Decoupling optimization of integrated energy system based on energy quality character

Abstract

Connections among multi-energy systems become increasingly closer with the extensive application of various energy equipment such as gas-fired power plants and electricity-driven gas compressor. Therefore, the integrated energy system has attracted much attention. This paper establishes a gas-electricity joint operation model, proposes a system evaluation index based on the energy quality character after considering the grade difference of the energy loss of the subsystem, and finds an optimal scheduling method for integrated energy systems. Besides, according to the typical load characteristics of commercial and residential users, the optimal scheduling analysis is applied to the integrated energy system composed of an IEEE 39 nodes power system and a 10 nodes natural gas system. The results prove the feasibility and effectiveness of the proposed method.

Keywords

integrated energy system / energy quality character / optimization / electric power system / natural gas system

Introduction

Compared with other energy resources, natural gas is economical, environmentally friendly, and widely used in energy area. Moreover, the proportion of combined cycle gas turbine generation has been gradually improved in recent years. Therefore, mutual influence between power grid and natural gas network is gradually deepened [¹]. The greatest advantage of the integrated energy system (IES) is the release of constraint freedoms, and different loads can be served by multi energy supply systems [²]. At the same time, the integrated energy system is composed of various subsystems with individual nonlinear characteristics. Difficulties in system scheduling will arise because the coupling nodes are unable to make the system interact among each other. The traditional system analysis methods are difficult to cope with these new challenges.

Considering the fact that coupling interaction and coordinated operation of energy subsystems is the key to achieving economic and reliable operation of the integrated energy system, many studies have been conducted on optimal dispatch and energy management of integrated energy system. Zheng et al. [³] focuses on the multi-objective optimization problem of the electrical integrated energy system. A simplified model is established, which is solved by using the MGSO-ACL and NSAG-II multi-objective method, and the results are compared with the single objective optimization. Considering the randomness of the energy system load and renewable energy supply, the linearization model of the energy hub is set up by Ghasemi et al. [⁴]. The impact of the load correlation on the system is compared and analyzed with the objective of minimizing the cost. Gu et al. [⁵] performs study on the impact of thermal inertia in natural gas network, and establishes a mixed integer nonlinear programming model for system analysis. Pan et al. [⁶] studies the interactions in an integrated energy system considering the time-scale characteristics of the main components. A quasi-steady multi-energy flow model is proposed to evaluate the effect of fast hydraulic process and slow thermal process. Some key problems of current integrated energy systems are revised by Collins et al. [⁷]. Rashidi and Khorshidi [⁸] compare and analyze the evaluation index of the integrated energy system, and analyze each index from the aspects of cost, emission, and system reliability.

The optimal dispatch of integrated energy system should consider the characteristics of energy subsystems. However, due to the difficulty of solving this complex model, a simplified model based on the energy hub is widely used in Refs. [⁹,¹⁰]. The nonlinear characteristics and coupling effect of the system, which will have a great influence on the optimization results, are not fully considered. In addition, most studies have adopted the minimization of operation cost as the optimization objective, which rarely reflects the improvement of energy utilization [¹¹,¹²]. Moreover, the diversity and impact of system load have not been considered.

Considering the problems in these papers, an optimal scheduling method of integrated energy system based on nonlinear mechanical model and energy quality character is proposed in this paper. The grade difference of energy loss in subsystems is full considered. System evaluation index based on the energy quality character are proposed to evaluate the benefits of an integrated energy system. Due the coupling between power grid and natural gas network including both gas-fired power plants and electricity-driven compressors, a computing framework combined with heuristic algorithm is established to solve the complex model. By dividing the load into commercial and residential users, the corresponding load characteristic curves are presented and the effect of the system load is fully discussed. The optimal scheduling analysis tested on an integrated energy system composed of the IEEE 39 nodes power system and the 10 nodes natural gas system is evaluated.

Description of energy system

The coupling of power grid and natural gas network is one of the important factors that cannot be ignored in the integrated energy system. With the increasing of gas-fired power plant and electricity-driven compressor, neglecting its influence will have a great effect on operation reliability and optimization effect of the system [¹³].

In the integrated energy system, the coupling between power grid and natural gas network is realized by the gas power plant and compressor, as shown in Fig. 1. The load includes not only commercial users and residential users, but also the electricity-driven compressor. Therefore, the scheduling process of the integrated energy system consists of a closed loop which includes the compressor unit–the power grid–gas power plant–gas network–the compressor unit, which arises a great difficulty in scheduling optimization.

Modeling

In this paper, the integrated energy system is mainly composed of an electrical network, a natural gas network, coupling nodes, and a renewable energy plant. To comprehensively consider the nonlinear characteristics of the subsystems, a corresponding mechanism model is established.

Model of electrical network

In this paper, the AC power flow model is used. By defining the type of nodes, including PQ node, PV node and reference node [¹⁴], the nodal admittance matrix is generated. The injected power and node voltage can be expressed as

(1)P_{\mathrm{g}i}=P_{\mathrm{d}i}+{\displaystyle \sum }\left|Y_{in}{V}_i{V}_n\right|\cos ({\theta }_{in}+{\delta }_n-{\delta }_i),

(2)Q_{\mathrm{g}i}=Q_{\mathrm{d}i}+{\displaystyle \sum }\left|Y_{in}{V}_i{V}_n\right|\sin ({\theta }_{in}+{\delta }_n-{\delta }_i),

where P_gi and Q_gi are the active and reactive power generated by the power plant; P_di and Q_di are the active and reactive power demand of the power plant; V_i is the voltage amplitude on the transmission line; Y_in and d_n are the admittance and impedance angle between the buses; and d_i is the voltage phase angle.

Model of natural gas pipeline

In this paper, a steady-state model of natural gas pipeline with long distance, equal height, and medium pressure is adopted. Thus, the temperature change of natural gas in pipeline during transportation is ignored, and the friction coefficient along the pipeline is considered as a constant.

Thus, the natural gas flow m is [¹⁵,¹⁶]

(3)m={\displaystyle \frac{\mathrm{\pi }}{\mathrm{4}}}\sqrt{{\displaystyle \frac{(p_{\mathrm{1}}^{\mathrm{2}}-p_{\mathrm{2}}^{\mathrm{2}})D^{\mathrm{5}}}{\lambda ZRTL}}}.

The volume flow q under standard condition is

(4)q={\displaystyle \frac{\mathrm{\pi }}{\mathrm{4}}}{\displaystyle \frac{\sqrt{R_{\mathrm{a}}}{T}_{\mathrm{0}}}{p_{\mathrm{0}}}}\sqrt{{\displaystyle \frac{(p_{\mathrm{1}}^{\mathrm{2}}-p_{\mathrm{2}}^{\mathrm{2}})D^{\mathrm{5}}}{\lambda Z\mathrm{\Delta }TL}}},

where q is the volume flow of gas in standard condition, p₁ and p₂ are the pressure of starting point and end point of pipeline, D is the inner diameter of the pipeline, l is the hydraulic friction coefficient, Z is the compression factor, R_a is the gas constant, T is the average temperature, and L is the length of pipeline.

Model of compressor

Two kinds of compressors adopted are the electricity-driven compressor and the gas-driven compressor.

The gas consumption q_GD and power P_GD of the gas-driven compressor are

(5)q_{\mathrm{GD}}={\displaystyle \frac{\mathrm{3600}\times P_{\mathrm{GD}}}{Q_{\mathrm{net}}\times {\eta }_{\mathrm{GT}}\times {\eta }_{\mathrm{C}}}},

(6)P_{\mathrm{GD}}={\displaystyle \frac{G_{\mathrm{in}}\cdot {\rho }_{\mathrm{a}}\cdot S_{\mathrm{G}}\cdot Z_{\mathrm{in}}\cdot R\cdot T_{\mathrm{in}}\cdot m}{m-\mathrm{1}}}\times [{\left({\displaystyle \frac{P_{\mathrm{out}}}{P_{\mathrm{in}}}}\right)}^{\frac{m-\mathrm{1}}{m}}-\mathrm{1}],

where G_in is the flow rate, r_a is the standard air density, S_G is the relative density of natural gas, Z_in is the natural gas compression factor, R is the gas constant, m is the compressor variable index, P_in and P_out are the inlet and outlet pressure, T_in is the inlet temperature, Q_net is the low calorific value of natural gas, h_GT is the efficiency of gas turbine driver, and h_C is the compressor efficiency.

The power consumption of the electricity-driven compressor is P_ED.

(7)P_{\mathrm{ED}}={\displaystyle \frac{P_{\mathrm{M}}}{{\eta }_{\mathrm{M}}\times {\eta }_{\mathrm{C}}}},

where h_C is the compressor efficiency, P_M and h_M are the power and efficiency of motor driver, and P_M is calculated as by using Eq. (6).

(8)P_{\mathrm{M}}={\displaystyle \frac{G_{\mathrm{in}}\cdot {\rho }_{\mathrm{a}}\cdot S_{\mathrm{G}}\cdot Z_{\mathrm{in}}\cdot R\cdot T_{\mathrm{in}}\cdot m}{m-\mathrm{1}}}\times [{\left({\displaystyle \frac{P_{\mathrm{out}}}{P_{\mathrm{in}}}}\right)}^{\frac{m-\mathrm{1}}{m}}-\mathrm{1}].

Model of renewable energy power plant

In this paper, wind power plant and solar power plant are modeled separately. Prediction data of wind speed and radiation intensity are introduced and converted into the power [¹⁷].

The power output of the wind power plant P_wt:

(9)P_{\mathrm{wt}}=\mathrm{0.5}\mathrm{\pi }\rho r^{\mathrm{3}}{v}^{\mathrm{2}}{C}_{\mathrm{p}},

where r is air density, r is the diameter of blade, and v and C_p are wind speed and conversion coefficient.

The power output of the solar power plant is

(10)P_{\mathrm{pv}}=E_{\mathrm{q}}A\eta ,

where E_q is radiation intensity, A is PV panel area, and h is conversion efficiency.

Constraint equations

System constraints are mainly divided into electrical network constraints, gas network constraints, and equipment constraints.

Electrical network constraints include line capacity constraints, and voltage and current constraints [¹⁸].

(11)P_{\mathrm{g}i,\min }\le P_{\mathrm{g}i}\le P_{\mathrm{g}i,\max },

(12)Q_{\mathrm{g}i,\min }\le Q_{\mathrm{g}i}\le Q_{\mathrm{g}i,\max },

(13)V_{i,\min }\le V_i\le V_{i,\max },

(14)\left|I_{i,j}\right|\le I_{i,j,\max },

where P_gi,min and P_gi,max are the minimum and maximum active power of the power plant, and Q_gi,min and Q_gi,max are the minimum and maximum reactive power of the node.

Gas network constraints include pressure constraints, flow constraints, and conservation constraints.

(15)p_{i,\min }\le p_i\le p_{i,\max },

(16)q_{i,\min }\le q\le q_{i,\max },

(17){\displaystyle {\sum }_j^M{q}_{i,j}}={\displaystyle {\sum }_k^N{q}_{k,i}},

where p_i,min and p_i,max are the minimum and maximum pressure of the node i, and q_{i,j, min} and q_i,j,max are the minimum and maximum flow in branch i,j.

The equipment constraints include the power constraint of the gas-fired power plant and the pressure constraint of the compressor.

(18)P_{\min }\le P_{\mathrm{GT}}\le P_{\max },

(19)P_{\mathrm{c},\min }\le P_{\mathrm{c},i}\le P_{\mathrm{c},\max },

(20)P{R}_{\min }\le P{R}_{\mathrm{c},i}\le P{R}_{\max },

where P_min and P_max are the minimum and maximum power of the gas power plant, P_c,min and P_c,max are the maximum and minimum power of the compressor unit, and PR_min and PR_max are the minimum and maximum of pressure ratio.

System evaluation index based on energy quality character

The energy utilization efficiency is one of the important evaluation criterions for the integrated energy system [¹⁹]. On the other hand, the grade difference of energy consumption of different subsystems should be fully considered. Therefore, energy quality character, which is defined as the portion of exergy in total energy, is introduced in this paper to demonstrate the influence of various energy consumption to the whole system.

The transfer form of energy in this system can be divided into work and heat. The transformation between work and heat is irreversible which indicates that different forms of energy are not only quantitatively related, but also qualitatively different [²⁰]. The efficient use of energy should be considered not only in terms of quantity but also in quality. From the perspective of fully utilization of energy, the ratio of work can be done by different energy sources to their total energy and is defined as the energy-quality coefficient \mathrm{EQC}, which is expressed as

(21)\mathrm{EQC}={\displaystyle \frac{W}{Q}},

where W is the exergy of energy, and Q is the total energy. For example, electric energy can be regarded as the highest-grade energy. Thus, the EQC of electricity is equal to 1.

In this system, the operation consumption of the system consists of electrical network consumption and gas network consumption.

The electrical network consumption is caused by the line impedance, which can be expressed as

(22)W_{\mathrm{E}}=({\displaystyle {\sum }_{i=\mathrm{1}}^m{W}_{\mathrm{g},i}}-{\displaystyle {\sum }_{j=\mathrm{1}}^n{L}_j){\mathrm{EQC}}_{\mathrm{E}}},

where W_g,i is the total output of the power plants, L_j is the total power of the load node j, m is the total number of power generation, n is the total load number, and EQC_E is the energy quality character.

The energy consumption of the gas network is caused by the frictional resistance in the transmission process. According to the law of conservation, the total loss of the gas network W_G can be expressed as

(23)W_{\mathrm{G}}=({\displaystyle {\sum }_{i=\mathrm{1}}^k{q}_{\mathrm{g},\mathrm{in},i}{H}_{\mathrm{g},i}}-{\displaystyle {\sum }_{j=\mathrm{1}}^l{q}_{\mathrm{g},\mathrm{out},j}{H}_{g,j}}){\mathrm{EQC}}_{\mathrm{g}}+W_{\mathrm{EC}}/{\mathrm{EQC}}_{\mathrm{g,EC}},

where q_g,in,i and H_g,i are the flow and enthalpy of the root node, k is the number of streams flowing into root nodes, l is the number of streams flowing out of root nodes, q_g,out,j and H_g,j are the flow and enthalpy of the gas network, EQC_g is the energy quality character of the gas network consumption, and EQC_g,EC and W_EC are energy quality character and power of the electricity-driven compressor respectively.

To meet the demand for gas pressure and flow of the node, the gas-driven compressor and the electricity-driven compressor provide the booster service along the pipeline, and part of natural gas is consumed by the gas-driven compressor. Therefore, the energy quality character of the gas network side can be calculated by

(24){\mathrm{EQC}}_{\mathrm{g},\mathrm{GD}}={\eta }_{\mathrm{GT}}{\eta }_{\mathrm{G}}{\eta }_{\mathrm{C}},

(25){\mathrm{EQC}}_{\mathrm{g},\mathrm{ED}}={\eta }_{\mathrm{M}}{\eta }_{\mathrm{C}},

where h_GT is the thermal efficiency of the gas turbine, h_G is the generation efficiency, h_C is the efficiency of the compressor, and h_M is efficiency of the motor.

Then the comprehensive evaluation index of the integrated system I_IES is obtained, which reflects the consumption of the system based on energy quality character.

(26)I_{\mathrm{IES}}=W_{\mathrm{G}}+W_{\mathrm{E}}.

Decoupling optimization for solving this problem

Optimization goal

Traditional optimization objectives for independence system do not need to consider the performance of other systems. However, in the integrated energy system, the consumption of multiple subsystems should be considered to maximize the energy utilization of the whole system. An optimization goal is constructed based on the energy quality character. Thus, the objective function is to minimize Eq. (26), with the constraints from Eqs. (1) – (25).

\mathrm{Min}{I}_{\mathrm{IES}}

(27)s.t.\mathrm{Eqs}.(1)–(\mathrm{25})\mathrm{.}

Solving framework

The traditional optimization process of the independence system is shown in Fig. 2. The optimal power flow of the electric network is calculated and the optimal power output of each power plant is obtained. The natural gas demand consumed by these generators is met by the gas network in real time [²¹], based on which, the optimal pressure distribution is achieved by controlling the pressure of each node using compressors [²²,²³].

With the wildly use of gas-fired power plant and electricity-driven compressor, the coupling between electric and gas network is increasing [²⁴]. The limitation of the traditional optimization method is becoming more and more severe. For example, the use of the electricity-driven compressor will affect the load of the electric network, making it difficult to obtain accurate load data and achieve a reliable optimization result. In addition, since gas network is only a subsidiary system, in global optimization, the advantages of integrated energy system in security and efficiency cannot be exerted.

The unified optimization scheduling of the integrated energy system combined with the optimization algorithm is demonstrated in Fig. 3. It should be noted that it is very difficult to obtain the global optimal solution when considering the complexity of the mathematics model. To solve this problem, a unified method based on the heuristic algorithm is proposed in this paper. The basic idea of this scheme is to transfer the system coupling variable as the control variable and adjust the variable by using the heuristic algorithm. After solving the model, the optimization objective function is obtained and iterated until convergence. The variables are divided into (1) external input which include user load data, renewable energy power forecast data, and (2) control variables which include power of each power plant, load capacity of electricity-driven compressor, and power of fuel-driven compressor.

A unified optimization solution framework for the integrated energy system is constructed, as depicted in Fig. 4. Considering the nonlinear characteristics of the optimization problem, GA (genetic algorithm) is used to solve this problem. GA is one of the heuristic algorithms which is convenient for implementation without gradient information [²⁵,²⁶].

The main steps of the optimization process are as follows:

Step 1: Achieve the load and power of the renewable energy station based on the weather data and historical load data in a typical day;

Step 2: For electric network, calculate the power flow according to a set of control variables, the power of the power plant, the load of the compressor unit, and the data of the renewable energy plant. Obtain the power generation capacity and network loss of each power plant. For gas network, calculate the amount of gas required according to the generating capacity of each power plant. This gas is supplied by distributed nodes in gas network. Obtain the loss in the gas network according to the flow of the node and the power of the compressor.

Step 3: Calculate the network loss index I_IES, and adjust the power of each power plant and compressor load by using GA.

Step 4: Stop the iteration according to the change rate of the optimization goal.

Case study

The electrical energy integrated energy system studied in this paper is depicted in Fig. 4.

The system is composed of an IEEE 39 nodes power grid and a 10 nodes natural gas network [¹⁶,²⁷,²⁸]. The power grid includes 10 gas-fired generators and 2 renewable energy power plants (including the wind power plant and the solar power plant), the reference voltage e_0,t is 345 kV, and reference power W_0,t is 100 MVA. These 10 gas power plants are connected to Nodes 30–39 respectively, while the wind power plant is connected to Node 38, and the solar power plant is connected to Node 37. The system also contains 21 power loads. To reflect the load characteristics, the loads are divided into the commercial one and the residential one, with different power characteristic curves respectively. In addition, the commercial loads are mostly arranged in the left part of the network to make the change of load center intuitively reflected.

The load categories and connection nodes are listed in Table 1.

The natural gas network consists of 10 nodes and is connected by 12 pipelines. The diameter of the natural gas pipeline is 500 mm and the gas pressure ranges from 2.5 MPa to 6 MPa in order to meet the pressure requirements of each gas-fired power plant. The natural gas network contains 3 pressure stations, two of them are the electricity-driven compressor. The electricity is obtained from Nodes 22 and 26 of the power grid. The C compressor station is a gas-driven compressor. The gas turbine drives the compressor using the natural gas consumed from the pipeline.

The system consists of 10 gas-fired power plants and three compressors. The information of the equipment is tabulated in Table 2. The load nodes are divided into commercial ones and residential ones, with different load curves. The load curves of the commercial and residential a reason a typical working day are illustrated in Fig. 5 [²⁹]. At the same time, the weather data of the wind power plant and the solar power plant on typical days are selected and the power coefficient is selected to be 0.85 [³⁰]. The power output is calculated and displayed in Fig. 6.

To prove the effectiveness of the proposed method, two optimization methods are compared.

Method 1: Independent optimization method, whose optimization goal and process are shown in Fig. 3.

Method 2: Integrated system optimization method, whose optimization goal and solution framework are adopted in this paper.

It is worth noting that the loss of each subsystem is calculated using Eqs. (21) to (25) at the end of the different methods, whose unit is MWh.

Performance analysis

To analyze the effect of unified optimization of the integrated energy system, the network loss of Methods 1 and 2 in 24 h are exhibited in Figs. 7 and 8.

It can be seen from Figs. 7 and 8 that in the 24 h period, Method 2 achieves a lower system loss compared with Method 1. Meanwhile, from 1:00 to 7:00, Method 2 shows a better performance. The load center is far away from the root nodes of the gas network, the loss of gas network when using Method 1 decreases significantly. At this time, Method 2, with unified optimization of the whole network considered, shows a greater advantage. Method 2 achieves the highest loss reduction of 1.78 MWh at 2:00. From the loss composition shown in Fig. 7, it is observed that the main optimization achievement is embodied in the gas network. During the whole study period, the power loss of Method 2 increases, but the optimization of the gas network compensates for the loss of the power grid and improves the overall performance of the system.

Table 3 is the total network loss in the 24 h time period. It is worth noting that the optimization goal of Method 1 is to minimize the loss of the power grid. Therefore, Method 1 achieves a smaller grid loss than Method 2, but the loss of the gas network is large at this time. Method 2 comprehensively considers the loss of the power grid and the gas network, the power consumption and network loss of each side of the gas network side can be reduced by reasonably adjusting the output of each gas power plant. Therefore, in joint optimal scheduling, Method 2 has better optimization performance, and the total network loss is reduced by 39.9 MWh in 24 h.

Influence of load demand distribution

To reflect the performance of the integrated energy system, the effectiveness of optimization should be comprehensively evaluated with consideration of special load distribution. In this system, this is achieved with the change of loads in the residential area and the commercial area. From Fig. 5, it can be seen that between 0:00 and 10:00, the load of residential area is larger than that in the commercial area. The load of these two areas is gradually tending to coincide after 10:00. It should be noticed that the residential loads are located in the left of this region while the commercial loads are located in the right. Therefore, the shift of spatial load distribution can be simulated by the timing change. Figures 9 and 10 show the power output of each gas power plant in two typical working conditions which correspond to 3:00 and 15:00, respectively.

From Fig. 9, it can be seen that power plants 8–10 have a lower power ratio optimized by Method 2. On the contrary, the output of power plants 1–4 is much higher. Power plant 10 is reduced by 105 MW compared to Method 1. Power plants 1 and 2 are increased by 63.2 and 54.6 MW respectively. The reason for this is that at this time, the load center is located in the left. To reduce the electric loss during transportation in Method 1, the power output of each power plant near the load center (power plants 8–10) is significantly increased, and the corresponding power plants near the commercial area (power plant 1–4) are decreased. On the other hand, because of the comprehensive consideration of the influence of the gas network in Method 2, the increase of power output for each power plant far away from the root nodes of the gas network will inevitably lead to the loss increase of the gas network. To balance the loss of the power network and the gas network, Method 1 increases the power output of the power plant far away from the load area to a certain extent, making the total loss of the integrated energy system minimum.

Figure 10 shows the power of each power plant in working condition 2. In this period, the load center of the system is gradually shifted to the commercial area and the whole network load is more balanced. At this time, the optimization direction of Methods 1 and 2 are the same. Therefore, the power output of each power plant near the commercial area is increased and the loss of power grid and gas network is simultaneously reduced. Compared with condition 1, the load fluctuation of each power plant in Method 2 is reduced. The load center of the system is close to the root nodes of the gas network, which leads to the decline of the optimization potential of the gas network.

Figures 11 and 12 are the power consumption of compressors. It can be seen that the power consumption of each compressor in Method 2 is lower than that in Method 1. The reason for this is that the power distribution of the generators in Method 2 is more reasonable. The power consumption and loss in the gas network are greatly reduced. The goal of Method 1 is to minimize the loss of the electric network, so the power loss of Method 1 is smaller. Meanwhile, Method 2 has a greater advantage in the system global optimization.

Conclusions

In this paper, an optimal scheduling method for an integrated energy system is proposed. Considering the grade difference of the loss energy of different subsystems, a system evaluation index based on energy quality character is established. Based on this index, the optimal scheduling method for combined operation of integrated energy system is constructed, and the method is applied to an integrated energy system composed of an IEEE 39 nodes power grid and a 10 nodes natural gas network. The following conclusions are drawn from this study.

System evaluation index and optimization method based on the energy coefficient can consider the grade difference of energy loss of different subsystems, and give a more reasonable scheduling scheme for integrated energy system.

Spatial load distribution will have a direct impact on the performance of the integrated energy system. When the load center of the system is far away from the root nodes of the gas network, it has a greater energy saving potential of the combined operation optimization scheduling.

A 24 h optimization analysis of this system indicates that the combined optimization method can reduce the total energy loss by 39.9 MWh compared to the independent optimization, which proves the superiority of the method proposed in this paper.

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