Energy hub-based optimal planning for integrated energy systems considering part-load characteristics and synergistic effect of equipment

0 Introduction

Energy has always been one of the basic human needs.With the advancement in various energy consumption technologies and the increasing dependence of the human lifestyle on energy, this need has become more apparent [1].Moreover, with the development of society and technology and improvements in living standards, the transition toward a clean, efficient, and stable energy supply system has become one of the main challenges.Electricity production through centralized power plants has become the dominant form of energy supply.However, the scarcity and environmental effects of fossil fuel resources have imposed considerable pressure on conventional energy suppliers to ensure energy conservation and environmental protection.Therefore, it is necessary to develop alternative energy supply solutions.

The concept of energy internet has been proposed as an internet-style solution to energy issues that involves integrating information and power flows bi-directionally [2].In the energy internet context, energy supply services include polarization development status, smart grids, and integrated energy systems (IES).Smart grids focus on the informatization and intellectualization of the existing power grid, in addition to conventional power generation, transmission, and distribution tasks.Benefiting from the development of distributed energy systems, especially renewable energy sources (RES) and multi-generation technologies, IES has the potential to aggregate distributed energy resources (DER), achieve energy cascade utilization and multiple energies complementarily, and improve energy efficiency.Moreover, it can facilitate renewable energy consumption through integrated planning and synergetic operation.

IES consists of multiple energy conversion devices, an energy distribution infrastructure, and energy storage facilities.The development of highly efficient technologies, such as micro-turbines and internal combustion engines, has enabled integration of DER through co-generation systems and utility heating networks.The stochastic and intermittent characteristics of RES can be moderated using energy storage devices.However, a key issue is rational configuration of IES for a stable energy supply and sustainable development of districts.

Several studies have focused on structure planning [3, 4], equipment configuration [5, 6], site placement [7, 8], and operational optimization [9, 10] for IES.Considering the attributes of IES, such as multi-energy demands, complex components, and advanced information communication, an integrated modeling and management framework is required.The efficient and promising energy hub (EH) concept proposed by Favre-Perrod [11] describes the production, conversion, storage and consumption of multienergy carriers [12].The compactness and effectiveness of EH-based modeling methods facilitate calculation of different energy flows in IES during initial configuration planning and optimization.This concept has been extended to various energy scenarios, such as RES absorption [13, 14], energy storage [15, 16], and demand-side management [16, 17].In EH-based models, the coupling matrix is modified to express a specific feature for different applications by adding additional energy exchange ports or adjusting the matrix dimension of the EH.Wang et al.[14, 18] proposed an EH-based standardized matrix modeling method for multi-energy systems and developed a mixedinteger linear programming-based optimal configuration planning method.Huang et al.[13] developed a two-stage linear programming approach for district-level multienergy system planning, combining EH and directed acyclic graphs with multiple layers.Optimizing the configuration and operation of IES involves a single EH or coordinated energy flows among multiple EHs, which is adopted for single homes, large residential complexes, commercial buildings, industrial units, and cross-regional IES [19-22].Mohammadi et al.[1] reviewed the concept and multiple applications of EH in various residential, commercial, industrial, agricultural, and integrated energy consumption sectors.

Optimal planning of EH, which is considered on three levels—synthesis, design, and operation—addresses the issues of size, time, and location for investing in energy equipment, to ensure the best economic and environmental benefits [23, 24].Voll et al.[25] proposed an automated superstructure-based synthesis and optimization method for distributed energy systems on a conceptual design level.Fabrizio et al.[20] developed a modeling approach for multi-energy systems in buildings at the design concept stage.Although several researchers have investigated the optimal planning and management of EH, to the best of our knowledge, very few researchers have considered the varying characteristics of energy equipment under off-design conditions, because of the time-consuming computation involved along with nonlinear factors—products of equipment sizes and load ratios.Thus, energy equipment characteristics are assumed to be constant in the coupling matrix of the EH, representing a relationship between the output energy and input energy resources [20, 26].Some studies [27, 28] have been conducted on synthesis and optimization of distributed energy systems, considering time-varying load profiles, continuous equipment sizing, and partload-dependent energy efficiencies.These studies are more suitable for simulating actual application situations with an initial reduction in capital investment and a stable energy supply.However, the available methods focus on subsystem integration and ignore the spatio-temporal synergetic effects and coupling mechanism of the internal energy equipment.Thus, a more scientific and systematic planning method is required.

Therefore, a two-level optimal configuration planning method based on an extended EH model and considering the part-load characteristics and synergistic effects of energy equipment, in addition to the operation strategy, is proposed herein.The upper level is used to identify the type and size of energy converters and energy storage devices, while the bottom level is used for scenario analysis for selected typical days.The EH is a “black-box” modeling method, which ignores internal energy-level matching and cascade utilization.By decomposing the sub-systems of IES into various energy devices or processes, each device can be observed as a node of the energy hub (NEH), and the spatio-temporal synergistic effects can be studied.The intermediate energy flows are added to the input and output ports of the NEH to construct the energy resources set and energy wares set of an extended EH.

Energy devices can achieve their highest efficiencies under the design conditions, and performance may be drastically reduced under extremely low loads and offdesign conditions.Therefore, the coefficients of the EH coupling matrix are nonlinear variables that represents the complex relationship among various components and their inherent characteristics.The load-ratio and performance function represent the part-load-dependent operating efficiencies.Flow of energy between the energy resources and energy wares set complies with the law of energy conservation and the fundamental laws of thermodynamics.Moreover, deviations in the energy flow between inputs and outputs are eliminated by a penalty function included in the objective functions.

The optimal operation of IES for a multi-energy flow dispatch is a complex, nonlinear, and nonconvex mixedinteger problem [29], with the classification of solution algorithms being deterministic and metaheuristic.For nonlinear optimization problems, deterministic methods require a suitable initial solution to achieve convergence, and the obtained optimal solution is not necessarily the global optimal solution.The commonly used solvers are based on successive quadratic programming or a generalized reduced gradient; the former generates Newton-like steps and requires minimum function evaluations, while the latter operates efficiently with cost-effective function evaluations [30].Metaheuristic optimization techniques, such as the genetic algorithm [31], particle swarm optimization [4], and immune firefly algorithm [32], can step out of the local optimal and robustly explore a decision space.Such techniques benefit from intelligent local sampling with a complex learning mechanism and represent another option for solving nonlinear problems.Moeini-Aghtaie et al.[33, 34] proposed a multi-agent genetic algorithm to decompose the multi-carrier optimal power flow problem into traditional questions.Shabanpour-Haghighi and Seifi developed a generalized heuristic approach to solve the optimal power flow problem in multi-carrier energy systems, in which the dispatch factors or dummy variables are eliminated using a modified teaching-learning-based optimization algorithm [35].To explore the optimal solutions for configuration planning of an IES, a hierarchical evolutionary algorithm based on the genetic algorithm and MATLAB OPTI toolbox is developed in this study to handle the two-level optimal configuration planning problem.

The remainder of this paper is organized as follows: The extended EH model is introduced in Section 2.Subsequently, the two-level optimal configuration planning method is described in Section 3, along with the procedure for obtaining the optimization solution.In Section 4, basic information regarding the illustrated example and equipment models of energy converters and storage devices is presented.Thereafter, the results of the case study are discussed in Section 5.Finally, the conclusions are drawn in Section 6.

1 Extended EH model

The EH aggregates all energy devices into a “black box” with the input energy resources and output energy wares ports.We developed an extended energy hub model for the IES considering the intrinsic energy conversion characteristics, to achieve better energy cascade utilization through systematic decomposition at the equipment level.

1.1 EH model

The relationship between the output energy wares L and input energy resources P can be formulated linearly using a coupling matrix C:

For an EH with M types of input energy resources and N types of output energy wares, Eq.(1) can be expanded as follows:

where Pm and Ln represent the m-th and n-th type of input energy resource and output energy wares, respectively, and cmn denotes the coupling factor.

For the energy storage devices, a storage coupling matrix S is defined to formulate the connection between the output power M and the changes in storage contents Ė within time Δt, i.e., Ė = E (t + Δt) - E(t).The relationship between the changes in storage contents and storage output flows is as follows:

where Ėv and Mn denote the v-th type of storage content change and n-th storage output flow, respectively, and snv denotes the storage coupling factor.

Energy storage output flows can be attributed to the output ports and are considered as a correction to the input matrix [16].The energy balance for the EH can be extended from Eq.(1) to Eq.(4):

With renewable energy access, two ports, R and T, are added to represent the renewable and residual energy flows, respectively.Considering energy storage devices and renewable energy injection, the EH model can be expressed using Eq.(5):

1.2 Extended EH model

Considering the part-load characteristics and spatiotemporal synergistic effects of the equipment, an extended EH model is developed.The sub-systems in the IES are decomposed into various energy devices or processes, with each device being defined as an NEH for the IES.The IES modeling based on the EH concept is illustrated in Fig.1.

The extended EH model includes three parts: a set of pre-defined NEHs for various types of energy equipment, energy resources set, and energy wares set.The IES modeling focuses on energy conversion for the NEH and energy balance among the various energy flows.The energy resources set is composed of natural energy sources and all the components of output energy flows, while the energy wares set consists of the intermediate energy flows and terminal energy demand.

For an NEH, the part-load characteristics of the equipment are expressed as an intrinsic part-load-dependent performance function.The dispatch factors are generally employed to describe the dispatch of energy flows in the EH and are independent variables for optimization.In the proposed EH model, dispatch factors are substituted by the equipment load-ratio; thereby, the available energy flow dispatch optimization is transferred to the original energy flow generation optimization, and the effects of the varying part-load characteristics can be analyzed.

Fig.1 Typical structure of an integrated energy system based on the proposed energy hub concept

The energy flow connections between the components are coupled and allocated through pre-defined labels related to the input and output ports for each NEH.These labels are defined by the physical property and constitute the energy resources and energy wares set for the proposed EH of the IES and NEH of the equipment.The label concept is illustrated in Fig.2 using a tri-generation system as an example.

Fig.2 Energy flow matching and allocation among various devices with defined labels in a tri-generation system

The tri-generation unit is decomposed into a gas turbine (GT), heat exchanger (HE), and an absorption chiller (AC).According to the energy flow types, the labels defined are natural gas, electricity, heat, and cooling.For the same type of energy, the labels are further divided into different levels depending on inherent features, e.g., the heat flow is divided into high-level and low-level according to the temperature.Apart from facilitating allocation of the energy flows among various components, labels can assist in process decomposition for various energy conversion technologies and can contribute to energy cascade utilization and synergetic optimization.

All devices and the overall IES can be formulated as EHs with the same size, e.g., the mathematical formulation of Ka is shown as Eq.(6), which is convenient for the energy balance calculation.Note that the coupling matrix NEH for each equipment is a sparse matrix with specific coefficients between the input and output ports.

where m denotes the number of energy resources from the energy resources set, and n denotes the number of energy wares from the energy wares set.

Considering the part-load characteristics of energy converters, the load-ratio ρ and part-load-dependent operating efficiency function f(ρ) are defined to demonstrate the actual operation of the IES.The coupling coefficients can be calculated as follows:

where denotes the load-ratio of the q-th energy ware, and denote the actual and rated energy flow, and denote the nominal efficiency and part-load-dependent performance function of the energy conversion from resource p to energy ware q.The energy efficiency under off-design conditions is defined as a function of the nominal efficiency with a multifactor interactive coefficient.Thus, the NEH of Ka can be expressed as follows:

Energy storage devices can be considered as energy demand users and energy supply resources during the charging and discharging, respectively.Therefore, the NEH for energy storage can be formulated as follows:

Note that the input energy flows PKb are zero during discharging, while the output energy flows M Kb are zero during charging.The constraints for the energy storage devices are

where is the maximum charging or discharging ratio of the energy storage devices, and represent the minimum and maximum charging status of energy storage, respectively.Similar to the load-ratio defined previously, a state of charging (SOC) coefficient μ is defined as follows:

where the range of μ is [-1,1], and a positive number represents charging, while a negative number indicates discharging.

The stochastic and intermittent characteristics of renewable energy are dependent on the available energy resources.The NEH for renewable energy is modified based on the original energy resources, as follows:

where ϑh denotes the key parameters representing the natural renewable energy resources.The extended EH for the overall IES is expressed as follows:

where Dwares denotes the aggregated energy wares from all the equipment, and p, q, and l are the number of traditional energy converters, energy storage devices, and renewable energy converters, respectively.The energy dispatch across the IES obeys the energy conservation law, as per Eq.(17).

2 Two-level optimal configuration planning method for integrated energy system

Based on the extended EH model, a two-level optimal configuration planning method for the IES is presented, with time-varying load profiles, continuous equipment size, and part-load-dependent energy efficiency, and considering a possible operation strategy and synergistic effects in the optimal planning.

2.1 Hierarchy framework of the optimal configuration planning method

IES optimization includes three aspects: synthesis, design, and operation [23, 24].In the proposed method, the upper level focuses on the synthesis and design to determine the appropriate equipment types and sizes.The bottom level involves the operation and is used to integrate the operation strategy with planning through a typical day analysis, in which the part-load characteristics and spatio-temporal synergistic effects of the energy equipment are considered.The hierarchy framework of the method is presented in Fig.3.

Fig.3 Hierarchy framework of the optimal planning method

The structure of the extended EH is determined in the upper level when the input and output ports are assigned the given labels.The operation optimization is aimed at finding the optimal energy production and dispatch solutions under the given equipment type and size.Generally, the hourly and typical day analysis method are employed to optimize multi-energy systems.The former method involves calculating 8760 timesteps to cover all the operation conditions, resulting in several variables and high complexity.Therefore, the latter method is chosen to handle the operation optimization problems at the bottom level.The k-means based clustering method can be applied to determine the typical days according to the energy demand curves.

2.2 Hierarchical mathematical model for formulating the integrated energy system

In the presence of a hierarchical framework, the mathematical models are formulated as a master problem in combination with a sub-problem, as follows:

where α is a vector for the binary design variables that represent the selection (or non-selection) of the types of equipment; β is a vector for the continuous design variables representing the equipment size; γt is a vector for the discrete operational variables that represent the quantitative decision variables at any time t (e.g., the load-ratio for various equipment); fd and fo denote the objective functions for the design and operation stage, respectively; for instance, the life cycle cost is the economic evaluation objective.φdc and ψdc are the equality and inequality design constraints, while φoc and ψoc are the equality and inequality operational constraints, respectively.To achieve a stable energy supply, the power balance constraints must be verified at any time, which means that the output power must cover the energy demands.For conventional fossil fuel-based energy converters, a lower limit ρmin should be assigned to ensure equipment safety, i.e., load-ratio at any time should be within the range [ρmin, 1].For energy storage devices, the status of and change in the stored energy must be within the upper limit.

2.3 Two-stage evolutionary algorithm for optimal configuration planning of integrated energy system

A two-stage evolutionary algorithm is proposed to solve the hierarchy optimization problem.The modified multi-mutation adaptive genetic algorithm (MMAGA) identifies the design variables, while the second-stage subproblems are solved using the interior point optimization (IPOPT) solver [36] in the free MATLAB OPTI Toolbox.At the upper level, MMAGA can strengthen the population diversity and improve the genetic search performance by increasing the mutation bit number, which is determined by the individual fitness values of the current population.

For MMAGA, the optimal solution search is accomplished by the selection, crossover, and mutation operators, especially the mutation operators that can enter a new search domain and increase the probability of obtaining the global optimal solution.However, a larger search domain reduces the search speed and the probability of convergence.Therefore, the self-adaptive genetic algorithm is essential for enhancing the search performance.The fitness value is an index of the fitness of the individuals in the population and is selected as a standard to adjust the mutation bit number.For instance, in the maximization problem, individuals with a lower fitness value need to mutate more gene loci, whereas individuals with a higher fitness value need to mutate fewer gene loci.The self-adaptive mutation probability is calculated as follows:

where fmax and favg are the maximum fitness and average fitness of the current population, respectively; fi is the fitness value of the i-th individual of the current population; and k1 and k2 are coefficients in the range [0, 1].The use of pm can prevent premature convergence and protect excellent individuals in the current population.Meanwhile, the elitist model can be used to preserve the optimal individuals in each generation through reproduction.

The mutation locus number Nml is calculated as follows:

where int is the round-off operation, and k3 is an integer constant ranging from 1/4 to 1/3 of the chromosome length.fmax - fmin denotes the fitness range of the current population, and fmax - fi denotes the difference between the individual and best fitnesses; the ratio of fmax - fi and fmax - fmin denotes the quality of individual i in the overall population, i.e., a large ratio indicates a high-quality individual.After determining the mutation probability and mutation locus number, the mutation locus is selected using the random number method.

At the bottom level, the energy equipment load-ratio for the selected days needs to be assigned; this represents a potential operation strategy.The optimization is a nonlinear problem and can be solved using the IPOPT solver with the given objective function and constraints such as energy balance, load-ratio change, and physical limitation.The detailed calculation diagram of the two-stage decomposition-based evolutionary algorithm is shown in Fig.4.

(1) Generation of initial population: After initialization, a group of individuals is generated randomly and encoded to represent the design variables, i.e., the equipment type and size.

Fig.4 Flowchart of the two-stage evolutionary algorithm for the optimal configuration planning problem

(2) Individual effectiveness validation: To accelerate algorithm convergence, each individual is evaluated according to certain criteria to satisfy the energy demand and energy balance.If the criteria are not met, the individuals must be replaced.

(3) Evaluation of fitness for each individual in the population: The life cycle cost of the IES (LCCIES) is the fitness function, which consists of the initial capital cost (ICC), operation and maintenance cost (CO&M), and fuel cost (CFuel).The fuel cost is optimized at the bottom level with the IPOPT solver and with load-ratios, SOC coefficients, and design variables as the decision variables.

(4) Selection: Select the individuals with high fitness values.

(5) Crossover: Calculate the crossover probability and execute the crossover operation.

(6) Mutation: Calculate the mutation probability using Eq.(20) and the mutation locus number and position using Eq.(21).Subsequently, execute the mutation operation except for the individual with the highest fitness value.

(7) Evaluate the fitness of the offspring.As in Step 3, calculate the fitness value for each individual in the new population.

(8) Stop criteria judgment: If the gap between the adjacent population is smaller than the assumed threshold value, the algorithm will stop and generate an optimal scheme and operational strategy.

The fitness function is calculated as follows:

For each component, the initial capital cost and operation & maintenance costs are calculated in the design stage, while the fuel cost is calculated in the operation stage, considering the specific operational strategy.Combining the cost generated in the operation stage and the typical day method, Eq.(22) can be rewritten as Eq.(23):

where n is the lifespan of the equipment; CO&M is calculated per annum at 4% of the initial capital investment; and s is the number of typical day according to the k-means clustering method.

Before the economic analyses, the equipment cost is estimated based on the vendor’s quotations and market research.Many factors affect the cost estimation, such as component size, materials, features, nominal working temperature and pressure,, which is usually chosen as the main parameter to establish the equipment cost function.The cost of the component divided by the component size is defined as the specific cost, which can be expressed as a hyperbola, a power function, or a logarithmically decreasing function.For instance, the power specific cost function was formulated by Chicco and Mancarella [19]:

where ICCKa is the referring cost of the component for a referring size pR.It is used to calculate the equipment cost for a given size when the cost of the same component at a reference size is known.p may be a single size variable, for example, the capacity, or a combination of multiple size variables.The exponent ω is the scaling exponent, which lies in the range [0, 1]; it reflects the scale effect of an increases in cost falls behind an increase in size.

3 Case Study

3.1 Energy demand

The two-level optimal configuration planning method is applied to design an IES for a case study.For the designated district, the energy demand for electricity, cooling, and heating are discussed.The hourly demand data are obtained from references [13] and [18], for which the selected three days are presented in Fig.5.

Fig.5 Hourly energy demand for electricity, cooling, and heating in the case-study district for three typical seasonal days [13]

Considering the weather conditions and energy supply policy, the energy supply is clustered seasonally.Spring and autumn are considered the intermediate seasons due to similar energy demand characteristics, and each typical day is assumed to sustain for four months, i.e., the heating period in winter starts on November 15th and ends on March 15th of the next year.

3.2 Assumptions and specifications for IES

To guarantee sufficient and stable energy, the IES provides electricity either from a single source or through any combination of a GT, photovoltaic (PV) arrays, and wind power (WT).The thermal load can be achieved using a water-to-water electric heat pump (EHP) and an electric boiler (EB), in addition to a heat exchanger (HE) deployed downstream of the GT.The cooling load can be achieved using an absorption chiller and a turbo-driven compression chiller (TCC).Considering the IES as an isolated energy system, storage batteries (SB) are employed to control the stochastic and intermittent characteristics of the renewable energy.The energy flows among various components with the input and output port labels are depicted in Fig.6.

Fig.6 Energy flows between the alternative components with the input and output port labels for NEH in the case study

Considering renewable energy, the key parameters are defined to quantify the time-varying energy resources.The hourly power generated from the PV array (PPV, W) is calculated using a modified version of the model developed by Duffie and Beckman [37]:

where ηPV,STC is the efficiency of the PV module under standard test conditions (STC) (%), μ is the temperature coefficient of the output power (%/℃), Ta is the ambient temperature (℃), TSTC is the temperature under standard test conditions (25 ℃), v is the wind speed (m/s), NOCT is the nominal operating cell temperature (℃), APV is the PV array area (m2) related to the array power peak, and Gg,t is the global solar radiation on the tilted surface (W/m2).

The hourly power generated from the wind turbine (PWT, W) is given by the following equations [38]:

where vi, vr, and vo are the cut-in, rated, and cut-out characteristic speeds of the wind power curve (m/s), respectively, ρair is the air density (1.225 kg/m3), A is the rotor area (m2), Cp is the power coefficient, v is the actual wind speed (m/s), and PWT is the wind turbine rated power (W).

For fossil fuel-based energy converters, the load-ratio and part-load-dependent operating efficiency function f(ρ) from the manufacturers’ data are used to model the partload characteristics.The power generation efficiency of the GT under the design condition is calculated as follows [39]:

where Epower is the rated power of the GT.The power generation efficiency under the off-design condition is calculated as follows:

where a0, a1, a2, a3 are the constant coefficients for a GT whose capacity ranges between 1000 kW and 10000 kW, and generally are assumed to be 0.1797, 2.329, -2.334, 0.8246, respectively [39].

For the absorption and turbo-driven compression chiller, the part-load performance curves (Fig.7) are available in reference [28].The part-load efficiency of the turbodriven compression chiller decreases with a reduction in the load-ratio, while that of the absorption chiller achieves a maximum at approximately 55% load-ratio.The energy conversion efficiency of an electric boiler is regarded as 0.95 according to the market survey.

Fig.7 Part-load characteristics curves of chillers [24].COP and
COPN are the actual and nominal coefficients of performance

The life cycle cost of the IES is used to evaluate the economic performance.Therefore, specific cost functions are designed to represent the investments for various components.The specific cost of PV modules is assumed to be 1.51 $/W based on market research in China, and that of WT modules is set at 1.02 $/W based on the onshore investment cost in China.The specific cost of GT is simulated using data collected from the manufacturer quotations and is illustrated in Fig.8.

Fig.8 Specific cost function for the gas turbine simulated using the market research data

The specific cost of the HE module is set at 181.54 $/kW heat flow [40].For other equipment, the specific costs are obtained from reference [13].The specific cost and nominal energy efficiency of the equipment are listed in Table 1.

4 Results and discussion

To verify the superiority of the hierarchical optimal configuration planning method and the two-stage evolutionary algorithm, we conducted a case study for two scenarios, considering the constant coefficients (S1) and varying coefficients (S2) of the part-load characteristics.In principle, the results of S1 are identical to those of the conventional EH model.Moreover, the scheme obtained from S1 is optimized again considering the varying partload characteristics of the energy equipment.The population size for the MMAGA is 80 at the upper level, and the maximum generation number is assumed to be 150.

Table 1 Energy efficiency and specific costs of the candidate system components

Component Energy efficiency Specific cost Photovolt images/BZ_68_460_562_570_638.pngs —1.51 $/W Wind power —1.02 $/W Battery 0.75 0.27 $/Wh Electric heat pump 3 0.15 $/W Electric boiler 0.95 0.15 $/W Water absorption chiller 0.7 0.18 $/W Turbo-driven compression chiller 3 0.15 $/W

Upon simulating the hierarchical IES planning procedures, the optimal solutions for the case study with eight candidate components were obtained.The evolution processes are illustrated in Fig.9.

After 60 iterations, the algorithm converged in the upper-level optimization.The life cycle costs of the IES in S1 and S2 are $4.26 million and $4.15 million, respectively.The $0.11 million difference is due to the initial investment capital and operation cost.For the operation cost, the assumed constant efficiency results in a deviation because the equipment efficiency drops under part-load conditions.The optimal configuration scheme of S1 is optimized again considering a variable efficiency, and the new life cycle cost of the IES obtained is $4.63 million, which is 11.57% and 8.69% higher than that for S1 and S2, respectively.Therefore, ignoring the varying part-load characteristics of the energy equipment during the design process will result in an expensive IES configuration scheme due to high operating costs.

Fig.9 Evolution of the proposed two-stage evolutionary algorithm considering constant and varying part-load performance coefficients

The equipment type and size are determined, and the optimal operating load-ratios of various components are specified at different periods for the selected typical days.Table 2 compares the optimized equipment configuration schemes considering both variable and constant part-load performance of the components.

Table 2 Optimal configuration schemes with and without the equipment part-load characteristics

Component S1 S2 Photovoltaic arrays——Wind power 710 kW 705 kW Gas turbine 60 kW 65 kW Electric hea t pump oiler 730 kW 510 kW Electric b20 kW 200 kW Heat exchanger 420 kW 350 kW Water absorption chiller 40 kW 120 kW Turbo-driven compression chiller 320 kW 240 kW Battery 460 kWh 380 kWh

For power generation, wind power is used in both the scenarios; the PV arrays are eliminated due to investment cost considerations.A small proportion of power is supplied by the GT; the initial investment capital for the GT is lower than that for the wind power; however, due to high fuel costs, the GT is not as advantageous.Considering the heat demand, an EHP is a better option in both scenarios, but for the peak heating load, an EB should be employed.The installed capacity of the EB is 200 kW in S2, which is 10 times that in S1.The heat exchanger is deployed downstream of the GT and coupled with the water absorption chiller.Considering the cooling demand, the configuration of the turbo-driven compression and water absorption chiller displays a consistent trend, in which the TCC plays a more significant role in the cooling sector.The installed capacity of the TCC is 320 kW in S1 and 240 kW in S2, while that of the AC is 40 and 120 kW in S1 and S2, respectively.Moreover, the capacity of the backup battery for wind power generation is 460 and 380 kWh, respectively.The maximum energy flows among various types of equipment in the IES with part-load characteristics are depicted in Fig.10.

Fig.10 Maximum energy flows among various components for the optimal configuration scheme of S1

For the operation strategy in the selected typical days, the load-ratio of each equipment is plotted in Fig.11.The load-ratio indicates the equipment status at any given time; and the load-ratio and the installed capacity can be used to calculate input and output energy power.On a spring or autumn day, the battery sets are charged for 2-4 h, discharged for 5-11 h, and charged again for 12-19 h until they reach full capacity, before being discharged again.The SOC change of the battery depends on the power generation and consumption, charging when the power generation more than the sum of the end-use demand and the equipment power input, and discharging on the contrary.The GT operates for 5-11 h because the wind power and battery sets cannot fulfil the power demand.However, the load-ratio in S2 is higher than in S1 because the capacity of the installed wind power and battery sets in S2 is smaller.Considering the heating supply, an EHP is used as the basic heat supply device, and an EB is used at specific periods for 12-19 h.The cooling demand for 9-19 h is met by the TCC in S2, while it is partly satisfied by the AC along with the GT for 9-11 h.

On a summer day, as shown in Fig.11 (c) and (d), the SOC change in battery sets is similar to that on a spring day.The heating demand decreases whereas the cooling demand increases for 7-20 h, when compared with those in the intermediate seasons.The thermal demand is fulfilled by the EHP and EB.The load-ratio in summer is much less than that in spring or autumn.In contrast, the cooling demand fulfilled by the TCC and AC presents a significant increase compared with that on the spring day.The TCC operates at the rated power for 12-14 h in S1.Meanwhile, the full running time for the same equipment in S2 is 11-15 h, due to the smaller installed capacity.Moreover, the GT operates for 7-20 h.

Fig.11 Load-ratios of energy converters and energy storage devices in the IES during the selected typical days

On a winter day, as shown in Fig.11 (e) and (f), the operation strategies for different components are different.In winter, the heating demand increases significantly, while the cooling demand is zero.Thus, the load-ratio of the TCC and AC is zero.In contrast, the load-ratio of the EHP and EB remain fairly high.In S1, the EHP units operate at the rated power for 12-20 h, and the EB operates at full load for 13-19 h.In S2, the EHP and EB units operate at the rated power for 11-20 h and 13-18 h; the difference is due to the larger installed capacity of the EB in S2.The GT plays an active role in the heat supply under a high load-ratio.

Based on the determined equipment type and capacity, the input energy resources and output energy wares can be calculated using Eq.(7)-(11), by combining the optimized load-ratio for each component at a given time.For the renewable energy sources, the power generation can be calculated using Eq.(25)-(26) and the available energy resources.To clarify the energy supply composition, the variations in the electrical and thermal loads distributed between the various components on a typical winter day are depicted in Fig.12.

We observe that on the winter day, the electricity stored in the battery sets is used in the first 2 h (until the third hour), the final 5 h (since the nineteenth hour), and the time between 5 and 12 h, when the real-time power generation from a wind power station cannot fulfil the terminal electricity demand.Moreover, a GT functions at a certain load-ratio to compensate for the electricity deficit.Considering the heating supply, as shown in Fig.11 (e) and (f), the EHP units operate at the rated power 12-20 h in both the scenarios, and the EB units operate at full load during the interval between 13 and 18 h.The heat generated from the EB contributes only a small proportion of the overall thermal load in S1, whereas in S2, it satisfies 24% of the overall thermal load at the fifteenth hour.This disparity is attributed to the different equipment sizes in the two scenarios.

5 Conclusions and prospects

Fig.12 Variations in electrical load and thermal load distributed between various components on a typical winter day

A two-level optimal configuration planning method was developed for IES, based on the extended EH concept and considering the part-load characteristics and spatiotemporal synergistic effects of the energy equipment.The hierarchy optimization problem was solved using a twostage evolutionary algorithm—the system component structure and size are determined through an MMAGA at the upper level, while the operation strategy for typical days is optimized by minimizing the operation costs and is solved using an IPOPT solver in the bottom level.

A case study showed the overall lifetime cost of the IES for similar optimal configuration schemes, S1 and S2.The off-design operation resulted in an additional 11.57% operation cost for the S1 optimal scheme, which demonstrates the necessity and feasibility of the optimal planning method.The results show that electricity is supplied by wind power and gas turbine, with the former being used for the main power supply tasks.An EHP performs the baseload heating by consuming the surplus wind power, while an EB and HE are used at the peak load.An AC is used before the TCC units once the GT becomes operational.Battery sets are necessary to balance the wind power.

This study provides an optimal configuration planning method for structure optimization, technology selection, and size determination for IES.However, the proposed model has certain limitations, which can addressed as follows:

· by integrating the location deployment;

· by developing a more computationally effective method;

· by considering the energy trade among distributed integrated energy systems.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant No.51821004), supported by the Major Program of the National Natural Science Foundation of China (Grant No.52090062).The author Chengzhou Li also thank the China Scholarship Council (CSC) for the financial support.

Declaration of Competing Interest

We declare that we have no conflict of interest.