 2 RO C2
ð15Þ
a4 ¼
ρw cp;w U PV P H −P RO C2
ð16Þ
a5 ¼
ρw cp;w P RO U 2 þ q RO C2
ð17Þ
ð6Þ
Req ¼ dT C 2 RO ¼ ρw cp;w ½ðP H −P RO ÞT H U PV þ ðP H −P RO ÞT C U 1 −P RO T RO U 2 −qRO T RO dt ð7Þ
where − PH is the pressure at the heat exchanger inlet, (the outlet of the circulating pump) assumed to be positive, − PRO is the pressure at the intake to the RO pump, also assumed positive, − UPV is the fluid flow resistance of the heat exchanger (L/s/bar), − U1 is the fluid flow resistance of Valve 1 (L/s/bar), and − U2 is the fluid flow resistance of Valve 2 (L/s/bar).
1 : U PV þ U 1
Eqs. (9)–(11) represent the uncontrolled system response. Assuming that actuating the control valves yields small, linear changes in the flow resistances u1 and u2, the system response can be written in state space form with two states, tH and tRO, and three outputs of interest, pRO, tRO and tH. The perturbations in heat flux and RO feed flow rate, δQwtr and δqRO, are functions of the solar radiation and RO unit properties, and are treated here as disturbances. The two control inputs are u1 and u2. The state and output equations are:
t_ H t_ RO ¼
The pressure at the RO pump inlet can also be written as a function of heat exchanger pressure and fluid resistances P RO ≈
P H ðU PV þ U 1 Þ−qRO : U PV þ U 1
ð8Þ
Eqs. (6)–(8) describe the thermal, flow and pressure behaviors of the system and are nonlinear. These equations can be linearized by assuming small perturbations about a steady state operating point. To linearize the model, it is assumed that the PV/RO system is operating at a point with feed water flow rate q RO and incoming , both functions of solar radiaheat to the heat exchanger water Q wtr tion, and that the incoming water temperature TC and circulating pump pressure PH are constant. Under these conditions, Valves 1 and 2 are set to positions with fluid resistances Ū1 and Ū2, respectively, which will result in steady state pressure P RO and temperatures T H and T RO . A cloud obscuring the sun causes perturbations in RO water flow rate δqRO and incoming heat δQwtr. Using a Taylor series expansion and discarding the higher-order terms, Eqs. (6)–(8) are rewritten in perturbation coordinates tH, tRO and pRO as: dt H δQ wtr ¼ þ a1 pRO −a2 t H dt C1
ð10Þ
pRO ¼ −Req δqRO
ð11Þ
−a2 a4 b1 þ b2
. 1 0 tH δQ wtr c2 0k2 þ C1 −a5 t RO δqRO u1 0 u2 b3
1 0 1 3 0 0 0 0 −Req pRO δQ wtr 4 t RO 5 ¼ @ 0 1 A t H þ @ 0 0 A t RO δqRO 1 0 0 0 tH 0 1 c1 0 u þ @ 0 0A 1 u2 0 0
ð19Þ
ð20Þ
where c1 ¼ Req P in −P out
ð21Þ
c2 ¼ −a1 c1 Req
ð22Þ
b1 ¼ −a3 c1
ð23Þ
k2 ¼ −k1 −a3 c1 Req
ð24Þ
ρw cp;w T C P in −P RO −a3 c1 C2
b3 ¼ − dt RO ¼ −k1 δqRO −a3 pRO þ a4 t H −a5 t RO dt
2
b2 ¼ ð9Þ
ð18Þ
ρw cp;w P RO T C : C2
ð25Þ
ð26Þ
As discussed, valve resistances u1 and u2 will change with valve positions and are controllable. This open loop system is passive, and is inherently stable.
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Fig. 7. Block diagram for thermal control.
5. Controller design The control problem described above is multiple input multiple output with two control inputs and three system outputs of interest, one of which (PRO) is not a system state. State feedback alone will not guarantee that the pressure constraint in Eq. (3) will be met, because the objective of limiting the PV panel temperature, Eq. (1), competes with the pressure constraint, Eq. (3), due to pressure limits on the heat exchanger. From the system physics, it can be seen that the pressure constraint can be met by a decoupled control law, where u1 is determined by the error between the desired and measured RO inlet pressure epRO and u2 determined by the error between the desired and measured RO water temperature, etRO , shown in the block diagram in Fig. 7. The errors are defined as
From the state-space model in Eqs. (19)–(20), the open loop transfer function from error epRO to perturbation in RO pressure pRO in the Laplace domain can be written with the PI controller as pRO ðsÞ K 1 ðs þ α 1 Þc1 ðs þ a2 Þðs þ a5 Þ ¼ ePRO ðsÞ sðs þ a2 Þðs þ a5 Þ where − K1 is the open loop gain and − α1 is the ratio between the proportional and integral gains. Similarly, the open loop transfer function relating the error eT RO to the perturbation in RO water temperature tRO is
ePRO ¼ P set −P RO;M
ð27Þ
t RO ðsÞ K 2 ðs þ α 2 Þb3 ðs þ a2 Þ ¼ eT RO ðsÞ sðs þ a2 Þðs þ a5 Þ
eT RO ¼ T RO;M −T set
ð28Þ
where
ð30Þ
− K2 is the open loop gain and − α2 is the ratio between the proportional and integral gains.
where − − − −
ð29Þ
Pset- is the commanded RO pump inlet pressure, PRO,M is the measured RO pump inlet pressure, TRO,M is the measured RO water temperature, and Tset is the commanded RO water temperature.
Proportional integral (PI) control is used to command the thermal subsystem to its desired operating point, which is at the constraint boundaries (see Fig. 7). Maximum fresh water production will occur at the highest allowable water temperature TRO, here limited to 40 °C to allow for some overshoot. The maximum water flow rate through the heat exchanger, and hence maximum heat transfer from the PV panel to the water, will occur when the RO inlet pressure is 0, but at 0 gauge pressure water will not flow through the discharge valve (Valve 2 in Fig. 6). Thus, the commanded RO pressure Pset is 0.068 bar (1 psi) to allow for flow through the discharge valve and still maintain sufficient flow of cooling water through the heat exchanger.
Although commanded to a desired operating point, some steadystate error may exist. For example, if the incoming water temperature is very low, the water exiting the heat exchanger may not reach 40 °C, but the PV panel will be cooled and the RO water warmed as much as possible for the given conditions. The PI controllers are designed for specific operating conditions using linear methods. However, since the operating conditions and system disturbances vary widely over time, the controller performance is evaluated in simulation. 6. Controller performance simulation The performance of a small-scale PV/RO system using the thermal controller was simulated for a step in solar radiation and for a day with varying solar radiation and air temperatures. The full nonlinear model of the system was used to represent performance of the
Table 1 Simulation input parameters.
Step response Full day
Duration
Solar radiation I (W/m2)
Ambient air temperature Tair (°C)
Source water temperature Twtr (°C)
1500 s 4 AM to 8 PM
1500 Solar profile based on [18] for Cambridge, MA
38 Data for Nov 9th for Cambridge, MA, from [19]
38 20
Table 2 Simulation initial conditions and commands.
Step response Full day
Initial PV panel temperature TPV (°C)
Initial heat exchanger pressure PH (bar)
Initial RO inlet pressure PRO (bar)
Commanded pressure PRO,c (bar)
Commanded temperature TRO,c (°C)
60 11 (Sunrise)
0.4137 0.4137
0.068 0
0.068 0.068
40 40
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Fig. 8. Controlled system response for a step in solar radiation.
system. The system contains one 230-W solar panel with a heat exchanger, concentrating mirrors that reflect 50% additional sunlight onto the panel, and an RO unit with a nominal daily production of 300–600 L of fresh water per day, depending on location [17]. The nominal steady state operating point used for controller design assumed that the incident solar radiation on the solar panel was 1500 W/m 2, the ambient air temperature was 38 °C, and the incoming water temperature was 38 °C. Under these conditions, the water temperature exiting the heat exchanger will be hotter than 40 °C, and the RO pump will require more water than can be supplied through the heat exchanger, and so both valves need to be actuated.
Based on stability analysis, the controller gains K1 and K2 are both set to 1, and α1 and α2 are set to 0.1. Simulations were implemented in MATLAB Simulink. Tables 1 and 2 summarize the simulation inputs and initial conditions, respectively. The step response of the simulated system is shown in Fig. 8. Fig. 8a shows the simulated temperatures of the solar panel TPV and the water entering the RO unit TRO. The solar panel is cooled to 58 °C under these conditions. The RO water temperature does not quite reach 40 °C, its commanded value, because the water exiting the heat exchanger qPV mixes with water flowing through the bypass valve q1. The flow rates are shown in Fig. 8c. Water flows through the
Fig. 9. Temperature responses for a full-day simulation.
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Fig. 10. Simulated flow rates with thermal control for full-day operation.
Fig. 12. Experimental and simulated results with and without thermal control.
bypass valve in response to the initial pressure drop at the RO pump inlet PRO, shown in Fig. 8b. Some steady state error in RO water temperature is acceptable, provided that the water temperature does not exceed the maximum allowable RO water temperature of 45 °C. Fig. 8b shows that the controller compensates for the initial pressure drop and that at steady state the pressure stabilizes at 0.03 bar. This is below its commanded pressure of 0.068 bar (1 psi). The linearization of Eq. (8) does not account for the coupling between the feed water flow rate and the control input to Valve 1. Eq. (8) was used directly in simulation, and so the coupling accounts for the steady state error. As with RO temperature, some steady state error in RO inlet pressure PRO is also acceptable, provided that it does not drop below its minimum allowable pressure of 0 bar. Fig. 8c shows the simulated flow rates. As the water demanded by the RO unit qRO increases, the water flow through the heat exchanger qPV quickly reaches its maximum allowable value. As the RO pressure PRO shown in Fig. 8b drops, the controller opens Valve 1 and water flows through the heat exchanger bypass q1 into the RO unit. As the temperature of the heat exchanger water (not shown) increases past 40 °C, Valve 2 opens, discharging some of the hot water q2. This forces more water through Valve 1 to meet the RO pressure demand. At steady state, the flow to the RO unit qRO is the sum of the flows through the heat exchanger qPV and Valve 1 q1, minus the flow through Valve 2 q2. The controller successfully manages both the pressure and temperature of the RO feed water at the RO pump inlet. Fig. 9 shows the simulated temperature responses for a full day's operation. The uncontrolled and controlled responses are shown in Fig. 9a and b, respectively. In Fig. 9a, the solar panel TPV gets too hot during the middle of the day, and the RO water TRO does not experience any heating. This case is unrealistic because the effect of concentrating
mirrors on solar panel temperature is included in the simulation without any solar panel cooling, hence the panel overheats. In Fig. 9b, the solar panel temperature TPV is kept much lower by the cooling water (temperature not shown). The RO water TRO is not substantially warmed. In this case the heat transferred from the hot solar panel to the water in the heat exchanger cannot raise the water temperature to its commanded value of 40 °C. Also, since the controller is managing the RO inlet water pressure PRO as well as temperature, some of the cool bypass water q1 mixes with the warmed water exiting the heat exchanger qPV (see Fig. 10), reducing RO water temperature. Fig. 10 shows the flow rates with thermal control for the full-day simulation. Just before 7 AM, the PV/RO system and its controller are turned on. All of the water demanded by the RO unit qRO flows through the heat exchanger qPV until just after 7 AM. This is shown by the overlapping curves for qRO and qPV. Just after 7 AM, the RO water demand causes the pressure at the RO inlet to drop, so the controller opens Valve 1. This is shown by the rapid rise in the flow q1. The RO water flow qRO is the sum of the water flow through the heat exchanger qPV and bypass q1. Since the water temperature never exceeds the commanded temperature of 40 °C, the controller does not open Valve 2 and so the flow through it q2 is 0. 7. Experimental validation The controller design was validated on an experimental PV/RO system in Cambridge, MA (see Fig. 11). The system is capable of producing 300–450 L of fresh water from sea water per day using only solar energy, and was developed to validate physical models and to test control algorithms. It uses one 230-W Sun Power Corporation solar panel with a rated conversion efficiency of 18%, mounted on a
Fig. 11. MIT experimental PVRO system showing the RO unit, left, and solar panel with concentrating mirrors attached, right.
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Fig. 13. Source and RO water temperatures from experiments with and without thermal control.
single axis tracker that is manually adjusted for different seasons. A simple maximum power point tracking algorithm is used to obtain maximum electrical power from the solar panel. A custom, computercontrolled, variable DC to DC converter is used to step down the solar panel voltage to power two positive displacement pumps, which operate in parallel. The pumps increase the pressure of the feed water from atmospheric and pump it into a dual-piston pressure exchanger that uses the energy from the high pressure brine exiting the RO pressure vessel to further increase the feed water pressure. The high pressure feed water flows into a fiberglass pressure vessel containing the RO membrane, where it is desalinated. The recovery ratio of fresh water produced to feed water is a fixed 9%. The system is fully instrumented with pressure, flow, salinity, temperature, current and voltage sensors. Embedded microcontrollers acquire sensor data and use them to control the DC to DC converter and tracker motor. Data logging is performed by a remote computer wirelessly connected to the microcontrollers. A stainless steel heat exchanger unit is mounted to the underside of the solar panel. The unit has a maximum inlet pressure of 0.41 bar (6 psi). A small 17-W circulator pump is used to circulate cooling water through the heat exchanger, through a proportional control valve bypassing the heat exchanger, and through a proportional valve bypassing the RO unit. Flat-plate solar concentrating mirrors (see Fig. 11) are mounted on the solar panel. Experiments with and without concentrated solar power can be performed. The mirrors are aluminum plate covered with reflective mirror film, and provide approximately 50% additional sunlight to the solar panel. The thermal PI controllers for the proportional valves were implemented on the embedded microcontrollers. A baseline experiment without thermal control, concentrating mirrors, solar panel cooling or RO feed water heating was also performed for a seasonal comparison. Fig. 12 shows typical experimental and simulated results for fresh water produced over an hour period in November, adjusted for the difference in experimental starting times. The experimental and simulated results agree well, although the experimental case with no thermal controller or concentrating mirrors produced less fresh water than the simulation predicts due to clouds. The simulation assumes clear-sky conditions. For the controlled case, the simulation predicts a 50% increase in fresh water production with the thermal controller. Experimentally, a 59% increase in fresh water production is achieved, which is due in part to passing clouds reducing the solar radiation received by the solar panel during the baseline experiment. These results compare favorably with other results presented in [3,17], where a 57% increase in water production was achieved experimentally with concentrating mirrors, solar panel cooling and RO feed water warming. It is not feasible to present a
case where thermal concentrating is used without control or cooling, since the PV panels will overheat. Fig. 13 shows the source and RO feed water temperatures recorded during experiments. When the heat exchanger is used, a 4 °C temperature difference between the source water and the heated RO feed water is achieved. It is apparent that during the course of operation, the source water does heat a little while sitting in its storage tank. The source water temperatures recorded at the heat exchanger inlet are much higher than the source water temperature during the baseline experiment since the brine and fresh water streams are both directed into a source water tank and the water is re-circulated during experiments. In Fig. 13, “Control, concentrating mirrors” refers to actively regulated RO inlet pressure, while “No control, concentrating mirrors” refers to passive regulation of the RO inlet pressure through an open bypass line. In both cases, the PV panel is cooled, and the pressure at the RO inlet is regulated to prevent cavitation. The active control system results in a slightly higher RO water temperature, although not enough to show an increase in permeate production. This result is expected, since during November operation the temperature at the heat exchanger outlet never exceeds 40 °C and so the blow-off valve never opens. Mineral scaling is a common problem in RO desalination. It is known that the solubility of certain minerals, including calcium carbonate, calcium sulfate and magnesium hydroxide, decreases with temperature. However, precipitation of scaling minerals is not expected to be problematic here, because the water temperature is limited by both the allowable RO membrane temperature and maximum solar panel temperature, and the water temperature difference between the heat exchanger inlet and outlet is small (4 °C). For typical seawater in this temperature range, scaling minerals such as calcium carbonate have negative Stiff & Davies Solubility Indices and are not likely to precipitate. This experimental validation focuses on thermal control for seawater PV/RO systems. Thermal control can also be applied to brackish water PV/RO systems, and can be validated with appropriate changes to the current experimental unit, such as replacement of a seawater membrane with a brackish membrane, and the use of a different energy recovery device. 8. Conclusions The daily water production of a PV/RO system can be substantially increased by exploiting the complementary thermal characteristics of PV panels and the RO membranes by cooling the solar panels using the RO feed water, warming it in the process. Cooling the solar panels and warming the RO feed water increase the electrical production of the solar panel and the flow rate of fresh water across the RO membrane, respectively. Further increases in electrical energy production are achievable with the addition of concentrating mirrors, which is only possible by cooling the solar panel. Active control of the solar panel and RO feed water temperatures is needed to maximize fresh water production while meeting physical system constraints. Classical methods are used to design a suitable controller, which is validated in simulation and in experiments. The controller presented here successfully manages temperatures while meeting system constraints, and achieves a 59% increase in water production experimentally. This is well above the target goal of a 25% increase in system efficiency. By actively controlling the temperatures of the PV panels and RO feed water, and by using concentrating mirrors, PV/RO can be made economically feasible for remote communities in much of the world. Acknowledgments The authors would like to thank the King Fahd University of Petroleum and Minerals in Dhahran, Saudi Arabia, for funding the research reported in this paper through the Center for Clean Water and Clean
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Energy at MIT and KFUPM under Project Number R6-DMN-08. Also Amy Bilton and Li Meng are acknowledged for their contributions to the experimental studies.
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