Energy Cascade Utilization of Electric-Thermal Port Microgrids

Abstract

In order to improve the energy utilization efficiency of electric-thermal port microgrid, this chapter proposed an energy comprehensive utilization optimization method on account of cascade utilization principle in this chapter. Firstly, we analyzed the structure of electric-thermal port microgrid and established the cascade utilization process during the cold, heat and electric energy production. The relationship between source, demand and storage was also considered. Then, according to different energy grades and their conversion modes, the energy flow coupling model and the energy grade conversion model were established to realize the energy exchange between electric energy and thermal energy and between different grades of thermal energy. The energy supply and demand model of different energy bus was built. Finally, based on the operational constraints of the energy cascade optimization utilization model, the optimal scheduling strategy of each equipment was solved with the goal of the lowest daily operating cost. Simulation showed that the proposed methodology effectively reduced the operating cost and improved the comprehensive energy utilization efficiency.

9.1 Introduction

Electric-thermal port microgrid is one of the typical applications of port integrated energy systems. Based on electrical and thermal demands, it integrates the supply, conversion, and storage equipment in electric and thermal energy flows, coordinates and optimizes protection and control methods, so as to achieve economical and reliable operation [1,2,3,4]. With the increasingly diverse energy needs of industrial, commercial, and residential users supplied by microgrids, there exist more complex multi-energy couplings, such as energy cascade utilization, which poses difficulties for energy optimization management of electric thermal microgrids [5, 6]. Energy cascade utilization is an effective method to improve energy utilization efficiency and supply quality. It is an important direction in current research on energy optimization management of electric-thermal port microgrids [7,8,9].

Currently, there has been a large number of researches on energy management in electric-thermal microgrids [10,11,12]. Literature [13] considered the coupling constraints of heating, cooling, and electricity, and used a clustering algorithm to obtain the optimal energy storage configuration for the integrated energy system to improve the system's economic performance. Literature [14] took into account the thermal storage characteristics of the heating network and established a system optimization and scheduling model to improve the consumption level of wind and solar energy in the region. Literature [15, 16] established a hybrid energy storage system model and proposed a coordinated operation strategy for electric and thermal energy storage. Literature [17] constructed an electric, thermal, and gas coupling network model and proposed an optimization strategy based on demand-side response, achieving optimized peak-shaving and valley-filling operation of the system. Literature [18] considered the dual uncertainties of renewable energy and load terminals and established a stochastic optimization model for cogeneration. The above literatures have provided relatively comprehensive models for the devices involved in electric-thermal microgrids, such as the sources, networks, loads, and storage. These researches enable the optimization configuration and operation of the system, and lay a research foundation for the coordinated complementarity of heterogeneous energy sources and the mutual substitution of different-grade energy sources.

Literature [19, 20] constructed a hierarchical optimization model for regional integrated energy systems considering multi-objective optimization in terms of economics, environmental protection, and energy efficiency. Literature [21, 22] proposed an energy management method for microgrids with energy storage devices, which enhanced system reliability while simultaneously reducing operating costs. Literature [23,24,25] established an economic dispatch model for energy systems with multiple energy supply sources, with the objective of minimizing operating costs. Literature [26] proposed a weighting method based on the Analytic Hierarchy Process to establish a comprehensive evaluation index for integrated energy systems from economic, reliability, environmental, and energy consumption aspects. Currently, scholars have suggested the utilization of flexible and controllable gas turbines in microgrid energy management based on the current production situation, which further improves energy utilization efficiency and is more in line with the development trend of actual production [27,28,29]. Literature [30] proposed a comprehensive energy system multi-energy collaborative optimization model that considers energy cascade utilization for industrial parks. This model followed the idea of “matching quality and cascade utilization” to achieve the comprehensive optimization of equipment operating parameters and industrial production processes.

The research on the comprehensive optimization and evaluation of multi-energy synergies in integrated energy systems has been increasingly matured. However, the energy utilization structure for energy cascading utilization is still relatively simple, lacking analysis of the substitution relationship between heterogeneous energy sources and energy sources with different grades, and the economic operating potential of the electric-thermal port microgrid has not been fully explored. In this chapter, different grades of energy sources in the electric-thermal microgrid are considered, and an energy cascade utilization flow structure based on the cascade utilization principle of gas turbines is constructed. An optimization model for energy cascade utilization in the electric-thermal microgrid is proposed with the objective of minimizing daily operating costs. On the Matlab platform, the system optimization operating model is established and the optimal operating scheme is solved. The effectiveness of the proposed strategy is verified through a case study of the “China-Italy Green Energy Experimental Center” at a university in southwest Shanghai.

9.2 Electric-Thermal Port Microgrids

9.2.1 Structure of Electric-Thermal Port Microgrids

An electric-thermal microgrid includes multiple forms of energy such as cold, heat, electricity, and gas. In addition to supplying electricity to user loads, it also includes steam loads, high/medium-temperature hot water loads, and chilled water loads. A typical microgrid structure that includes industrial, commercial, and residential users is shown in Fig. 9.1. Among them, the steam load corresponds to the demand of industrial users; in addition to meeting the heating needs of commercial and residential users, high-temperature hot water also satisfies the hot water needs of some industrial users; medium-temperature hot water meets the domestic water needs of commercial and residential users; and chilled water supplies the cooling load needs of all users.

Fig. 9.1

The structure and energy flow of electric-thermal microgrid

Electric thermal microgrids can be divided into micro-power grids and micro-thermal grids (including cooling and heating), which couples different forms of energy through integrated energy stations. The integrated energy station includes various energy equipment such as gas turbines, absorption heat pumps, absorption refrigeration, and energy storage, consuming natural gas and interacting with the power grid through transmission lines to supply or store cold, heat, and electrical energy. Wind power generation equipment is connected to the micro-power grid, and its output has certain fluctuations and randomness. Solar thermal power plants use solar thermal co-generation to supply electricity to the micro-power grid and to supply heat to the micro-thermal grid.

Considering the diverse energy needs of users in the electric thermal microgrid, in addition to electrical loads, there are also steam loads, high-temperature hot water loads, and medium-temperature hot water loads. Different heat load requires different water supply temperatures. Multiple forms of energy flows require the configuration of various types of energy coupling and conversion equipment in the electric thermal microgrid, making the operating mode of the electric thermal microgrid more complex than that of traditional distribution networks. However, considering energy cascade optimization, multiple energy flows and the abundance of controllable energy coupling equipment also make it more flexible for mutual support among various of energy forms. When purchasing electricity prices, natural gas prices, and renewable energy generation change, the adjustment and control methods of electric-thermal microgrids are also more diverse. Therefore, the principle of energy cascade utilization has broader optimization space for electric-thermal microgrids with diversified load demands.

9.2.2 Cascaded Utilization of the Electric-Thermal Microgrids

The cascaded utilization of electric-thermal microgrid follows the principles of “electric-thermal complementarity, temperature matching, and cascaded utilization.” Thermal energy is divided into different grades based on temperature, and the higher the temperature, the higher the thermal energy grade. Furthermore, according to the temperature requirements of different thermal loads, efforts are made to meet the heat utilization of temperature matching as much as possible. In cascaded utilization, higher-grade thermal energy is recycled, recovered and gradually converted to lower-grade thermal energy, thereby achieving high-efficiency energy utilization. Additionally, the advantages of “electric-thermal complementarity” are leveraged in the electric-thermal microgrid, and the reliability and efficiency of cascaded utilization are improved based on the deep coupling of electric-thermal energy flow.

The energy cascading utilization method in gas turbines is shown in Fig. 9.2, where the extracted air heat and exhaust heat are utilized separately. The exhaust heat is recovered by the waste heat boiler to produce low-temperature hot water of around 34 ℃. Since the value of storage and transfer low-temperature hot water are low, a portion of the waste heat is used as the low-temperature heat source of the absorption heat pump, and the remaining portion is used to heat the boiler feedwater or space heating load. The extracted air heat is high-temperature steam, and a portion of it drives the absorption heat pump to heat a large amount of low-temperature hot water to mid-temperature of 75 ℃, and another portion is heated to high-temperature of 120 ℃ through the peak heater heat exchanger to supply steam load and produce cold water through the absorption refrigeration.

Fig. 9.2

The energy cascade utilization method of gas turbine

Based on the above cascaded utilization process and considering the electric-thermal coupling relationship, the energy equipment and loads of the electric-thermal microgrid are shown in Fig. 9.3. The sources of power and heat supply include gas turbines, waste heat boilers, gas boilers, absorption heat pumps, absorption refrigeration, peak heaters, electric heat pumps, electric refrigeration, and electricity purchased from the main power grid. Cold, heat, and electricity storage include cold water storage tanks, hot water storage tanks, and battery storage. The loads include high-temperature steam loads, high-temperature hot water loads, mid-temperature hot water loads, and cold water loads.

Fig. 9.3

The source-demand-storage relationship in energy cascade utilization

9.3 Energy Flow Analysis of Cascaded Utilization in Electric-Thermal Port Microgrids

Considering the electric-thermal coupling relationship at different thermal energy levels and utilizing the advantages of multi-energy complementarity, the energy flow structure of electric-thermal coupling cascaded utilization is shown in Fig. 9.4. From the energy perspective, it can be divided into electric power bus, steam bus, low-temperature hot water bus, medium-temperature hot water bus, and high-temperature hot water bus. The electric power bus is connected to gas turbine power generation, solar thermal power generation, wind power generation, and interacts with the main power grid and battery energy storage, supplying electric loads, electric heat pumps, and electric refrigeration equipment. The steam bus is connected to gas turbine exhaust and gas boilers, supplying absorption heat pumps, peak heating equipment, absorption refrigeration equipment and high-temperature steam loads. The low-temperature hot water bus is connected with waste heat boilers and absorption refrigeration, supplying absorption heat pumps and electric heat pumps. The low-temperature hot water in medium-temperature hot water bus is heated to supply the peak heating equipment and medium-temperature hot water loads. The high-temperature hot water bus is connected with peak heating equipment and solar thermal energy, satisfying high-temperature hot water loads.

Fig. 9.4

The energy flow structure in heat and power cascade utilization

The energy flow structure of the cascade utilization of the electric-thermal microgrid includes electricity, steam, high-temperature hot water, medium-temperature hot water, low-temperature hot water, and cold water. The next section will analyze the cascade utilization model from three aspects: energy flow coupling relationship, energy grade conversion model, and energy supply-demand relationship.

9.3.1 The Coupling Relationship of Energy Flow

Different from traditional microgrids, there are multiple forms of energy flow in the electric-thermal microgrid, and there are also various coupling relationships between them. Taking full advantage of these relationships and achieving heterogeneous energy flow coupling and mutual aid in different operating conditions is an effective way to improve energy utilization efficiency and save operating costs. The energy coupling models used in this section are introduced as follows.

• (1) Gas Turbine

The back-pressure gas turbine is selected as the modeling object, which has high efficiency in power generation. Throughout the operation, the power generation, gas consumption, and exhaust ratios are fixed. The waste gas from the gas turbine is recovered by the waste heat boiler while filtering out pollutants to reduce emissions. The cogeneration model of gas turbine is shown in Eq. (9.1).

$$ \begin{array}{*{20}c} {\left\{ \begin{aligned} P_{{{\text{GT}}}}^{t} & = \eta_{{{\text{GT}}}} \cdot \lambda F_{{{\text{GT}}}}^{t} \\ H_{{{\text{GT\_L}}}}^{t} & = \eta_{{{\text{exh}}}} \cdot \left( {1 - \eta_{{{\text{GT}}}} } \right) \cdot \lambda F_{{{\text{GT}}}}^{t} \\ H_{{{\text{GT\_S}}}}^{t} & = \eta_{{{\text{ext}}}} \cdot \left( {1 - \eta_{{{\text{GT}}}} } \right) \cdot \lambda F_{{{\text{GT}}}}^{t} \\ \end{aligned} \right.} \\ \end{array} $$

(9.1)

In (9.1), P_GT is the power output of the gas turbine, λ is the lower heating value of natural gas, F_GT is the gas turbine's air intake flow rate, and η_GT is the gas turbine's power generation efficiency. H_{GT_L} is the recovered heat power from the waste gas, and η_exh is the waste heat recovery efficiency. H_{GT_S} is the steam power generated by the gas turbine's exhaust gas, and η_ext is the exhaust coefficient. The superscript t denotes time.

• (2) Gas Boiler

The gas boiler also consumes natural gas, but lacks the power generation process. The combustion process generates high temperature steam directly for heating. The heating model is shown in Eq. (9.2).

$$ \begin{array}{*{20}c} {H_{{{\text{GB}}}} \left( t \right) = \eta_{{{\text{GB}}}} \cdot \lambda F_{{{\text{GB}}}} \left( t \right)} \\ \end{array} $$

(9.2)

where F_GB is the intake amount of the gas boiler, H_GB is the heat energy contained in the steam generated by the gas boiler, and η_GB is the efficiency of the gas boiler.

• (3) Electric Heat Pumps and Electric Refrigeration

Electric heat pumps and electric refrigeration have similar working principles, and their models can be represented by coefficients of energy efficiency ratio, as shown in Eqs. (9.3) and (9.4).

$$ \begin{array}{*{20}c} {H_{{{\text{HP\_M}}}}^{t} = C_{{{\text{HP}}}} \cdot P_{{{\text{HP}}}}^{t} } \\ \end{array} $$

(9.3)

$$ \begin{array}{*{20}c} {H_{{{\text{RE\_C}}}}^{t} = C_{{{\text{RE}}}} \cdot P_{{{\text{RE}}}}^{t} } \\ \end{array} $$

(9.4)

where H_{HP_M} represents the heating power of the electric heat pump, P_HP represents the power consumption of the electric heat pump, and C_HP represents the energy efficiency ratio of the electric heat pump. H_{RE_C} represents the cooling power of the electric refrigeration, P_RE represents the power consumption of the electric refrigeration, and C_RE represents the energy efficiency ratio of the electric refrigeration.

• (4) Absorption Heat Pump and Absorption Refrigeration

The working principles of absorption heat pump and absorption refrigeration are similar. The absorption heat pump consumes a small amount of high temperature heat energy to produce abundant medium temperature heat energy, while the absorption refrigeration consumes high temperature heat energy to produce cold energy, accompanied by a large amount of low temperature hot water by-product. Their mathematical models are shown in Eqs. (9.5) and (9.6).

$$ \begin{array}{*{20}c} {H_{{{\text{AHP\_M}}}}^{t} = C_{{{\text{AHP}}}} \cdot H_{{{\text{AHP\_S}}}}^{t} } \\ \end{array} $$

(9.5)

$$ \begin{array}{*{20}c} {\left\{ \begin{aligned} H_{{{\text{ACH\_C}}}}^{t} & = C_{{{\text{ACH}}}} \cdot H_{{{\text{ACH\_S}}}}^{t} \\ H_{{{\text{ACH\_L}}}}^{t} & = k_{{{\text{ACH}}}} \cdot C_{{{\text{ACH}}}} \cdot H_{{{\text{ACH\_S}}}}^{t} \\ \end{aligned} \right.} \\ \end{array} $$

(9.6)

In the above equations, H_{AHP_M} represents the heating power of the absorption heat pump, C_AHP represents the energy efficiency ratio of the absorption heat pump, and H_{AHP_S} represents the steam heat consumption of the absorption heat pump. H_{ACH_C} represents the cooling power of the absorption refrigeration, C_ACH represents the energy efficiency ratio of the absorption refrigeration, H_{ACH_L} represents the low temperature heat energy produced by the absorption refrigeration, and k_ACH is a proportional constant based on the characteristics of the absorption refrigeration equipment.

• (5) Peak Heater

The peak heater can use steam to heat hot water to a high temperature. Its mathematical model is similar to that of a heat exchanger, as shown in Eq. (9.7).

$$ \begin{array}{*{20}c} {H_{{{\text{PH\_H}}}}^{t} = C_{{{\text{PH}}}} H_{{{\text{PH\_S}}}}^{t} } \\ \end{array} $$

(9.7)

In (9.7), H_{PH_H} represents the heat energy transferred by the peak heater, C_PH represents the heat transfer efficiency, and H_{PH_S} represents the steam heat energy consumed by the peak heater.

• (6) Solar Thermal Equipment

Solar thermal power generation uses concentrated solar light to generate high-temperature steam. A part of it is used for power generation through a steam turbine, and the remaining part is used for heating. Its mathematical model is shown in Eq. (9.8).

$$ \begin{array}{*{20}c} {\left\{ \begin{aligned} P_{{{\text{PT}}}} & = \eta_{{{\text{ST}}}} x_{{\text{p}}} E_{{{\text{solar}}}} \\ H_{{{\text{PT\_H}}}} & = \eta_{{{\text{ex}}}} (\left( {1 - x_{{\text{p}}} {) + }\eta_{{{\text{WH}}}} \left( {1 - \eta_{{{\text{ST}}}} } \right)x_{{\text{p}}} } \right)E_{{{\text{solar}}}} \\ \end{aligned} \right.} \\ \end{array} $$

(9.8)

In (9.8), P_PT represents the solar thermal power generation capacity, η_ST represents the steam turbine power generation efficiency, E_solar represents the heat energy provided by the solar collector system, and x_p is the proportion coefficient of thermal energy entering the steam turbine. H_{PT_H} represents the solar thermal heating capacity, η_ex represents the efficiency of the heat exchanger, and η_WH represents the recovery efficiency of the steam turbine waste heat.

• (7) Battery Energy Storage

The battery energy storage model is represented by the state of charge, as shown in Eq. (9.9).

$$ \begin{array}{*{20}c} {SOC_{{{\text{ess}}}}^{t} = \left\{ {\begin{array}{*{20}c} {\left( {1 - \sigma_{{{\text{ess}}}} } \right)SOC_{{{\text{ess}}}}^{t - 1} + \eta_{{{\text{chr}}}} \frac{{P_{{{\text{ess}}}}^{t - 1} \cdot \Delta t}}{{E_{{\text{ess,max}}} }}} \\ {\left( {1 - \sigma_{{{\text{ess}}}} } \right)SOC_{{{\text{ess}}}}^{t - 1} + \frac{1}{{\eta_{{{\text{dch}}}} }}\frac{{P_{{{\text{ess}}}}^{t - 1} \cdot \Delta t}}{{E_{{\text{ess,max}}} }}} \\ \end{array} } \right.} \\ \end{array} $$

(9.9)

where SOC_ess represents the state of charge of the battery energy storage, P_ess represents the charging/discharging power (positive for charging and negative for discharging), E_ess,max represents the maximum capacity, η_chr represents the charging efficiency, η_dch represents the discharging efficiency, σ_ess represents the self-discharge coefficient, and Δt represents the time interval.

• (8) Thermal Energy Storage Using Cold and Hot Water

Cold and hot water energy storage is stored at a constant temperature, and the change in water storage reflects the energy storage status. Its mathematical model is shown in Eq. (9.10).

$$ \begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {Q_{{\text{M}}}^{t} = \left( {1 - \sigma_{{\text{M}}} } \right)Q_{{\text{M}}}^{t - 1} + H_{{{\text{tank\_M}}}}^{t - 1} \Delta t} \\ {Q_{{\text{C}}}^{t} = \left( {1 - \sigma_{{\text{C}}} } \right)Q_{{\text{C}}}^{t - 1} + H_{{{\text{tank\_C}}}}^{t - 1} \Delta t} \\ \end{array} } \right.} \\ \end{array} $$

(9.10)

where Q_M represents the thermal energy stored in the water tank, σ_M is the heat self-loss coefficient, and H_{tank_M} is the thermal power of the water tank (positive for input and negative for output); Q_C represents the cold energy stored in the water tank, σ_C is the cold self-loss coefficient, and H_{tank_C} is the cooling power of the water tank (positive for input and negative for output).

9.3.2 Energy Grade Conversion Model

Electric energy and thermal energy, as well as different grades of thermal energy, can be transformed from high to low grade by equipment such as electric heat pumps, absorption heat pumps, and peak heaters. During the conversion process, a certain proportion of the high-grade energy input on the driving side of the device is converted to the heating side, raising the grade of thermal energy on the heating side. The process of grade conversion and thermal energy transfer in the energy flow is shown in Fig. 9.5. Based on the energy conservation law and the definition of specific enthalpy, the multi-energy coupling relationships between different grades of thermal energy are analyzed as shown in Eqs. (9.11–9.13).

Fig. 9.5

Multi-grade energy conversion diagram

$$ \begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {H_{{x{\text{,out}}}}^{t} = C_{x} \cdot H_{{x{\text{,in}}}}^{t} + H_{{x{\text{,heated}}}}^{t} } \\ {m_{{x{\text{,in}}}}^{t} \cdot \left( {h_{{{\text{in}}}} - h_{{{\text{base}}}} } \right) \cdot \Delta t = H_{{x{\text{,in}}}}^{t} } \\ {m_{{x{\text{,out}}}}^{t} \cdot \left( {h_{{{\text{heated}}}} - h_{{{\text{base}}}} } \right) \cdot \Delta t = H_{{x{\text{,heated}}}}^{t} } \\ {m_{{x{\text{,out}}}}^{t} \cdot \left( {h_{{{\text{out}}}} - h_{{{\text{base}}}} } \right) \cdot \Delta t = H_{{x{\text{,out}}}}^{t} } \\ \end{array} } \right.} \\ \end{array} $$

(9.11)

$$ \begin{array}{*{20}c} {R_{x} = \frac{{H_{{x{\text{,heated}}}}^{t} }}{{H_{{x{\text{,in}}}}^{t} }} = \frac{{C_{x} \cdot \left( {h_{{x{\text{,heated}}}} - h_{{{\text{base}}}} } \right)}}{{h_{{x{\text{,out}}}} - h_{{x{\text{,heated}}}} }}} \\ \end{array} $$

(9.12)

$$ \begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {H_{{x{\text{,out}}}}^{t} = \left( {C_{x} + R_{x} } \right) \cdot H_{{x{\text{,in}}}}^{t} } \\ {H_{{x{\text{,heated}}}}^{t} = R_{x} \cdot H_{{x{\text{,in}}}}^{t} } \\ \end{array} } \right.} \\ \end{array} $$

(9.13)

In Eq. (9.11), x represents the type of energy equipment, H_x,out is the output thermal energy, C_x is the energy efficiency ratio constant, H_x,in is the input energy on the driving side, and H_x,heated is the input thermal energy on the heated side. m_x,in and m_x,out are the working fluid flow rates on the driving and heated sides, respectively, and h_in, h_heated, and h_out are the specific enthalpies of input on the driving side, input on the heated side, and output on the heated side, respectively. h_base is the specific enthalpy of water at normal temperature and is used as a reference.

In Eq. (9.12), R_x is the ratio of input thermal energy on the heated side to the input energy on the driving side. It can be seen that this proportionality factor depends on the energy efficiency ratio and the design input-output specific enthalpy of the equipment and can be treated as a constant for a specific equipment. Equation (9.13) analyzes the coupling and conversion relationship between different thermal energy grades based on the proportionality factor R_x. The input-output mathematical models of electric heat pumps, absorption heat pumps, and peak heating equipment are rewritten based on the original mathematical model.

9.3.3 Energy Supply and Demand Analysis

Based on the energy flow structure shown in Fig. 9.4, the energy flow coupling relationships and the energy grade conversion model described above, the energy supply and demand on different energy buses are analyzed from the perspective of energy cascade utilization. The energy sources on each bus are shown in Eq. (9.14).

$$ \begin{array}{*{20}c} {\left\{ \begin{aligned} P_{{{\text{E\_supply}}}}^{t} & = P_{{{\text{grid}}}}^{t} + P_{{{\text{GT}}}}^{t} + P_{{{\text{PT}}}}^{t} + P_{{{\text{wind}}}}^{t} \\ H_{{{\text{S\_supply}}}}^{t} & = H_{{{\text{GB\_S}}}}^{t} + H_{{{\text{GT\_S}}}}^{t} \\ H_{{{\text{H\_supply}}}}^{t} & = H_{{{\text{PT\_H}}}}^{t} + H_{{{\text{PH\_H,out}}}}^{t} \\ H_{{{\text{M\_supply}}}}^{t} & = H_{{{\text{HP\_M,out}}}}^{t} + H_{{{\text{AHP\_M,out}}}}^{t} \\ H_{{{\text{L\_supply}}}}^{t} & = H_{{{\text{GT\_L}}}}^{t} + H_{{{\text{ACH\_L}}}}^{t} \\ H_{{{\text{C\_supply}}}}^{t} & = H_{{{\text{RE\_C}}}}^{t} + H_{{{\text{ACH\_C}}}}^{t} \\ \end{aligned} \right.} \\ \end{array} $$

(9.14)

where P_{E_supply}, H_{S_supply}, H_{H_supply}, H_{M_supply}, H_{L_supply}, H_{C_supply} are the total energy sources of the power, steam, high-temperature hot water, medium-temperature hot water, low-temperature hot water, and chilled water buses, respectively.

From the equation above, it can be seen that electricity and steam, the two high-grade energy sources, are directly supplied by power generation equipment or natural gas; high-temperature hot water is not only directly supplied by solar thermal energy but also by utilizing the surplus steam and medium-temperature hot water energy through the peak heating equipment. Medium-temperature hot water is supplied by consuming electricity through electric heat pumps and steam and low-temperature hot water through absorption heat pumps. Low-temperature hot water is supplied by the waste heat recovery power of gas turbines and the consumption of steam through absorption refrigeration. Cold water is supplied by consuming electricity through electric refrigeration and steam through absorption refrigeration. During the energy supply process, surplus high-grade energy can supply low-grade energy, and low-grade heat energy can also be heated into high-grade heat energy.

The energy consumption of each bus is shown in Eq. (9.15), which takes into account the energy interaction between electricity, cooling, thermal storage, and their corresponding buses.

$$\begin{array}{*{20}c} {\left\{ \begin{aligned} P_{{{\text{E\_load}}}}^{t} & = P_{{{\text{EL}}}}^{t} + P_{{{\text{HP}}}}^{t} + P_{{{\text{RE}}}}^{t} + P_{{{\text{ess}}}}^{t} \\ H_{{{\text{S\_load}}}}^{t} & = H_{{{\text{SL}}}}^{t} + H_{{{\text{ACH\_S}}}}^{t} + H_{{{\text{AHP\_S,in}}}}^{t} + H_{{{\text{PH\_S,in}}}}^{t} \\ H_{{{\text{H\_load}}}}^{t} & = H_{{{\text{HL}}}}^{t} \\ H_{{{\text{M\_load}}}}^{t} & = H_{{{\text{ML}}}}^{t} + H_{{{\text{PH\_M,heated}}}}^{t} + H_{{{\text{tank\_M}}}}^{t} \\ H_{{{\text{L\_load}}}}^{t} & = H_{{{\text{HP\_L,heated}}}}^{t} + H_{{{\text{AHP\_L,heated}}}}^{t} \\ H_{{{\text{C\_load}}}}^{t} & = H_{{{\text{CL}}}}^{t} + H_{{{\text{tank\_C}}}}^{t} \\ \end{aligned} \right.} \\ \end{array}$$

(9.15)

where P_{E_load}, H_{S_load}, H_{H_load}, H_{M_load}, H_{L_load}, H_{C_load} represent the total energy consumption of the power, steam, high-temperature hot water, medium-temperature hot water, low-temperature hot water, and chilled water buses respectively. P_EL, H_SL, H_HL, H_ML, and H_CL represent the loads of electric power, steam, high-temperature hot water, medium-temperature hot water, and chilled water, respectively.

As shown in the above equation, the total energy consumption of each energy bus including power, steam, high-temperature hot water, medium-temperature hot water, low-temperature hot water, and cold water, is considered while taking into account the energy interaction with the corresponding energy storage system. PEL, HSL, HHL, HML, HCL represent the electrical, steam, high-temperature hot water, medium-temperature hot water, and cold water loads, respectively.

As can be seen from the above equation, the two high-grade energy sources, electric power and steam, are not only consumed by the corresponding loads, but also consumed by energy coupling devices to supply low-grade energy demands. The surplus of medium-temperature and low-temperature hot water can also supply higher-grade energy demands through energy coupling devices. The energy supply and demand under the cascade utilization mode is not limited to a single form of energy, but achieves complementarity between different grades of energy.

9.4 Optimization Strategy for Cascaded Utilization of Electric-Thermal Microgrids

9.4.1 Objective Function

The objective of the optimization strategy takes into account the minimum daily operating cost, which is composed of the costs of purchasing natural gas and electricity, as well as equipment operating costs, as shown in Eq. (9.16).

$$ \begin{array}{*{20}c} {C_{{{\text{all}}}} = C_{{{\text{ng}}}} + C_{{{\text{grid}}}} + C_{{{\text{device}}}} } \\ \end{array} $$

(9.16)

Natural gas is consumed by gas turbines and gas boilers, and the cost of purchasing natural gas is shown in Eq. (9.17). Here, i represents the internal number of the same type of equipment.

$$ \begin{array}{*{20}c} {C_{{{\text{ng}}}} = \mathop \sum \limits_{i} \mathop \sum \limits_{t} F_{{{\text{GT}},i}}^{t} + \mathop \sum \limits_{i} \mathop \sum \limits_{t} F_{{{\text{GB}},i}}^{t} } \\ \end{array} $$

(9.17)

When the microgrid is in parallel operation with the main grid, electricity is purchased and sold from the main grid based on time-of-use pricing. The cost of purchasing and selling electricity from the grid is shown in Eq. (9.18). Here, p^t_buy represents the time-of-use purchase price of electricity.

$$ \begin{array}{*{20}c} {C_{{{\text{grid}}}} = \mathop \sum \limits_{t} p_{{{\text{buy}}}}^{t} \cdot P_{{{\text{buy}}}}^{t} } \\ \end{array} $$

(9.18)

Equipment operating costs can be divided into energy equipment maintenance costs and battery energy storage depreciation costs. Equipment maintenance costs are defined by the cost per unit of equipment power. Battery energy storage depreciation costs are related to the amount of charged and discharged electricity, and the depreciation is assumed to be linear with increasing charged and discharged electricity. Therefore, the equipment operating cost is shown in Eq. (9.19).

$$ \begin{array}{*{20}c} {C_{{{\text{device}}}} = \left( {\mathop \sum \limits_{x} \mathop \sum \limits_{i} \mathop \sum \limits_{t} p_{x} \cdot P_{x,i}^{t} + \mathop \sum \limits_{t} c_{{{\text{bat}}}} \frac{{P_{{{\text{ess}}}}^{t} }}{{Q_{{\text{ess,max}}} }}} \right) \cdot \Delta t} \\ \end{array} $$

(9.19)

where x represents the cost per unit output power of different energy equipment, c_ess represents the replacement cost of the battery energy storage system, and Q_ess,max represents the total charge and discharge amount of the battery over its entire lifecycle.

9.4.2 Constraints

Energy supply and demand must be balanced on each bus during operation, and the constraints on each bus are shown in Eq. (9.20). Here, the storage of large amounts of low-temperature hot water is uneconomical, and the study do not consider factors such as space heating demand in the plant area and boiler return water heating. Therefore, the constraint is set to ensure that supply is greater than demand.

$$ \begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {P_{{{\text{E\_supply}}}}^{t} = P_{{{\text{E\_load}}}}^{t} } \\ {H_{{{\text{S\_supply}}}}^{t} = H_{{{\text{S\_load}}}}^{t} } \\ {H_{{{\text{H\_supply}}}}^{t} = H_{{{\text{H\_load}}}}^{t} } \\ {H_{{{\text{M\_supply}}}}^{t} = H_{{{\text{H\_load}}}}^{t} } \\ {H_{{{\text{L\_supply}}}}^{t} \ge H_{{{\text{L\_load}}}}^{t} } \\ {H_{{{\text{C\_supply}}}}^{t} = H_{{{\text{C\_load}}}}^{t} } \\ \end{array} } \right.} \\ \end{array} $$

(9.20)

In addition, the operation of energy equipment must satisfy constraints on maximum and minimum power and ramp rate, as shown in Eq. (9.21).

$$ \begin{array}{*{20}c} {\left\{ {\begin{array}{*{20}c} {P_{{x,{\text{min}}}} \le P_{x,i}^{t} \le P_{{x,{\text{max}}}} } \\ { - D_{x} \cdot \Delta t \le P_{x,i}^{t} - P_{x,i}^{t} \le B_{x} \cdot \Delta t} \\ \end{array} } \right.} \\ \end{array} $$

(9.21)

where P_x,min and P_x,max represent the minimum and maximum operating power of different energy equipment, while D_x and B_x represent the downward and upward ramp rates of different energy equipment, respectively.

9.4.3 Solution Methodology

This chapter studies a linearized modeling approach, which belongs to the mixed-integer linear programming problem, and uses the commercial solver Gurobi for solving. The energy flow mathematical model and constraints of the integrated energy system are constructed using the Matlab platform and Yalmip toolbox. During the simulation process, the day is divided into 96 time nodes, and the scheduling plan for each device is developed with the objective of minimizing daily operating costs.

During the solution process, there is some randomness in the solver's selection of output devices for multiple devices of the same type due to the same constraint definition. In order to make the device selection more distinctive, Eq. (9.22) is used to process the operating and maintenance costs of devices of the same type, with the operating costs of devices of the same type increasing sequentially, thus prioritizing devices with lower numbers. Here, x represents the device type, i represents the device number, and e_r represents the cost increment. The cost increment is defined to be extremely small (10^–4 in this study) and only serves to differentiate devices, so its numerical value is negligible in the final solution.

$$ \begin{array}{*{20}c} {p_{x,i + 1} = p_{x} \cdot \left( {1 + i \cdot {\text{e}}_{{\text{r}}} } \right)} \\ \end{array} $$

(9.22)

9.5 Case Studies

9.5.1 Case Description

The simulation case is based on the structural topology and parameters of the “China-Italy Green Energy Experimental Center” at a university in southwest Shanghai, which corresponds to an electric-thermal microgrid scenario that includes industrial, commercial, and residential users. The simulation analysis is performed with a 15-min interval, which satisfies the time scale requirement for optimizing scheduling considering the dynamic characteristics of multiple energy flows and the response capabilities of each device. The example includes devices such as gas turbines, gas boilers, absorption heat pumps, absorption refrigeration, electric heat pumps, electric refrigeration, peak heating equipment, battery energy storage, hot water storage tanks, and chilled water storage tanks. These devices cooperate to supply users with electric power, steam, high- temperature and medium-temperature hot water, and chilled water loads. The key parameters of each device are shown in Table 9.1, while the maintenance costs, time-of-use electricity prices, and natural gas purchase costs are shown in Table 9.2. The microgrid load and renewable energy daily output predictions are shown in Fig. 9.6, where wind power and electric load are in electric power, while the rest are in thermal power.

Table 9.1 Equipment parameter

Table 9.2 Operating cost parameter

Fig. 9.6

Renewable energy output and load prediction of microgrid with heat and power system

9.5.2 Results Analysis

Based on the simulation case described above, the comprehensive energy station's thermal-electric dispatch is shown in Figs. 9.7, 9.8, 9.9, 9.10, and 9.11, where energy input to the bus is represented by positive values, and energy acquired from the bus is represented by negative values. Based on the electricity and steam dispatch plan results, Analysis are conducted from the perspective of electricity prices during peak and off-peak hours:

Fig. 9.7

Power dispatch plan

Fig. 9.8

Steam dispatch plan

Fig. 9.9

High-temperature hot water dispatch plan

Fig. 9.10

Medium-temperature hot water dispatch plan

Fig. 9.11

Cold water dispatch plan

• (1) 23:00 to 7:00 is the off-peak electricity pricing period. It is economically efficient to directly purchase electricity from the grid, so the gas turbine is not started. The power supply side is composed of solar-thermal power generation, wind power, and the main power grid, while the power load side is composed of electric heat pumps, electric refrigeration, and uncontrollable electric loads. During this period, only the gas boiler supplies steam, and the steam load side is composed of absorption refrigeration, peak heating equipment, and steam loads. The reason for using absorption refrigeration during this period is that the electricity price is low, and the low-temperature hot water produced by the absorption refrigeration can be heated and utilized by the electric heat pump, which has good economic benefits. The battery energy storage is fully charged at maximum power before the end of the off-peak period.

• (2) 7:00 to 23:00 is the peak and flat electricity pricing period, and the power supply by the gas turbine is more economical. During this period, the power supply side is mainly composed of gas turbines, solar-thermal power generation, and wind power. Note that at around 10:00, due to the intermittent decrease in wind power output, both the gas turbine and the battery energy storage reach maximum output, and electricity is purchased from the grid to meet the load demand. The power load side is mainly composed of electric refrigeration and uncontrollable electric loads, and electric heat pumps are only selectively used. The steam supply side is provided by the gas turbine and gas boiler, and the steam load side is composed of absorption heat pumps, absorption refrigeration, peak heating equipment, and steam loads. Due to the large amount of steam provided by the gas turbine combined heat and power and the high electricity price, absorption heat pumps and absorption refrigeration have better economic benefits. During the period from 7:00 to 15:00, due to high electric load and the decrease in wind power output, the battery energy storage is discharged to assist in peak shaving until the state of charge reaches the lower limit.

Based on the cold and hot water scheduling plan results in Figs. 9.9, 9.10, and 9.11, analysis are conducted from the perspective of the energy supply composition of cold and hot loads:

• (1) For high-temperature hot water supply, since the solar thermal power station does not participate in scheduling control, the steam turbine's electricity generation is relatively stable, and the remaining solar thermal energy is used for heating. Therefore, the peak heating equipment adjusts the heat production according to the heating supply of the solar thermal power station. Its steam consumption is a rigid demand, and the steam production of gas turbines and gas boilers needs to be prioritized.

• (2) For medium-temperature hot water supply, it is supplied by electric heat pumps during the valley electricity price period and by absorption heat pumps during the peak and flat electricity price periods. Electric heat pumps are used for heating when steam supply is tight. Due to energy self-loss, the heat storage water tank first releases water during the valley electricity price period and then heats up through electric heat pumps before the end of the valley electricity price period, storing water to the maximum capacity and releasing heat during the peak electricity price period.

• (3) For cold water supply, electric refrigeration is mainly used, and the proportion of absorption refrigeration supply increases during the peak and flat electricity price periods. This is because the energy efficiency ratio of absorption refrigeration is lower than that of electric refrigeration, but considering that absorption refrigeration can provide low-temperature hot water while cooling, it can be used for further heating by electric heat pumps during the valley electricity price period. When steam supply is sufficient during the peak and flat electricity price periods, the comprehensive benefits of consuming steam refrigeration by absorption refrigeration are higher. The operation mode of the cold storage water tank is similar to that of the hot storage water tank. It stores water to the maximum capacity before the end of the valley electricity price period and releases cold during the peak electricity price period.

9.5.3 Economic Analysis of Diverse Energy Supply Structures

The energy supply of electric-thermal microgrid is realized by electric-thermal coupling cascade utilization (structure 1), cascade utilization without electric-thermal coupling (structure 2) and traditional tri-generation supply structure (structure 3), and the daily cost of the three energy supply structures is shown in Table 9.3 below. The daily operating cost includes natural gas costs, electricity purchase costs and maintenance costs. At the same time, because the equipment used in the three structures is not identical, the total cost also includes the equipment cost converted to the daily price.

Table 9.3 Daily cost comparison

Structure 2 only adopts the energy cascade utilization strategy without considering the coupling between electric and thermal energy, so it does not use electric heat pumps, electric refrigeration and other electric-thermal coupling equipment. In terms of energy supply, absorption heat pumps provide all medium temperature hot water, and absorption refrigeration provides all cold water. The power and steam dispatch plan for structure 2 is shown in Figs. 9.12 and 9.13. Gas turbines and gas boilers operate around the clock, providing steam for absorption heat pumps, absorption refrigeration and steam loads. The steam supply is mainly gas boilers during the valley electricity price period, and gas turbines are mainly used during the peak electricity price period. During the valley tariff period, the purchase of electricity from the grid is reduced because the gas turbine runs to generate electricity. The operation mode of battery energy storage is consistent with structure 1, that charging during the valley electricity price period and discharging during the peak electricity price period.

Fig. 9.12

Power dispatch plan of structure 2

Fig. 9.13

Steam dispatch plan of structure 2

Structure 3 adopts the traditional tri-generation supply mode without dividing the thermal energy grade. Its specific supply strategy is referred to in literature [31]. The power and steam dispatch plan of Structure 3 is shown in Figs. 9.14 and 9.15. Since the thermal energy grade is not divided, the load of medium-temperature hot water and hot water in the heat network are unified as high-temperature heat load, and the hot water is supplied through the heat network. In terms of supply strategy, during the off-peak electricity price period, the steam generated by gas turbines and gas boilers is supplied to the peak heater and high-temperature steam load. The peak heater produces high-temperature hot water to meet the hot water load of the heat network, and electric refrigeration provides all the required cold water. During the peak and flat electricity price period, gas turbines and gas boilers operate at high loads, providing the steam required for absorption refrigeration, peak heater, and high-temperature steam load. Electric refrigeration is turned on after the uncontrollable electrical load in the microgrid decreases, consuming surplus electricity and reducing the steam demand of absorption refrigeration, thus balancing the power and steam demand of the microgrid.

Fig. 9.14

Power dispatch plan of structure 3

Fig. 9.15

Steam dispatch plan of structure 3

Based on the information presented in the table and figures, the following conclusions can be drawn:

• (1) The cascade utilization strategy of electric-heat coupling can effectively improve the economic performance of electric-thermal microgrids. As microgrids have demand for both heating and cooling, the benefit of using natural gas for cogeneration is significant, hence natural gas expenses are relatively high. Structure 1 consumes more electricity at lower rates and thus saves on natural gas expenses, resulting in lower overall energy costs. Furthermore, the high-efficiency equipment such as absorption heat pumps, electric heat pumps, and electric refrigeration are utilized to minimize maintenance costs. In terms of daily operating costs, structures 2 and 3 have increased by 8.31% and 17.58% respectively compared to structure 1.

• (2) As structure 1 utilizes the most equipment, it has the highest daily equipment cost. However, as the prices of the various equipment types are relatively low among the three structures, it has not had a significant impact on the total cost. The total cost of structures 2 and 3 have increased by 7.60% and 16.78% respectively compared to structure 1.

• (3) The lack of electric-thermal coupling equipment negatively impacts the flexibility of electric-thermal combined microgrid operations. In structure 2, due to the single type of heating and cooling supply equipment, the operation of absorption heat pumps and absorption refrigeration needs to be carried out based on load requirements, while the gas turbine and gas boiler need to operate at high load throughout the day, leaving no room for optimization.

• (4) Without considering the cascade utilization of energy, the operating efficiency of electric-thermal combined microgrid is low. In structure 3, direct heat exchange is used for heating, resulting in low efficiency, and a large amount of steam is consumed for heating and cooling supply in the microgrid, causing high natural gas expenses. Without distinguishing the heat quality requirements of microgrid users, the actual heating efficiency of the system is low, and it cannot achieve efficient and targeted high-quality heating.

9.6 Conclusion

This chapter aims to address the issue of the comprehensive optimization and utilization of various forms of energy in electric-thermal microgrids. Based on the principle of cascade utilization, a cascade utilization energy flow structure for electric-thermal coupling conversion is constructed to achieve energy utilization and supply with matched thermal energy grade, and to enhance the operational economy and flexibility of cold and heat supply equipment by leveraging the complementary advantages of electric and thermal energy. For the source-load-storage of electric-thermal microgrids, an energy flow supply and demand model with different energy buses is established. Based on the operational constraints of the energy cascade optimization utilization model and with the objective of minimizing daily operating costs, this mixed integer optimization problem is solved via the establishment of constraints and objectives in Matlab. By coordinating and scheduling various energy sources and coupling devices, the optimized economic operation of the electric-thermal microgrid system is achieved. The method used in this study fully considers the principles of mutual coupling and complementary optimization of various forms of energy, making effective use of energy with different grades in the production process, providing good engineering application prospects. Future research will further improve the energy optimization and scheduling capabilities of electric-thermal microgrid systems through rolling optimization or by establishing optimization models that take into account uncertain factors.