Multi-objective optimization of a hybrid distributed energy system using NSGA-II algorithm

Abstract

In this paper, a multi-objective optimization model is established for the investment plan and operation management of a hybrid distributed energy system. Considering both economic and environmental benefits, the overall annual cost and emissions of CO₂ equivalents are selected as the objective functions to be minimized. In addition, relevant constraints are included to guarantee that the optimized system is reliable to satisfy the energy demands. To solve the optimization model, the non-dominated sorting generic algorithm II (NSGA-II) is employed to derive a set of non-dominated Pareto solutions. The diversity of Pareto solutions is conserved by a crowding distance operator, and the best compromised Pareto solution is determined based on the fuzzy set theory. As an illustrative example, a hotel building is selected for study to verify the effectiveness of the optimization model and the solving algorithm. The results obtained from the numerical study indicate that the NSGA-II results in more diversified Pareto solutions and the fuzzy set theory picks out a better combination of device capacities with reasonable operating strategies.

Keywords

multi-objective optimization / hybrid distributed energy system / non-dominated sorting generic algorithm II / fuzzy set theory / Pareto optimal solution

Introduction

Nowadays, the demand for energy is increasing due to rapid industrialization and urbanization. Conventional power plants depending on fossil fuels have caused increasing urgent issues including energy shortages and greenhouse effects. Meanwhile, large centralized power stations are always vulnerable to natural disasters, and may cause large-scale power cut in the region [¹,²]. To solve the above issues, since the late 1970s, based on the theory of energy cascade utilization, the gas fired distributed energy system in forms of CHP (combined heating and power) or CCHP (combined cooling, heating and power), has been proposed and paid more attention to in developed countries or regions such as the United States, Japan and Europe [³]. On the other hand, since the beginning of this century, as one of the most important ways to deal with the climate change issues, distributed renewable energy technologies (distributed photovoltaic system, etc.) have achieved explosive growth under strong policy incentives [⁴]. By examining the development of the distributed energy system, it is easy to find that the conventional system based on a single technology has shown its limitation due to the poor flexibility. Under these backgrounds, the hybrid distributed energy system, integrating traditional thermal power generation technologies with renewable ones, is proposed [⁵]. Specifically, the hybrid distributed energy system is not the simple superposition of various energy sources, but the integrated and complementary utilization of various energy sources according to their grades. In this way, the overall efficiency may be improved from the systematic level.

The hybrid distributed energy system may have interactive and complementary effects by integrating diversified energy technologies. However, it also increases the system complexity and poses a big challenge to the system plan and design. Generally, the design of a hybrid distributed energy system is a multiple and complex system engineering, which may refer to multi-disciplinary fields such as energy, environment, economy, society and so on. It should cover the entire optimization process from energy structure design, equipment configuration, and capacity selection until operation strategy determination [⁶,⁷]. Therefore, a scientific decision-making method should be employed. To solve this problem, a number of studies have been reported by proposing models and methods from different perspectives. Cardoso et al. [⁸] developed an investment and operation optimization model for a distributed energy system while considering the uncertain moving of electric vehicles. Voll et al. [⁹] realized the collaborative optimization of structure, scale, and operation of a distributed energy system by establishing an automatic modeling and optimization framework. Bakken et al. [¹⁰] proposed a nested optimization method composed of the operation strategy optimization model based on linear programming as well as the investment strategy optimization model based on dynamic programming.

Generally, most previous studies focused on the determination of a set of decision parameters under a specific objective with certain internal and external constraints. However, the plan and design of a hybrid distributed energy system may usually have multiple goals with no uniform measurement unit and even conflict value system [¹¹,¹²]. For this reason, Di Somma et al. [¹³] developed a multi-objective programming (MOP) model of the distributed energy systems for a large-scale utility customer. Hu and Cho [¹⁴] optimized the CCHP operation strategy based on a weighted sum utility function which considered three objectives including minimizing operational cost, primary energy consumption, and carbon dioxide emissions. The conventional solving method of a multi-objective optimization problem is transferring it into a single-objective optimization problem while taking other objectives as constraints. However, the optimization results of the above method are partly determined by the preference of the decision makers, and the scientific objectivity is not fully reflected.

In recent years, along with the development of computer technology and optimization algorithm, some modern heuristic algorithms such as genetic algorithm (GA), particle swarm optimization (PSO), etc., have been employed for the optimal design of distributed energy systems [¹⁵–¹⁷]. Fazlollahi et al. [¹⁸] applied the integer reduction constraint algorithm, evolutionary algorithm and other methods to solve the multi-objective investment and operation optimization model for a regional energy system. Wang et al. [¹⁹] employed the PSO algorithm to optimize the operation strategy of a CCHP system under electric-tracking mode. Soheyli et al. [²⁰] applied a co-constrained multi objective particle swarm optimization (CC-MOPSO) algorithm to optimize a novel CCHP system for minimizing fossil fuel consumption and pollution.

In summary, along with the continuing innovation of the energy system engineering, the design optimization of the hybrid distributed energy system has been paid more and more attention to. To examine the trade-off relationship of multiple and conflict objectives, the MOP models and corresponding solving methods have been proposed in previous studies. However, most of previous works remain in getting the Pareto solutions without further selection, which may bring troubles for final decision-making. Moreover, a comprehensive and systematic framework of the solution is always escaped, which makes the solving procedure confusing and complicated. In this study, focusing on the simultaneous optimization of equipment configuration and operation strategy of the hybrid distributed energy system, a MOP model is developed considering both economic and environmental objectives. Besides, a systematic solving procedure is detailed. Moreover, accounting for the good search ability and high optimization speed, the non-dominated sorting generic algorithm II (NSGA-II) is employed to solve the optimal model, where the elite strategy and crowding distance theory are dedicated to finding the diversified Pareto solution sets. Furthermore, in order to enhance the objectivity of selecting the optimal solution set from multi-objective solution sets, the fuzzy set theory is used to provide auxiliary selection work after optimization.

Framework of the hybrid distributed energy system

For simplicity, in this paper, the hybrid distributed energy system is composed of a gas engine unit, photovoltaic (PV) cells, a gas boiler, an absorption chiller, and a heat exchanger, as shown in Fig. 1.

In this system, the electric load is partly supplied by the gas engine and the PV system, and the deficiency can be met by the utility grid. In addition, the excess power may be sold back to the grid while simultaneous buy and sell is not allowed. On the other hand, the waste heat from the gas engine is recovered and sent to the heat exchanger and absorption chiller to meet the heating and cooling loads, respectively. When the thermal loads cannot be fully satisfied by the waste heat, the auxiliary boiler can be operated.

Mathematical formulation of the MOP model

Objective functions

In this paper, the overall annual cost and emissions of CO₂ equivalents are selected as the economic and environmental index for optimizing and analyzing the configuration and operation strategy of the hybrid distributed energy system.

Economic objective function

As expressed in Eq. (1), the overall annual cost involves the cost of equipment investment C_inv, the cost of consumed fuels C_gas, the cost of grid interaction C_ele (including the cost of purchasing electricity from the electric utilities as well as the revenue from selling electricity from the on-site generation back into the grid), and the policy subsidy of the PV system C_sub.

(1)f_{\mathrm{cost}}{=C}_{\mathrm{inv}}{+C}_{\mathrm{gas}}{+C}_{\mathrm{ele}}{-C}_{\mathrm{sub}}.

The annual investment cost is determined by multiplying the unit cost of each equipment with its rated capacity and then annualized by multiplying with the capital recovery factor (CRF). Assuming the capacity of each equipment is a continuous variable, the cost of equipment investment can be calculated by Eqs. (2) and (3).

(2)\begin{array}{l}{C}_{\mathrm{inv}}=CR{F}_{\mathrm{PV}}·U{C}_{\mathrm{PV}}·S_{\mathrm{PV}}·A_{\mathrm{PV}}+CR{F}_{\mathrm{GE}}·U{C}_{\mathrm{GE}}·Ca{p}_{\mathrm{GE}}\hfill \\ +CR{F}_{\mathrm{GB}}·U{C}_{\mathrm{GB}}·Ca{p}_{\mathrm{GB}}+CR{F}_{\mathrm{AC}}·U{C}_{\mathrm{AC}}·Ca{p}_{\mathrm{AC}},\hfill \end{array}

(3)CRF={\displaystyle \frac{r·{(\mathrm{1}+r)}^l}{{(\mathrm{1}+r)}^l-\mathrm{1}}}.

The fuel cost is related to the fuel consumption of the gas engine and the boiler, which can be determined by Eq. (4).

(4)C_{\mathrm{gas}}=g_{\mathrm{m}}·({\displaystyle \sum _t^{}\frac{H_{\mathrm{GB},t}}{{\beta }_{\mathrm{GB}}}}+{\displaystyle \sum _t^{}\frac{E_{\mathrm{GE},t}}{{\alpha }_{\mathrm{GE}}}}).

The cost of grid interaction can be calculated by Eq. (5).

(5)C_{\mathrm{ele}}={\displaystyle \sum _t^{}(e_{\mathrm{pur}}·E_{\mathrm{pur},\mathrm{t}}})-{\displaystyle \sum _t^{}(e_{\mathrm{sell}}·E_{\mathrm{sell},t}}).

The distributed PV system will be subsidized by the national and local government, and the total subsidy can be calculated by Eq. (6).

(6)C_{\mathrm{sub}}={\displaystyle \sum _t^{}Q·E_{\mathrm{PV},t}}.

Environmental objective function

(7)f_{{\mathrm{CO}}_2\mathrm{eq}}=ECI·{\displaystyle \sum _t^{}{E}_{\mathrm{pur},t}}+GCI·({\displaystyle \sum _t^{}\frac{H_{\mathrm{GB},t}}{{\beta }_{\mathrm{GB}}}}+{\displaystyle \sum _t^{}\frac{E_{\mathrm{GE},t}}{{\alpha }_{\mathrm{GE}}}}).

Main constraints

There are two categories of constraints related to the energy balance between demand and supply as well as the availability of generating units.

Energy balances

Energy balance means that the energy inputs must be equal to the outputs in each period, which includes the balance of electricity, heating, and cooling. The constraints are defined as

(8)E_{\mathrm{load},t}=E_{\mathrm{pur},t}+E_{\mathrm{GE},t}+E_{\mathrm{PV},t}-E_{\mathrm{sell},t},

(9)H_{\mathrm{load},t}=H_{\mathrm{GE},t}+H_{\mathrm{GB},t}-H_{\mathrm{AC},t},

(10)C_{\mathrm{load},t}^{\text{'}}=C_{\mathrm{AC},t}^{\text{'}}.

Availability of generating units

The relation between power generation and capacity of gas engine is expressed by Eq. (11). The output relation of heating and electricity is determined by Eq. (12), in which the heat-to-power ratio (l) of the gas engine is assumed to be the fixed value.

(11)\mathrm{0}\le E_{\mathrm{GE},t}\le Ca{p}_{\mathrm{GE}},

(12)H_{\mathrm{GE},t}=E_{\mathrm{GE},t}·\lambda .

The relation between heat generation and capacity of gas boiler is expressed by Eq. (13). In addition, it is assumed that the efficiency of the boiler is a constant value during operation periods and its start-stop can be operated at any time.

(13)\mathrm{0}\le H_{\mathrm{GB},t}\le Ca{p}_{\mathrm{GB}}.

The relation between the cooling output and capacity of the absorption chiller is expressed by Eq. (14), and the relation between heat input and cooling output is estimated by Eq. (15).

(14)\mathrm{0}\le C_{\mathrm{AC},t}^{\text{'}}\le Ca{p}_{\mathrm{AC}},

(15)H_{\mathrm{AC},t}={\displaystyle \frac{C_{\mathrm{AC},t}^{\text{'}}}{\mathrm{COP}}}.

The power output of the PV system can be calculated by Eq. (16). In addition, the total installation areas of the PV system can be determined by Eq. (17)

(16)E_{\mathrm{PV},t}=S_{\mathrm{PV}}·{\eta }_{\mathrm{PV}}·R_t,

(17)S_{\mathrm{PV}}\le S_{\max }.

Solution to the MOP model

Pareto dominance theory

Unlike the single objective programming, in the multi-objective optimization model, it is difficult to get a solution which can meet multiple goals at the same time, because of the diversity of objective functions. In this case, the concept of Pareto dominance is used to evaluate the solutions and can be defined as follows.

For a multi-objective minimization problem, a vector u = [u₁,u₂,...,u_M]^T is recognized to dominate another vector v = [v₁,v₂,...,v_M]^T, if and only if, \forall i\in \left\{\mathrm{1},\mathrm{2},...,M\right\},u_i\le v_i; \exists i\in \left\{\mathrm{1},\mathrm{2},...,M\right\},u_i＜v_i, where M is the dimension of the objective space. A solution u∈U, where U is the universe set, is recognized to be Pareto optimum if, and only if, there is no other solution v∈U, such that u is dominated by v. Such solutions (u) are called no-dominated solutions. These solutions present compromised values of objective functions. In other words, it is impossible to improve one of the objective functions in a no-dominated solution without deteriorating at least one of the other objective functions. All the non-dominated solutions constitute the Pareto set or non-dominated set, and the image of Pareto set in the function space is called the Pareto front [²¹,²²].

Solution algorithm

Procedure of the algorithm

The multi-objective genetic algorithm is one of evolutionary algorithms to solve the MOP problems, whose core is coordinating the relation between various objective functions and finding the Pareto set. For the optimization problem with two objectives, the procedure of finding the optimal solution set is shown in Fig. 2.

In this study, the fast and elitist NSGA-II is employed to find the Pareto set. In detail, it adopts the generic algorithm for evolutionary population, the fast and no-dominated method for individual ranking, the elite strategy for improving the precision of optimization results, and the crowding distance operator for keeping the diversity of population. The flowchart of the algorithm for solving the physical model is depicted in Fig. 3.

Elite strategy

The elite strategy is the core of NSGA- II, and its operation procedure is demonstrated in Fig. 4. First, the combined population R_t is formed with the size of 2N and composed by the current dominating set P_t and generation Q_t. Next, the population R_t is sorted according to the non-domination and forms a non-dominant set F=F_{\mathrm{1}}\cup F_{\mathrm{2}}\cup \cdots \cup F_k. Since all previous and current population members are included in R_t, the elitism is ensured. For choosing exactly population members, the non-dominant set is arranged by the crowding distance in descending order, then the best solutions are chosen as parent population passed to the next generation [²³].

Crowding distance calculation

To keep system diversity and prevent individuals from local accumulation, the concept of crowding distance is introduced into the NSGA-II. The crowding distance is used to estimate the size of the largest cuboid enclosing this point without including any other point in the population [²⁴]. As exhibited in Fig. 5, the crowding distance of i in its front (marked with solid circles) is the average side-length of the cuboid (shown with a dashed box). This method can adjust the niche automatically, resulting in uniform dispersion in the target space.

Constraint-handling approach

The traditional genetic algorithm usually employs a penalty parameter to deal with constraints for single-objective optimization. However, it does not work for multi-objective optimization. For the NSGA-II algorithm, the constraint-handling method adopts the binary tournament selection, where two solutions are picked from the population and the better one is selected. In detail, the selection mechanism are as follows: (1) when both solutions are feasible, the crowding-distance comparison operator is used as mentioned before; (2) when one is feasible and other is not, the feasible solution is chosen; (3) when both are infeasible, the constrained-domination principle is used, i.e., the solution with a smaller constraint violation has a better non-domination rank. In this way, all feasible solutions are ranked according to their non-domination level based on the objective function values and constraints.

Fuzzy set theory

The multi-objective programming usually finds the non-dominated solutions. After that, the most satisfactory solution may be determined according to certain preferences or principles. To avoid the subjective selection, in this paper, the fuzzy set theory is adopted to select the most satisfactory solution [²⁵,²⁶].

First, a member function τ_i is defined as the weight of target i in a solution:

(18){\tau }_i={\displaystyle \frac{f_i^{\max }-f_i}{f_i^{\max }-f_i^{\min }}},f_i^{\min }\le f_i\le f_i^{\max }.

The dominance function τ_k for each non-dominated solution k in the Pareto solution set is expressed as

(19){\tau }_k={\displaystyle \sum _{i=\mathrm{1}}^m{\tau }_k^i}/{\displaystyle \sum _{j=\mathrm{1}}^n{\displaystyle \sum _{i=\mathrm{1}}^m{\tau }_j^i}}.

Numerical study

Research object

To analyze the performance of a hybrid distributed energy system and verify the validity of the proposed optimization model and solving algorithm, in this section, a hotel building with a floor area of 29816 m² in Shanghai (within hot summer and cold winter climate zone) is selected as the research case for optimization and discussion. By combining the building envelop and local climate, the all-year hourly load can be simulated. Because the energy demands fluctuate both daily and seasonally, the hourly demand profiles of typical days in winter (November–December, January–February), summer (June–September), and mid-season (March–May, October) are shown in Fig. 6 [²⁷].

Fuel and electricity prices

In Shanghai, a time-of-use (TOU) tariff is usually employed for commercial users, as listed in Table 1 [²⁸].

As mentioned above, the on-site power generation is used to meet local demands in priority, and the excess power is sold back to the utility grid. Generally, on-grid price is equal to the local stake electrovalence of coal-fired power generator, and this price is approximately $0.0591/kWh at present in Shanghai [²⁸]. On the other hand, the government provides subsidies for PV systems. As for commercial users, the state subsidy is $0.0613/kWh [²⁹]. For promoting the development of renewable energies, the local government provides an additional subsidy of $0.0365/kWh [³⁰].

Another important input for the model is the gas price, which is $0.3942/m³. The calorific value of gas is 35.59 MJ/m³.

Equipment parameters

The list of candidate technologies considered in this study and the corresponding generation efficiencies, unit costs, and lifetimes are presented in Table 2 [³¹].

Other parameters

Besides the photoelectric conversion efficiency, the biggest influencing factor for PV cells is the local solar irradiation. In Shanghai, the irradiation value in winter is relatively small, and the average daily irradiation is only 1.9 kW/m² in January. On the contrary, the average irradiation value is about 4.9 kW/m² in May [³²].

Results and discussion

Optimal results

In this case, the parameters for the NSGA- II are set as follows: the population size is 80; single point crossover and mutation probability with 0.8 and 0.1, respectively; and the max-generation is 500. In addition, the calculation procedure is realized in Matlab r2016a; the computing environment is based on the CPU with 3.5 GHz (Inter core (TM) i7-4790) and DDR3 RAM with 4 G. After running the program 20 times separately, the population distribution is approximately the same, and the average running time is 710 s. Actually, the population has accumulated obviously and formed the non-dominated front when the evolutionary generations are over 200, which indicates the well global optimization capability and convergent stability of the proposed algorithm.

Figure 7 displays the respective aggregated Pareto efficiency measures. From Fig. 7, it can be found that the Pareto solutions are evenly distributed in the target space. Owing to the acuity of the equality constraints in this example, the distribution range of Pareto solutions is relatively small. Moreover, the Pareto front presents a declining trend, which reflects the opposite relation between the economic and environmental aspects. The decision-makers can select the optimization scenarios from this result. For instance, if they care about the economic profits, a scheme with a small annual total cost may be chosen while sacrificing some environmental profits. On the contrary, the pursuit of environmental profits comes at the expense of cost increasing.

Based on the fuzzy set theory, the most satisfactory solution is selected in non-dominated solution set, and the results are tabulated in Table 3.

Operation strategy

Figures 8 and 9 show the thermal and electrical balances of typical days in winter, mid-season, and summer, respectively.

In the winter, because of the sunlight intensity, low temperature, large amount of space-heating, and hot-water load, the gas engine unit operates throughout the day to satisfy most of the thermal demand. The gas boiler is also used to compensate for the thermal deficiency. In addition, due to the relatively high heat-to-power ratio in the hotel, in order to satisfy the thermal demand, especially during some peak hours (e.g., 6:00–9:00 am), the power output from the gas engine unit may be greater than the local electricity demand, and the oversupply is sold back to the grid (see Fig. 9). Furthermore, at daytime, the PV cells can generate power to meet part of the electrical load. At night, with low electricity price, it is better to purchase power from the grid rather than generate on-site. During the high price period, increasing the output of the gas engine unit to meet the electric demand is the best choice.

In summer, with the high sunlight intensity, sunshine duration, and large electricity and cooling demands, the cooling load is satisfied by the absorption chiller which is heated by the recovered heat from the gas engine unit. Unlike winter, the cooling and power demands usually peak around 8:00 pm in summer, which results in the high efficiency of the gas engine unit without power excess. At daytime, the electricity load is met by the PV system and the gas engine unit. Due to the relatively high load ratio of the gas engine unit to satisfy the thermal demand, the excess electricity is sold back to the utility grid.

In mid-season, because of the moderate cooling and heating loads, most of the thermal load can be provided by the gas engine unit. With the limitation of thermal output from the engine during the transition season, the power output is also less. Therefore, in addition to the gas engine unit and the PV system, most of the electricity demand comes from the unity grid. Moreover, due to the TOU tariff for outside electricity purchase, most of the electricity requirement at night is satisfied by the utility grid to reduce the running cost.

According the above discussion, by executing the optimization model, all generators can cooperate with each other to meet the energy demands under the guidance of the objective functions. Compared with the traditional boiler, the gas engine unit can reduce the unit cost and increase the flexibility of the system by recovering waste heat. In addition, the system is also optimized under the guidance of the electricity price, i.e., purchasing the electricity in the valley period and selling in the peak time, which will reduce the peak-valley difference of electricity and improve the economic benefit of the system. The PV cells run in the daytime, which can reduce the purchasing power from the grid during the flat load time and save the running cost effectively. In addition, introducing the PV system with zero carbon emission makes the system more environmentally friendly.

Comparative analysis

To inspect the performance of the NSGA-II algorithm, the traditional weighting method and the NSGA-II algorithm are compared by choosing one day in the mid-season as an example. The optimization results with the two methods are shown in Fig. 10. It can be found that the NSGA-II algorithm has better results than the weighting method (both the weighting factor of running cost and CO₂ emissions are equal to 0.5). In detail, compared with the weighting method, the running cost optimized by the NSGA-II algorithm has a sharp decrease of 17.43% ($48.76), and the CO₂ emission reduction is 4.57% (275 kg). Therefore, the optimization by the NSGA-II algorithm can help the decision-makers get more reasonable and effective optimization results.

Conclusions

In this study, based on the basic framework of a hybrid distributed energy system, a multi-objective optimization model is developed for investment planning and operation management while considering both economic and environmental objectives. In addition, the NSGA-II algorithm combined with the fuzzy set theory is used to find the most satisfactory solutions. Regarding to the specific case study, the following conclusions can be reached:

The multi-objective programming model tends to approach the actual comprehensive assessment index. The optimization scheme not only gives full play to the economic advantages of the hybrid distributed energy system, but also reduces the environmental pollutions to a certain extent.

The crowding distance and its comparison operator are introduced in the NSGA-II algorithm, and the elite strategy is used to improve the precision of the results. The simulation results show that the algorithm has better optimization performances and the Pareto solutions are distributed evenly in Pareto front.

By employing the fuzzy set theory, the final solution can be achieved in a more objective way, without confirming manually after getting the Pareto set.

By comparing the optimization results obtained from different algorithms, to solve the multi-objective problem, the NSGA-II is superior to the traditional weighting method on validity.

In the future, to understand the availability and superiority of various solutions, especially some intelligent algorithms (PSO, etc.), a comprehensive and systematic comparative study will be executed while considering multiple criteria.

References

[1] International Energy Agency. Energy, Climate Change & Environment: 2016 Insights. Technical Report, 2016

[2] World Economic Forum and Accenture. Digital Transformation of Industries Electricity Industry. Technical Report, 2016

[3] Liu M, Shi Y, Fang F. Combined cooling, heating and power systems: a survey. Renewable & Sustainable Energy Reviews, 2014, 35: 1–22

[4] Qiu Y, Jiang J, Chen D. Development and present status of multi-energy distributed power generation system. In: IEEE Power Electronics and Motion Control Conference, Florence, Italy, 2016

[5] Ju L, Tan Z, Li H, Tan Q K, Yu X B, Song X H. Multi-objective operation optimization and evaluation model for CCHP and renewable energy based hybrid energy system driven by distributed energy resources in China. Energy, 2016, 111: 322–340

[6] Evins R. Multi-level optimization of building design, energy system sizing and operation. Energy, 2015, 90: 1775–1789

[7] Mehleri E D, Sarimveis H, Markatos N C, Papageorgiou L G. Optimal design and operation of distributed energy systems: application to Greek residential sector. Renewable Energy, 2013, 51(2): 331–342

[8] Cardoso G, Stadler M, Bozchalui M C, Sharma R, Marnay C, Barbosa-Póvoa A, Ferrão P. Optimal investment and scheduling of distributed energy resources with uncertainty in electric vehicle driving schedules. Energy, 2014, 64(1): 17–30

[9] Voll P, Klaffke C, Hennen M, Bardow A. Automated superstructure-based synthesis and optimization of distributed energy supply systems. Energy, 2013, 50(1): 374–388

[10] Bakken B H, Skjelbred H I, Wolfgang O. Transport: Investment planning in energy supply systems with multiple energy carriers. Energy, 2007, 32(9): 1676–1689

[11] Falke T, Krengel S, Meinerzhagen A K, Schnettler A. Multi-objective optimization and simulation model for the design of distributed energy systems. Applied Energy, 2016, 184:1508–1516

[12] Duan Z, Yan Y, Yan X, Liao Q, Zhang W, Liang Y T, Xia T. An MILP method for design of distributed energy resource system considering stochastic energy supply and demand. Energies, 2017, 11(1): 22

[13] Di Somma M, Yan B, Bianco N, Luh P B, Graditi G, Mongibello L, Naso V. Multi-objective operation optimization of a Distributed Energy System for a large-scale utility customer. Applied Thermal Engineering, 2016, 101: 752–761

[14] Hu M, Cho H. A probability constrained multi-objective optimization model for CCHP system operation decision support. Applied Energy, 2014, 116(116): 230–242

[15] Zeng R, Li H, Liu L, Zhang X, Zhang G. A novel method based on multi-population genetic algorithm for CCHP–GSHP coupling system optimization. Energy Conversion and Management, 2015, 105: 1138–1148

[16] Gan L K, Shek J K H, Mueller M A. Optimised operation of an off-grid hybrid wind-diesel-battery system using genetic algorithm. Energy Conversion and Management, 2016, 126: 446–462

[17] Ghaem Sigarchian S, Orosz M S, Hemond H F, Malmquist A. Optimum design of a hybrid PV–CSP–LPG microgrid with Particle Swarm Optimization technique. Applied Thermal Engineering, 2016, 109: 1031–1036

[18] Fazlollahi S, Mandel P, Becker G, Maréchal F. Methods for multi-objective investment and operating optimization of complex energy systems. Energy, 2012, 45(1): 12–22

[19] Wang J, Zhai Z, Jing Y, Zhang C. Particle swarm optimization for redundant building cooling heating and power system. Applied Energy, 2010, 87(12): 3668–3679

[20] Soheyli S, Shafiei Mayam M H, Mehrjoo M. Modeling a novel CCHP system including solar and wind renewable energy resources and sizing by a CC-MOPSO algorithm. Applied Energy, 2016, 184: 375–395

[21] Zitzler E, Thiele L. Multiobjective evolutionary algorithms: a comparative case study and the strength Pareto approach. IEEE Transactions on Evolutionary Computation, 1999, 3(4): 257–271

[22] Zitzler E, Thiele L.An Evolutionary Algorithm for Multiobjective Optimization: The Strength Pareto Approach. TIK-Report, 1998

[23] Deb K, Pratap A, Agarwal S, Meyarivan T. A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation, 2002, 6(2): 182–197

[24] Wang H, He C, Liu Y. Pareto optimization of power system reconstruction using NSGA-II algorithm. In: Asia-Pacific Power and Energy Engineering Conference, Chengdu, China, 2010

[25] Farina M, Amato P. A fuzzy definition of optimality for many-criteria optimization problems. IEEE Transactions on Systems, Man, and Cybernetics. Part A, Systems and Humans, 2004, 34(3): 315–326

[26] Sheng W, Liu Y, Meng X, Zhang T. An Improved Strength Pareto Evolutionary Algorithm 2 with application to the optimization of distributed generations. Computers & Mathematics with Applications (Oxford, England), 2012, 64(5): 944–955

[27] Weber C, Keirstead J, Samsatli N, Shah N, Fisk D. Trade-offs between layout of cities and design of district energy systems. In: Proceedings of the 23rd international conference on efficiency, cost, optimization, simulation and environmental impact of energy systems, Lausanne, Switzerland, 2010

[28] Shanghai Municipal Development & Reform Commission. Notice on implementing linkage adjustment of coal and electricity prices by Shanghai Price Bureau. 2016–01–05,

[29] National Development and Reform Commission. Notice on giving full play to price leverage to promote the healthy development of photovoltaic industry by the State Development and Reform Commission. 2013–08–26,

[30] Shanghai Municipal Development & Reform Commission. Notice on issuing the special supporting fund for renewable energy and new energy development in Shanghai. 2016–11–16,

[31] Huo X L, Zhou W G, Ying-Jun R. The integrated optimization of sizing and operation strategy for BCHP (Buildings Cooling, Heating and Power) systems. Natural Gas Industry, 2009, 29(8): 119–122

[32] Ren H, Wu Q, Gao W, Zhou W. Optimal operation of a grid-connected hybrid PV/fuel cell/battery energy system for residential applications. Energy, 2016, 113: 702–712

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature