Abstract
The traditional energy hub based model has difficulties in clearly describing the state transition and transition conditions of the energy unit in the integrated energy system (IES). Therefore, this study proposes a state transition modeling method for an IES based on a cyber-physical system (CPS) to optimize the state transition of energy unit in the IES. This method uses the physical, integration, and optimization layers as a three-layer modeling framework. The physical layer is used to describe the physical models of energy units in the IES. In the integration layer, the information flow is integrated into the physical model of energy unit in the IES to establish the state transition model, and the transition conditions between different states of the energy unit are given. The optimization layer aims to minimize the operating cost of the IES and enables the operating state of energy units to be transferred to the target state. Numerical simulations show that, compared with the traditional modeling method, the state transition modeling method based on CPS achieves the observability of the operating state of the energy unit and its state transition in the dispatching cycle, which obtains an optimal state of the energy unit and further reduces the system operating costs.
BUILDING a new power system dominated by renewable energy sources (RESs) is critical for achieving carbon peaking and carbon neutrality. An integrated energy system (IES) integrates various energy sources such as cooling, heating, electricity, and gas. As a major utilization form of RESs, IES is a representative of new power system [
Studies have been conducted on the modeling of IES, including modeling from a single energy unit to the system level. For example, [
In short, some preliminary results have been achieved in the IES modeling, but there are still some limitations that need to be addressed.
1) There are a large number of energy units in the IES, and their states vary during operation. The starting, operating, and stopping states constitute a set of different operating states for energy units in the IES. It is challenging to use a unified model to characterize the multiple operating states and the transitions between the states to improve the observability of IES.
2) The economy of the dispatching of IES depends on the accuracy of the IES model. However, the existing studies tend to simplify the IES model to a certain extent and lack an accurate description of the operating state of each energy unit. Thus, they fail to reflect the changes in the operating states of energy units and the energy conversion process of the energy unit under different states, which affect the accuracy of the dispatching scheme of IES.
3) The aforementioned studies only model the physical system of an IES from the internal coupling characteristics of energy flow, ignoring the effects of information flow during IES operation. To fully reveal the interplay of the information flow and energy flow in the IES, and to visualize the operating state and state transition of energy unit in the IES, the cyber and physical systems should be studied as an integrated system for modeling analysis.
To address these issues, researchers have begun to seek new modeling methods, among which the modeling based on cyber-physical systems (CPSs) has received wide attention. The theory of CPS provides a technical means for realizing the integrated modeling of physical and cyber systems in an IES. A CPS, through a closed-loop mechanism of sensing, analysis, decision-making, and execution, can detect the operating state of an energy unit in an IES in real time, and thus realize the observability and controllability of IES. The power grid CPS has been widely studied in recent years [
Existing power grid CPS models have achieved the integrated modeling of cyber and physical systems; however, they fail to realize the description of the state transition of energy unit. The integration of information flow into the physical model of energy units in the IES and the construction of the state transition model of IES based on CPS are the key issues addressed in this study.
Thus, this study proposes a state transition model for an IES based on CPS and applies it to the day-ahead optimal dispatching of IES. The main contributions of this study are summarized as follows.
1) A CPS-based hierarchical modeling framework for an IES is proposed, and different methods are utilized to model each layer. The hierarchical modeling framework integrates energy and information flows and can be extended to other energy systems with the integration of CPS.
2) A method for the division of operating states of energy units based on the load ratio is proposed. The refined division can delineate the operating characteristics of energy units more precisely, which makes the dispatching scheme of IES more reasonable and reduces the operating costs of IES.
3) The information flow is integrated into the physical model of energy unit in IES, and the state transition model of energy unit based on the CPS is established, which can visualize the operating state and state transition of energy unit.
The remainder of this paper is organized as follows. Section II describes the architecture of IES based on CPS and hierarchical modeling framework. Section III discusses the state transition model of the IES based on CPS. Case studies are presented in Section IV. Section V concludes this study.
The architecture of IES based on CPS studied in this paper is shown in
Fig. 1 Architecture of IES based on CPS.
The physical system consists of energy production units (EPUs), energy conversion units (ECUs), energy storage units (ESUs), and energy consumption units (ECSUs), which are used in the production, conversion, storage, and consumption of different energy sources, respectively.
The cyber system consists of data collection and control (DCC) of energy units, computing center, control center, and a communication network that connects these cyber devices. As the control center of IES, the cyber system is responsible for data monitoring and optimization decisions of IES as well as the analysis of information uploaded from the physical system and for the generation of the corresponding control commands for issuance.
To fully reveal the interplay between the information and energy flows in an IES and to visualize the operating state and state transition of each energy unit in the IES, we propose a hierarchical modeling framework for an IES integrated with a CPS, as shown in
Fig. 2 Hierarchical modeling framework of IES integrated with CPS.
1) Physical layer: this layer integrates the information flow into the physical model of energy unit and establishes an information flow driven state transition model of energy unit.
2) Integration layer: this layer mainly collects the operating states of different energy units si in the physical layer to establish the state transition model of the IES and obtains the optimal state transfer path of energy unit according to the optimal dispatch scheme issued by the optimization layer.
3) Optimization layer: this layer considers the operating constraints of the IES and presents the optimization objectives of the IES. It then solves the optimal dispatching scheme based on the optimization objective and sends it to the integration layer.
The physical, integration, and optimization layers interact through information flow. Information flow is achieved by closing the loop of four links: sensing, analysis, decision-making, and execution, as shown in
Fig. 3 Interaction between different layers.
In
(1) |
In summary, the integration layer senses the operating states of energy units in the physical layer through sensors in real time. It then analyzes and processes the information and finally constructs the state transition model of IES-based on the operating state of each energy unit and other historical data to provide n transferable paths for the optimization layer to determine the optimal operation strategy of the IES. The entire state transition trajectory of the IES at different stages can then be observed. Based on different optimization objectives of IES and the transferable path provided by the integration layer, the optimization layer considers the operating constraints of IES, solves the optimal dispatching scheme of the IES, and sends it to the integration layer. The integration layer then obtains the optimal state transfer path of the energy unit according to the optimal dispatching scheme issued by the optimization layer. Based on the optimal state transfer path provided by the integration layer, the physical layer changes the operating state of the energy unit through actuators and completes the conversion of information flow into energy flow. The aforementioned closed-loop process ensures that the traction control of the operating state of the energy unit can be performed according to the optimal state transfer path, thereby enabling the IES to develop in a more optimal direction.
A time delay actually occurs during the process of converting the energy flow into information flow as well as when establishing the state transition model of energy units and the transition between different states in the integration layer. However, the state transition model developed in this study is mainly applied to the day-ahead optimal dispatching of IES, and the time scale (one hour) of day-ahead optimization is longer. This study ignores the time delay in the integration layer because its effects on day-ahead optimal dispatching are negligible. If the state transition model is applied to real-time optimal dispatching of IES, the time delay cannot be ignored because the time scale of real-time optimal dispatching is very short.
This section details the models of the physical, integration, and optimization layers, as presented in
The generation efficiency of GT is nonlinearly related to the electric load ratio , which can be described by the following fourth-order polynomial fitting [
(2) |
where is the fitting order; and are the order fitting coefficients of GT; is the thermoelectric ratio at time t; is the electric power generated by GT at time t; and is the rated electric power of GT. The power generated by GT can then be obtained as:
(3) |
where is the thermal power generated by GT at time t; is the natural gas input to GT at time t; and is the calorific value of natural gas.
The model of GB can be expressed as:
(4) |
where and are the thermal efficiency and thermal load ratio of GB at time t, respectively; is the order fitting coefficient of GB; is the rated themal power of GB; is the thermal power generated by GB at time t; and is the natural gas input to GB at time t.
The model of AC can be expressed as:
(5) |
where and are the conversion efficiency and cold load ratio of AC at time t, respectively; is the order fitting coefficient of AC; is the rated cold power of AC; and and ) are the cold power generated and thermal power consumed by AC at time t, respectively.
The model of EC can be expressed by:
(6) |
where and are the conversion efficiency and cold load ratio of EC at time t, respectively; is the order fitting coefficient of EC; is the rated cold power of EC; and and are the cold power generated and electric power consumed by the EC at time t, respectively.
The model of ESU can be expressed by:
(7) |
where and are the stored energies of ESUs at time and , respectively; and are the upper and lower limits of stored energy in ESUs, respectively; and are the charging power and charging efficiency of ESUs at time t, respectively; ) and are the discharging power and discharging efficiency of ESUs at time t, respectively; and are the upper limit of the charging and discharging power of ESUs, respectively; Si is the rated capacity of ESUs; and are binary variables that take only the values of 0 or 1; is the time scale of dispatching; and and are the stored energies of ESUs at the beginning and end of dispatching, respectively.
The integration layer describes different state combinations of energy units in the IES at different operating stages and establishes a state transition model of IES based on CPS. We consider only the modeling of dispatchable energy units in the IES, such as ECUs, ESUs, and ECSUs.
1) State Transition Modeling of Energy Units
1) ECUs
The information flow (information collection, processing and analysis, and decision-making) is integrated into the physical model of energy unit, and the state transition model of ECU is established based on the CPS, as shown in
Fig. 4 State transition model of ECU based on CPS.
The operating states of ECU are divided into stopping state and on-load operating state . However, in actual operation, an ECU has an obvious partial-load performance; that is, when the ECU is not in operation under rated conditions, its efficiency changes with the load ratio. The efficiency of ECU decreases as the load ratio decreases. For example, the power generation efficiency of GT at a low load ratio is only 80% of that in the full load operation or even lower. In addition, compared with the efficiency of ECU as a constant, the partial-load performance when considering the efficiency of ECU can more accurately and efficiently characterize the operation of ECU, which makes the dispatching scheme of IES more accurate and reasonable. Therefore, in this study, the on-load operating state is divided into four operating states according to its load ratio, i.e., light load state , medium load state , heavy load state , and full load state , and their energy conversion efficiencies are different. The thresholds for distinguishing the above four operating states are listed in
Operating state | Threshold (%) | Operating state | Threshold (%) |
---|---|---|---|
(8) |
(9) |
where and are the control variables that control the start-up and shut-down of ECUs, respectively; and and are the control variables that control the ECUs to enter and exit the corresponding state, respectively, which are 0-1 variables and cannot be 1 simultaneously. For example, and are 0-1 variables that control the ECUs to enter and exit a medium load operating state, respectively.
The transition between different states of information flow driven ECUs can be achieved by controlling the control variables in (9), where the state transition path of the information flow driven ECUs during the entire optimization period is shown in
Fig. 5 State transition path of information flow driven ECUs.
The transition conditions in
Condition | Description | Logical judgment expression |
---|---|---|
δ1 | From to start | |
δ2 | Enter | |
δ3 | Enter | |
δ4 | Enter | |
δ5 | Enter | |
δ6 | From to |
When the logical judgment expression in
2) ESUs
The ESUs include battery storage (BS), thermal storage (TS), and cold storage (CS). According to the mathematical model of ESU [
Fig. 6 State transition model of ESU based on CPS.
Similarly, the state transfer equations of ESU similar to those of GT in
Condition | Description | Logical judgment expression |
---|---|---|
δ7 | Enter s5 | |
δ8 | Enter s4 | |
δ9 | Enter s6 | |
δ10 | Enter s3 | |
δ11 | Enter s7 |
can be expressed as:
(10) |
where and are the 0-1 binary variables, which indicate purchasing and selling electricity from and to the power grid, respectively; is the output power of photovoltaic (PV); is the output power of wind turbine (WT); is the power purchased from power grid; and is the power sold to power grid.
3) ECSUs
The ECSUs can be classified as critical, shiftable, transferable, and interruptible loads. Part of loads can be transferred moderately under the condition of satisfying IES constraints, which can play the role of peak-shaving and valley-filling, called demand response (DR). In this part, the DR of electric load is considered, and thus an ECSU can be divided into two operating states: normal operating state s8 and transferable operating state s9. The state transition model of ECSU is established based on CPS, as shown in
Fig. 7 State transition model of ECSU based on CPS.
The state transition of an ECSU is determined by the time-of-use prices, i.e., the electric load is transferred from high to low electricity price periods. Therefore, the transition condition , as shown in
2) State Transition Modeling of IES
In this study, the operating states of IES are divided into shut-down state , start-up state , dispatchable state , and fault state . The state transition model of IES, as shown in
Fig. 8 State transition model of IES.
In general, an IES mainly operates in the dispatchable state to ensure the energy supply quality and to improve the economical operation of IES; therefore, in this study, we mainly consider the dispatchable state of IES. Because the PV and WT are non-dispatchable units, n dispatchable operating states of IES are shown in
Fig. 9 n dispatchable operating states of IES.
In
The IES can be in any of the aforementioned dispatchable operating states in
Fig. 10 Example of state transition of IES.
In
Fig. 11 State transition paths of IES.
In summary, compared with the traditional input-output model of IES, the establishment of state transition model of IES has many advantages: ① the complexity of IES can be reduced by representing its operating control with a set of finite states; ② the observability of IES can be improved by providing a graphical representation of the operating state of energy unit; and ③ a simpler means of modifying the predefined transition conditions to make the IES towards the desired state can be achieved.
The optimization layer is based on the state transition model given in the integration layer. It considers the constraints to be satisfied by the operation of energy unit and solves the optimal model at the lowest operating cost of IES as the optimization objective.
The objective function is expressed as:
(11) |
where is the total daily operating cost of IES; and , , and are the cost of purchasing electricity, cost of purchasing gas, and DR cost, respectively, which are expressed as:
(12) |
where and are the electricity prices of purchasing and selling electricity, respectively; is the price of natural gas purchased by the IES from the natural gas network; is the load unit compensation cost; is the amount of load participating in the DR at time t; and is the dispatching period.
The IES must satisfy the energy balance, energy unit output, and power exchange constraints of power grid in operation, which are described in [
(13) |
where is the maximum proportion of load change at time t; and is the load power at time t.
The first constraint in (13) indicates that the total load power before and after the implementation of DR should remain unchanged in one dispatch cycle, i.e., the sum of the DR power should be zero. The second constraint in (13) is used to limit the variation range of the load participating in the DR at a certain time.
The model of the optimization layer in IES composed of the aforementioned objective function and constraints is a mixed-integer nonlinear programming (MINP) problem, and an effective tool called IPOPT is used to solve this kind of optimization problem. Because the IPOPT can only solve continuous programming problems, the optimization model in this study is an MINP problem containing binary variables. For example, for ESUs, the mathematical model in (7) contains two binary variables and , and we can eliminate the binary variables and convert them to the following equivalent form:
(14) |
The solution flow for day-ahead optimal dispatching of the IES is presented in
Fig. 12 Solution flow for day-ahead optimal dispatching of IES.
1) At the beginning of regulation, the information of energy unit including electric, cold, and thermal power outputs from each energy unit of IES is collected through the sensors, and the parameter information including the gas price, electricity purchase and sale prices, and electric, cold, and thermal loads is obtained through the network.
2) The minimum daily operating cost of IES is selected as the optimization objective, and constraints are set to establish the day-ahead optimal dispatching of IES.
3) Based on the collected data, the computing center solves the day-ahead optimal dispatching model using the IPOPT and generates the optimal control commands.
4) The control system receives the control commands and controls each energy unit to change its operating state along the optimal state transition path.
5) Judge whether the regulation cycle is finished. If not, wait for the next regulation time.
6) The optimization is terminated and the day-ahead optimal dispatching of the IES is output.
To verify the feasibility of the proposed modeling method, numerical simulations are conducted based on the IES, as shown in
Fig. 13 Structure of IES.
The main parameters of energy unit in IES, as given in
Energy unit | Parameter | Value |
---|---|---|
GT | 1200 kW | |
Rated | 0.34 | |
Rated | 1.48 | |
, , , | ||
, , | ||
GB | 1000 kW | |
Rated | 0.85 | |
, | ||
EC | 650 kW | |
Rated | 3 | |
, , βEC,2= | ||
AC | 800 kW | |
Rated kAC | 1.5 | |
βAC,i |
, , , |
Electricity period | Time interval | Electricity price (¥/kWh) | |
---|---|---|---|
Purchasing | Selling | ||
Peak | Hours 8-12 | 1.12 | 1.18 |
Hours 19-23 | |||
Flat | Hours 12-19 | 0.84 | 0.84 |
Valley | Hours 23-8 | 0.35 | 0.28 |
Fig. 14 Actual data curves of loads on a certain day.
Based on the parameters in
Fig. 15 Fitting curve of conversion efficiency for ECUs. (a) GT and GB. (b) EC and AC.
To test the superiority of the proposed modeling method, two cases are considered for comparison.
1) Case 1: the optimal dispatching of IES based on the proposed modeling method of IES based on CPS.
2) Case 2: the optimal dispatching of IES based on the traditional modeling method of EH.
Note that both cases do not consider the DR.
Fig. 16 Optimal dispatching results of electric power. (a) Case 1. (b) Case 2.
In Case 2, for each energy unit, the optimal dispatching results are similar to those in Case 1. The sole difference during the flat periods is: the electric load in Case 1 is supplied by the GT, whereas that in Case 2 is supplied by both the GT and power grid. This is mainly because the traditional modeling method considers the conversion efficiency of the energy unit as the rated efficiency, which is generally the optimal operating point of the energy unit with the highest operating efficiency. However, due to the limitations of the thermal load and thermal electricity ratio, the GT fails to supply all of electric loads in Case 1.
Fig. 17 Optimal dispatching results of thermal power. (a) Case 1. (b) Case 2.
The operating state of energy unit is considered in Case 1. When the electricity price and thermal load are determined, the optimal dispatching result is related to the load ratio of energy unit. When the thermal load is small, both the GT and GB are at low load levels, and their operating efficiencies are lower than those operate at full load. However, because the GT can generate both electric and thermal energy, it is more economical than GB at a low load level. Therefore, the GT is used to meet the thermal load demand during hours 12-16. When the thermal load increases, the thermal energy generated by the GT cannot satisfy the thermal load and the thermal output of GB gradually increases and its efficiency is at a high load level. At hour 3, the GB covers the main thermal load demand. However, during the peak periods, the GT operates at full load due to the increase in electricity purchase cost. Therefore, the thermal load is mainly supplied by the GT, and the insufficient thermal load is supplied by the GB. The TS releases heat during periods of insufficient heat and stores it during periods of excess heat.
By contrast, Case 2 does not consider the operating state of energy unit, where the conversion efficiency of energy unit is considered as rated efficiency. Under the rated efficiency, the GT is more economical, so GT is used as the main thermal energy unit. GB and TS are used for supplying the thermal load during peak thermal load periods when the GT is undersupplied. During the valley periods, the electric load is mainly supplied by the power grid. Therefore, the output of GT is reduced, and the lacking thermal load is supplied by the GB and TS.
Fig. 18 Optimal dispatching results of cold power. (a) Case 1. (b) Case 2.
In Case 2, during the valley periods, the EC covers the entire cold load. During the peak periods, the AC covers most of the cold load, and an insufficient part is provided by CS.
It is worth noting that the conversion efficiency of the energy unit in Case 2 is regarded as the rated efficiency, which is the desired dispatching scheme. However, the actual conversion efficiency of energy unit is usually not the rated value. Therefore, the optimal dispatching results obtained in Case 2 often exhibit large errors, resulting in a shortage of load supply in actual operation.
Fig. 19 Shortages of electric, thermal, and cold power during each period in Case 2. (a) Electric power. (b) Thermal power. (c) Cold power.
Case | Operating cost () |
---|---|
1 | 24603 |
2 | 19014 (ideal); 25133 (actual) |
As can be observed from
Fig. 20 Load ratio of each energy unit in Cases 1 and 2. (a) Case 1. (b) Case 2.
In addition, the proposed modeling method of CPS realizes the observability for the operating state of energy unit and its state transition process in one dispatch cycle.
Fig. 21 State transition processes of ECU and ESU. (a) ECU. (b) ESU.
Energy unit | Duration under different operating states (hour) | ||||
---|---|---|---|---|---|
Stopping | Light load | Medium load | Heavy load | Full load | |
GT | 0 | 7 | 2 | 0 | 15 |
GB | 0 | 13 | 11 | 0 | 0 |
EC | 0 | 0 | 24 | 0 | 0 |
AC | 2 | 0 | 20 | 2 | 0 |
In summary, the proposed modeling method of CPS can visualize the operating state of energy unit and its state transition, and the operating state of energy unit can be controlled according to the planned transfer path to achieve the optimal state and state transition of energy unit.
Considering the characteristics of thermal and cold loads, it is difficult to change the users’ habits. Therefore, we consider only the DR of electric load.
Fig. 22 Electric load curves with and without considering DR.
1) Case 3: the proposed modeling method without considering DR.
2) Case 4: the proposed modeling method with considering DR.
Fig. 23 Optimal dispatch results of IES in Case 4. (a) Electric power. (b) Thermal power. (c) Cold power.
Case | Cost of purchasing gas and electricity (¥) | DR cost (¥) | Total operating cost (¥) |
---|---|---|---|
3 | 24603.0 | 0 | 24603 |
4 | 22887.8 | 358.2 | 23246 |
For a further analysis of the effects of DR on the optimal dispatch of IES, the efficiency curves of ECU in Cases 3 and 4 are shown in
Fig. 24 Efficiency curves of ECU in Cases 3 and 4. (a) . (b) . (c) . (d) . (e) .
As shown in
As shown in
The operating efficiency curves of EC and AC are inverted as U-shaped. With an increase in the load ratio, the operating efficiencies of EC and AC first increase and then decrease, i.e., the best operating efficiencies of EC and AC are in the partial load region. As shown in
In summary, the implementation of DR can further improve the operating interval and overall efficiency of energy unit, and reduce the energy loss of the IES.
This study proposes a state transition modeling method of IES based on a CPS, and the feasibility of the proposed modeling method is verified through case studies. The main conclusions are as follows.
1) The proposed state transition model can visualize the regulation of the operating state and state transition of the energy unit. It can also identify the operating state of the energy unit at each moment and the duration of the energy unit under a given operating state, which is conducive to the reasonable configuration of the energy unit in the IES.
2) The proposed state transition model can accurately and efficiently characterize the energy unit operation, which makes the dispatching scheme of IES more accurate and reasonable and reduces the operating costs of IES by 2.1%.
3) The implementation of DR further improves the operating points of energy unit, enabling it to operate in a more efficient load ratio range while improving the overall efficiency of IES.
As the number of energy units in an IES increases, the proposed state transition model will have irreplaceable advantages. Future research will consider the effects of additional factors on the operating state of energy unit and further refine the state transition model of the energy unit to improve the optimal dispatching method proposed in this study.
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