A multiple-objective capacity allocation optimisation method for cogeneration integrated energy systems considering life cycle carbon emission

ABSTRACT

With the increasing penetration of renewable sources, the cogeneration integrated energy system (CIES) is much more efficient and flexible to achieve various types of energy supply for remote loads. Due to uncertainties in both sources and loads, the CIES should be carefully planned and optimised to keep it working at the suitable operation condition. Therefore, this paper proposes a multi-objective capacity allocation optimisation method for the islanded CIES, which is composed of renewable energy generation unit, electric-thermal conversion unit, electric storage, thermal storage and various loads. Firstly, three optimisation objectives are selected as typical indexes, including economic cost, solar energy utilisation, and life cycle carbon emission. An improved radar chart evaluation (RCE) solution is subsequently utilised for calculating a fitness function and building the multi-objective optimisation model. Besides, several compulsory constraints are supplemented to ensure the overall CIES performance satisfy energy supply requirement. As a mature and widely accepted algorithm, a genetic algorithm is chosen as an example to obtain the optimal capacity allocation scheme. Case study of an islanded CIES is provided on the basis of real data from the remote region of northwestern China, which successfully verifies the effectiveness of the proposed optimal capacity allocation method.

KEYWORDS:

• Cogeneration integrated energy system
• capacity allocation
• islanded mode
• radar chart evaluation solution
• carbon emission

1. Introduction

With the development and utilisation of renewable energy sources, the integrated energy system based on renewable sources has become a viable solution for energy supply in many remote and off-grid regions (May Alvarez et al. 2023; Ren et al. 2023; Yuan et al. 2023). Generally, photovoltaic or wind power generation units are adopted together with electric storages to form an islanded microgrid or integrated system, which is responsible for self-regulation of power flow. On the basis, various types of thermal producing units, electric-thermal conversion units and thermal storages can be further added to implement heat supply. As a result, the cogeneration integrated energy system (CIES) is established with many advantages including electric and thermal energy supply, energy saving, environmental protection and high utilisation efficiency, which is attracting extensive attentions from industry and academia (Dou et al. 2020; J. Li et al. 2020).

In the islanded CIES, renewable energy based distributed generators are key components, which may impair power quality and cause system operating constraint violations due to their power intermittency and uncertainty. Reasonable capacity allocation is essential for the islanded CIES to keep it working at the suitable operation condition and satisfying energy requirements. However, conventional optimisation methods focus on improving the solution robustness on constraints under uncertainties but ignoring that on the optimisation objective. Single optimisation objective is usually considered, e.g. investment or energy cost, which is not sufficient to comprehensively evaluate the overall system performances (Shawon and Liang 2023). Thus, multi-objective optimisation methods are preferred for obtaining a superior capacity allocation scheme. In C. Li et al. (2020), Li et. al formulated a multiple-objective planning model for a solar-biogas integrated energy system and advantaged on both investment cost reduction and peak load shaving by the Benders Decomposition algorithm. In Azizivahed et al. (2019), a multi-objective framework was presented to solve the dynamic feeder reconfiguration problem in automated distribution networks as well as a hybrid evolutionary algorithm, where the operation cost and energy loss were both considered in the objective function. Upon (Azizivahed et al. 2019), voltage stability index was further selected as a security objective and was added in the multi-objective framework to achieve a more comprehensive energy management approach of distribution grid (Lotfi 2020). Moreover, a modified honey bee matting optimisation algorithm based on the new mating mechanism was presented in Lotfi and Ghazi (2021) to solve the multi-objective dynamic feeder reconfiguration problem, and a fuzzy decision-maker was simultaneously adopted to select the best compromise solution among the non-dominated solutions. Among the above methods, optimisation objectives are mainly chosen in terms of distributed energy management. As for integrated energy system planning, Wang et al. (J. Wang et al. 2019) proposed a capacity allocation optimisation method for a cogeneration microgrid considering demand response, which successfully improved operation income and energy saving on typical summer and winter days. In Liu et al. (2023), a sensitivity region-based optimisation method was proposed considering microgrid frequency variation and microturbine droop control functionality, which could maximise renewable generation hosting capacity of an islanded microgrid with high solution robustness on both objective and operating constraints. In (Zou, Xu, and Zhang 2023), a stackelberg game-theoretic bi-level optimisation model was established for a multi-energy microgrid. With this method, operator optimised the energy scheduling and pricing strategies at the upper level, and the industrial, commercial and residential agents optimised their energy trading strategies at the lower level. In summary, the capacity allocation optimisation model of CIES should take into account constraints caused by equipment and load, and meanwhile, multiple objectives should be carefully selected aiming at reflecting the comprehensive system performances, e.g. reliable energy supply, high renewable energy utilisation and low economic cost. Besides, due to a fact that the global pursuit of carbon neutrality intensifies, carbon emission is also recommended as a superior option in designing CIES, which has not been discussed in C. Li et al. 2020; Y. Wang, Qiu, and Tao 2022.

As mentioned above, it is found that for the capacity allocation problem of microgrid or CIES, the mainstream solution is to comprehensively consider the planning configuration cost and operation cost, establish a unified mathematical optimisation model, and then use single objective or multi-objective optimisation algorithm to resolve this model. Thus, the optimal planning result including capacity allocation scheme and operation strategy is generated (Zhu, Peng, and Geng 2022). Sometimes, the operation strategy of microgrid or CIES can be firstly determined to simplify the mathematical optimisation model. For example, the load tracking management strategy is preferred for the islanded CIES, which has the simple logic and gives priority to meet energy supply requirements of loads. Nevertheless, due to the existence of many logic judgement links and discrete equations, it is difficult to obtain the optimal scheme or ensure that this optimisation scheme is located at the Pareto front of multi-objective function (Xu et al. 2021). Besides, for the multi-objective fitness function problem of CIES, many solutions have been studied for determining the weighting factors and calculating the fitness function, e.g. empirical parameter tuning solution (Lu et al. 2020; Zheng, Sun, and Li 2019), fuzzy membership function solution (Kumar and Freudenthaler 2020; Teo et al. 2021), and triangular evaluation solution (P. Li et al. 2016, 2017). In these solutions, the multi-objective optimisation model is actually simplified as the single-objective model by assigning proper weighting factors on these optimisation objectives in the fitness function. In fact, the radar chart evaluation (RCE) solution combining numerical calculation and graph is typically used to constitute the reasonable optimisation function and assess the overall system performances (Yang et al. 2022; Zhang et al. 2022). However, the conventional radar chart solution faces a problem of information sharing among multiple optimisation objectives. Meanwhile, both the area and perimeter of the radar chart will change with different arrangement orders of the optimisation objectives, which easily causes the inconsistent optimisation results and is difficult for direct application.

Upon (C. Li et al. 2020)- (Zhang et al. 2022), this paper proposes a multi-objective optimisation method for the capacity allocation problem of islanded CIES. Firstly, a typical framework of CIES is built, which consists of renewable energy generation unit, electric-thermal conversion unit, electric storage, thermal storage and various loads. Three optimisation objectives including economic cost, solar energy utilisation and life cycle carbon emission are respectively chosen to cover the overall system performances. In order to constitute a reasonable fitness function and overcome the problems of information sharing and objective arrangement order, an improved RCE solution is subsequently utilised so that a multi-objective optimisation mathematical model is built. Besides, several compulsory constraints are supplemented to keep the CIES satisfying energy supply requirements and working at the suitable operational condition. As a mature and widely accepted algorithm, the genetic algorithm is chosen as an example to obtain the optimal capacity allocation scheme. Case study of the islanded CIES is provided on the basis of real data from the remote region of northwestern China, which successfully verifies the effectiveness of the proposed capacity allocation optimisation method.

2. Islanded CIES and optimisation objectives

Figure 1 shows a representative framework of the islanded CIES. Photovoltaic thermal (PV/T) element serves as the sole energy source and converters solar energy into electricity and heat. PV/T element, converter, electric storage, and electric load constitute the electric transmission layer. Meanwhile, the thermal transmission layer consists of PV/T element, heat pump, boiler, thermal storage, and heat load. In the thermal transmission layer, PV/T element and heat pump serve as the primary heat source together, and boiler serve as the supplementary heat source. A water cycle device is equipped to transfer heat from sources and storage to load through heat pipe network. Besides, both the electric load and thermal load are seen as concentrated together rather than dispersed across nodes.

Figure 1. The representative framework of islanded CIES.

For the islanded CIES in Figure 1, three optimisation objectives are chosen with the minimum cost, the maximum renewable utilisation, and the minimum life cycle carbon emission.

2.1. Annualised system cost

Annualised system cost (ASC) F₁ is defined to reflect the overall system economic performance, which considers the initial investment and maintenance costs of PV/T element, converter, electric storage, heat pump, boiler, thermal storage and is expressed as

(1) $min{F}_1=\sum _{\mathit{j}=1}^n\left[C_{\mathit{inv}}\left(\mathit{j}\right)+C_{\mathit{mai}}\left(\mathit{j}\right)\right]$(1)

where C_inv(j) and C_mai(j) are the initial annualised investment cost and the annualised maintenance cost of the jth component, respectively, and n is the component number.

2.2. Wastage of solar power

Wastage of solar power (WSP) F₂ is defined to reflect the renewable utilisation condition of system, which is expressed as

(2) $min{F}_2=\sum _{\mathit{t}=1}^T{P}_{\mathit{los}}\left(\mathit{t}\right)/\sum _{\mathit{i}=1}^T{P}_{\mathit{pvt}}\left(\mathit{t}\right)$(2)

where P_los(t) demonstrates the wasted solar power and P_pv(t) shows the generated power of PV/T element at time t.

2.3. Life cycle carbon emission

Life Cycle Carbon Emission (LCCE) F₃ is defined to reflect the carbon emission condition through input-output life cycle assessment and expressed as

(3) $min{F}_3=\sum _{\mathit{j}=1}^{n_e}\sum _{\mathit{t}=1}^T{P}_j\left(\mathit{t}\right)\mathrm{\Delta t}{R}_j+\sum _{\mathit{k}=1}^{n_h}\sum _{\mathit{t}=1}^T{H}_k\left(\mathit{t}\right)\mathrm{\Delta t}{R}_k$(3)

where P_j(t) and R_j are the electric power and the carbon emission coefficient of the jth electric transmission layer element, H_k(t) and R_k are the heat power and the carbon emission coefficient of the kth thermal transmission layer component, n_e and n_h are the component numbers of electric transmission layer and thermal transmission layer.

Note that the above optimisation objectives have the normalisation processing is required to deal with different dimensions and orders of magnitude of. Since it is expected to obtain the minimum F₁, F₂, and F₃, they are all normalised as follows:

(4) $F^{\prime }=\frac{{\mathit{F}}_{max}-\mathit{F}}{F_{max}-F_{min}}$(4)

where F∈{F₁, F₂, F₃}. F^’, F_max and F_min are the normalised, maximum and minimum values of optimisation objectives, respectively.

3. Compulsory Optimisation Constraints

Compulsory optimisation constraints are considered to ensure the safe and reliable operation of islanded CIES as follows.

3.1. Power balance constraint

(5) $P_{\mathit{pvt}}\left(\mathit{t}\right)=P_{\mathit{esu}}\left(\mathit{t}\right)+P_{\mathit{est}}\left(\mathit{t}\right)+P_{\mathit{boi}}\left(\mathit{t}\right)+P_{\mathit{pum}}\left(\mathit{t}\right)+P_{\mathit{los}}\left(\mathit{t}\right)$(5)

where P_pvt(t) denotes the generation power of PV/T element at time t, P_esu(t) denotes the electric supply power for electric load at time t, P_est(t) denotes the charging/discharging power of electric storage at time t, P_boi(t) denotes the boiler power at time t, P_pum(t) denotes power of heat pump at time t, and P_los(t) denotes the abandoned power of renewable generation at time t.

3.2. Heat balance constraint

(6) $\left\{\begin{array}{c}{H}_{\mathit{pum}}\left(\mathit{t}\right)+H_{\mathit{boi}}\left(\mathit{t}\right)=H_{\mathit{hsu}}\left(\mathit{t}\right)+H_{\mathit{hst}}\left(\mathit{t}\right)+H_{\mathit{los}}\left(\mathit{t}\right)\\ H_{\mathit{pum}}\left(\mathit{t}\right)\le H_{\mathit{pvt}}\left(\mathit{t}\right)\end{array}\right.$(6)

where H_pvt(t) denotes the heat power of PV/T element at time t, H_pum(t) denotes the heat power of heat pump at time t, H_boi(t) denotes the heat power of boiler at time t, H_hsu(t) denotes the heat supply power for heat load at time t, H_hst(t) denotes the absorbing/releasing heat power of thermal storage at time t, and H_los(t) denotes the lost heat power of water cycle device at time t.

As can be seen, the heat power of heat pump in (6) is limited by the heat power of PV/T element. Besides, H_los(t) should be accurately calculated by the water flow, heat capacity and temperature difference of different sections of water cycle device. Given that the heat load, thermal storage and other heat equipment of islanded CIES are close to each other, H_los(t) demonstrates approximately proportional to the heat supply power of water cycle device in this paper for simplifying analysis.

3.3. Energy conversion constraint

To simplify analysis, the average coefficient of performance (COP) is applied to approximately evaluate the relationship between P_pum(t), P_boi(t), H_pum(t) and H_boi(t), which can be expressed as

(7) $\left\{\begin{array}{c}{H}_{\mathit{pum}}\left(\mathit{t}\right)=\mathit{CO}{P}_{\mathit{pum}}\cdot P_{\mathit{pum}}\left(\mathit{t}\right)\\ H_{\mathit{boi}}\left(\mathit{t}\right)=\mathit{CO}{P}_{\mathit{boi}}\cdot P_{\mathit{boi}}\left(\mathit{t}\right)\end{array}\right.$(7)

where COP_pum and COP_boi are the COP values of heat pump and boiler, respectively.

3.4. Capacity constraint of electric storage

(8) $0.2\mathit{SO}{C}_{\mathit{rat}}\le \mathit{SOC}\left(\mathit{t}\right)\le 0.8\mathit{SO}{C}_{\mathit{rat}}$(8)

where SOC(t) is the real-time state of charge of electric storage at time t, SOC_rat is the rated state of charge. The lower and upper limits of SOC(t) are constrained to avoid over-charging/over-discharging phenomenon and life reduction.

3.5. Power constraints of electric storage

(9) $-P_{\mathit{est}\_max}\le P_{\mathit{est}}\left(\mathit{t}\right)\le P_{\mathit{est}\_max}$(9)

where P_{est_max} denotes the maximum charging/discharging power of electric storage and is limited by the power of converter P_con. Especially, P_est(t)>0 at the charging state, while P_est(t)≤0 at the discharging state.

3.6. Efficiency constraint of electric storage

(10) $\mathit{SOC}\left(\mathit{t}\right)=\mathit{SOC}\left(\mathit{t}-1\right)+\mathit{\eta }{P}_{\mathit{est}}\left(\mathit{t}-1\right)\mathrm{\Delta t}$(10)

where SOC(t-1) and SOC(t) denotes the real-time states of charge of electric storage at time (t-1) and time t, respectively. η denotes the charging/discharging efficiency and is selected as 0.9 here. P_est(t-1) denotes the charging/discharging power of electric storage at time (t-1), and Δt denotes the time interval.

3.7. Capacity constraint of thermal storage

(11) $0\le \mathit{Q}\left(\mathit{t}\right)\le Q_{\mathit{rate}}$(11)

where Q(t) denotes the real-time capacity of thermal storage at time t, and Q_rat denotes the rated capacity of thermal storage.

3.8. Heat power constraint of thermal storage

(12) $-H_{\mathit{out}\_\max }\le H_{\mathit{hst}}\left(\mathit{t}\right)\le H_{\mathit{in}\mathrm{\_}max}$(12)

where H_{in_max} is the maximum absorbing heat power of thermal storage, and H_{out_max} are the maximum releasing heat power, which are both limited by the transfer heat power of heat exchanger. Especially, H_hst(t)>0 at the absorbing state, while H_hst(t)≤0 at the releasing state.

3.9. Energy supply constraints

The probability that electrical supply power P_esu(t) is less than the electrical load P_load(t) within a period of T and the probability that heat supply power H_hsu(t) is less than the heat load H_load(t) within a period of T are constrained to guarantee reliable power and heat supply for loads, i.e.

(13) $\left\{\begin{array}{c}\sum _{\mathit{t}=1}^T\mathit{p}\left(P_{\mathit{esu}}\left(\mathit{t}\right)<P_{\mathit{load}}\left(\mathit{t}\right)\right)\le r_1\mathit{T}\\ \sum _{\mathit{t}=1}^T\mathit{p}\left(H_{\mathit{hsu}}\left(\mathit{t}\right)<H_{\mathit{load}}\left(\mathit{t}\right)\right)\le r_2\mathit{T}\end{array}\right.$(13)

where 0≤r₁ ≤1 and 0≤r₂ ≤1 are the power and heat supply reliability coefficients. Thus, they are both chosen as 0.05 to ensure the relatively reliable energy supply for load.

4. Fitness calculation using the RCE model

In this subsection, a RCE model is employed to constitute the fitness function and assess the overall islanded CIES performances.

4.1. Calculate the sector angles of optimisation objectives with G1 method

In order to determine the weights of three optimisation objectives reasonably, a typical analytic hierarchy process (AHP), i.e. G1 method, is utilised with the steps as follows:

Firstly, sort F₁’, F₂’ and F₃’ by their own importance degrees. Here, F₁’ is ranged as the most important optimisation objective, while F₃’ is ranged as the least important optimisation objective.

Then, the ratio of importance degrees between two adjacent optimisation objectives R_ri-m is defined as

(14) $R_{\mathit{ri}-}{\mathit{\hspace{0.17em}}}_m=\frac{X_{\mathit{m}-1}}{X_m},\mathit{m}=2,3,$(14)

where X₁, X₂ and X₃ represent the importance degree of F₁’, F₂’ and F₃’, respectively. 1.0, 1.2, 1.4 or 1.6 is commonly selected as the value of R_ri-m. R_ri-m = 1.0 means that two adjacent optimisation objectives have the same importance degrees. Besides, the larger R_ri-m is, the more important X_m is than X_m-1. In this paper, R_ri-2 and R_ri-3 are both selected as 1.2.

Then, the weight of each optimisation objective can be derived as

(15) $\left\{\begin{array}{c}{w}_{\mathit{m}-1}=R_{\mathit{ri}-\mathit{m}}{w}_m,\mathit{m}=2,3\\ w_3={\left(1+{\mathit{R}}_{\mathit{ri}-2}{{\mathit{R}}_{\mathit{ri}-}}_3+R_{\mathit{ri}-3}\right)}^{-1}\end{array}\right.$(15)

and the sector angle of each optimisation objective θ_k in the radar chart is decided as

(16) ${\theta }_k=2\mathit{\pi }{w}_k,\mathit{k}\in \left\{1,2,3\right\}$(16)

Finally, the weights and sector angles of three optimisation objectives are calculated as follows:w₁ = 0.3956, w₂ = 0.3297, w₃ = 0.2747, θ₁ = 2.486 rad, θ₂ = 2.071 rad, and θ₃ = 1.726 rad.

4.2. Plot radar chart

Firstly, plot a half-line OZ, which starts from the centre of unit circle O and intersects with unit circle at A. Similarly, plot another two half-lines OX, OY on the basis of sector angle and in the order of weights from largest to smallest. Furthermore, we can obtain three sectors, i.e. ZOX, XOY, ZOY, which corresponds to F₁, F₂, F₃.

Then, plot the angle bisectors OZ’, OX’, OY’ of all sectors, which Z’, X’, Y’ are the intersection points with unit circle, and adopt these angle bisectors as the axis of optimisation objectives.

Based on F₁’, F₂’ and F₃’, plot their corresponding points z, x, y in each axis, and obtain a triangular zxy. As a result, the radar chart is plotted as Figure 2.

Figure 2. The plotted radar chart.

4.3. Fitness calculation

Based on Figure 2, the area S_rc and perimeter L_rc of the radar chart are derived as

(17) $S_{\mathit{rc}}=\frac{1}{2}\left[\sum _{\mathit{i}=1}^2{F_i}^{\prime }{F}_{i+1}^{\prime }sin\left(\frac{{\theta }_i+{\theta }_{\mathit{i}+1}}{2}\right)+{{\mathit{F}}_1}^{\prime }{{\mathit{F}}_3}^{\prime }sin\left(\frac{{\theta }_1+{\theta }_3}{2}\right)\right]$(17)

Based on Figure 2, the area S_rc and perimeter L_rc of the radar chart are derived as

(18) $L_{\mathit{rc}}=\sum _{\mathit{i}=1}^2\sqrt{\mathit{F}{{ }_i^{\prime }}^2+\mathit{F}{{ }_{i+1}^{\prime }}^2-2F_i^{\prime }{F}_{i+1}^{\prime }cos\left(\frac{{\theta }_i+{\theta }_{\mathit{i}+1}}{2}\right)}+\sqrt{\mathit{F}{{ }_1^{\prime }}^2+\mathit{F}{{ }_3^{\prime }}^2-2F_1^{\prime }{F}_3^{\prime }cos\left(\frac{{\theta }_1+{\theta }_3}{2}\right)}$(18)

Accordingly, the corresponding fitness function can be derived by S_rc and L_rc as

(19) $\mathit{F}=\sqrt{S_{\mathit{rc}}\cdot L_{\mathit{rc}}}$(19)

5. Optimisation implementation

Based on the aforementioned optimisation objectives, fitness function and constraints, a capacity allocation optimisation model is built with the target of minimising the value of fitness function as

(20) $max\mathit{F}=\sqrt{S_{\mathit{rc}}\cdot L_{\mathit{rc}}}\mathit{s}.\mathit{t}.\left(5\right)-\left(13\right)$(20)

The proposed optimisation algorithm is a hybrid methodology that synergistically combines principles from multi-objective optimisation, the radar chart evaluation solution, and a natural selection-based optimisation algorithm, such as genetic algorithm and its alternatives (particle algorithm etc.). This approach is designed to address the complexity and diversity inherent in optimisation problems, leveraging the strengths of different optimisation paradigms for enhanced. As a mature algorithm, the genetic algorithm (GA) is a heuristic search and optimisation technique that imitates the process of natural selection to evolve potential solutions to a problem, by iteratively evolving a population of potential solutions towards optimal or near-optimal solutions. To enhance reliability and comprehensiveness, this paper incorporates the genetic algorithm as a foundational method within its framework to solve the capacity allocation optimisation model in (20). As a result, the optimisation implementation process is shown in Figure 3 and illustrated as follows:

Figure 3. The flowchart of optimisation implementation process.

Step 1: Data Input.

Input the generation power data of PV/T unit, power load data and heat load data to obtain the maximum implemental range of each component for the islanded CIES.

Step 2: Condition Assuming.

To reflect the common daily operation process of electric storage and thermal storage, their initial conditions at t = 0 should be equal to the final conditions at t=T, which can be expressed as

(21) $\left\{\begin{array}{c}\mathit{SOC}\left(0\right)=\mathit{SOC}\left(\mathit{T}\right)\\ \mathit{Q}\left(0\right)=\mathit{Q}\left(\mathit{T}\right)\end{array}\right.$(21)

Step 3: Load Tracking Managing.

For the islanded CIES, the load tracking management strategy is an effective solution to keep the optimisation following load changing and regulate the real-time energy flow of all system components. Meanwhile, the energy supply and usage priorities of system components in this scheduling strategy are given as:

1) Power supply priority:

(22) $\mathrm{PV}/\mathrm{T}>\mathrm{Electric}\mathrm{storage}$(22)

2) Heat supply priority:

(23) $\mathrm{Pump}>\mathrm{Heat}\mathrm{storage}>\mathrm{Boiler}$(23)

3) Power usage priority:

(24) $\mathrm{Pump}=\mathrm{Boiler}>\mathrm{Electric}\mathrm{load}>\mathrm{Electric}\mathrm{storage}$(24)

1. Heat usage priority:

2. Power usage priority:

   (25) $\mathrm{Heat}\mathrm{load}>\mathrm{Heat}\mathrm{storage}$(25)

Step 4: Iteration Solving.

The paper applies a widely accepted genetic algorithm (GA) to the solution of the capacity allocation optimisation model in (20). The number of population is set to 300, the number of evolution iteration equals to 400, the crossover rate is set to 0.5, and the mutation rate is fixed at 0.01. With this algorithm, the optimal capacity allocation result can be obtained through iterative solution for the islanded CIES.

6. Case study

To verify the proposed optimal capacity allocation method, case study is presented on the basis of real data from the remote region of northwestern China and (J. Wang et al. 2019). In this case, the maximum power and heat loads on a typical summer day are 822 kW and 451 kW, while the maximum power and heat loads on a typical winter day are 835 kW and 1266 kW. Figure 3 illustrates the predictive generation power of unit megawatt (MW) PV/T component, power load, and heat load on the typical summer day and winter day. For PV/T element, its solar-power conversion rate and solar-heat conversion rate are set as 15% and 20%, respectively. The lithium battery is adopted for electric storage, and the molten salt is adopted for thermal storage. Tables 1 and 2 list the annualised system cost, the life cycle carbon emission coefficients and the annual utilisation hours of CIES elements, respectively.

Table 1. Annualised system cost of CIES elements.

Parameter		Value
PV/T element	Cinv (¥/kW)	3500
	Cmai (¥/kW·year)	120
Electric storage	Cinv (¥/kWh)	1840
	Cmai (¥/kWh·year)	40
Thermal storage	Cinv (¥/kW)	510
	Cmai (¥/kWh·year)	15
Boiler	Cinv (¥/kW)	500
	Cmai (¥/kW·year)	25
	COP	0.96
Heat pump	Cinv (¥/kW)	850
	Cmai (¥/kW·year)	30
	COP	3
Converter	Cinv (¥/kW)	200
	Cmai (¥/kW·year)	12

Table 2. Life cycle carbon emission coefficient and annual utilisation hours of CIES elements.

Element	Carbon emission coefficient R (kg/kWh)	Annual utilisation hours (h/year)
PV/T	0.086	1056
Electric storage	0.112	448
Thermal storage	0.101	466
Heat pump	0.028	877
Boiler	0.031	655
Converter	0.022	448

6.1. Simulation result with the proposed optimisation method

Based on real data in Figure 4(a) and assuming a 20-year life cycle, the optimal capacity allocation scheme of islanded CIES on a typical summer day are as follows: 3.92 MW PV/T element, 12683kWh electric storage, 1.71 MW converter, 934 kW heat pump, 1503 kW boiler, 10825kWh thermal storage. In this case, three optimisation objectives are F₁ = 3.45 × 10⁶¥/year, F₂ = 0.1570, F₃ = 1.19 × 10⁶kg/year. Under this optimal capacity scheme, Figure 5(a) demonstrates the energy flow of islanded CIES on a typical summer day. Due to the higher H_load and the lower P_pvt at the initial 0–4h, boiler and thermal storage are responsible for heat supply with Q rapidly and approximately decreasing to 0, while electric storage is responsible for electric supply with SOC decreasing relatively slowly. Then, P_boi decreases with P_pvt gradually increasing at 5–7h, while SOC and Q both increases at 9–18h. Notably, PV/T element and heat pump are mainly responsible for electric and heat supply at 5–20h. Finally, at 19–24h, electric storage, thermal storage and boiler are responsible for energy supply again. It is obvious that electric and heat supply are reliable within the whole operation process, which verifies that the optimal capacity allocation scheme can overwhelmingly realise good system performances on a typical summer day.

Figure 4. The predictive generation power of 1MW PV/T component, electrical load and heat load. (a) Typical summer day, (b) typical winter day.

Figure 5. Energy flow of the islanded CIES with the proposed optimisation method.(a) Typical summer day, (b) Typical winter day.

Based on real data in Figure 4(b) and assuming a life cycle of 20 years, the optimal capacity allocation scheme of islanded CIES on a typical winter day are as follows: 4.69 MW PV/T element, 18769kWh electric storage, 1.88 MW converter, 1224 kW heat pump, 1770 kW boiler, 10155kWh thermal storage. In this case, three optimisation objectives are F₁ = 4.49 × 10⁶¥/year, F₂ = 0.0093, F₃ = 1.47 × 10⁶kg/year. It is noted that since H_load is larger in winter, the capacities of PV/T element and electric-thermal conversion device are much larger than those in summer. With this optimal capacity scheme, Figure 5(b) shows the energy flow of islanded CIES on a typical winter day. As seen, similar to the previous case, at the initial 0–8h, boiler and thermal storage are responsible for heat supply with Q rapidly decreasing to 0 at 4h, while SOC decreases relatively slowly. Then, P_pvt keeps a high level with SOC and Q both increasing at 9–18h, while P_boi even decrease to 0 at 9–19h. Finally, at 20–24h, electric storage, thermal storage and boiler are responsible for energy supply again. Thus, this optimal capacity allocation scheme is also able to ensure satisfactory overall system performances on a typical winter day.

According to Figure 4, the proposed optimal capacity allocation method is effective for the islanded CIES to achieve satisfactory overall performances.

6.2. Comparison with single-objective optimisation methods

To compare the proposed method with single-objective optimisation methods, this paper lists different optimal capacity allocation schemes of islanded CIES on a typical winter day in Table 3 with real data in Figure 4(b), and a life cycle of 20 years. Meanwhile, Figure 6 further shows the energy flow of islanded CIES on a typical winter day with different optimisation methods.

Table 3. Capacity allocation results with different optimisation methods.

Result			Optimisation Method
			Proposed method	Minimum F1	Minimum F2	Minimum F3
Capacity Allocation	PV/T (MW)	4.69		6.29	4.53	7.94
	Electric storage (kWh)	18769		11207	19770	14342
	Converter (MW)	1.88		1.16	1.98	1.36
	Heat pump (kW)	1224		695	1537	1738
	Boiler (kW)	1770		397	1888	1592
	Thermal storage (kWh)	10156		26600	10233	10233
Optimisation Objective	F1 (¥/year)	4.49×10^6		4.47×10^6	5.35×10^6	4.70×10^6
	F2	0.0093		0.3744	0	0.3958
	F3 (kg/year)	1.47×10^6		1.83×10^6	2.40×10^6	1.27×10^6

Figure 6. Energy flow of the islanded CIES on a typical winter day. (a) Minimum F₁, (b) Minimum F₂, (c) Minimum F₃.

Combing Table 3 and Figure 6, although the capacity allocation schemes by optimising F₁ or F₃ are able to achieve the minimum cost or carbon emission, the solar energy abandonment phenomenon is more serious than that of the proposed optimisation method. Comparatively, the capacity allocation schemes by optimising F₂ can achieve the nearly full use of solar energy, but its cost and carbon emission are unsatisfactory. Thus, the proposed optimisation method can obtain a superior capacity allocation scheme with comprehensive system performances in comparison with single-objective optimisation methods.

6.3. Comparison with the multi-objective weighted optimisation method

In order to prove the superiority of the improved RCE solution for fitness function establishment, the multi-objective weighted optimisation method is presented here for comparison, which aims at minimising the area S of the radar chart model. The same optimisation implementation process is adopted with GA to obtain the capacity allocation result.

To ensure the year-round electricity and heat supply in remote regions, the optimal capacity allocation scheme on a typical winter day is only given as follows: 4.53 MW PV/T element, 19927kWh electric storage, 1.99 MW converter, 1910 kW heat pump, 1861 kW boiler, 27615kWh thermal storage. In this case, three optimisation objectives are F₁ = 5.26 × 10⁶¥/year, F₂ = 0.0028, F₃ = 2.29 × 10⁶kg/year. Under this optimal capacity scheme, Figure 7 demonstrates the energy flow of islanded CIES on a typical winter day.

Figure 7. Energy flow of the islanded CIES with the weighted optimisation method on a typical winter day.

As can be seen, there is basically no certain phenomenon of renewable energy abandonment in the islanded CIES, the energy utilisation efficiency is high, and the power loss problem does not exist. Compared with the single-objective optimisation results in Section 5.2, the multi-objective weighted method can obtain a proper capacity allocation scheme for CIES with the better overall performance. However, in comparison with the improved RCE solution-based multi-objective optimisation method in Section 5.1, the objective F₁, which is of greater importance, has not realised its satisfying optimisation result. Thus, the proposed multi-objective capacity allocation optimisation method based on the improved RCE solution has better applicability than the multi-objective weighted method.

7. Conclusion

This paper focuses on the representative islanded CIES, which is composed of renewable energy generation unit, electric-thermal conversion unit, electric storage, thermal storage and various loads, and investigates the reasonable capacity allocation scheme to keep it satisfying energy requirements. In this study, a multi-objective optimisation method is proposed on the basis of the improved RCE solution, and conclusions are drawn as follows.

1. Three optimisation objectives are carefully selected from the aspects of economic cost, solar energy utilisation and life cycle carbon emission, which responds to the global pursuit of carbon neutrality and fully reflects the essential system performances.

2. The reasonable fitness function is proposed on the basis of the improved RCE solution, which is easy to implement and can overcome the inherent problems of information sharing and objective arrangement order. Especially, this fitness function establishment method is still applicable when more optimisation objectives are adopted.

3. The multi-objective capacity allocation optimisation model is finally established with reliable energy supply constraints and the mature GA for optimisation implementation, which is successfully validated through case study.

In addition, the load tracking management strategy has simple logic and gives priority to ensuring the energy supply demand of loads, which is adopted in the mathematical optimisation model. Nevertheless, due to the existence of many logic judgement links and discrete equations, it is difficult to obtain the optimal scheme or ensure that this optimal scheme is located at the Pareto front of multi-objective fitness function. Thus, the planning optimisation method including capacity allocation scheme and energy management strategy is worth further studying.

Nomenclature

CIES	=	Cogeneration Integrated Energy System
REC	=	Radar Chart Evaluation
PV/T	=	Photovoltaic Thermal
ASC	=	Annualised System Cost
WSP	=	Wastage of Solar Power
LCCE	=	Life Cycle Carbon Emission
COP	=	Coefficient of Performance
SOC	=	State of Charge
GA	=	Genetic Algorithm

Disclosure statement

No potential conflict of interest was reported by the author(s).