Optimal Sizing and Design of Hybrid Power Systems - ACS

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Optimal Sizing and Design of Hybrid Power Systems Jui-Yuan Lee, Kathleen Aviso, and Raymond R. Tan ACS Sustainable Chem. Eng., Just Accepted Manuscript • DOI: 10.1021/ acssuschemeng.7b03928 • Publication Date (Web): 29 Dec 2017 Downloaded from http://pubs.acs.org on December 31, 2017

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ACS Sustainable Chemistry & Engineering

Optimal Sizing and Design of Hybrid Power Systems Jui-Yuan Lee,*,† Kathleen B. Aviso,‡ and Raymond R. Tan‡ †

Department of Chemical Engineering and Biotechnology, National Taipei University of Technology, 1, Sec. 3, Zhongxiao E. Rd., Taipei 10608, Taiwan, ROC

‡

Chemical Engineering Department, De La Salle University, 2401 Taft Avenue, Malate, Manila, 0922, Philippines ABSTRACT: Climate change is a major concern of this generation, with energy use in various sectors of the economy remaining the main culprit. Various strategies are thus being developed to reduce greenhouse gas (GHG) emissions, including schemes to improve energy efficiency and to maximize the use of renewable energy (RE). However, RE suffers from its inherent variability due to its dependence on weather and climatic conditions. Hybrid power systems (HPSs) are thus recommended to provide a solution for reducing GHG emissions while ensuring energy availability by using a mix of RE technologies and conventional energy sources. This work develops a mathematical model for optimal HPS design with detailed cost considerations. The model accounts for the variability of RE sources and power demands, and selection between different energy storage technologies, as well as power losses. Results for two case studies, which consider different sources of RE and different types of energy storage, illustrate the trade-offs between cost and RE utilization. Significant reductions in total cost can be achieved with the appropriate mix of outsourced electricity supply and proper sizing of RE generators and energy storage systems. KEYWORDS: Climate change, Renewables, Energy storage, Process integration (PI), Superstructure, Mathematical programming

Corresponding Author *Tel.: +886-2-27712171 ext. 2524. Fax: +886-2-27317117. E-mails: [email protected] (J.-Y. Lee), [email protected] (K.B. Aviso), [email protected] (R.R. Tan). 1

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INTRODUCTION Combustion of fossil fuels causes environmental pollution and climate change. Growing concerns have prompted countries to commit to reducing greenhouse gas (GHG) emissions, hence the recent adoption of the Paris Agreement. Effective measures to mitigate and adapt to climate change include the use of renewables, such as solar, wind and biomass, which provide the prospect of low-carbon energy generation. According to Energy Technology Perspectives 2016,1 renewables would contribute 32% of the cumulative emissions reductions in the 2°C Scenario (2DS) over the period 2013-50. Furthermore, renewables will be deployed mainly in the power sector, where wind and solar photovoltaic (PV) have the potential to provide 22% of annual emissions reduction in 2050 under the 2DS.2 However, a major issue of renewables is the inherent variability due to their dependence on weather and climatic conditions (e.g., wind speed and solar irradiance), which invariably results in a mismatch between the power generation and the load demand. While fluctuations in the output of renewables make it challenging to utilize renewable energy (RE) efficiently, integrating complementary sources such as solar and wind can significantly improve the system efficiency and availability, thereby reducing the dependence on backup energy devices (e.g., batteries, diesel generators etc.). This approach has led to the study of hybrid power systems (HPSs).3 The HPS is an application variant of distributed generation, defined as a system utilizing two or more energy sources. An HPS can be on-grid or off-grid, and may incorporate energy storage or a conventional source (e.g., diesel) to further improve the system availability. Different types of HPSs are feasible depending on the local demand and resource availability. Solar and wind are the most promising RE sources especially because of their complementary nature. This advantage makes such HPSs a popular topic of research,4 with the main focus on sizing and optimization to ensure a cost-effective system.5 Recently, the approaches of process integration (PI) have been extended to the optimal design of HPSs.6 PI techniques can be classified as pinch analysis and mathematical programming. The former may be used to set performance targets and provide high-level insights for the design problem, while the latter is preferred for handling detailed problems. Since HPS design is analogous to the synthesis of batch resource conservation networks, well-established PI techniques can be adapted to HPS design and optimization problems. For HPS targeting, Wan Alwi et al.7 established power pinch analysis (PoPA) using power composite curves to determine the minimum outsourced electricity supply and the available excess electricity during start-up and normal operations. Mohammad Rozali et al.8 later developed power cascade analysis and the storage 2


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cascade table (SCT) to determine the maximum power demand and storage capacity in addition to the electricity targets. However, both works assume an ideal case of 100% power transfer and battery storage efficiency.7,8 To relax this simplifying assumption, Mohammad Rozali et al.9 further developed the SCT for HPS design with consideration of energy losses. With different types of energy storage systems, Mohammad Rozali et al.10 presented a generic PoPA-based framework to select the most cost-effective storage technology for an HPS. Mathematical programming techniques have been developed to optimize the sustainability of process systems,11-13 and power allocation in HPSs. Chen et al.14 proposed two transshipment model-based formulations for HPS targeting and design. Their formulations account for the effect of power losses from transfer and storage by introducing a fixed energy recovery ratio, although conversion losses are not considered. This drawback has been overcome in a later proposed model.15 Lee et al.16 presented a superstructure-based optimization model for HPS design with energy loss considerations. The superstructure approach makes the model generic and flexible to accommodate additional design options, constraints or objectives. Furthermore, the optimization framework allows all the power allocation options to be considered at the same time and the true optimum to be identified, although minimizing the outsourced electricity supply as the primary objective may not necessarily achieve the minimum total cost. The model of Lee et al.16 was then modified for remote island17 and eco-industrial park (EIP) applications.18 Sreeraj et al.19 proposed a PI-based methodology to find the minimum battery capacity required for an isolated HPS. The authors also considered the stochastic nature of the RE resources and the system reliability requirements using a chance-constrained programming approach. Bandyopadhyay20 highlighted the use of the grand composite curve representation of stored energy to design isolated PV-battery and wind-battery systems. In addition, the battery sizing methodology proposed in both works helps to plan further load growth without increasing the system size.19,20 Ho et al.21 developed electric system cascade analysis (ESCA) for designing and optimizing isolated energy systems with a non-intermittent power source (biomass) and energy storage. ESCA was later applied to isolated PV systems.22 So far, ESCA is limited to systems with only one power source, and is not applicable to wind energy systems. Ho et al.23 proposed a graphical PoPA tool to determine the capacities of power generators and energy storage for the design of off-grid HPSs. Mohammad Rozali et al.24 applied the modified SCT9 for sizing an HPS. Recent studies have explored the use of probability theory to simplify the process

of

PoPA

in

considering

efficiency

losses,25

3


and

incorporated


chance-constrained programming into the PoPA framework to account for uncertainty.26 Other recent works analyzed the effect of renewables and load variability on the system design and performance,27,28 the reliability of polygeneration,29 and the trade-off between total annualized cost and electrical system unavailability.30 It should be noted that there are fewer mathematical programming techniques developed for HPS sizing. The only relevant contributions are either limited to biomass and solar systems31 or lacking in cost considerations.17 With all its advantages, pinch analysis lacks the capability to address various design constraints and cost trade-offs. Moreover, pinch analysis could be cumbersome when applied to large-scale problems involving multiple sources and demands varying with time. Thus, there is a need for the development of mathematical programming techniques to complement the pinch-based techniques in HPS design and optimization; this paper aims to develop a generic mathematical model that is applicable to both off-grid and on-grid HPSs with all types of power sources and energy storage technologies, and potentially capable of dealing with multiple objectives. In the following sections, a formal problem statement is given first. The mathematical model is presented next. Three case studies are then solved to illustrate the proposed approach. Finally, conclusions and prospects for future work are given at the end of the paper. PROBLEM STATEMENT The problem addressed in this paper can be stated as follows.

An HPS consists of a set of power sources i∈I and a set of power demands j∈J. Power sources can be conventional (e.g., diesel) or renewable (e.g., wind, biomass and solar) to generate power for demands.

The availability and power generation of renewable sources are determined by local weather conditions and the equipment used, assuming conventional sources can be used as backup to produce power whenever needed. It is also assumed that the load profiles of power demands are available.

Considering the variability of renewables and load demands, a set of energy

storage systems s∈S (e.g., batteries) are also given. When there is insufficient renewable power, there is the option of importing

electricity from the grid, or alternatively using conventional sources onsite. Since power sources and demands as well as energy storage systems can be alternating (AC) or direct current (DC), a power conditioning system is needed. Specifically, the conversion between AC and DC involves a rectifier (AC-DC) 4


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and an inverter (DC-AC). The objective is to determine the optimal HPS size and configuration that minimizes the outsourced electricity supply or the total cost. Simplifying assumptions made for the problem include the following:

Power generators and energy storage systems have piecewise linear capital cost functions. The HPS cost is approximated by the sum of capital and operating costs of major system elements. Outsourced electricity has a fixed price. The annualization factor (i.e., the capital recovery factor) is fixed, calculated from the interest rate and project life.

MODEL FORMULATION The modeling of an HPS is based on the superstructure in Figure 1, taking into account all possible connections between power sources, power demands and energy storage systems. A set of time intervals t∈T are also defined. The mathematical formulation presented below consists mainly of energy balance equations. Notation used is given in the Nomenclature. Energy Balance for Power Sources and Demands. As shown in Figure 1, the power generated from source i ( ) can be sent directly to power demands j ( )

e and stored in energy storage systems s ( ) for later use, while excess power ( ) would be dumped or exported. Equation 1 describes the energy balance for power source i in time interval t. e = + + ∀ ∈ I, ∈ T

∈J

∈S

(1)

where the power output from source i is given by eq 2 as a function of the maximum power rating ( ) and the ratio of the installed capacity ( ) to the maximum

capacity (max ). Here it is assumed that generators of different sizes are available to make the total generation capacity a continuous variable. Capacity constraints for power sources are given in eq 3. (2) = ⁄max ∀ ∈ I, ∈ T

≤ max ∀ ∈ I

(3)

The power required for demand j ( ) may come from power sources i, energy o storage systems s ( ) and outsourced electricity ( ). Equation 4 describes the energy balance for power demand j in time interval t. Note that efficiency factors 5



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( , and o ) are included to account for power losses from conversion. These

factors are set to the inverter efficiency (inv ) for DC-AC conversion, to the rectifier efficiency (rec ) for AC-DC conversion, or to 100% (no efficiency losses) if no power conversion is needed for the demand. o o = + + ∀ ∈ J, ∈ T

∈I

∈S

(4)

Energy Balance for Electricity Storage. Energy storage may be used to collect surplus power from sources and dispatch it to demands when there is a deficit of power. Equations 5 and 6 describe the inlet and outlet energy balances for storage

out in system s in time interval t, respectively. Note that and are the total amounts of power to be charged and discharged before charging/discharging losses.

Similar to the efficiency factors in eq 4, accounts for power losses from conversion for energy storage, while out is the discharging efficiency. in = ∀ ∈ S, ∈ T

∈I

out out = ∀ ∈ S, ∈ T

∈J

(5)

(6)

The overall energy balance for storage system s is given by eq 7. It is stated that the amount of energy stored at the end of time interval t ( ) equals that at the end of the previous time interval (,) or the initial charge (, for = 1) adjusted

in in by the storage loss (self-discharge) and the amounts charged into ( ) and out discharged from the system ( ) during time interval t.

= op ,

out in in + , ! " × $1 − & Δ ( + ) − *Δ

(7)

∀ ∈ S, ∈ T where is a binary parameter indicating the operation mode ( op = 0 for start-up or the first-day operation; op = 1 for normal daily operation), & is the op

hourly self-discharge rate, Δ is the time interval length, and in is the charging efficiency. In normal operation, the energy stored at the end of the last time interval

( = ,) of a day is taken as the initial charge for the next day. Since the startup is only a moment in the operating period, the design of HPSs in this work will be based on normal operation. It is worth noting that the current formulation applies to

energy storage technologies to be modeled in the same way as batteries (including pumped hydro, compressed air, superconducting magnetic and flywheel energy storage),10,18 and can be extended for virtual storage in the form of desalinated water32 and hydrogen.33 However, additional case-specific constraints would be needed for more detailed storage design. 6


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Capacity constraints for energy storage are given in eqs 8-10. For storage system design, the power-related capacity ( ) considers the maximum rate of cap charging and discharging, while the energy-related capacity ( ) allows for the maximum amount of energy stored during the operation. cap

in ≤ ∀ ∈ S, ∈ T cap out ≤ ∀ ∈ S, ∈ T

cap

≤

cap ∀

(8) (9)

∈ S, ∈ T

(10)

Objective Functions. This work considers both sequential and simultaneous approaches in HPS sizing and design. While sequential optimization applies when there is a hierarchy of priority, simultaneous optimization allows the trade-off between various cost elements. In order to exploit the local energy sources, the HPS may be designed through a three-step optimization approach. The primary objective in step 1 is to minimize the outsourced electricity supply (-OES ): o min -OES = Δ

(11)

∈J ∈T

Next, step 2 determines the required generator capacities by minimizing the total cost of power generation (-PGC ):

min -PGC = 12 )1fix 3 + 1var * ∈I

+

456fix ∈I

(12)

+ 56var 7 Δ 8 ∈T

where 3 is a binary variable indicating the use of power source i, correlated with the installed capacity using eq 13. Note that eq 3 becomes redundant with the inclusion of eq 13. In this step, an additional constraint (eq 14) is needed to limit the ∗ outsourced electricity supply to the previously determined minimum (-OES ).

≤ max 3 ∀ ∈ I

(13)

o ∗ Δ ≤ -OES

(14)

∈J ∈T

Step 3 then determines the required storage capacities by minimizing the total cost of energy storage (-ESC ):

min -ESC = 12 )1fix3 + 1E + 1P * + 56 cap

cap

∈S

cap

∈S

(15)

where 3 is a binary variable indicating the use of energy storage system s,

correlated with the power-related capacity using eq 16. In this step, the minimum generator sizes identified in step 2 (∗ ) are used as upper limits in eq 17. cap

7



min 3 ≤ ≤ max 3 ∀ ∈ S ≤ ∗ ∀ ∈ I cap

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(16) (17)

It should be noted that fixed capital costs (1fix and 1fix) are included in eqs 12 and 15 to account for economies of scale. However, these terms may not be needed for technologies with limited economies of scale, or when such effect has

been reflected in the variable capital cost coefficients (1var , 1E and 1P ), which vary with the capacity. In addition, step 2 may be skipped if there is no excess of power in normal daily operation.

Alternatively, the objective function may be to minimize the total annual cost (-TAC ) of the HPS, taking into account the trade-offs between outsourced electricity, onsite power generation and energy storage costs:

min -TAC = -OEC + -PGC + -ESC where the cost of outsourced electricity (-OEC ) is given by eq 19. o -OEC = ,: × 7 Δ

∈J ∈T

(18)

(19)

Whichever approach is used, the overall model is a mixed integer linear program (MILP), for which global optimality can be guaranteed without major computational difficulties for cases of typical size. ILLUSTRATIVE CASE STUDIES In this section, two case studies are presented to illustrate the proposed approach. The developed model is implemented and solved in GAMS34 on a Core i5-4340M, 2.90 GHz processor, using CPLEX as the solver. All solutions were found with negligible processing time. Case Study 1. The first case study is taken from Mohammad Rozali et al.24 The HPS consists of a wind turbine, a biomass generator and PV modules, with a lead-acid battery for electricity storage. Initially, the installed capacities of the wind, biomass and PV generators are assumed at their maximum: 80 kW, 70 kW and 60 kW, respectively. The limiting power data are shown in Tables S1 and S2. In this case study, the battery charging/discharging efficiency is assumed to be 90%, the battery self-discharge rate to be 0.004%/h, while the inverter/rectifier efficiency to be 95%. Tables S3 and S4 show the cost data for the power generation and energy storage technologies considered in this case study, respectively. The tariff rate for electricity (,:) is taken to be $0.12/kWh, while the capital cost is to be annualized over a 10-year period at a fixed rate of interest of 10%. It is further assumed that the 8


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effect of economies of scale (if any) is factored into the variable capital expenditure of the equipment. Therefore, the fixed capital cost terms in eqs 12 and 15 are not needed, and the MILP model can be reduced to a linear program (LP). The sequential approach is applied first to determine the minimum outsourced electricity supply and the corresponding HPS sizing. Solving the LP model for steps 1-3 yields the results in Table 1. It can be seen that outsourced electricity is not needed, given more power to be generated (2920 kWh/day) than is consumed (2680 kWh/day). Thus, the installed capacity of PV may be reduced to 59.11 kW to eliminate excess power, while wind and biomass remain at their initial (i.e., maximum) capacities. The required energy-related and power-related capacities of the lead-acid battery are then determined to be 622.02 kWh and 92.5 kW respectively. Figure S1 shows the energy storage profile. For power allocation, Figure 2 shows that most of the electricity to the demands is supplied directly from the sources, with only a small portion via the battery, to minimize efficiency losses from energy storage. Furthermore, comparing the demand and supply profiles indicates additional power supply, which is needed to compensate for the various efficiency losses. In comparison with the results of Mohammad Rozali et al.,24 this work reports a larger capacity for PV (59.11 kW). However, their minimum PV capacity (58.47 kW) proved to be an underestimate. Tables S5a and S5b show the modified SCT for this case study. It can be seen that reducing the PV capacity to 58.47 kW leads to insufficient power generation and hence the need for 6.43 (= 6.11/0.95) kWh/day of outsourced electricity for normal operation. This exceeds the target of zero set with the maximum generator capacities. Similarly, the minimum outsourced electricity supply for normal operation with the reduced PV capacity is determined to be 5.8 kWh/day using the proposed model. These verification results indicate not only the failure of the method of Mohammad Rozali et al.24 to give the correct sizing, but also the capability of the proposed model to determine the true electricity targets. Incorrect sizing is also found in the other case study of Mohammad Rozali et al.,24 as discussed in the Supporting Information. It is worth noting that if step 2 were to minimize the energy storage cost and step 3 the power generation cost, the required energy-related and power-related capacities of the battery would be slightly smaller (614.06 kWh and 90.73 kW respectively), with wind, biomass and PV all remaining at their maximum capacities. Minimizing the cost of power generation or energy storage as the first step is not considered in this work, because the primary objective of the sequential approach is 9



to determine the minimum outsourced electricity supply. However, it is expected that if step 1 were to minimize the cost of power generation, there would be no onsite generation or energy storage, and all power demands would be satisfied by outsourced electricity. The same goes for minimizing the energy storage cost in the first step and the power generation cost in the second. Interestingly, if the energy storage cost is to be minimized first, the outsourced electricity supply next and then the power generation cost (i.e., a special case of HPS design in the absence of energy storage), the minimum outsourced electricity supply would be 529.26 kWh/day and the required generator capacities would be 60.5 kW, 70 kW and 60 kW for wind, biomass and PV respectively. Considering cost trade-offs for the HPS, the simultaneous approach is then used to minimize the total cost. Solving the LP model (eq 18 subject to eqs 1-10) gives the results in Table 1. It can be seen that only biomass (52.63 kW) is to be used and no energy storage is required, with an outsourced electricity supply of 1480 kWh/day, or 540200 kWh/y. The resulting TAC is much lower (−38.37%) than that of the design produced by the sequential approach, because the cost of outsourced electricity is low compared to the costs of wind/PV power generation and battery storage. The impact of the electricity tariff rate on the optimal HPS configuration is further analyzed using the simultaneous approach. Figure 3 shows that the use of wind and PV is economically feasible only when the electricity tariff is no less than $0.25/kWh. With the electricity tariff increasing therefrom, wind is deployed first as PV is more expensive. Increased use of the RE sources increases the capacity required for battery storage, as shown in Figure 4, while decreasing the need for outsourced electricity. When the outsourced electricity supply reaches zero for electricity tariffs of $0.33/kWh and above (see Figure 4), the total cost levels off at $171,140/y, as shown in Figure 5. At this point, both design approaches give the same HPS configuration. Furthermore, Figure 5 also shows the penetration of RE with the increase in the electricity tariff rate. Case Study 2. The second case study is taken from Theo et al.,18 involving the optimization of electric power dispatch and energy storage for an on-grid HPS serving an EIP. The power outputs of the renewable sources are shown in Table S6. There are four major plants in the EIP, namely aluminum casting, plastic injection molding, meat processing and cement plants. Table S7 shows the plant-wide power demands from the machinery, while Table S8 presents the overall load profiles. Further details can be found in the original paper.18 In this case study, the design of the HPS considers the net present cost rather 10


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than the annual cost. Therefore, the cost-related objective functions in eqs 12, 15 and 18 are rewritten as in eqs 20-22, respectively. Note that the 2 factors (2 , 2 ,

2 inv and 2 rec ) are included to allow for the replacement cost of the HPS components (if the component life is shorter than the project life), while the 1 factor converts the annual worth to the present worth. In addition, the depth of discharge (;

Optimal Sizing and Design of Hybrid Power Systems - ACS

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