Keywords

1 Introduction

In recent years, energy internet has been developing vigorously in China. As the basic cell of the energy internet, the integrated energy system covers energy consumption systems and distributed energy supply equipment [1]. It is an effective method to realize multi-energy complementation and energy cascade utilization [2, 3]. In actual operations, problems such as unreasonable planning and configuration were gradually exposed. Reasonable and optimized configuration in the early stage of project construction is the key to the continuous operation of the integrated energy system.

Scholars in China and abroad have carried out extensive research on the optimal configuration method of integrated energy systems: Reference [4, 5] comprehensively considers configuration and operation optimization. The optimization objective in the upper-layer is the minimum cost, and the optimization objective in the lower-layer is the minimum cost. The two-layer optimization solution method often adopts the combination of upper-layer intelligent optimization algorithms, such as genetic algorithm [4,5,6], particle swarm algorithm [7, 8], and lower-layer linear programming, etc. Reference [9,10,11,12,13] comprehensively considers configuration optimization and operation optimization variables, and uses a large-scale mixed integer linear programming method to achieve synchronous optimization of configuration and operation. In order to enhance the engineering practicability of the optimized configuration results and avoid unreasonable investment, some scholars have improved the optimized configuration model from the perspectives of construction sequence, equipment pre-selection, and simulation analysis. Reference [14] proposed a multi-stage planning method for the integrated energy system considering the construction sequence. Reference [15] through equipment pre-selection, configures the available capacity of equipment in advance, and avoids the problem of a large gap between results and actual results caused by continuous changes of optimized configuration variables.

In this paper, through extensive research on the commercially available products of the integrated energy system, the optimal configuration method of the integrated energy system in the industrial park considering the constraints of engineering equipment is proposed. The maximum net present value of the system is used as the optimization objective. The source-load balance and equipment operating characteristic constraints are used as the basic constraints. A large-scale mixed-integer linear programming optimization model is established under the constraints of engineering equipment. The configuration results and operation strategies are analyzed by numerical examples, and the influence of investment constraints on the optimal configuration of the system is studied.

2 System Model Building

2.1 The Structure of Integrated Energy System

The structure of the integrated energy system is shown in Fig. 1. It contains three busbars: power, cold and heat bus. And the energy system is made of energy layer, equipment layer and load layer.

Fig. 1.
figure 1

Schematic diagram of the structure of the integrated energy system

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2.2 Engineering Equipment Products

The capacity, performance and price of the energy conversion, storage and supply equipment involved in the construction of the integrated energy system in the industrial park are directly determined by the equipment products in the market. And the prices and performance levels of equipment products of different companies or different models are uneven. This paper establishes a commercial equipment product library based on market research and the equipment products commonly used in the park’s comprehensive energy. The library covers the equipment model’s type, efficiency, startup load and other performance parameters, operation and maintenance cost, sales price and other price parameters. The equipment product library used in this paper is detailed in Table 2 of Appendix.

3 The Optimization Model and Solution

3.1 The Optimize Configuration Variable

The operation variable is directly constrained by the installation of the equipment. Therefore, the setting of the configuration optimization variable directly affects the scientificalness and reliability of the optimization model. In order to make a comparative analysis, this paper adds the method of taking the continuous variable of equipment capacity as the optimization variable, and compares it with the method of considering the constraints of engineering equipment in this paper. The configuration variable settings of the two methods are described as follows:

As shown in method 1 in Table 1, \(V\left( i \right)\) is a continuous optimization variable, which represents the capacity of the ith device, \(\left[ {minV,\,\,maxV} \right]\) represents the set capacity optimization interval.

As shown in method 2 in Table 1, \(n\left( {i,j} \right)\) represents the number of equipment of the \(i\)-th class and the \(j\)-th type. Compared with the first method, method 2 has more integer variables. However, this method fully considers the situation of engineering products and has strong engineering practicability. \(I\) refers to the number of equipment classes, and \(J\) refers to the number of equipment types.

Table 1. The setting of configuration optimization variables
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3.2 The Objective Function

The evaluation of the optimal allocation results of the integrated energy system needs to comprehensively consider its early-stage investment and the income within the project operation cycle. We convert the cost or income generated by the system operation to the present value at the beginning of the planning cycle, and comprehensively consider the early-stage investment, and establish an objective function with the net present value as the optimization objective, as follows.

$$ NPV = \sum\nolimits_{n = 1}^{n = N} {NCF\left( n \right)/\left( {1 + IRR} \right)^{n - 1} } $$
(1)
$$ \begin{gathered} NCF\left( n \right) = \sum\nolimits_{l = 1}^{l = L} Income\left( l \right) - \sum\nolimits_{e = 1}^{e = E} Cost\left( e \right) - \frac{{\sum\nolimits_{i = 1}^{i = I} \sum\nolimits_{j = 1}^{j = J} \left( {Equi\left( {i,j} \right)n\left( {i,j} \right)} \right)}}{k} \hfill \\ \quad \quad \quad \quad + \sum\nolimits_{i = 1}^{i = I} \sum\nolimits_{j = 1}^{j = J} \left( {Subsidy\left( {i,j} \right) - Replace\left( {i,j} \right)} \right)*n\left( {i,j} \right) \hfill \\ \end{gathered} $$
(2)

where, \(NPV\) refers to the net present value within the planning cycle of the project, \(N\) refers to the planning cycle of the project, \(IRR\) refers to the benchmark internal rate of return, \(NCF\left( n \right)\) refers to the net cash flow in the \(n\) th year of the planning cycle, \(Income\left( l \right)\) refers to the income of the 1st kind of sales load, \(Cost\left( e \right)\) refers to the purchase cost of the e kind of energy, and \(Subsidy,Replace,Equi\) refer to the subsidy, replacement, and purchase unit price of a certain type of product respectively. \(k\) refers to the conversion coefficient of equipment purchase cost relative to total investment.

3.3 The Constraint Conditions

The integrated energy system optimization model realizes the combination selection of equipment and the optimization of its operation strategy at the same time, so its constraints are also divided into two levels. The first level is the constraints for equipment selection and sizing, mainly including: energy source load balance constraints, installed reliability constraints, financial demand constraints, environmental constraints, etc. The second layer is the equipment operation constraints, mainly including: the power constraints of the equipment, the start and stop constraints, and the state of charge constraints of energy storage equipment.

System Constraints

  1. 1)

    Energy balance constraint. The optimization model needs to meet the power balance of electric, cold and heat, and its source-load balance model can be ex-pressed as:

    $$ \left\{ {\begin{array}{*{20}c} {\sum\nolimits_{i = 1}^{i = I} \sum\nolimits_{j = 1}^{j = J} P_{ij} \left( t \right)*n\left( {i,j} \right) = P\left( t \right)} \\ {\sum\nolimits_{i = 1}^{i = I} \sum\nolimits_{j = 1}^{j = J} Qc_{ij} \left( t \right)*n\left( {i,j} \right) = Q_c \left( t \right)} \\ {\sum\nolimits_{i = 1}^{i = I} \sum\nolimits_{j = 1}^{j = J} Qh_{ij} \left( t \right)*n\left( {i,j} \right) = Q_h \left( t \right)} \\ \end{array} } \right. $$
    (3)

    where, \(P\left( t \right),Q_c \left( t \right),Q_h \left( t \right)\) respectively represents the electric/cooling/heating load at the time of t. \(P_{ij} \left( t \right),Qc_{ij} \left( t \right),Qh_{ij} \left( t \right)\) respectively represents the electric/cold/hot output of the i-th class and the j-th type equipment at the time of t.

  2. 2)

    Installation reliability constraints. The installed reliability constraints described in this paper mainly include stable electric, cold and hot installations, and renewable energy power generation installation constraints. Related constraints can be described as:

    $$ \sum\nolimits_{i = 1}^{i = I} \sum\nolimits_{j = 1}^{j = J} V\left( {i,j,l} \right)*n\left( {i,j} \right) \ge Maxload\left( l \right) $$
    (4)
    $$ V_{wind} \left( j \right)n_{wind} \left( j \right) + V_{pv} \left( j \right)n_{pv} \left( j \right) \le rV_{grid} \left( j \right)n_{grid} \left( j \right) $$
    (5)

    where, \(maxload\left( l \right)\) represents the design load of the l-th load. \(V\left( {i,j,l} \right)\) represents the rated capacity of the i-th class and the j-th type equipment on the load of l-th. \(V_{wind} \left( j \right)\), \(V_{pv} \left( j \right)\), \(V_{grid} \left( j \right)\), \(n_{wind} \left( j \right)\), \(n_{pv} \left( j \right)\), \(n_{grid} \left( j \right)\) respectively indicate the rated capacity and installed number of the j-th fan, the j-th photovoltaic and the j-th transformer models. R refers to the proportion coefficient between the installed capacity of wind turbine/photovoltaic and the installed capacity of transformer in the park.

  3. 3)

    The constraint of financial demand. The constraint of financial demand is the constraint of total investment, which is the total investment cost of system construction shall not be higher than the expected project investment value \(Ftotal\).

    $$ \sum\nolimits_{n = 1}^{n = N} \left( {\sum\nolimits_{i = 1}^{i = I} \sum\nolimits_{j = 1}^{j = J} Equi\left( {i,j} \right){\text{n}}\left( {{\text{i}},{\text{j}}} \right)/k} \right) \le Ftotal $$
    (6)

The Equipment Operation Constraints

  1. 1)

    Power constraint. The output of the equipment is limited by the upper and lower limits of its output, which are generally determined by the installed capacity and its starting load of the equipment. The power constraints of each equipment can be described as shown in formula (20).

    $$ \left\{ {\begin{array}{*{20}c} {MinP\left( {i,j} \right) \le P\left( {i,j} \right) \le MaxP\left( {i,j} \right)} \\ {MinQ_c \left( {i,j} \right) \le Q_c \left( {i,j} \right) \le MaxQ_c \left( {i,j} \right)} \\ {MinQ_h \left( {i,j} \right) \le Q_h \left( {i,j} \right) \le MaxQ_h \left( {i,j} \right)} \\ \end{array} } \right. $$
    (7)

    where, \(P\left( {i,j} \right),Q_c \left( {i,j} \right),Q_h \left( {i,j} \right)\) respectively represents the electric/cold/heat power of the \(j\)-th type equipment, and \(Max,Min\) respectively represent their minimum starting load and maximum output.

  2. 2)

    Constraints of energy storage equipment. The energy storage equipment also has constraints of charging state, as shown in formula (11–12), and the constraints of charging and discharging times can be described as shown in formula (21).

    $$ U_{cell} \left( {i,j} \right) \le minU_{cell} \left( {i,j} \right) $$
    (8)

    where: \(U_{cell} \left( {i,j} \right)\) is the charging and discharging times of the \(j\)-th type battery, \(minU_{cell} \left( {i,j} \right)\) is the optimal charging and discharging times allowed.

3.4 Solution Method

By linearizing the nonlinear constraints in the solution model, the optimal allocation model of park integrated energy system considering engineering practicality can be considered as a large-scale mixed integer linear programming problem covering continuous variables and integer variables:

$$ \left\{ {\begin{array}{*{20}l} {\,\ } \hfill & {min F\left( x \right)} \hfill \\ {s.t. } \hfill & {h_m \left( x \right) = 0 m = 1,2, \ldots \ldots ,M} \hfill \\ \, \hfill & {g_r \left( x \right) \le 0 r = 1,2, \ldots \ldots ,R} \hfill \\ \, \hfill & {x_{min} \le x \le x_{max} } \hfill \\ \, \hfill & {x_k \in \left\{ {0,1,2,3 \ldots \ldots } \right\}} \hfill \\ \end{array} } \right. $$
(9)

where \(F\left( x \right)\) is the objective function and x is the variable to be optimized. \(h_m \left( x \right) = 0 \) are the equality constraints, \(g_r \left( x \right) \le 0\) are the inequality constraints. \(x_{min}\), \(x_{max}\) are the upper and lower limits of variables respectively. \(x_k\) is the integer variable. M, R are the number of equality constraints and inequality constraints respectively. The commercial solver CPLEX can be called to optimize the model.

4 Example Analysis

4.1 Examples and Scenarios

An office park in Beijing is selected as an example. The annual hourly load curve is shown in Fig. 2. In the comprehensive energy system planning, the amount of data is too large when optimizing based on the annual 8760 h hourly load curve. There are two 630 kVA transformers in the park. The electricity price is the local industrial and commercial time of use electricity price. The available roof area of the park is 1600 m2. The site does not have the conditions for the construction of fans and water energy storage, and has the conditions for natural gas access. In order to verify the practicability and effectiveness of the optimized configuration of the integrated energy system based on the equipment product library, three scenarios were set up for analysis.

Fig. 2.
figure 2

Annual hourly load curve of the whole region

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Scenario 1: Method 1 in Table 1 is used for the selection of configuration optimization variables. Set uniform performance and price parameters for various types of equipment. Refer to Table 2.

Table 2. Unified performance parameters of various equipment.
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Table 3. Information of some commercial equipment.
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Scenario 2: Since the optimized configuration results of the devices in scenario 1 are not practical, model are selected in the commercially available library based on the principle of similar capacity to form scenario 2.

Scenario 3: Method 2 in Table 1 is used for the selection of configuration optimization variables. Each equipment parameter is based on the commercially available equipment product library. Refer to Table3. Taking the direct combustion engine as an example, the settings of each scenario are shown in Table 4 and Table 5.

Table 4. Part of the performance parameters of the direct combustion engine in scenario 1
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Table 5. Information on some commercial products of DC gas turbines in scenario 2
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4.2 Configuration Optimization Result Analysis

The results of each optimized configuration are shown in Table 6: Since Beijing is a typical area with low gas prices and high electricity prices, a high-power gas trigeneration system is installed in both scenarios, and a heat pump system or a direct-fired turbine is equipped. The supplement of supply has good economic benefits. From the analysis of the optimization results, the configuration results of Scenario 1 and Scenario 3 have a certain gap in equipment types and equipment installed capacity. Scenario 1 does not consider engineering products during optimization, the equipment capacity is biased towards the theoretical value, and the equipment types are more too much, which is not conducive to later operation and maintenance.

From the analysis of the economic evaluation results, scenario 1 has large net present value NPV, large internal rate of return (IRR), short payback period, and relatively good economy. The net present value of the operation optimization is significantly lower than that of the Scenario 3, which verifies the effectiveness of the configuration optimization based on the equipment product library.

Table 6. Configuration optimization results in different scenarios
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4.3 Analysis of Running Results

Taking a typical weekday in July in summer as an example, the hourly operation of each device in Scenario 3 is shown in Figs. 3 and 4. During the peak and peacetime of electricity price during the day, the electricity load of the park is mainly supplied by photovoltaics and trigeneration system. During the valley time of electricity price at night, the electricity load is mainly supplied by the transformer through the city grid, and the part with the supply greater than the load is mainly the power consumption of the ground source heat pump. The cooling load supply is given priority to trigeneration system, and the insufficient part is supplemented by the ground source heat pump.

Fig. 3.
figure 3

Electric balance optimization strategy

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Fig.4.
figure 4

Cool balance optimization strategy

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4.4 Investment Sensitivity Analysis

As shown in Table 7, under different reasonable investment constraints, the optimal configuration scheme can be optimized, and the scheme difference is obvious. When the total investment constraint exceeds the corresponding investment of the optimal allocation scheme, the total investment no longer has an impact on the optimal scheme. After that, as the total investment constraint decreases, the optimal allocation scheme of the project varies greatly. The trigeneration system and ground source heat pump have the characteristics of good economic benefits and high initial investment, and in the equipment warehouse. The cooling and heating load supply equipment is gradually replaced from ground source heat pump to direct combustion engine with lower initial investment. Therefore, the setting of the total investment constraint directly determines the different types of equipment in the optimal configuration scheme, which has an important impact on the optimal configuration of the system.

Table 7. Allocation optimization results under different investment constraints
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5 Conclusion

In this paper, an optimal equipment configuration method of integrated energy system considering engineering practicability is proposed. A large-scale mixed integer linear optimization model is established by taking the net present value as the optimization objective. The model takes the number of products of each equipment in the actual engineering equipment library as the configuration optimization variable. And the operational and planning constraints are considered. Combining with the case, the configuration and operation results are compared and analyzed, and the following conclusions are drawn as: 1) In the method of optimal equipment configuration of integrated energy system considering the engineering practicability, the nonlinear discrete characteristics of equipment price and performance are fully considered. Therefore the price and performance of products in line with the actual engineering changes with the capacity and model witch ensured the accuracy of the operation results. 2) Compared with other methods, the equipment configuration optimization method considering the engineering equipment products can fully consider the operating characteristics of a single equipment. The optimal product combination is matched from the engineering products, which improves the practicability of the optimization results. 3) In the configuration optimization of integrated energy system considering the constraints of engineering equipment, the constraints of total investment directly affect the type selection of engineering equipment. The economic bene-fit of the equipment configuration optimization scheme is sensitive to the total in-vestment.