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Resolving conflict objectives between environment impact and energy efficiency – An optimization modeling on multiple-energy deployment
Journal Pre-proofs Resolving conflict objectives between environment impact and energy efficiency - an optimization modeling on multiple-energy deployment Kung-Jeng Wang, Le Duc Dao PII: DOI: Reference:
S0360-8352(19)30580-7 https://doi.org/10.1016/j.cie.2019.106111 CAIE 106111
To appear in:
Computers & Industrial Engineering
Received Date: Revised Date: Accepted Date:
10 March 2019 18 August 2019 3 October 2019
Please cite this article as: Wang, K-J., Dao, L.D., Resolving conflict objectives between environment impact and energy efficiency - an optimization modeling on multiple-energy deployment, Computers & Industrial Engineering (2019), doi: https://doi.org/10.1016/j.cie.2019.106111
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Resolving conflict objectives between environment impact and energy efficiency - an optimization modeling on multiple-energy deployment Kung-Jeng Wang (Corresponding author) and Le Duc Dao Department of Industrial Management National Taiwan University of Science and Technology Taipei 106, Taiwan, ROC [email protected], [email protected] Highlights:
Developing electricity portfolio to tradeoff electricity generation and CO2 emission.
Designing a non-dominated sorting genetic solution algorithm for multiple objectives.
Presenting the optimal capacity plan for electricity generation efficiency.
Resolving conflict objectives between environment impact and energy efficiency - an optimization modeling on multiple-energy deployment
Abstract Energy consumption increases dramatically due to economic development, leading to the raising of toxic materials such as CO2 during electricity generation process. This study aims at solving the electricity generation portfolio issue to maximize electricity generation while minimizing the CO2 emission to protect the environment. In this research, multiple types of power plants to produce electricity, such as by gas, coal, solar, are alternatives for electricity generation portfolio. Especially, uncertainty in electricity demand is included and dealt by a stochastic chance constrained method. Further. The proposed model is solved by a non-dominated sorting genetic algorithm for multiple objectives. The result 1
presents the optimal capacity portfolio plan for electricity generation and suggests a tradeoff decision between conflicting goals to balance electricity generation efficiency and environmental protection. Keyword: Energy conservation; environmental protection; capacity portfolio planning; stochastic programming.
2
Resolving conflict objectives between environment impact and energy efficiency - an optimization modeling on multiple-energy deployment 1. Introduction Energy consumption is an indicator of economic development (Huang, et al., 2017; Surendra, et al., 2014; Wang, et al., 2018) and closely associated with high-quality living standard. The electricity demand prediction for the next 25-30 years has an upward tendency and mostly comes from developing nations, and this situation in turn presents a serious energy demand (Wolfram, et al., 2012; Kaplan & Aladağ, 2016; Mehrara, 2007). However, the objectives of energy, economy, and environment are proved conflicting (Feng, et al., 2016). While producing electricity, natural resources are not only mined but CO2 is emitted, causing severe environment impacts (Peters, et al., 2012). For example, in many countries, an increasing in the sea levels or strong storm annually destroys crops, houses and leads people to poverty. In addition, many dangerous viruses originated from polluted air, e.g., Zika or SARS threaten the lives of living creatures (Mendelsohn, et al., 2016; O'Neill, et al., 2017) To solve the environmental issues caused by generating electricity, several actions have been done, but they have certain limitations, e.g., using renewable resources to partially replace traditional ones, consequently, reducing environmental impacts (Grubb, et al., 2015; Zografidou, et al., 2016). It is noted that, although clean resources possess advantages, compared to traditional resources, they cannot fully meet demands with cost-efficiency. The major source for electricity up to now in various countries still comes from nonrenewable resources. For instance, in Mexico, natural gas and coal are the major fuels of primary electricity generation. Gas accounted for 40% of the total amount of electricity 3
generated, followed by oil (45%) and coal (8%). The use of renewable energy is still little (Pérez-Denicia, et al., 2017). In addition, reducing pollution by adopting appropriate energy options and optimizing their production process becomes critical (Chevallier & Goutte, 2017; Zhang, et al., 2016). Actually, to deal with the relationship between environmental impacts and electricity generation efficiency, the amounts of renewable and non-renewable energy should be balanced. Such proportions can be handled by establishing the electricity reform agreement (e.g., the electricity generation plan) between energy consumer community and producer. However, this raises issues from concerned parties, e.g., the impact to the power generation firm’s profit and motivation to green power generation need to be addressed due to costefficiency. To conclude, to resolve conflicting objectives between environmental impacts and energy efficiency is an issue that needs to further investigate. To contribute to this research area, this study builds a quantitative model considering how to maximize the volume of electricity produced while minimizing the amount of CO2 emitted. In detail, multiple approaches (further provided in section 4) will be conducted to propose a electricity generation portfolio dealing with chaotic demands. The framework of our research is presented in Figure 1. The rest of the article is organized as follows. Section 2 reviews related literatures. The problem is modelled in Section 3. Section 4 develops the solution approach. Our experiments are conducted in Section 5. Finally, Section 6 gives some conclusion and future research.
4
Firm expectation profit
Input
Stochastic Energy demand Energy Profit Technology Climates parameter (carbon dioxide emission)
Chance constraint method
Model
Output
Min environment hazard Max energy received Meet the expectation profit for Firm
Technology capacity planning Optimal energy produced Trade-off between maximize energy and minimize CO2
Electricity generation strategy
GA, NSGA II
Figure 1. The proposed framework of optimal energy adoption and production model 2. Literature review Electricity generation is a capital- intensive investment with long operating period (Kaygusuz, 2012). Right investment related to electricity generation should be carefully inspected (Jamasb, et al., 2017). The emission of toxic material, such as CO2, is unavoidable by some electricity generation portfolios, resulting excessive CO2 and an estimate of rising global temperature by 1.3o C in 2060 (Davis, et al., 2010). To deal with this issue, several researches proposed the ways to protect the environment in terms of controlling CO2 emission by capturing its sequestration from electricity generation plants (e.g., Gao, et al., 2016; Grubb, et al., 2015). Others methods reserved energy loss in the case of low demand, which reduces the amount of CO2 emission from 5
electricity generation (e.g., Steffen, 2012; Succar & Williams, 2011; Wang & Qie, 2018) . Some studies focused on measuring the carbon footprint generated from different regions to design the strategies that can be devised to reduce CO2, e.g., technology development, environment protection regulation and others (Mahmoudi & Rasti-Barzoki, 2018; Hu, et al., 2016; Urata, et al., 2017; Zha, et al., 2016). Only limited studies addressed strategic methods to minimize CO2, while considering revenue optimization. Taking energy modeling for example, Shrouf, et al. (2014) applies genetic algorithm (GA) to determine the optimal production scheduling of single machine to minimize the cost of energy consumption, and to reduce CO2 from power generator sites. Wang, et al. (2008) proposed a resource portfolio planning model using GA to optimize profit, but environmental factor is ignored. Although previous studies have provided a number of solutions related to environmental protection, energy storage and production planning, the link between them is still underresearched. Further, few researches engages in multiple objectives, e.g., maximizing the amount of energy produced and minimizing the environment impact issue simultaneously. The agreement between energy generation firms and consumer communities remains to be resolved. 3. Problem formulation This paper proposes a solution to compromise electricity generation by reducing the total CO2 emission. We assume the proportion of electricity generated from various resources such as oil, gas, and wind, is first determined by the government to fulfill the community demand. Nine different electricity generation plants are available. Details of the electricity demand is shown in Appendix 1. 6
3.1 Modelling Each electricity generation plant owns raw material type to produce electricity. The materials are presented as illustrated in Table 1. Table 1. Electricity produced from various options t=1 t=2
Gasoline Petrol
t=4 t=5
t=3
Oil
t=6
Coal t=7 Hydrogen t=8 fuel Diesel t=9
Wind power Solar power Nuclear power
This study will handle three different perspectives from electricity generation plant, electricity consumption community, and government. Each of them has their own objective, which may conflict with each other. Environment protection is an important issue which the government is interested in. Plants want to maximize their profit, while the community focuses on the benefit of receiving more energy. In the present research, multiple periods of time have been processed in the experiments with the stochastic demand in energy, the change of raw material cost and the variation in production strategy. Results will be the optimal strategy for each stakeholder. The model is illustrated in Figure 2. The electricity generators are defined by using specific raw materials as stated in Table 1 to produce energy. The project will be implemented through multiple periods with fixing initial resources. Demand is assumed to be followed by a normal distribution. The plant will have their own electricity generators to produce energy. For example, electricity from gas was produced in the gas plant by using gas generators.
7
. Community
Make survey for electricity demand (MGW)
Delivering electricity (MGW)
gas
oil
diesel
Gas, petrol
coal
hydrogen
wind
sun
nuclear
Feed back the demand (MGW)
Objective perspective Plant: max profit Community: max power received Government: min CO2 emission
classified Electricity demand (MGW) to various option based on policy Gas, oil ,diesel, petrol, coal, hydrogen, wind, sun, nuclear
Required electricity for firm (MGW)
Figure 2: A model illustration Notation for indexes is as follows. 𝑝: Index of period (p=1, 2, 3,…, P) 𝑚: Index of machines (m=1, 2, 3,…, M) 𝑡: Index of electricity produced from resource t (t=1, 2, 3,…, T) Notation for decision variables is as follows. 𝑄𝑝,𝑚,𝑡: Amount of electricity from resource t produced by electricity generator m in period p. 𝐾𝑚: Number of main electricity generator type m in each period. The electricity generator will be kept in all period.
8
Notation for parameters is as follows. 𝑐𝑚,𝑡: Parameter to indicate that main electricity generator m can produce energy from resource t or not. 𝑐𝑚,𝑡 = {0,1}. 𝑟𝑚,𝑡: Theoretical throughput of electricity from resource t manufactured by electricity generator type m. 𝑤𝑝,𝑚:Working hours of main electricity generator m in period p. 𝑦𝑝,𝑚: Target utilization of main electricity generator m in period p. 𝑀𝑇𝑆: Make-to-stock. MTO: make-to-order. 𝑗𝑝,𝑡: The unit excess production cost of electricity from resource t in period p. 𝑙𝑝,𝑡:The unit lack production cost of electricity from resource t in period p. 𝑏𝑝,𝑡: Unit profits of the electricity from resource t produced in period p. 𝑒𝑚:Unit cost of purchasing an electricity generator m. 𝑑𝑚:Unit salvage value of phasing out an electricity generator m. 𝐾0,𝑚:Number of main electricity generator m in the initial period. 𝑂𝑝,𝑡: the mean of uncertainty demands of energy t from market in period p. 𝐼𝑝: The interest rate for capacity planning and resource allocation in eight periods TCs: A threshold value of the amount of CO2 received from all producing energy from a government perspective. TPs: A threshold value of the amount of profit received from producing electricity from a firm perspective. 𝑆𝑝,𝑡: Capacity loading quantity of electricity from resource t in the end of period p. 𝑉𝑝,𝑡: Capacity loading cost of electricity from resource t in period p. 9
𝐹𝑝: Cash flow at period p 𝜃: Profit after period of running 𝑃𝑆𝐶(𝑡): CO2 produced when producing electricity from resource t Objective of energy efficiency optimization model – community perspective
[
𝑀𝑎𝑥 𝑇𝐸 =
𝑃
𝑀
]
𝑇
∑ ∑ ∑(𝑄
𝑝,𝑚,𝑡)
𝑝 = 1𝑚 = 1𝑡 = 1
(1)
Total energy objective function (TE): From the community’s perspective, they possess the interest of receiving as much energy as possible to serve their needs. The energy efficiency is formulated as the Eq. (1) illustrating the benefit received when producing energy from T type material in P period. Objective of CO2 emission optimization model- government perspective Total carbon dioxide emission objective function (𝑇𝐶𝑂2): From the nation’s point of view, they expect to limit the CO2 emission to protect the habitat. The amount of CO2 released when producing energy will be represented by the Total CO2 emission (TCO2) caused by transforming raw material (type 1 to type T) to energy in period 1 to the period P, the objective function is shown in Eq (2).
[
𝑃
𝑀
]
𝑇
𝑀𝑖𝑛 𝑇𝐶𝑂2 = ∑𝑝 = 1∑𝑚 = 1∑𝑡 = 1(𝑄𝑝,𝑚,𝑡𝑃𝑆𝐶(𝑡))
(2)
The next consideration is about the profit that a firm can earn if it generates energy under uncertain demand. From the firm’s perspective, they purchase electricity generators for the power plants to 10
produce energy and earn revenue. In our case, many types of materials to produce energy, take gas, oil or coal as examples, to meet the demand of consumers are investigated. The processing of them is very complex and affects the manufacturing capacity and Firm’s policy. In addition, the costs of shortage and excesses units of energy produced when applying production strategy need to be concerned. These costs negatively lower the firm’s profit. Furthermore, since our model includes uncertainty demand, a chance constrained method is applied to convert this stochastic factor to the deterministic before implementing the metaheuristic research (GA, NSGA II). Constraints Required number of electricity generators: The number of electricity generators need to be equal to or larger than the required one that its capacity fulfils the promised electricity needs. 𝑇
𝑐𝑚,𝑡𝑄𝑝,𝑚,𝑡
(3)
𝐾𝑚 ≥ ∑𝑡 = 1𝑟𝑚,𝑡𝑤𝑝,𝑚𝑦𝑝,𝑚 , ∀ 𝑝,𝑚
Inventory balance from net market demands: In the make to stock process, the inventory in level p will be calculated by the inventory p-1 plus the net production in period p and minus the demand from the market in period p. 𝑀
𝑆𝑝,𝑡 = 𝑆𝑝 ― 1,𝑡 +
∑𝑐
𝑚,𝑡𝑄𝑝,𝑚,𝑡
― 𝑂𝑝,𝑡 𝑡 ∈ 𝑀𝑇𝑆
(4)
𝑚=1
Production balance from net market demands: in the make to order process, the amount of electricity manufactured needs to be less than the demand from the market. That means the amount of energy in period p should be less than or equal to the market demand in period p. 11
𝑀
∑𝑐
𝑚,𝑡𝑄𝑝,𝑚,𝑡
≤ 𝑂𝑝,𝑡 𝑡 ∈ 𝑀𝑇𝑂, ∀𝑝
(5)
𝑚=1
Cost due to excess or inadequate inventory: Different inventory levels have different costs for both excess and shortage inventory and it will decrease the unit profit.
{
𝑗𝑝,𝑡𝑆𝑝,𝑡 , 𝑖𝑓 𝑆𝑝,𝑡 ≥ 0 𝑉𝑝,𝑡 = 𝑙 |𝑆 | , 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 𝑡 ∈ 𝑀𝑇𝑆 , ∀𝑝 𝑝,𝑡 𝑝,𝑡
(6)
Capital balance equation: Capital balance presents the cash flow over a period of time. The profit in period p is calculated by adding the remaining budget from the previous period (the first term in Eq. 7), the income from production profit and the money received from selling m energy (the second and third term) before subtracting the inventory cost ( the fourth term). 𝑀𝑇𝑆
𝐹𝑝 = 𝐹𝑝 ― 1(1 + 𝐼𝑝) + ∑𝑡 , ∀𝑝
𝑀
𝑀𝑇𝑂
𝑏𝑝,𝑡𝑂𝑝,𝑡 + ∑𝑚 = 1∑𝑡
𝑀𝑇𝑆
𝑏𝑝,𝑡𝑄𝑝,𝑚,𝑡, ― ∑𝑡 = 1𝑉𝑝,𝑡 (7)
Profit Objective function- Firm perspective Profits after periods of running: Profits are calculated by adding the net profits in period 1 to those in the final period (p_end), which are equivalent to the sum of the net value of the salvaged electricity generators and the residual capital in the final period. We will try to help Firm to achieve their expected profit. However, our research puts more effort into the relationship between environmental impact and energy efficiency, compared to firm’s perspective. Therefore, this objective function will be converted and always set as the constraint.
[
𝑀𝑎𝑥 𝜃 =
𝐹𝑝_𝑒𝑛𝑑 𝑃 ∏𝑝 = 1(1
+ 𝐼𝑝)
]
𝑀
― ∑𝑚 = 1(𝑒𝑚 ― 𝑑𝑚)(𝐾𝑚 ― 𝐾0,𝑚)
(8)
Where 𝜃 is a function of decision variables 𝐾𝑚, 𝑄𝑝,𝑚,𝑡, and random variable 𝑂𝑝,𝑡. 12
3.2 Model conversation by a chance constrained method In this paper, since demand is random probabilistic instead of deterministic quantities, some traditional studies have been discussed methods to solve this issue such as stochastic sampling or fuzzy techniques (Inuiguchi & Ramık, 2000; Linderoth, et al., 2006). Although these methods bring lots of advantages, some drawbacks in computing still exist. Take sampling solution for example, each sample needs to run one time to get the optimal solution. It leads to the heavy computation. Hence, we need a new and advanced model to deal with random parameters. In this case, a chance constrained method with the basic idea of transforming the stochastic problem into an equivalent deterministic is the best candidate (Rao, 2009). The general form of chance constrained method is shown below (Rao, 2009). Generally, when some of the parameters involved in the objective function and constraints vary about their mean values, a general optimization problem has to be formulated as a stochastic nonlinear programming problem. For the present purpose, we assume that all the random variables are independent and follow normal distribution. A stochastic nonlinear programming problem can be stated in standard form as Objective function: Find X which minimizes f (Y)
(9)
subject to Subject to 𝑃[𝑔𝑗(𝑌) ≥ 0] ≥ 𝑝𝑗, 𝑗 = 1,2,…,𝐽
(10)
where Y is the vector of N random variables 𝑦1,𝑦2…𝑦𝑁 and it includes the decision variables 𝑥1,𝑥2…𝑥𝑁. Further, constraint indicates that the 𝑗𝑡ℎ with 𝑔𝑗(𝑌) ≥ 0 should be equal or larger than probability of 𝑝𝑗 , where 0 ≤ 𝑝𝑗 ≤ 1. 13
By using chance constrained method, the new objective function and constraints are reformed as below Eqs. (11) and (13). The detail of transformation is referred in (Rao, 2009- page 652). Objective function: 𝐹(𝑌) = 𝑘1𝜓(𝑌) + 𝑘2𝜎𝜓
(11)
2
( │)
∂𝑓 𝑁 ∑𝑖 = 1 ∂𝑦 𝑖
where: 𝜓(𝑌) = 𝑓(𝑌); 𝜎𝜓 =
𝑌
𝜎2𝑦𝑖
(12)
𝑘1,𝑘2 are positive numbers: 𝑘1 ≥ 0, 𝑘2 ≥ 0. Their numerical values show the important relation of 𝜓 and 𝜎𝜓 for minimization. 𝑘2 = 0 indicates that the expected value of 𝜓 is to be minimized without considering the standard deviation of 𝜓. If 𝑘1 = 0, the variability of 𝜓 is minimized regardless of the mean of 𝜓. If 𝑘1 = 𝑘2 = 1, the means and standard deviations are also minimized. Constraints:
[ ( │) ] 2
𝑁
𝑔𝑗 ― ∅𝑗(𝑝𝑗) ∑𝑖 = 1
∂𝑔𝑗
∂𝑦𝑖
𝑌
1 2
𝜎2𝑦𝑖 ≥ 0
(13)
where 𝑔𝑗 = 𝑔𝑗(𝑌); 𝑔𝑗 = 𝑔𝑗(𝑌) and ∅𝑗(𝑝𝑗) is the value of the standard normal variable corresponding to the probability 𝑝𝑗. New equivalent deterministic objective function In our model, only the profit objective (the third one) includes the uncertainty demand. Indeed, if we apply Eq.(11) and Eq.(12) to the first-two objectives, they remain the same. However, if we apply them to the third objective, its original form is changed to the new
14
one. Our case sets
𝑘1 = 𝑘2 = 1 (further provided in section 5.1). The transformed
procedures are illustrated bellow Objective 1: Max 𝑂𝐹1 = 𝑘1𝜓(𝑂𝑝,𝑡) + 𝑘2𝜎𝜓
( )
[
(14)
𝑃
𝑀
𝑇
]
where 𝜎𝜓 = 0, 𝑘1,𝑘2 = 1, 𝜓 𝑂 = ∑𝑝 = 1∑𝑚 = 1∑𝑡 = 1(𝑄𝑝,𝑚,𝑡) 𝑝,𝑡 Objective 2: 𝑀𝑖𝑛 𝑂𝐹2 = 𝑘1𝜓(𝑂𝑝,𝑡) + 𝑘2𝜎𝜓
[
(15)
𝑃
𝑀
𝑇
]
where 𝜎𝜓 = 0,𝑘1,𝑘2 = 1, 𝜓(𝑂 ) = ∑𝑝 = 1∑𝑚 = 1∑𝑡 = 1(𝑄𝑝,𝑚,𝑡𝑃𝑆𝐶(𝑡)) 𝑝,𝑡
[
Objective 𝟑: 𝑀𝑎𝑥 𝑂𝐹3 = 𝑀𝑎𝑥 𝜃 =
𝐹𝑝𝑒𝑛𝑑 𝑃
∏𝑝 = 1(1 + 𝐼𝑝)
𝑀
]
― ∑𝑚 = 1(𝑒𝑚 ― 𝑑𝑚)(𝐾𝑚 ― 𝐾0,𝑚)
= 𝑘1𝜓(𝑂𝑝,𝑡) + 𝑘2𝜎𝜓
(16)
applying the Eq. (11) and Eq. (12) to Eq. (8). We have 𝜓(𝑌) = 𝜃(𝑂𝑝,𝑡), while 𝑉𝑎𝑟(𝜓)is defined as below 2
𝑃
𝑇
(│)
𝑉𝑎𝑟(𝜓) = 𝜎2𝜓 = ∑𝑝 = 1∑𝑡 = 1
∂𝜃
∂𝑂𝑝,𝑡
𝜎2𝑂𝑝,𝑡
(17)
𝑂𝑝,𝑡
where 𝜃(𝑂𝑝,𝑡) is function of decision variables 𝐾𝑚, 𝑋𝑝,𝑚,𝑧, 𝑄𝑝,𝑚,𝑡, with mean of random variable 𝑂𝑝,𝑡. The Eq. (17) is paraphrased following the traditional derivative. By applying this theory, 2
(│) ∂𝜃
∂𝑂𝑝,𝑡
𝜎2𝑂𝑝,𝑡 is converted to the new form
𝑂𝑝,𝑡
15
(│) ∂𝜃
∂𝑂𝑝,𝑡
= lim
𝜃(𝑂𝑝,𝑡 + ∆𝑂𝑝,𝑡) ― 𝜃(𝑂𝑝,𝑡)
𝑂𝑝,𝑡
(18)
∆𝑂𝑝,𝑡
∆𝑂𝑝,𝑡→0
After that, by mixing the Eq. (17) and Eq. (18) together, the new Eq. (19) is shown below 𝑃
𝑉𝑎𝑟(𝜓) = 𝜎2𝜓 =
𝑇
∑ ∑( lim
𝜃(𝑂𝑝,𝑡 + ∆𝑂𝑝,𝑡) ― 𝜃(𝑂𝑝,𝑡)
𝑝 = 1𝑡 = 1
)
∆𝑂𝑝,𝑡
∆𝑂𝑝,𝑡→0
2
𝜎2𝑂𝑝,𝑡
(19)
Finally, if we choose the very small ∆𝑂𝑝,𝑡. Eq. (19) becomes 𝑃
𝑉𝑎𝑟(𝜓) =
𝜎2𝜓
=
𝑇
𝜃(𝑂𝑝,𝑡 + ∆𝑂𝑝,𝑡) ― 𝜃(𝑂𝑝,𝑡)
∑ ∑(
)
∆𝑂𝑝,𝑡
𝑝 = 1𝑡 = 1
2
𝜎2𝑂𝑝,𝑡
(20)
Since Eq. (20) is easily calculated, the final objective function can be depicted as Eq. (21) 𝑶𝑭𝟑 = 𝒌𝟏𝜃(𝑂𝑝,𝑡) + 𝒌𝟐 𝑉𝑎𝑟(𝜓) = 𝒌𝟏𝜃(𝑂𝑝,𝑡) + 𝑘2𝜎𝜓
( 21)
New equivalent deterministic constraints In constraint model, only Eq. (5) includes uncertainty variable (𝑂𝑝,𝑡), Hence, if we apply Eq. (13) to other constraints, all of them remain the same except Eq. (5). The new form is shown in Eq. (22)
[ ( │) ] 2
∑𝐶
𝑂𝑝,𝑡 ―
𝑝 𝑀𝑇𝑂
𝑚,𝑡𝑄𝑝,𝑚,𝑡
― ∅𝑗(𝑝𝑗)
𝑝 = 1𝑡 = 1
𝑚∈𝑀
[
𝑚,𝑡𝑄𝑝,𝑚,𝑡
∂𝐸𝑞 (5) ∂𝑂𝑝,𝑡
( │) ] 2
𝑝 𝑀𝑇𝑂 Since ∅𝑗(𝑝𝑗) ∑𝑝 = 1∑𝑡 = 1
∑𝐶
∑∑
∂𝐸𝑞 (5) ∂𝑂𝑝,𝑡
1 2
𝜎2𝑂𝑝,𝑡 ≥ 0
(22)
𝑂𝑝,𝑡
1 2
𝜎2𝑂𝑝,𝑡 = ∅𝑗(𝑝𝑗)𝜎𝑂𝑝,𝑡. Then Eq. (5) is reduced to 𝐸𝑞.(23)
𝑂𝑝,𝑡
≤ 𝑂𝑝,𝑡 ― ∅𝑗(𝑝𝑗)𝜎𝑂𝑝,𝑡
𝑡 ∈ 𝑀𝑇𝑂, ∀𝑝
𝑚∈𝑀
16
(23)
Final equivalent deterministic multi-objective function and constraints for easy calculation In the first experiment, Environmental score and expectation profit are given. Because of the decreasing tendency of CO2 emission from government and increasing profit from Firm, the left hand side of Eq. (15) and Eq. (21) should be smaller than and larger than the given values, respectively. Then applying GA algorithms, energy for community has been generated. Clearly, the electricity generation process should satisfy the limited CO2 emission policy and guarantee their expected revenue. To be more specific, the new optimal energy model is Maximize Eq. (14) Subject to: Eq. (3), (15), (21), (23) where Eqs. (15), (21) are 𝑃
𝑇𝐶𝑂2 =
𝑀
𝑇
∑ ∑ ∑(𝑄
𝑝,𝑚,𝑡𝑃𝑆𝐶(𝑡))
≤ 𝑇𝐶𝑠
𝑝 = 1𝑚 = 1𝑡 = 1
k1𝜃(𝑂𝑝,𝑡) + 𝑘2𝜎𝜓 ≥ 𝑇𝑃𝑠
In the second experiment, we will show another way to solve the multi objective optimization by NSGA II, this method is based on the Pareto frontier analysis to find the optimal set of solutions with details illustrated in the section 4.2 . As for the programming, to accelerate the computation time, we will firstly check the energy producing ability of each electricity generator 𝑐𝑚,𝑡. When 𝑐𝑚,𝑡 = 0, that means the power plant cannot produce this type of energy and 𝑄𝑝,𝑚,𝑡 can be set at zeros. At this time, we will check the value of 𝐾𝑚 . to ensure that the Eq. (3) is always satisfied . Furthermore, for Eq. (4) and Eq. (6), 𝑆𝑝,𝑡 and 𝑉𝑝,𝑡 can be directly computed from values of 𝑄𝑝,𝑚,𝑡 . These 17
values will be put in the Eq. (7). This step can reduce lots of computation quantity and speed up the algorithms solving. 4. Solution approach Owing the non-linear complexity and multiple-objective property, the addressed did not follow a deterministic solution method. Instead, GA-based metaheuristic is adopted. The proposed GA has been justified by previous literatures such as Wang et al. (2007) and Wang et al. (2008). To execute the present model with multiple objective functions, two approaching methods are conducted: given the expected amount of CO2 defined by government or expected profit defined by plants, using the proposed GA to solve the other objective. In addition, we use a non-sorting genetic algorithm (NSGAII) to develop a Pareto frontier to present the trade-off between CO2 and energy generated. 4.1 Solving single objective by genetic algorithm The initial electricity generation portfolio is randomly created and defined as population P1. Then, in the selection stage, the GA selects good offspring on the basis of energy received before mixing the solutions to create population P2 in the crossover stage. Finally, potential chromosomes are used to enhance the offspring and make it better than the parents
18
in the mutation stage. The GA algorithm continues the loop until a stopping criterion, as the maximum of running time or generations is approached (Figure 3).
Selection Create the initial solutions (Km,Qp,m,t)
Mutation
Choosing the good solutions based on energy score
Combine the solutions together to form new population
Crossover
Stopping criteria = false Stopping criteria
Add potential value to ensure the next population is better than older
Stopping criteria = true Record the best solution
Figure 3: Single objective optimization based computation procedure 4.2 Solving multi-objective by non-sorting genetic algorithm Multi-objective optimization has many feasible solutions instead of one in the single objective optimization. The framework of our computational procedure is adopted from NSGA II (Deb, et al., 2002) and is shown in Figure 4.
The offspring Qt size N is firstly produced by the parent Pt size N. Then, the combination between Qt and Pt is processed and population Pt with size 2N has been created. Afterwards, non-dominated Pareto set (F1, F2, Fm) is formed by ranking the population Pt following the objectives scores before using crowding sorting method to create the new population Pt+1 (Deb, et al., 2002). After ranking the population, one will check the population size of the new generation, if the population size F1 is smaller than the population size N, the 19
algorithm chooses all the members of F1 for the next population, which is similar to the next-best population F2. If F1 + F2 is still smaller than N, all the members of F2 are fulfilled in the next population.
Report the optimal Pareto trade off soluion Yes
Generate random population Pt size N ( electricity portfolio solution)
Stoping criteria
No
Selection Genetic operators
Mutation
Non optimal-Pareto frontier and next generation population
Crossover Non-dominated sorting based on TE and TCO2 score Creating Offspring population Qt Size N
Creating population Pt size 2N by combing Qt and Pt
NSGA II operators
Crowding distance
Figure 4: The proposed computational procedure for multi-objective optimization Once the population is larger than N, the crowding sorting method calculates the crowding distance to decide which offspring should be kept in the next generation (Deb, et al., 2002). A longer distance corresponds to a higher chance of survival for further use. Take F3 for example, once the sum of F1+F2+F3 is larger than N, this method will reduce the quantity of population to ensure that the size of next generation Pt+1 is N. In the next step, the member in the population Pt+1 is used for selection, mutation and cross-over to create Qt+1 and the loop is continued until the termination condition is reached. The above-mentioned procedure is implemented in our model. The initial electricity population portfolio is created. Then, mutation, selection, and crossover are applied to create the size of other electricity generation portfolios with size N. Afterwards, these 20
solutions are mixed together to form next-population size 2N. Next, The size of Pt+1 must be equal to N, and the crowding distance is used. The loop will be repeated until the stopping criteria is reached and the non-dominated set Pareto is recorded. 5. The experiment Firstly, GA is applied to optimize Eq. (14) and gives the electricity generation portfolio as well as the amount of electricity produced. Then, to illustrate the trade-off between maximizing electricity generation and minimizing CO2 emission, we use NSGA II to achieve Pareto optimality. These issues are discussed in section 4.1 and 4.2 respectively. 5.1 Optimal electricity generation given total allowance of CO2 and marginal profit The algorithm is implemented in Matlab. The algorithmic parameters are set for GA as follows: 200 for population size, 100 for generation size 0.9 and 0.01 for rates of crossover and mutation, respectively. All experiments are run on a personal computer with Intel Core i5-5200GHz with 12 GB of RAM. Moreover, for the termination criteria, the time limit for running is 14,000s. The initial data are shown in Appendix 1 and 2. It contains 9 types of electricity generators, located in different plants to produce electricity. The quantity of electricity generators is flexible based on the production strategy of the plant. The interest rate 𝐼𝑝 = 1.02. The working hours of electricity generator m in period p (𝑤𝑝,𝑚) and target utilization of main electricity generator m in period p( 𝑦𝑝,𝑚) are set to 1,900 and 0.8, respectively. At the same time, the unit excess production cost of electricity from resource t in period p (𝑗𝑝,𝑡), and the unit lack production cost of electricity from resource t in period p (𝑙𝑝,𝑡) account for 10% and 20% from unit profits of electricity from resource t produced in period p (bp,t) 21
The electricity demand from different energy resources follows a normal distribution with the standard deviation 𝜎𝑂𝑝,𝑡 = 7,000. The mean is listed in the appendix 1 (𝑂𝑝,𝑡). Demands are randomly sampled from the abovementioned normal distribution and verified again by a goodness-of-fit test. These numbers presented as the average demand of the energy from different resources in each period of time. The probability of satisfied constraints is set to 𝑝𝑗 = 95%, which leads to the probability ∅𝑗(𝑝𝑗) = 1.645. By referring to (Rao, 2009), the value of probability is found as ∅𝑗(𝑝𝑗) = 1.645. Finally, (𝑘1 = 𝑘2 = 1) is chosen to present the equal priority for the maximization of the mean and the minimization of the standard deviation. The optimal electricity for community is depicted in Figure 5. This figure presents the fitness evolution of the mean electricity and the optimal amount of electricity produced. The mean fitness represents the average fitness value in each GA generation, while the best fitness shows the best function value. To be more specific, by giving the expected value of TCs and TPs equal to 400,000,000 and $100,000,000, respectively, the optimal energy 1,974,500 MGW is generated. The detail of electricity generation portfolio is shown in Table 2.
22
Figure 5. Performance convergence of GA (given that expected TCO2 is 400,000,000, TPs is $100,000,000, the optimal energy is 1,974,500 MGW) Table 2: Solution of the example case (a) Amount of electricity (MGW) produced by plants, 𝑄𝑝,𝑚,𝑡 Q(:,:,.) Period 1 2 3 4 5 6 7 8
Plant 1 44216 40108 44116 25078 33502 38621 35386 38291
Plant 2 41226 44320 41190 39530 20160 29350 28163 44136
Plant 3 1498 34522 40446 43199 3519 3958 23972 32036
Plant 4 44221 41403 22094 33120 22451 44138 35142 42521
Plant 5 25068 44747 20039 21426 17036 34739 41053 32207
Plant 6 41938 1300 29173 35099 27216 28262 31938 3872
Plant 7 17794 17964 15927 17916 14489 16489 17761 17374
Plant 8 18785 15397 19081 18134 16904 17631 20372 14814
Plant 9 23966 20579 23686 21980 23082 22150 23722 23763
(b) Quantity of electricity generators in plants (𝐾𝑚) (c) Quantity of in-house energy generator Plant 1
Plant 2
Plant 3
Plant 4
Plant 5
23
Plant 6
Plant 7
Plant 8
Plant 9
7
7
5
6
7
5
6
6
6
5.2 Trade-off between the energy received and TCO2 for a nation The NSGA II is utilized to tradeoff between two objectives as shown in Eqs. (14) and (15). The parameter settings and constraints are the same with those in section 5.1. To be more specific, the key issue in our model is to resolve conflict objectives between environment impact and energy efficiency when deploying multiple-energy resource. Therefore, profit objective in this case has been considered as the second priority one and set in the constraint. However, the two-first trade-off priority objectives shown in Pareto chart should satisfy the expected profit defined by the concern Eq. (21). From the perspective of community: Objective 1: Maximize the energy generaton efficiency, Eq. (14) 𝑀𝑎𝑥 𝑂𝐹1 = 𝑘1𝜓(𝑂𝑝,𝑡) + 𝑘2𝜎𝜓
( )
[
𝑃
𝑀
]
𝑇
where 𝜎𝜓 = 0, 𝑘1,𝑘2 = 1, 𝜓 𝑂 = 𝑇𝐸 = ∑𝑝 = 1∑𝑚 = 1∑𝑡 = 1(𝑄𝑝,𝑚,𝑡) 𝑝,𝑡 From the perspective of government: Objective 2: Minimize the TCO2 emission, Eq. (15), 𝑀𝑖𝑛 𝑂𝐹2 = 𝑘1𝜓(𝑂𝑝,𝑡) + 𝑘2𝜎𝜓
( )
[
𝑃
𝑀
𝑇
]
where 𝜎𝜓 = 0,𝑘1,𝑘2 = 1, 𝜓 𝑂 = 𝑇𝐶𝑂2 = ∑𝑝 = 1∑𝑚 = 1∑𝑡 = 1(𝑄𝑝,𝑚,𝑡𝑃𝑆𝐶(𝑡)) 𝑝,𝑡 Subject to: Eq. (3), Eq. (21) and Eq. (23), 𝑇
𝑐𝑚,𝑡𝑄𝑝,𝑚,𝑡
𝐾𝑚 ≥ ∑𝑡 = 1𝑟𝑚,𝑡𝑤𝑝,𝑚𝑦𝑝,𝑚 , ∀ 𝑝,𝑚, 24
k1𝜃(𝑂𝑝,𝑡) + 𝑘2𝜎𝜓 ≥ 𝑇𝑃𝑠
∑𝐶
𝑚,𝑡𝑄𝑝,𝑚,𝑡
≤ 𝑂𝑝,𝑡 ― ∅𝑗(𝑝𝑗)𝜎𝑂𝑝,𝑡
𝑚∈𝑀
After running the NSGA II algorithms, the seventy optimal results are shown in Figure 6. Each point illustrates the trade-off feasible solution for the community and government when producing energy. As discussed, the more CO2 emitted will let the energy increase significantly, but it also bring negative effects to the environment. The Figure shows that based on the stakeholder’s perspective, the optimal solution can be obtained through their agreements. It indicates that if government wants to increase their energy, the less rigid policy to protect the environment must be accepted.
Figure 6: The sensitivity analysis between the energy producton and CO2 emission
25
6. Conclusion This study proposed a stochastic model to allocate various electricity generators for the community energy usage. Uncertainty demand was considered. To efficiently produce energy, two types of production strategy, make-to-stock and make-to-order policies, are considered. This study presented a solution to trade-off between the energy efficiency produced and the environment hazards caused. After using the proposed algorithm to solve the problem, our paper shows two results, which balance the perspectives of government, firm and community. The first result showed the optimal energy for community (1,974,500 MGW) given specific threshold of the amount of CO2 from a government perspective and threshold of the amount of profit from a firm perspective. (TCs=400,000,00) and (TPs=$100,000,000). Further, the study presented a multi-objective optimization to give alternatives for different stakeholders, as indicated in Figure 6. Future research can extend to several directions. More uncertain parameters can be investigated, such as the reliability of the stochastic electricity generator and their yield rates. Secondly, the patterns of stochastic demands, such as discrete distributions, mixed discrete/continuous distributions, and various joint distributions, can be further investigated. Thirdly, one can consider energy distribution, for example, producing mass energy to supply for communities located in different areas. In this case, many variables are needed to be concerned, e.g., energy production, storage and delivery costs. In addition, the community also has the satisfaction level which flexibly changes during the quality of service. The late energy delivery will lead to the increasing of customer loyalty loss.
26
Further, advanced model can be built up to decide the location of power plants and production strategies to satisfy different stakeholders. Appendix Appendix 1: The data set of the benchmark example 𝑐𝑚,𝑡: Parameter to indicate that, electricity generator m can produce energy from material t or not t=1 t=2 t=3 t=4 t=5 t=6 t=7 t=8 t=9 m=1 1 0 0 0 0 0 0 0 0 m=2 0 1 0 0 0 0 0 0 0 m=3 0 0 1 0 0 0 0 0 0 m=4 0 0 0 1 0 0 0 0 0 m=5 0 0 0 0 1 0 0 0 0 m=6 0 0 0 0 0 1 0 0 0 m=7 0 0 0 0 0 0 1 0 0 m=8 0 0 0 0 0 0 0 1 0 m=9 0 0 0 0 0 0 0 0 1 𝒓𝒎,𝒕: Theoretical throughput of energy from material t manufactured by main electricity generator type m t=1 t=2 t=3 t=4 t=5 t=6 t=7 t=8 t=9 8 8 8 8 8 8 8 8 8 m=1 5 5 5 5 5 5 5 5 5 m=2 7 7 7 7 7 7 7 7 7 m=3 8 8 8 8 8 8 8 8 8 m=4 5 5 5 5 5 5 5 5 5 m=5 7 7 7 7 7 7 7 7 7 m=6 8 8 8 8 8 8 8 8 8 m=7 5 5 5 5 5 5 5 5 5 m=8 7 7 7 7 7 7 7 7 7 m=9 𝑂𝑝,𝑡: market demand (mean) t=1 t=2 t=3 t=4 t=5 t=6 t=7 t=8 t=9 p=1 33100 30240 35500 37700 33240 29500 29500 32240 35500 p=2 33100 30240 35500 37700 33240 29500 29500 32240 35500 p=3 33100 30240 35500 37700 33240 29500 29500 32240 35500 p=4 33100 30240 35500 37700 33240 29500 29500 32240 35500 p=5 33100 30240 35500 37700 33240 29500 29500 32240 35500 p=6 33100 30240 35500 37700 33240 29500 29500 32240 35500 p=7 33100 30240 35500 37700 33240 29500 29500 32240 35500 p=8 33100 30240 35500 37700 33240 29500 29500 32240 35500 𝑏𝑝,𝑡: Profit for each period 27
t=1 t=2 t=3 t=4 t=5 t=6 p=1 200 180 150 200 180 150 p=2 190 170 140 190 170 140 p=3 180 160 130 180 160 130 p=4 200 180 150 200 180 150 p=5 190 170 140 190 170 140 p=6 180 160 130 180 160 130 p=7 200 180 150 200 180 150 p=8 190 170 140 190 170 140 𝑒𝑚:Unit cost of purchasing a main electricity generator type m m=1 3900000
m=2 1350000
m=3 2840000
m=4 3900000
m=5 1350000
m=6 2840000
t=7 200 190 180 200 190 180 200 190
t=8 180 170 160 180 170 160 180 170
t=9 150 140 130 150 140 130 150 140
m=7 3900000
m=8 1350000
m=9 2840000
m=8 650000
m=9 980000
𝑑𝑚:Unit salvage value of phasing out a main electricity generator type m m=1 1300000
m=2 650000
m=3 980000
m=4 1300000
m=5 650000
F0=20000000 S0=[-3113,0,0,0,0,0,0,0,0] Others K0m =[2 1 1 2 1 1 2 1 1]
28
m=6 980000
m=7 1300000
Appendix 2: Production policy and CO2 emission
Type of energy
Type of
CO2 emission
manufacturing
Kg/MGW
Gasoline
MTS
250
Petrol
MTS
230
Oil
MTS
280
Coal
MTS
260
Kerosene
MTS
260
Diesel
MTS
270
Wind
MTO
40
Solar
MTO
40
Nuclear
MTO
40
Source: * (Quaschning, 2015) * J .W.Storm van Leeuwen (2008, may 25) retrieved from timeforchange.org
29
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S0360-8352(19)30580-7 https://doi.org/10.1016/j.cie.2019.106111 CAIE 106111
To appear in:
Computers & Industrial Engineering
Received Date: Revised Date: Accepted Date:
10 March 2019 18 August 2019 3 October 2019
Please cite this article as: Wang, K-J., Dao, L.D., Resolving conflict objectives between environment impact and energy efficiency - an optimization modeling on multiple-energy deployment, Computers & Industrial Engineering (2019), doi: https://doi.org/10.1016/j.cie.2019.106111
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Resolving conflict objectives between environment impact and energy efficiency - an optimization modeling on multiple-energy deployment Kung-Jeng Wang (Corresponding author) and Le Duc Dao Department of Industrial Management National Taiwan University of Science and Technology Taipei 106, Taiwan, ROC [email protected], [email protected] Highlights:
Developing electricity portfolio to tradeoff electricity generation and CO2 emission.
Designing a non-dominated sorting genetic solution algorithm for multiple objectives.
Presenting the optimal capacity plan for electricity generation efficiency.
Resolving conflict objectives between environment impact and energy efficiency - an optimization modeling on multiple-energy deployment
Abstract Energy consumption increases dramatically due to economic development, leading to the raising of toxic materials such as CO2 during electricity generation process. This study aims at solving the electricity generation portfolio issue to maximize electricity generation while minimizing the CO2 emission to protect the environment. In this research, multiple types of power plants to produce electricity, such as by gas, coal, solar, are alternatives for electricity generation portfolio. Especially, uncertainty in electricity demand is included and dealt by a stochastic chance constrained method. Further. The proposed model is solved by a non-dominated sorting genetic algorithm for multiple objectives. The result 1
presents the optimal capacity portfolio plan for electricity generation and suggests a tradeoff decision between conflicting goals to balance electricity generation efficiency and environmental protection. Keyword: Energy conservation; environmental protection; capacity portfolio planning; stochastic programming.
2
Resolving conflict objectives between environment impact and energy efficiency - an optimization modeling on multiple-energy deployment 1. Introduction Energy consumption is an indicator of economic development (Huang, et al., 2017; Surendra, et al., 2014; Wang, et al., 2018) and closely associated with high-quality living standard. The electricity demand prediction for the next 25-30 years has an upward tendency and mostly comes from developing nations, and this situation in turn presents a serious energy demand (Wolfram, et al., 2012; Kaplan & Aladağ, 2016; Mehrara, 2007). However, the objectives of energy, economy, and environment are proved conflicting (Feng, et al., 2016). While producing electricity, natural resources are not only mined but CO2 is emitted, causing severe environment impacts (Peters, et al., 2012). For example, in many countries, an increasing in the sea levels or strong storm annually destroys crops, houses and leads people to poverty. In addition, many dangerous viruses originated from polluted air, e.g., Zika or SARS threaten the lives of living creatures (Mendelsohn, et al., 2016; O'Neill, et al., 2017) To solve the environmental issues caused by generating electricity, several actions have been done, but they have certain limitations, e.g., using renewable resources to partially replace traditional ones, consequently, reducing environmental impacts (Grubb, et al., 2015; Zografidou, et al., 2016). It is noted that, although clean resources possess advantages, compared to traditional resources, they cannot fully meet demands with cost-efficiency. The major source for electricity up to now in various countries still comes from nonrenewable resources. For instance, in Mexico, natural gas and coal are the major fuels of primary electricity generation. Gas accounted for 40% of the total amount of electricity 3
generated, followed by oil (45%) and coal (8%). The use of renewable energy is still little (Pérez-Denicia, et al., 2017). In addition, reducing pollution by adopting appropriate energy options and optimizing their production process becomes critical (Chevallier & Goutte, 2017; Zhang, et al., 2016). Actually, to deal with the relationship between environmental impacts and electricity generation efficiency, the amounts of renewable and non-renewable energy should be balanced. Such proportions can be handled by establishing the electricity reform agreement (e.g., the electricity generation plan) between energy consumer community and producer. However, this raises issues from concerned parties, e.g., the impact to the power generation firm’s profit and motivation to green power generation need to be addressed due to costefficiency. To conclude, to resolve conflicting objectives between environmental impacts and energy efficiency is an issue that needs to further investigate. To contribute to this research area, this study builds a quantitative model considering how to maximize the volume of electricity produced while minimizing the amount of CO2 emitted. In detail, multiple approaches (further provided in section 4) will be conducted to propose a electricity generation portfolio dealing with chaotic demands. The framework of our research is presented in Figure 1. The rest of the article is organized as follows. Section 2 reviews related literatures. The problem is modelled in Section 3. Section 4 develops the solution approach. Our experiments are conducted in Section 5. Finally, Section 6 gives some conclusion and future research.
4
Firm expectation profit
Input
Stochastic Energy demand Energy Profit Technology Climates parameter (carbon dioxide emission)
Chance constraint method
Model
Output
Min environment hazard Max energy received Meet the expectation profit for Firm
Technology capacity planning Optimal energy produced Trade-off between maximize energy and minimize CO2
Electricity generation strategy
GA, NSGA II
Figure 1. The proposed framework of optimal energy adoption and production model 2. Literature review Electricity generation is a capital- intensive investment with long operating period (Kaygusuz, 2012). Right investment related to electricity generation should be carefully inspected (Jamasb, et al., 2017). The emission of toxic material, such as CO2, is unavoidable by some electricity generation portfolios, resulting excessive CO2 and an estimate of rising global temperature by 1.3o C in 2060 (Davis, et al., 2010). To deal with this issue, several researches proposed the ways to protect the environment in terms of controlling CO2 emission by capturing its sequestration from electricity generation plants (e.g., Gao, et al., 2016; Grubb, et al., 2015). Others methods reserved energy loss in the case of low demand, which reduces the amount of CO2 emission from 5
electricity generation (e.g., Steffen, 2012; Succar & Williams, 2011; Wang & Qie, 2018) . Some studies focused on measuring the carbon footprint generated from different regions to design the strategies that can be devised to reduce CO2, e.g., technology development, environment protection regulation and others (Mahmoudi & Rasti-Barzoki, 2018; Hu, et al., 2016; Urata, et al., 2017; Zha, et al., 2016). Only limited studies addressed strategic methods to minimize CO2, while considering revenue optimization. Taking energy modeling for example, Shrouf, et al. (2014) applies genetic algorithm (GA) to determine the optimal production scheduling of single machine to minimize the cost of energy consumption, and to reduce CO2 from power generator sites. Wang, et al. (2008) proposed a resource portfolio planning model using GA to optimize profit, but environmental factor is ignored. Although previous studies have provided a number of solutions related to environmental protection, energy storage and production planning, the link between them is still underresearched. Further, few researches engages in multiple objectives, e.g., maximizing the amount of energy produced and minimizing the environment impact issue simultaneously. The agreement between energy generation firms and consumer communities remains to be resolved. 3. Problem formulation This paper proposes a solution to compromise electricity generation by reducing the total CO2 emission. We assume the proportion of electricity generated from various resources such as oil, gas, and wind, is first determined by the government to fulfill the community demand. Nine different electricity generation plants are available. Details of the electricity demand is shown in Appendix 1. 6
3.1 Modelling Each electricity generation plant owns raw material type to produce electricity. The materials are presented as illustrated in Table 1. Table 1. Electricity produced from various options t=1 t=2
Gasoline Petrol
t=4 t=5
t=3
Oil
t=6
Coal t=7 Hydrogen t=8 fuel Diesel t=9
Wind power Solar power Nuclear power
This study will handle three different perspectives from electricity generation plant, electricity consumption community, and government. Each of them has their own objective, which may conflict with each other. Environment protection is an important issue which the government is interested in. Plants want to maximize their profit, while the community focuses on the benefit of receiving more energy. In the present research, multiple periods of time have been processed in the experiments with the stochastic demand in energy, the change of raw material cost and the variation in production strategy. Results will be the optimal strategy for each stakeholder. The model is illustrated in Figure 2. The electricity generators are defined by using specific raw materials as stated in Table 1 to produce energy. The project will be implemented through multiple periods with fixing initial resources. Demand is assumed to be followed by a normal distribution. The plant will have their own electricity generators to produce energy. For example, electricity from gas was produced in the gas plant by using gas generators.
7
. Community
Make survey for electricity demand (MGW)
Delivering electricity (MGW)
gas
oil
diesel
Gas, petrol
coal
hydrogen
wind
sun
nuclear
Feed back the demand (MGW)
Objective perspective Plant: max profit Community: max power received Government: min CO2 emission
classified Electricity demand (MGW) to various option based on policy Gas, oil ,diesel, petrol, coal, hydrogen, wind, sun, nuclear
Required electricity for firm (MGW)
Figure 2: A model illustration Notation for indexes is as follows. 𝑝: Index of period (p=1, 2, 3,…, P) 𝑚: Index of machines (m=1, 2, 3,…, M) 𝑡: Index of electricity produced from resource t (t=1, 2, 3,…, T) Notation for decision variables is as follows. 𝑄𝑝,𝑚,𝑡: Amount of electricity from resource t produced by electricity generator m in period p. 𝐾𝑚: Number of main electricity generator type m in each period. The electricity generator will be kept in all period.
8
Notation for parameters is as follows. 𝑐𝑚,𝑡: Parameter to indicate that main electricity generator m can produce energy from resource t or not. 𝑐𝑚,𝑡 = {0,1}. 𝑟𝑚,𝑡: Theoretical throughput of electricity from resource t manufactured by electricity generator type m. 𝑤𝑝,𝑚:Working hours of main electricity generator m in period p. 𝑦𝑝,𝑚: Target utilization of main electricity generator m in period p. 𝑀𝑇𝑆: Make-to-stock. MTO: make-to-order. 𝑗𝑝,𝑡: The unit excess production cost of electricity from resource t in period p. 𝑙𝑝,𝑡:The unit lack production cost of electricity from resource t in period p. 𝑏𝑝,𝑡: Unit profits of the electricity from resource t produced in period p. 𝑒𝑚:Unit cost of purchasing an electricity generator m. 𝑑𝑚:Unit salvage value of phasing out an electricity generator m. 𝐾0,𝑚:Number of main electricity generator m in the initial period. 𝑂𝑝,𝑡: the mean of uncertainty demands of energy t from market in period p. 𝐼𝑝: The interest rate for capacity planning and resource allocation in eight periods TCs: A threshold value of the amount of CO2 received from all producing energy from a government perspective. TPs: A threshold value of the amount of profit received from producing electricity from a firm perspective. 𝑆𝑝,𝑡: Capacity loading quantity of electricity from resource t in the end of period p. 𝑉𝑝,𝑡: Capacity loading cost of electricity from resource t in period p. 9
𝐹𝑝: Cash flow at period p 𝜃: Profit after period of running 𝑃𝑆𝐶(𝑡): CO2 produced when producing electricity from resource t Objective of energy efficiency optimization model – community perspective
[
𝑀𝑎𝑥 𝑇𝐸 =
𝑃
𝑀
]
𝑇
∑ ∑ ∑(𝑄
𝑝,𝑚,𝑡)
𝑝 = 1𝑚 = 1𝑡 = 1
(1)
Total energy objective function (TE): From the community’s perspective, they possess the interest of receiving as much energy as possible to serve their needs. The energy efficiency is formulated as the Eq. (1) illustrating the benefit received when producing energy from T type material in P period. Objective of CO2 emission optimization model- government perspective Total carbon dioxide emission objective function (𝑇𝐶𝑂2): From the nation’s point of view, they expect to limit the CO2 emission to protect the habitat. The amount of CO2 released when producing energy will be represented by the Total CO2 emission (TCO2) caused by transforming raw material (type 1 to type T) to energy in period 1 to the period P, the objective function is shown in Eq (2).
[
𝑃
𝑀
]
𝑇
𝑀𝑖𝑛 𝑇𝐶𝑂2 = ∑𝑝 = 1∑𝑚 = 1∑𝑡 = 1(𝑄𝑝,𝑚,𝑡𝑃𝑆𝐶(𝑡))
(2)
The next consideration is about the profit that a firm can earn if it generates energy under uncertain demand. From the firm’s perspective, they purchase electricity generators for the power plants to 10
produce energy and earn revenue. In our case, many types of materials to produce energy, take gas, oil or coal as examples, to meet the demand of consumers are investigated. The processing of them is very complex and affects the manufacturing capacity and Firm’s policy. In addition, the costs of shortage and excesses units of energy produced when applying production strategy need to be concerned. These costs negatively lower the firm’s profit. Furthermore, since our model includes uncertainty demand, a chance constrained method is applied to convert this stochastic factor to the deterministic before implementing the metaheuristic research (GA, NSGA II). Constraints Required number of electricity generators: The number of electricity generators need to be equal to or larger than the required one that its capacity fulfils the promised electricity needs. 𝑇
𝑐𝑚,𝑡𝑄𝑝,𝑚,𝑡
(3)
𝐾𝑚 ≥ ∑𝑡 = 1𝑟𝑚,𝑡𝑤𝑝,𝑚𝑦𝑝,𝑚 , ∀ 𝑝,𝑚
Inventory balance from net market demands: In the make to stock process, the inventory in level p will be calculated by the inventory p-1 plus the net production in period p and minus the demand from the market in period p. 𝑀
𝑆𝑝,𝑡 = 𝑆𝑝 ― 1,𝑡 +
∑𝑐
𝑚,𝑡𝑄𝑝,𝑚,𝑡
― 𝑂𝑝,𝑡 𝑡 ∈ 𝑀𝑇𝑆
(4)
𝑚=1
Production balance from net market demands: in the make to order process, the amount of electricity manufactured needs to be less than the demand from the market. That means the amount of energy in period p should be less than or equal to the market demand in period p. 11
𝑀
∑𝑐
𝑚,𝑡𝑄𝑝,𝑚,𝑡
≤ 𝑂𝑝,𝑡 𝑡 ∈ 𝑀𝑇𝑂, ∀𝑝
(5)
𝑚=1
Cost due to excess or inadequate inventory: Different inventory levels have different costs for both excess and shortage inventory and it will decrease the unit profit.
{
𝑗𝑝,𝑡𝑆𝑝,𝑡 , 𝑖𝑓 𝑆𝑝,𝑡 ≥ 0 𝑉𝑝,𝑡 = 𝑙 |𝑆 | , 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒 𝑡 ∈ 𝑀𝑇𝑆 , ∀𝑝 𝑝,𝑡 𝑝,𝑡
(6)
Capital balance equation: Capital balance presents the cash flow over a period of time. The profit in period p is calculated by adding the remaining budget from the previous period (the first term in Eq. 7), the income from production profit and the money received from selling m energy (the second and third term) before subtracting the inventory cost ( the fourth term). 𝑀𝑇𝑆
𝐹𝑝 = 𝐹𝑝 ― 1(1 + 𝐼𝑝) + ∑𝑡 , ∀𝑝
𝑀
𝑀𝑇𝑂
𝑏𝑝,𝑡𝑂𝑝,𝑡 + ∑𝑚 = 1∑𝑡
𝑀𝑇𝑆
𝑏𝑝,𝑡𝑄𝑝,𝑚,𝑡, ― ∑𝑡 = 1𝑉𝑝,𝑡 (7)
Profit Objective function- Firm perspective Profits after periods of running: Profits are calculated by adding the net profits in period 1 to those in the final period (p_end), which are equivalent to the sum of the net value of the salvaged electricity generators and the residual capital in the final period. We will try to help Firm to achieve their expected profit. However, our research puts more effort into the relationship between environmental impact and energy efficiency, compared to firm’s perspective. Therefore, this objective function will be converted and always set as the constraint.
[
𝑀𝑎𝑥 𝜃 =
𝐹𝑝_𝑒𝑛𝑑 𝑃 ∏𝑝 = 1(1
+ 𝐼𝑝)
]
𝑀
― ∑𝑚 = 1(𝑒𝑚 ― 𝑑𝑚)(𝐾𝑚 ― 𝐾0,𝑚)
(8)
Where 𝜃 is a function of decision variables 𝐾𝑚, 𝑄𝑝,𝑚,𝑡, and random variable 𝑂𝑝,𝑡. 12
3.2 Model conversation by a chance constrained method In this paper, since demand is random probabilistic instead of deterministic quantities, some traditional studies have been discussed methods to solve this issue such as stochastic sampling or fuzzy techniques (Inuiguchi & Ramık, 2000; Linderoth, et al., 2006). Although these methods bring lots of advantages, some drawbacks in computing still exist. Take sampling solution for example, each sample needs to run one time to get the optimal solution. It leads to the heavy computation. Hence, we need a new and advanced model to deal with random parameters. In this case, a chance constrained method with the basic idea of transforming the stochastic problem into an equivalent deterministic is the best candidate (Rao, 2009). The general form of chance constrained method is shown below (Rao, 2009). Generally, when some of the parameters involved in the objective function and constraints vary about their mean values, a general optimization problem has to be formulated as a stochastic nonlinear programming problem. For the present purpose, we assume that all the random variables are independent and follow normal distribution. A stochastic nonlinear programming problem can be stated in standard form as Objective function: Find X which minimizes f (Y)
(9)
subject to Subject to 𝑃[𝑔𝑗(𝑌) ≥ 0] ≥ 𝑝𝑗, 𝑗 = 1,2,…,𝐽
(10)
where Y is the vector of N random variables 𝑦1,𝑦2…𝑦𝑁 and it includes the decision variables 𝑥1,𝑥2…𝑥𝑁. Further, constraint indicates that the 𝑗𝑡ℎ with 𝑔𝑗(𝑌) ≥ 0 should be equal or larger than probability of 𝑝𝑗 , where 0 ≤ 𝑝𝑗 ≤ 1. 13
By using chance constrained method, the new objective function and constraints are reformed as below Eqs. (11) and (13). The detail of transformation is referred in (Rao, 2009- page 652). Objective function: 𝐹(𝑌) = 𝑘1𝜓(𝑌) + 𝑘2𝜎𝜓
(11)
2
( │)
∂𝑓 𝑁 ∑𝑖 = 1 ∂𝑦 𝑖
where: 𝜓(𝑌) = 𝑓(𝑌); 𝜎𝜓 =
𝑌
𝜎2𝑦𝑖
(12)
𝑘1,𝑘2 are positive numbers: 𝑘1 ≥ 0, 𝑘2 ≥ 0. Their numerical values show the important relation of 𝜓 and 𝜎𝜓 for minimization. 𝑘2 = 0 indicates that the expected value of 𝜓 is to be minimized without considering the standard deviation of 𝜓. If 𝑘1 = 0, the variability of 𝜓 is minimized regardless of the mean of 𝜓. If 𝑘1 = 𝑘2 = 1, the means and standard deviations are also minimized. Constraints:
[ ( │) ] 2
𝑁
𝑔𝑗 ― ∅𝑗(𝑝𝑗) ∑𝑖 = 1
∂𝑔𝑗
∂𝑦𝑖
𝑌
1 2
𝜎2𝑦𝑖 ≥ 0
(13)
where 𝑔𝑗 = 𝑔𝑗(𝑌); 𝑔𝑗 = 𝑔𝑗(𝑌) and ∅𝑗(𝑝𝑗) is the value of the standard normal variable corresponding to the probability 𝑝𝑗. New equivalent deterministic objective function In our model, only the profit objective (the third one) includes the uncertainty demand. Indeed, if we apply Eq.(11) and Eq.(12) to the first-two objectives, they remain the same. However, if we apply them to the third objective, its original form is changed to the new
14
one. Our case sets
𝑘1 = 𝑘2 = 1 (further provided in section 5.1). The transformed
procedures are illustrated bellow Objective 1: Max 𝑂𝐹1 = 𝑘1𝜓(𝑂𝑝,𝑡) + 𝑘2𝜎𝜓
( )
[
(14)
𝑃
𝑀
𝑇
]
where 𝜎𝜓 = 0, 𝑘1,𝑘2 = 1, 𝜓 𝑂 = ∑𝑝 = 1∑𝑚 = 1∑𝑡 = 1(𝑄𝑝,𝑚,𝑡) 𝑝,𝑡 Objective 2: 𝑀𝑖𝑛 𝑂𝐹2 = 𝑘1𝜓(𝑂𝑝,𝑡) + 𝑘2𝜎𝜓
[
(15)
𝑃
𝑀
𝑇
]
where 𝜎𝜓 = 0,𝑘1,𝑘2 = 1, 𝜓(𝑂 ) = ∑𝑝 = 1∑𝑚 = 1∑𝑡 = 1(𝑄𝑝,𝑚,𝑡𝑃𝑆𝐶(𝑡)) 𝑝,𝑡
[
Objective 𝟑: 𝑀𝑎𝑥 𝑂𝐹3 = 𝑀𝑎𝑥 𝜃 =
𝐹𝑝𝑒𝑛𝑑 𝑃
∏𝑝 = 1(1 + 𝐼𝑝)
𝑀
]
― ∑𝑚 = 1(𝑒𝑚 ― 𝑑𝑚)(𝐾𝑚 ― 𝐾0,𝑚)
= 𝑘1𝜓(𝑂𝑝,𝑡) + 𝑘2𝜎𝜓
(16)
applying the Eq. (11) and Eq. (12) to Eq. (8). We have 𝜓(𝑌) = 𝜃(𝑂𝑝,𝑡), while 𝑉𝑎𝑟(𝜓)is defined as below 2
𝑃
𝑇
(│)
𝑉𝑎𝑟(𝜓) = 𝜎2𝜓 = ∑𝑝 = 1∑𝑡 = 1
∂𝜃
∂𝑂𝑝,𝑡
𝜎2𝑂𝑝,𝑡
(17)
𝑂𝑝,𝑡
where 𝜃(𝑂𝑝,𝑡) is function of decision variables 𝐾𝑚, 𝑋𝑝,𝑚,𝑧, 𝑄𝑝,𝑚,𝑡, with mean of random variable 𝑂𝑝,𝑡. The Eq. (17) is paraphrased following the traditional derivative. By applying this theory, 2
(│) ∂𝜃
∂𝑂𝑝,𝑡
𝜎2𝑂𝑝,𝑡 is converted to the new form
𝑂𝑝,𝑡
15
(│) ∂𝜃
∂𝑂𝑝,𝑡
= lim
𝜃(𝑂𝑝,𝑡 + ∆𝑂𝑝,𝑡) ― 𝜃(𝑂𝑝,𝑡)
𝑂𝑝,𝑡
(18)
∆𝑂𝑝,𝑡
∆𝑂𝑝,𝑡→0
After that, by mixing the Eq. (17) and Eq. (18) together, the new Eq. (19) is shown below 𝑃
𝑉𝑎𝑟(𝜓) = 𝜎2𝜓 =
𝑇
∑ ∑( lim
𝜃(𝑂𝑝,𝑡 + ∆𝑂𝑝,𝑡) ― 𝜃(𝑂𝑝,𝑡)
𝑝 = 1𝑡 = 1
)
∆𝑂𝑝,𝑡
∆𝑂𝑝,𝑡→0
2
𝜎2𝑂𝑝,𝑡
(19)
Finally, if we choose the very small ∆𝑂𝑝,𝑡. Eq. (19) becomes 𝑃
𝑉𝑎𝑟(𝜓) =
𝜎2𝜓
=
𝑇
𝜃(𝑂𝑝,𝑡 + ∆𝑂𝑝,𝑡) ― 𝜃(𝑂𝑝,𝑡)
∑ ∑(
)
∆𝑂𝑝,𝑡
𝑝 = 1𝑡 = 1
2
𝜎2𝑂𝑝,𝑡
(20)
Since Eq. (20) is easily calculated, the final objective function can be depicted as Eq. (21) 𝑶𝑭𝟑 = 𝒌𝟏𝜃(𝑂𝑝,𝑡) + 𝒌𝟐 𝑉𝑎𝑟(𝜓) = 𝒌𝟏𝜃(𝑂𝑝,𝑡) + 𝑘2𝜎𝜓
( 21)
New equivalent deterministic constraints In constraint model, only Eq. (5) includes uncertainty variable (𝑂𝑝,𝑡), Hence, if we apply Eq. (13) to other constraints, all of them remain the same except Eq. (5). The new form is shown in Eq. (22)
[ ( │) ] 2
∑𝐶
𝑂𝑝,𝑡 ―
𝑝 𝑀𝑇𝑂
𝑚,𝑡𝑄𝑝,𝑚,𝑡
― ∅𝑗(𝑝𝑗)
𝑝 = 1𝑡 = 1
𝑚∈𝑀
[
𝑚,𝑡𝑄𝑝,𝑚,𝑡
∂𝐸𝑞 (5) ∂𝑂𝑝,𝑡
( │) ] 2
𝑝 𝑀𝑇𝑂 Since ∅𝑗(𝑝𝑗) ∑𝑝 = 1∑𝑡 = 1
∑𝐶
∑∑
∂𝐸𝑞 (5) ∂𝑂𝑝,𝑡
1 2
𝜎2𝑂𝑝,𝑡 ≥ 0
(22)
𝑂𝑝,𝑡
1 2
𝜎2𝑂𝑝,𝑡 = ∅𝑗(𝑝𝑗)𝜎𝑂𝑝,𝑡. Then Eq. (5) is reduced to 𝐸𝑞.(23)
𝑂𝑝,𝑡
≤ 𝑂𝑝,𝑡 ― ∅𝑗(𝑝𝑗)𝜎𝑂𝑝,𝑡
𝑡 ∈ 𝑀𝑇𝑂, ∀𝑝
𝑚∈𝑀
16
(23)
Final equivalent deterministic multi-objective function and constraints for easy calculation In the first experiment, Environmental score and expectation profit are given. Because of the decreasing tendency of CO2 emission from government and increasing profit from Firm, the left hand side of Eq. (15) and Eq. (21) should be smaller than and larger than the given values, respectively. Then applying GA algorithms, energy for community has been generated. Clearly, the electricity generation process should satisfy the limited CO2 emission policy and guarantee their expected revenue. To be more specific, the new optimal energy model is Maximize Eq. (14) Subject to: Eq. (3), (15), (21), (23) where Eqs. (15), (21) are 𝑃
𝑇𝐶𝑂2 =
𝑀
𝑇
∑ ∑ ∑(𝑄
𝑝,𝑚,𝑡𝑃𝑆𝐶(𝑡))
≤ 𝑇𝐶𝑠
𝑝 = 1𝑚 = 1𝑡 = 1
k1𝜃(𝑂𝑝,𝑡) + 𝑘2𝜎𝜓 ≥ 𝑇𝑃𝑠
In the second experiment, we will show another way to solve the multi objective optimization by NSGA II, this method is based on the Pareto frontier analysis to find the optimal set of solutions with details illustrated in the section 4.2 . As for the programming, to accelerate the computation time, we will firstly check the energy producing ability of each electricity generator 𝑐𝑚,𝑡. When 𝑐𝑚,𝑡 = 0, that means the power plant cannot produce this type of energy and 𝑄𝑝,𝑚,𝑡 can be set at zeros. At this time, we will check the value of 𝐾𝑚 . to ensure that the Eq. (3) is always satisfied . Furthermore, for Eq. (4) and Eq. (6), 𝑆𝑝,𝑡 and 𝑉𝑝,𝑡 can be directly computed from values of 𝑄𝑝,𝑚,𝑡 . These 17
values will be put in the Eq. (7). This step can reduce lots of computation quantity and speed up the algorithms solving. 4. Solution approach Owing the non-linear complexity and multiple-objective property, the addressed did not follow a deterministic solution method. Instead, GA-based metaheuristic is adopted. The proposed GA has been justified by previous literatures such as Wang et al. (2007) and Wang et al. (2008). To execute the present model with multiple objective functions, two approaching methods are conducted: given the expected amount of CO2 defined by government or expected profit defined by plants, using the proposed GA to solve the other objective. In addition, we use a non-sorting genetic algorithm (NSGAII) to develop a Pareto frontier to present the trade-off between CO2 and energy generated. 4.1 Solving single objective by genetic algorithm The initial electricity generation portfolio is randomly created and defined as population P1. Then, in the selection stage, the GA selects good offspring on the basis of energy received before mixing the solutions to create population P2 in the crossover stage. Finally, potential chromosomes are used to enhance the offspring and make it better than the parents
18
in the mutation stage. The GA algorithm continues the loop until a stopping criterion, as the maximum of running time or generations is approached (Figure 3).
Selection Create the initial solutions (Km,Qp,m,t)
Mutation
Choosing the good solutions based on energy score
Combine the solutions together to form new population
Crossover
Stopping criteria = false Stopping criteria
Add potential value to ensure the next population is better than older
Stopping criteria = true Record the best solution
Figure 3: Single objective optimization based computation procedure 4.2 Solving multi-objective by non-sorting genetic algorithm Multi-objective optimization has many feasible solutions instead of one in the single objective optimization. The framework of our computational procedure is adopted from NSGA II (Deb, et al., 2002) and is shown in Figure 4.
The offspring Qt size N is firstly produced by the parent Pt size N. Then, the combination between Qt and Pt is processed and population Pt with size 2N has been created. Afterwards, non-dominated Pareto set (F1, F2, Fm) is formed by ranking the population Pt following the objectives scores before using crowding sorting method to create the new population Pt+1 (Deb, et al., 2002). After ranking the population, one will check the population size of the new generation, if the population size F1 is smaller than the population size N, the 19
algorithm chooses all the members of F1 for the next population, which is similar to the next-best population F2. If F1 + F2 is still smaller than N, all the members of F2 are fulfilled in the next population.
Report the optimal Pareto trade off soluion Yes
Generate random population Pt size N ( electricity portfolio solution)
Stoping criteria
No
Selection Genetic operators
Mutation
Non optimal-Pareto frontier and next generation population
Crossover Non-dominated sorting based on TE and TCO2 score Creating Offspring population Qt Size N
Creating population Pt size 2N by combing Qt and Pt
NSGA II operators
Crowding distance
Figure 4: The proposed computational procedure for multi-objective optimization Once the population is larger than N, the crowding sorting method calculates the crowding distance to decide which offspring should be kept in the next generation (Deb, et al., 2002). A longer distance corresponds to a higher chance of survival for further use. Take F3 for example, once the sum of F1+F2+F3 is larger than N, this method will reduce the quantity of population to ensure that the size of next generation Pt+1 is N. In the next step, the member in the population Pt+1 is used for selection, mutation and cross-over to create Qt+1 and the loop is continued until the termination condition is reached. The above-mentioned procedure is implemented in our model. The initial electricity population portfolio is created. Then, mutation, selection, and crossover are applied to create the size of other electricity generation portfolios with size N. Afterwards, these 20
solutions are mixed together to form next-population size 2N. Next, The size of Pt+1 must be equal to N, and the crowding distance is used. The loop will be repeated until the stopping criteria is reached and the non-dominated set Pareto is recorded. 5. The experiment Firstly, GA is applied to optimize Eq. (14) and gives the electricity generation portfolio as well as the amount of electricity produced. Then, to illustrate the trade-off between maximizing electricity generation and minimizing CO2 emission, we use NSGA II to achieve Pareto optimality. These issues are discussed in section 4.1 and 4.2 respectively. 5.1 Optimal electricity generation given total allowance of CO2 and marginal profit The algorithm is implemented in Matlab. The algorithmic parameters are set for GA as follows: 200 for population size, 100 for generation size 0.9 and 0.01 for rates of crossover and mutation, respectively. All experiments are run on a personal computer with Intel Core i5-5200GHz with 12 GB of RAM. Moreover, for the termination criteria, the time limit for running is 14,000s. The initial data are shown in Appendix 1 and 2. It contains 9 types of electricity generators, located in different plants to produce electricity. The quantity of electricity generators is flexible based on the production strategy of the plant. The interest rate 𝐼𝑝 = 1.02. The working hours of electricity generator m in period p (𝑤𝑝,𝑚) and target utilization of main electricity generator m in period p( 𝑦𝑝,𝑚) are set to 1,900 and 0.8, respectively. At the same time, the unit excess production cost of electricity from resource t in period p (𝑗𝑝,𝑡), and the unit lack production cost of electricity from resource t in period p (𝑙𝑝,𝑡) account for 10% and 20% from unit profits of electricity from resource t produced in period p (bp,t) 21
The electricity demand from different energy resources follows a normal distribution with the standard deviation 𝜎𝑂𝑝,𝑡 = 7,000. The mean is listed in the appendix 1 (𝑂𝑝,𝑡). Demands are randomly sampled from the abovementioned normal distribution and verified again by a goodness-of-fit test. These numbers presented as the average demand of the energy from different resources in each period of time. The probability of satisfied constraints is set to 𝑝𝑗 = 95%, which leads to the probability ∅𝑗(𝑝𝑗) = 1.645. By referring to (Rao, 2009), the value of probability is found as ∅𝑗(𝑝𝑗) = 1.645. Finally, (𝑘1 = 𝑘2 = 1) is chosen to present the equal priority for the maximization of the mean and the minimization of the standard deviation. The optimal electricity for community is depicted in Figure 5. This figure presents the fitness evolution of the mean electricity and the optimal amount of electricity produced. The mean fitness represents the average fitness value in each GA generation, while the best fitness shows the best function value. To be more specific, by giving the expected value of TCs and TPs equal to 400,000,000 and $100,000,000, respectively, the optimal energy 1,974,500 MGW is generated. The detail of electricity generation portfolio is shown in Table 2.
22
Figure 5. Performance convergence of GA (given that expected TCO2 is 400,000,000, TPs is $100,000,000, the optimal energy is 1,974,500 MGW) Table 2: Solution of the example case (a) Amount of electricity (MGW) produced by plants, 𝑄𝑝,𝑚,𝑡 Q(:,:,.) Period 1 2 3 4 5 6 7 8
Plant 1 44216 40108 44116 25078 33502 38621 35386 38291
Plant 2 41226 44320 41190 39530 20160 29350 28163 44136
Plant 3 1498 34522 40446 43199 3519 3958 23972 32036
Plant 4 44221 41403 22094 33120 22451 44138 35142 42521
Plant 5 25068 44747 20039 21426 17036 34739 41053 32207
Plant 6 41938 1300 29173 35099 27216 28262 31938 3872
Plant 7 17794 17964 15927 17916 14489 16489 17761 17374
Plant 8 18785 15397 19081 18134 16904 17631 20372 14814
Plant 9 23966 20579 23686 21980 23082 22150 23722 23763
(b) Quantity of electricity generators in plants (𝐾𝑚) (c) Quantity of in-house energy generator Plant 1
Plant 2
Plant 3
Plant 4
Plant 5
23
Plant 6
Plant 7
Plant 8
Plant 9
7
7
5
6
7
5
6
6
6
5.2 Trade-off between the energy received and TCO2 for a nation The NSGA II is utilized to tradeoff between two objectives as shown in Eqs. (14) and (15). The parameter settings and constraints are the same with those in section 5.1. To be more specific, the key issue in our model is to resolve conflict objectives between environment impact and energy efficiency when deploying multiple-energy resource. Therefore, profit objective in this case has been considered as the second priority one and set in the constraint. However, the two-first trade-off priority objectives shown in Pareto chart should satisfy the expected profit defined by the concern Eq. (21). From the perspective of community: Objective 1: Maximize the energy generaton efficiency, Eq. (14) 𝑀𝑎𝑥 𝑂𝐹1 = 𝑘1𝜓(𝑂𝑝,𝑡) + 𝑘2𝜎𝜓
( )
[
𝑃
𝑀
]
𝑇
where 𝜎𝜓 = 0, 𝑘1,𝑘2 = 1, 𝜓 𝑂 = 𝑇𝐸 = ∑𝑝 = 1∑𝑚 = 1∑𝑡 = 1(𝑄𝑝,𝑚,𝑡) 𝑝,𝑡 From the perspective of government: Objective 2: Minimize the TCO2 emission, Eq. (15), 𝑀𝑖𝑛 𝑂𝐹2 = 𝑘1𝜓(𝑂𝑝,𝑡) + 𝑘2𝜎𝜓
( )
[
𝑃
𝑀
𝑇
]
where 𝜎𝜓 = 0,𝑘1,𝑘2 = 1, 𝜓 𝑂 = 𝑇𝐶𝑂2 = ∑𝑝 = 1∑𝑚 = 1∑𝑡 = 1(𝑄𝑝,𝑚,𝑡𝑃𝑆𝐶(𝑡)) 𝑝,𝑡 Subject to: Eq. (3), Eq. (21) and Eq. (23), 𝑇
𝑐𝑚,𝑡𝑄𝑝,𝑚,𝑡
𝐾𝑚 ≥ ∑𝑡 = 1𝑟𝑚,𝑡𝑤𝑝,𝑚𝑦𝑝,𝑚 , ∀ 𝑝,𝑚, 24
k1𝜃(𝑂𝑝,𝑡) + 𝑘2𝜎𝜓 ≥ 𝑇𝑃𝑠
∑𝐶
𝑚,𝑡𝑄𝑝,𝑚,𝑡
≤ 𝑂𝑝,𝑡 ― ∅𝑗(𝑝𝑗)𝜎𝑂𝑝,𝑡
𝑚∈𝑀
After running the NSGA II algorithms, the seventy optimal results are shown in Figure 6. Each point illustrates the trade-off feasible solution for the community and government when producing energy. As discussed, the more CO2 emitted will let the energy increase significantly, but it also bring negative effects to the environment. The Figure shows that based on the stakeholder’s perspective, the optimal solution can be obtained through their agreements. It indicates that if government wants to increase their energy, the less rigid policy to protect the environment must be accepted.
Figure 6: The sensitivity analysis between the energy producton and CO2 emission
25
6. Conclusion This study proposed a stochastic model to allocate various electricity generators for the community energy usage. Uncertainty demand was considered. To efficiently produce energy, two types of production strategy, make-to-stock and make-to-order policies, are considered. This study presented a solution to trade-off between the energy efficiency produced and the environment hazards caused. After using the proposed algorithm to solve the problem, our paper shows two results, which balance the perspectives of government, firm and community. The first result showed the optimal energy for community (1,974,500 MGW) given specific threshold of the amount of CO2 from a government perspective and threshold of the amount of profit from a firm perspective. (TCs=400,000,00) and (TPs=$100,000,000). Further, the study presented a multi-objective optimization to give alternatives for different stakeholders, as indicated in Figure 6. Future research can extend to several directions. More uncertain parameters can be investigated, such as the reliability of the stochastic electricity generator and their yield rates. Secondly, the patterns of stochastic demands, such as discrete distributions, mixed discrete/continuous distributions, and various joint distributions, can be further investigated. Thirdly, one can consider energy distribution, for example, producing mass energy to supply for communities located in different areas. In this case, many variables are needed to be concerned, e.g., energy production, storage and delivery costs. In addition, the community also has the satisfaction level which flexibly changes during the quality of service. The late energy delivery will lead to the increasing of customer loyalty loss.
26
Further, advanced model can be built up to decide the location of power plants and production strategies to satisfy different stakeholders. Appendix Appendix 1: The data set of the benchmark example 𝑐𝑚,𝑡: Parameter to indicate that, electricity generator m can produce energy from material t or not t=1 t=2 t=3 t=4 t=5 t=6 t=7 t=8 t=9 m=1 1 0 0 0 0 0 0 0 0 m=2 0 1 0 0 0 0 0 0 0 m=3 0 0 1 0 0 0 0 0 0 m=4 0 0 0 1 0 0 0 0 0 m=5 0 0 0 0 1 0 0 0 0 m=6 0 0 0 0 0 1 0 0 0 m=7 0 0 0 0 0 0 1 0 0 m=8 0 0 0 0 0 0 0 1 0 m=9 0 0 0 0 0 0 0 0 1 𝒓𝒎,𝒕: Theoretical throughput of energy from material t manufactured by main electricity generator type m t=1 t=2 t=3 t=4 t=5 t=6 t=7 t=8 t=9 8 8 8 8 8 8 8 8 8 m=1 5 5 5 5 5 5 5 5 5 m=2 7 7 7 7 7 7 7 7 7 m=3 8 8 8 8 8 8 8 8 8 m=4 5 5 5 5 5 5 5 5 5 m=5 7 7 7 7 7 7 7 7 7 m=6 8 8 8 8 8 8 8 8 8 m=7 5 5 5 5 5 5 5 5 5 m=8 7 7 7 7 7 7 7 7 7 m=9 𝑂𝑝,𝑡: market demand (mean) t=1 t=2 t=3 t=4 t=5 t=6 t=7 t=8 t=9 p=1 33100 30240 35500 37700 33240 29500 29500 32240 35500 p=2 33100 30240 35500 37700 33240 29500 29500 32240 35500 p=3 33100 30240 35500 37700 33240 29500 29500 32240 35500 p=4 33100 30240 35500 37700 33240 29500 29500 32240 35500 p=5 33100 30240 35500 37700 33240 29500 29500 32240 35500 p=6 33100 30240 35500 37700 33240 29500 29500 32240 35500 p=7 33100 30240 35500 37700 33240 29500 29500 32240 35500 p=8 33100 30240 35500 37700 33240 29500 29500 32240 35500 𝑏𝑝,𝑡: Profit for each period 27
t=1 t=2 t=3 t=4 t=5 t=6 p=1 200 180 150 200 180 150 p=2 190 170 140 190 170 140 p=3 180 160 130 180 160 130 p=4 200 180 150 200 180 150 p=5 190 170 140 190 170 140 p=6 180 160 130 180 160 130 p=7 200 180 150 200 180 150 p=8 190 170 140 190 170 140 𝑒𝑚:Unit cost of purchasing a main electricity generator type m m=1 3900000
m=2 1350000
m=3 2840000
m=4 3900000
m=5 1350000
m=6 2840000
t=7 200 190 180 200 190 180 200 190
t=8 180 170 160 180 170 160 180 170
t=9 150 140 130 150 140 130 150 140
m=7 3900000
m=8 1350000
m=9 2840000
m=8 650000
m=9 980000
𝑑𝑚:Unit salvage value of phasing out a main electricity generator type m m=1 1300000
m=2 650000
m=3 980000
m=4 1300000
m=5 650000
F0=20000000 S0=[-3113,0,0,0,0,0,0,0,0] Others K0m =[2 1 1 2 1 1 2 1 1]
28
m=6 980000
m=7 1300000
Appendix 2: Production policy and CO2 emission
Type of energy
Type of
CO2 emission
manufacturing
Kg/MGW
Gasoline
MTS
250
Petrol
MTS
230
Oil
MTS
280
Coal
MTS
260
Kerosene
MTS
260
Diesel
MTS
270
Wind
MTO
40
Solar
MTO
40
Nuclear
MTO
40
Source: * (Quaschning, 2015) * J .W.Storm van Leeuwen (2008, may 25) retrieved from timeforchange.org
29
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