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Global Energy Interconnection
Volume 2, Issue 4, Aug 2019, Pages 310-317
Optimal capacity planning of combined renewable energy source-pumped storage and seawater desalination systems
Abstract
As water scarcity is becoming a growing threat to human development, finding effective solutions has become an urgent need.To make better use of water resources, seawater desalination and storage systems using renewable energy sources (RES) are designed and implemented around the world.In this paper, an optimal capacity planning method for RES-pumped storage-seawater desalination (RES-PS-D) system is introduced.The configuration of the RES-PS-D system is clarified first, after which a cost-benefit analysis is performed using all cost and benefit components.A function for determining maximum economic benefits of the RES-PS-D system is then established, and the constraints are proposed based on various limitations.The mixed-integer linear programming algorithm is applied to solve the optimal function.A case study is introduced to validate the feasibility and effectiveness of the method.The conclusion shows that the strategy is suitable for solving the configuration optimization problem, and finally both merits and defects of the method are discussed.
1 Introduction
Throughout history, water scarcity has been a critical issue for mankind, and currently the situation is worse than it has been before.At least two billion people lack access to safe drinking water at present, and the demand for clean water is increasing due to population growth [1].As an effective approach to relieve the stress of water shortage, seawater is widely desalinated around the world, principally in the Middle East and northern Africa [2].There are multiple ways to desalinate seawater; for cost-effectiveness and other considerations, reverse osmosis (RO) membranes are commonly used for seawater desalination and have dominated the desalination market in recent years [3].On the other hand, technology based on renewable energy sources (RES) is gradually maturing, which makes it possible to establish wind turbines and distribute photovoltaic (PV) arrays on a large scale.In power grids, a RES-pumped storage system can utilize its pumped storage units to shoulder regulation duty due to their reliability and rapidity [4].Besides peak shavingand valley filling, pumped storage units can also operate as an emergency backup of the power grid.As more and more RES units are connected to the power grids, pumped storage units are of significant importance.There are many advantages to a RES-pumped storage system.For a coastal region, RESpumped storage systems can be combined with desalination plants to form a RES-pumped storage-seawater desalination (RES-PS-D) system.
There is a considerable amount of literature studying RES, pumped storage, seawater desalination and their combinations.In order to balance the economic benefits and power fluctuation, Li and Tang [5] proposed an interactive optimization model of the RES-pumped storage system.This model transferred multi-objective optimization functions into single-objective optimization functions.Li et al.[6] studied microgrids accounting for RES, fossil fuel generators, and batteries.This study adapted comprehensive annual costs and pollution conversion fees as the objective function and established constraints based on the configuration studied.The study adopted an improved gravitational search algorithm to solve the objective function and eventually obtained the optimized configuration.Ren and Zheng [7] studied the intelligent control of an RES-PS-D system, and their work provided a complete control strategy process.However, since it is not reasonable for pump turbines to start and stop frequently, limits for the number of starts and stops of the pumped storage units need to be included in the optimization strategy.Turki et al.[8] proposed an autonomous desalination unit fed by a combined wind and solar energy system.Since the desalination unit is isolated from the main grid and lacks energy storage components, it can only be applied as an auxiliary or backup system.Novosel [9] introduced energyPLAN, a comprehensive system developed based on an RES-PS-D system.The paper considered the real situation in Jordan and discussed the effect of establishing the system to reduce critical excess of electricity production.The paper demonstrated the positive effect of the desalination plant with respect to the increase of RES penetration rate.Zhang et al.[10] demonstrated the configuration optimization for island microgrids with RES, diesel generators, batteries, and desalination units.The objective functions concern the system operation cost and RES utilization rate.The optimization problem was solved using a self-adaptive multi-object differential evolution algorithm.Segurado et al.[11] proposed a desalination plant with pumped storage units powered by both wind turbines and conventional generators.Although this theoretical system combines RES, desalination and pumped storage, it is the desalinated water that the pump storage units utilize to reserve upwards or downwards.Such a design scheme severely limits the scale of pumped storage units; the energy stored in the upper reservoir cannot be large enough to accommodate local RES generation.Thus, the economic benefit of the system can be considered insufficient.Ren et al.[12] introduced a configuration optimization of the RESPS-D system.They provided a set of data to perform the optimization.However, there is no detailed optimization method in the paper.
In fact, to date, few previous works have attempted to explain the configuration optimization strategy of the RES-PS-D system.Therefore, this paper focuses on the configuration optimization problem of the RES-PS-D system.A cost-benefit based optimal function, considering RES, pumped storage, and seawater desalination, is established to describe the capacity planning problem of the RES-PS-D system.The mixed-integer linear programming algorithm is adopted to solve the problem.By using this optimization strategy, the optimal capacities of wind farms, PV cells and pumped storage units can be obtained.Also, the annual benefit of the system and payback period of investment can be determined.which are helpful for establishing an RES-PS-D system in coastal regions and accommodate renewable energies in a better way.
The remains of this paper are organized as follows.In Section 2, a methodology to determine the annual maximum economic benefit of an RES-PS-D system is established.Section 3 uses a case study to validate the methodology.The conclusions and future work are presented in Section 4.
2 Determining the annual maximum economic benefit of an RES-PS-D system
2.1 System configuration
The configuration of an RES-PS-D system is shown in Fig.1.In the system, all generators and loads are controlled by the central controller via wireless communication.The central controller collects all essential system data, such as the power output of the RES, the operating condition of the pumps and turbines, and water levels of the reservoirs.The central controller also delivers control strategies to other parts of the system.In practical applications, wind turbines and PV arrays may not be used in the same RESPS-D system, as the specific RES will be determined by geographical resources and other aspects.The lower reservoir can be replaced by the sea and this would save the cost of building two reservoirs, but seawater corrosion of the pump storage equipment has to be taken into account.If the system is applied on an island, then the position of the main grid should be replaced by conventional power generators.To simplify the model, the single pump in the desalination plant represents all water feed pumps in a desalination process line.Because the other parts of the desalination plant do not use power on a large scale, these minor power usages are not considered in the model.
Fig.1 Configuration of RES-PS-D system
2.2 Annual maximum economic benefit function
The annual maximum economic benefit function of the RES-PS-D system is:
where B represents different kinds of annual benefits, and C represents different kinds of annual costs.The sum of all benefits of the system B∑ consists of the benefit from the power generated by RES and pumped storage units.A local PV subsidy is also considered into the benefit, thus B∑ can be given by:
where, 
, 
, and 
are the power generated by PV array, wind turbine, and pumped storage units in the i-th hour of j-th day in a year, respectively.
is local timeof-use (TOU) electricity tariff in the i-th hour of a day, and TFIT is a feed-in tariff of the PV array.In this model, it is assumed that all power generated by RES is transmitted to the main grid.
The sum of all costs C∑ can be expressed as:
where CI and COM are the equivalent annual cost of initial investment (1), and operation and maintenance cost (2) of all parts in the system, respectively.CR is the equivalent annual cost of replacement equipment in the RES units (3), CSS is the annual start and stop cost of reversible pump turbines (4), and CP is the annual cost caused by power consumption of regular loads, water feed pumps and reversible pump turbines (5).
(1) The equivalent annual cost of initial investment CI is:
where, NPV, NWF, and NPS are the installed capacity of PV modules, wind turbines, and reversible pump turbines, respectively.
, and
are the initial investment cost of a single PV module, a wind turbine, and a reversible pump turbine, respectively.
is the initial investment cost of the desalination equipment, 
is the land investment cost of the entire RES-PS-D system, and K is the annual capital recovery factor, which is defined as
where m is the service time of the RES-PS-D system, and r is the discount rate, which is adopted here to measure the net present value of investment.
Besides the cost of land purchase, the initial investment cost also includes construction cost of the RES, pumped storage units, and desalination plant.
(2) The equivalent annual cost of operation and maintenance COM is given by
Here,
and 
are the operation and maintenance cost of a single PV module, a wind turbine, and a reversible pump turbine, respectively.
is the operation and maintenance cost of the desalination plant.
For simplicity, all operation and maintenance costs areaveraged down to each unit in the system.
(3) The equivalent annual cost of equipment replacement CR is:
and 
are the replacement cost of a single PV module and a wind turbine, respectively.nPV and nWF are the number of times PV modules and wind turbines are replaced, respectively, and these can be calculated using Equation (8):
where YPV, YWF are the service time of a PV module and a wind turbine, respectively.
(4) The annual start/stop cost of reversible pump turbines is given by
Here, 
and 
are the number of reversible pump turbines that start/stop in the i-th hour of j-th day in a year, respectively.CSTART and CSTOP are the cost per start and stop of the reversible pump turbines, respectively.
(5) The annual cost of power consumption CP is
where 
and 
is the power consumed by reversible pump turbines, regular loads, and water feed pumps the i-th hour of j-th day in a year, respectively.
2.3 Constraints
Since the system is limited by multiple constraints from geographical, meteorological, social, and political factors, etc., relevant constraints must be considered.In this paper, only essential constraints are discussed, nonessential constraints, such as constraints depending on local policy, are not within the scope of discussion.The essential constraints are presented and discussed below.
(1) System power balance
The system power balance is represented by
where 
,
and 
are the power used by pumped storage units, regular load and desalination units in the i-th hour of j-th day in a year, respectively.
The sum of all power generated and transmitted from the main grid is equal to the sum of the power consumed by loads at any time.The value of 
and its fluctuation reflects the power stability of the RES-PS-D system.
(2) RES-PS-D system power constraints
The RES-PS-D system power constraints are:
Here, 
and 
are the lower and upper boundaries of the power generated by PV arrays and wind turbines, respectively
and 
are the lower and upper boundaries of the power consumed by water feed pump, reversible pump turbines, and the regular load, respectively.The upper boundaries depend on the installation capacity of their respective units.
(3) Reservoir capacity constraint
The constraints on the reservoir capacity is expressed as
where 
and 
are the minimum and maximum water volume of the lower reservoir, respectively, and 
is the water volume of the lower reservoir in the i-th hour of j-th day in a year.
However, if the RES-PS-D system is built near the sea, the lower reservoir can be replaced by the sea itself.Under this circumstance, there is no relevant upper boundary of the water volume 
for the lower reservoir.
For simplicity, the constraint for the upper reservoir is defined in the form of electrical energy that can be generated instead of water volume:
where
an≤d 
are the minimum and maximum energy stored in the upper reservoir, respectively, an≤d 
≤ is the energy stored in the upper reservoir in the i-th hour of j-th day in a year.
Both 
and 
depend on the scale of their respective reservoirs.
(4) Reservoir water balance
The constraint relating to the reservoir water balance is given by:
where t is the time interval, and ηP and ηT are the pumping and power generation efficiency of reversible pump turbines, respectively.
Equation (19) represents the water balance of the upper reservoir, where the energy stored in the upper reservoir at the (i+1)-th hour equals to the sum of the energy stored in the i-th hour and the energy increment from pumping water in the i-th hour minus the energy reduction from turbining water in the i-th hour.
(5) Pumped storage power generation constraint
The constraint governing pumped storage power generation is given by
where 
and 
are the lower and upper boundaries of the power generated by reversible pump turbines, respectively.
(6) Pumped storage units function constraint
The constraint of the pumped storage unit function is expressed as
This constraint is applied to prevent reversible pump turbines from pumping water and generating power at the same time, which would constitute a pointless waste of energy.
(7) Pumped storage units start/stop constraint
The start/stop constraint of the pumped storage unit is
where Ti is the number of starts and stops in the i-th day.This constraint is applied to limit the times of starts and stops of the reversible pump turbines.
(8) Desalinated water storage constraint
The desalinated water storage constraint is given by
Here, 
and 
are the minimum and maximum water volume of the storage tank for desalinated water, respectively, and 
is the water volume of the storage tank for desalinated water in the i-th hour of j-th day in a year.
(9) Desalinated water storage balance
The constraint governing the desalinated water storage balance is
where ηDS is the pumping efficiency of the water feed pump, HDS is the lift of the water feed pump, 
is the volume of desalinated water needed in the i-th hour of j-th day in a year, and 
s the volume of water pumped under the condition of ηDS,
and 
Equation (24) represents the water balance of the desalinated water.Similar to constraint (4), the water volume in the i-th hour plus the volume of newly desalinated water minus the water usage in that hour equals the volume in the next hour.
3 Case study
3.1 System parameters
The method for optimal capacity planning of the RESPS-D system is established, with Equations (1)-(10) describing the optimization function and Equations (11)-(24) expressing the constraints.Using MILP algorithm, the optimal capacity of the RES and the pumped storage units, 
, 
, and 
, can be obtained.Additionally, the annual net economic benefit of the system can be determined, and the duration of the payback period can be confirmed, which reflects the recovery speed of all costs and investments.
In this section, the initial parameters of the RES-PS-D system are provided as shown in Table 1.All essential parameters are set based on realistic data.Equivalent modeling of PV, wind turbines, and pump storages are considered and the value of NPV, NWF, and NPS are set to 1 to simplify the calculation and the TOU tariff applied in this case is shown in Fig.2.
Table 1 Initial parameters for the case
Parameter Value Parameter Value CI P V (USD/kW) 745.15 OM PV C (USD/(kW·yr)) 13.22 CI W F (USD/kW) 548.73 OM WF C (USD/(kW·yr)) 5.27 CI P S (USD/kW) 521.61 OM PS C (USD/(kW·yr)) 3.36 CI D S (USD) 1222.05 OM DS C (t·yr) 0.92 CSTART (USD/MW) 5.96 R PV C (USD/kW) 298.06 CSTOP (USD/MW) 5.96 R WF C (USD/kW) 271.23 Cland (USD/m2) 11.17 r 6.7%YPV (yrs) 25 m (yrs) 30 YWF (yrs) 20 TFIT (USD/kWh) 0.062 NDS 1 Ti 2 NPV 1 ηP 0.75 NWF 1 ηT 0.75 NPS 1 ηDS 0.75
Fig.2 TOU tariff for the case study
The regular load represents the supporting and other regular facilities in the RES-PS-D system, such as municipal infrastructure and communities, etc.In this case, data of civilian power consumption in a region in Huludao, China, has been adopted as the regular load in the system.General fluctuations in the regular load in one day is shown in Fig.3.
Fig.3 The regular load during one day used in this case study
The PV and wind generation in Huludao, China, as shown in Fig.4 and 5, respectively, were also adopted for this study.
Fig.4 PV generation used in this case study
Fig.5 Wind generation used in this case study
Finally, the desalinated water demand was adopted as 
, as shown in Fig.6.This data was also sourced from Huludao, China.
Fig.6 The fluctuation in the demand for desalinated water in a 24-hour period used in this case study
3.2 Simulation results
The results obtained when the collated data was applied to the method outlined in Section 2 are listed in Table 2.
Table 2 Results of the optimal capacity planning
P max PV P max WF P max PS 76.32 MW 36.89 MW 31.60 MW Annual net economic benefit Payback period 412,665 USD 15.3 yrs
The results show that under this capacity configuration, the entire RES-PS-D system will reach its maximum annual economic benefit, and in 15.3 years the cost can be fully recovered.Taking the RES service time into consideration, the total benefits of the RES-PS-D system are 6,313,775 USD in total over 15.3 years.Considering the service time of PV cells and wind turbines, RES equipment will need to be replaced after 20 years.
Several plans based on different RES and pumped storage capacities were designed to verify the performance of our model, as shown in Fig.7 and Table 3.
Fig.7 Comparison of different capacity plans
Table 3 Comparison of different capacity plans
max PV P max WF P max PS P Annual net benefit (USD)Payback period (yrs)Plan 1 76.32 36.89 0 423,140 17.5 Plan 2 90.568 22.642 31.6 385,112 18.6 Plan 3 22.642 90.568 31.6 352,764 17.2 Plan 4 76.32 36.89 31.6 412,665 15.3
It can be observed that Plan 4 had the optimal capacity in this Plan; both Plan 2 and Plan 3 had the same total RES capacity but different proportions of PV capacity and wind capacity in the RES.Plan 1 was set to exclude pumpedstorage units.
The above results prove that the pumped storage units accounted for a part of the economic benefit of the RESPS-D system.Although the total investment is decreased when the pumped storage units are not included, however, the total benefits declines as well, and payback period becomes longer.
It can also be concluded that there is an optimal proportion for both wind power and solar power in the RES capacity.The reason Plan 3 was not as beneficial as Plan 4 was that solar power can not only generate power from PV arrays but also be subsidized by governments.However, Plan 2 had a greater proportion of solar capacity but was less beneficial than Plan 4.This is because the costs of PV units are larger than wind turbines, including initial investment costs, equipment replacement, and operation and maintenance costs.
3.3 Discussion
The optimal capacity planning method for an RESPS-D system achieved the expected effect of determining the value of annual maximum net benefit.Assuming that all parameters are kept constant, it can also help determine the payback period of the system.
For simplicity, the value of NPV, NWF, and NPS were set to 1 in this case study.Although they have little influence on the result, they could be important when comparing the effects of different types of wind turbines, PV arrays, or pump turbines on system economic benefits.This shows that the method can also be used to compare between different plans.
4 Conclusion
In this paper, an optimal capacity planning method for the RES-PS-D system is proposed, which focuses on the maximum economic benefit of the RES-PS-D system.By taking various benefits and costs into consideration, the method can be applied to evaluate the profitability of an RES-PS-D construction project.Initial investment costs and other costs are converted into equivalent annual costs in order to obtain the total annual cost.We also introduced relevant constraints into the method to account for natural or artificial limitations.Overall, our method can be used to calculate the optimal capacity of the RES and the pumped storage units and to determine the payback period of a specific configuration.This is useful for practical decisionmaking.The feasibility and effectiveness of the proposed method was validated using a case study.Results show that the optimization strategy proposed is suitable for solving the problem.The study can be applied in the capacity planning problem when an RES-PS-D system is under programming in a coastal region.
Future work will include the methodology of evaluation of the RES-PS-D benefits and the control strategy of the pump storage units.
Acknowledgements
This work was supported by the National Natural Science Foundation of China (No.61703081), the Natural Science Foundation of Liaoning Province (No.20170520113), and the State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources (No.LAPS19005).The authors would also like to thank the State Grid Huludao Power Supply Company for providing confidential data.
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Fund Information
supported by the National Natural Science Foundation of China (No.61703081)； the Natural Science Foundation of Liaoning Province (No.20170520113)； the State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources (No.LAPS19005)；
supported by the National Natural Science Foundation of China (No.61703081)； the Natural Science Foundation of Liaoning Province (No.20170520113)； the State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources (No.LAPS19005)；
Author
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Boyu Liu
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Bowen Zhou
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Dongsheng Yang
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Zhile Yang
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Mingjian Cui