Optimal dispatch of multi energy system using power-to-gas technology considering flexible load on user side

Abstract

The relation between power-to-gas technology (P2G) and energy interconnection becomes increasingly close. Meanwhile, the participation of flexible load on user side in system optimization has attracted much attention as an efficient approach to relieve the contradiction between energy supply and energy demand. Based on the concept of energy hub, according to its series characteristic, this paper established a generic multi-energy system model using the P2G technology. The characteristic of flexible load on user side was considered and optimal dispatch analysis was made, so as to reduce the cost, to reasonably dispatch the flexible load, to reduce the discharge, to enhance the new energy output, and to increase the power-to-gas conversion efficiency. Finally, a concrete analysis was made on the optimal dispatch result of the multi-energy system using the P2G technology considering flexible load on user side in the calculating example, and optimal dispatch of the system was verified via four different scenarios. The results indicate that cooperative dispatch of multi-energy system using the P2G technology considering flexible load on user side is the most economic, and can make a contribution to absorption of new energy and P2G conversion. In this way, environmental effects and safe and stable operation of the system can be guaranteed.

Keywords

multi-energy system / energy hub / series characteristic / optimal dispatch / flexible load

Introduction

In the hot trend of energy internet research and development [¹], the concept of energy hub proposed by Geidl et al. from ETH Zurich [²] has attracted extensive attention from academic circles and industrial circles, and relevant researches have been launched by focusing on energy hub. The energy hub which can distribute, transform, store energy of multiple forms, meet load requirements of different forms, and enhance the economic benefit and environmental benefit of energy systems, has become an important direction of energy system development in the future [³]. Therefore, optimal operation of energy hub has become an essential issue. Reference [⁴] proposes an energy flow calculation method for micro energy grid including CCHP based on energy hub, and puts forward the function rate index of CCHP to reflect the coupling degree of the power distribution network and natural gas network. Based on the energy hub model, Ref. [⁵] puts forward an optimal operation method for the integrated energy system. In Ref. [⁶], an energy center with P2G equipment is established, and a study is made on the issue of market equilibrium when various energy centers participate in several energy markets at the same time in the framework of game theory. In Refs. [⁷–⁸], an optimal dispatch model of P2G multi-energy system is built, and an analysis is made on the economic benefit brought about by P2G to the absorption of electric system for wind power energy. In Ref. [⁹], an energy concentrator model with P2G is established, and verification is conducted for the necessity of calculating P2G operation cost in the integrated energy system and the feasibility of considering economic efficiency and wind power receptivity. At present, multi-energy system modeling based on energy hub is not orderly enough, and a new model needs to be established for energy hubs under different scenarios, which will increase the modeling time and reduce the efficiency.

With the gradual increase of environmental pressure and development bottleneck of energy, more and more scholars have paid attention to the utilization and development of new energy. The study on P2G technology also becomes increasingly mature. The combination of P2G and energy interconnection field has realized the transformation between electric energy and natural gas, and can effectively enhance the coupling of the multi-energy system. In addition, the P2G technology can obviously improve the absorption ability of the system for renewable energy sources [¹⁰]. In Refs. [¹¹–¹²], the power-gas networks are interconnected through the coordinating function of P2G and gas turbine, it is verified that the P2G and peak load shifting model can stabilize the net load fluctuation effectively, which improves the wind power absorption ability of the system. Reference [¹³] establishes a power-gas interconnection system with P2G, analyzes the influence of P2G process on combined operation of power-gas system, and displays its potential for absorbing renewable energy sources. According to the above references, the P2G technology can improve the absorption ability of the multi-energy system for new energy in load trough, enhance the effect of power-gas coupling link in the system, and improve the function of coupling link between power and natural gas systems.

Potential schedulable resources exist on the load side in the multi-energy system. Considering the characteristics of flexible load on user side actually means to guide users to initiatively change their electricity use habit, optimize the electricity use mode, and alter the electricity use time through price signals or incentive policies, so as to reduce or delay the effect of electric load in a certain period [¹⁴]. In Ref. [¹⁵], flexible load is introduced, and in Refs. [¹⁶–¹⁸], research achievements about flexible load participating in energy management are illustrated. Reference [¹⁹] discusses the influence of flexible electricity and heating load in the family-type multi-energy system, and transforms the change of flexible load into the comfort level index, but the diversity of flexible load is not considered and the load model is relatively simple. At present, most studies only consider flexible power load on user side in optimal dispatch of the multi-energy system. However, flexible cooling and heating loads do not participate in optimal dispatch of the system. Therefore, this paper further divides cooling, heating, and power load into flexible load and rigid load, and makes flexible load participate in optimal dispatch as an important resource of multi-energy system.

Based on the above references, this paper fully considers the coupling property of several devices and series characteristic of energy hub. Besides, by combining the P2G technology with flexible cooling, heating and power load features on user side, it establishes a generic multi-energy system model based on energy hub. In establishment of constraint conditions and scenario analysis, the series characteristic of energy hub was also fully utilized. It aims to explore the coupling mechanism of energy hub and the interactive coordinated dispatch of supply and demand more conveniently and effectively, to express the function of multi-energy cooperation, and to realize optimum utilization of energy.

Mathematic model of multi-energy system with P2G considering flexible load on user side

Multi-energy system comprises the input of multiple energy forms, coupling of different energy devices and demands of various energy needs. Based on the concept of energy hub, this paper establishes a generic multi-energy system to describe the exchange and coupling relationship among energy, load, and network in the system [⁴]. Moreover, the features of flexible load on user side are considered, and flexible load on user side is used to participate in system optimization, as shown in Fig. 1. Electric energy and natural gas are set as two major energy inputs, and coupling devices include P2G equipment, a micro-gas turbine, a boiler, refrigeration equipment, and energy storage equipment. Besides, energy needs are abstracted into electric, cooling, heating types, each of which is divided into flexible and rigid loads.

The energy hub abstracts the multi-energy system into a two-port network of input-output, and the coupling relationship between relevant internal components can be described using the coupling matrix

(1)L=CP,

where C is the coupling matrix; L represents the user load at the output end of the energy hub; and P means the energy power at the input end of the energy hub.

To reflect the series characteristic of energy supply, transformation, storage and consumption in the energy hub [²⁰], the energy hub is divided into four modules including supply, transformation, storage, and consumption. Hence, more detailed mathematical description is given to the energy hub. In this way, devices in the energy hub can be added and removed effectively and conveniently, and different energy utilization scenarios can be switched rapidly.

Mathematical description of supply module

The supply module includes the energy input of power grid and natural gas network, the input of new energy, the P2G equipment, and the gas storage equipment. The new energy is solar energy and wind energy. The supply relationship is can be expressed as

(2)\underset{P^{\mathrm{t}}}{\underbrace{\left[\begin{array}{l}{P}_{\mathrm{e}}^{\mathrm{t}}\\ P_{\mathrm{g}}^{\mathrm{t}}\end{array}\right]}}=\underset{P^{\mathrm{n}\mathrm{e}\mathrm{t}}}{\underbrace{\left[\begin{array}{l}{P}_{\mathrm{e}}^{\mathrm{n}\mathrm{e}\mathrm{t}}\\ P_{\mathrm{g}}^{\mathrm{n}\mathrm{e}\mathrm{t}}\end{array}\right]}}+\underset{P^{\mathrm{in}}}{\underbrace{\left[\begin{array}{l}{P}_{\mathrm{e}}^{\mathrm{new}}\\ P_{\mathrm{g}}^{\mathrm{s}}\end{array}\right]}}+\underset{P^{\mathrm{P}\mathrm{2}\mathrm{G}}}{\underbrace{\left[\begin{array}{l}-P_{\mathrm{e}}^{\mathrm{P}\mathrm{2}\mathrm{G}}\\ P_{\mathrm{g}}^{\mathrm{P}\mathrm{2}\mathrm{G}}\end{array}\right]}},

(3)P^{\mathrm{t}}=P^{\mathrm{net}}+P^{\mathrm{in}}+P^{\mathrm{P2G}},

where P^t, P^net, Pⁱⁿ, and P^P2G represent the supply output matrix, the energy network input matrix, the new energy and gas storage input matrix, and the P2G matrix; P_{\mathrm{e}}^{\mathrm{t}} and P_{\mathrm{g}}^{\mathrm{t}} represent the output of electric energy and natural gas in the supply module; P_{\mathrm{e}}^{\mathrm{net}} and P_{\mathrm{g}}^{\mathrm{net}} means the input of electric energy and natural gas in the supply module; P_{\mathrm{e}}^{\mathrm{new}} and P_{\mathrm{g}}^{\mathrm{s}} indicate the input of new energy and gas storage tank; and P_{\mathrm{e}}^{\mathrm{P2G}} and P_{\mathrm{g}}^{\mathrm{P2G}} signify the electrolysis power in P2G process and gas volume produced.

The P2G process will transform electric energy into natural gas, which is characterized by the quick response and flexible dispatch characteristic. Therefore, ignoring the transformation time of this process, only the relation between electrolysis power and gas volume is considered [¹³].

(4)P_{\mathrm{P}\mathrm{2}\mathrm{G}}^{\mathrm{g}}={\eta }_{\mathrm{P}\mathrm{2}\mathrm{G}}{P}_{\mathrm{P}\mathrm{2}\mathrm{G}}^{\mathrm{e}}/HH{V}_{\mathrm{C}\mathrm{H}\mathrm{4}},

where HHV_CH4 means the high calorific value of CH₄, which is 0.0155 MWh/m³ in standard state; and η_P2G is the efficiency of P2G equipment producing CH₄.

For the gas tank model, suppose that the gas storage and degassing power is constant in the time period t, and the equipment energy relation before and after gas storage and degassing [²¹] is

(5)W_{\mathrm{g}}(t)=W_{\mathrm{g}}(t-\mathrm{1})+P_{\mathrm{g}}^{\mathrm{s}},

(6)P_{\mathrm{g}}^{\mathrm{s}}=[P_{\mathrm{g}}^{\mathrm{c}}{\eta }_{\mathrm{g}}^{\mathrm{c}}{\mu }_{\mathrm{g}}-{\displaystyle \frac{P_{\mathrm{g}}^{\mathrm{d}\mathrm{i}\mathrm{s}}}{{\eta }_{\mathrm{g}}^{\mathrm{d}\mathrm{i}\mathrm{s}}}}(\mathrm{1}-{\mu }_{\mathrm{g}})]\times t,

where W_g(t–1) and W_g(t) are the energy stored by the equipment before and after gas storage and degassing respectively; P_{\mathrm{g}}^{\mathrm{c}} and P_{\mathrm{g}}^{\mathrm{dis}} represent the energy stored and released by the gas storage tank; {\eta }_{\mathrm{g}}^{\mathrm{c}} and {\eta }_{\mathrm{g}}^{\mathrm{dis}} mean the gas storage and degassing efficiency; μ_g is a variable of 0 or 1, in which 1 and 0 indicate the air inflation state and degassing state respectively.

Mathematical description of transformation module

The transformation module includes a micro-gas turbine, an electric boiler, a gas-fired boiler, an electric refrigerator, and a lithium bromide refrigerator. The transformation relationship is

(7)\underset{\mathrm{conversion\; output\; matrix}{P}^{\mathrm{T}}}{\underbrace{\left[\begin{array}{l}{P}_{\mathrm{e}}^{\mathrm{T}}\\ P_{\mathrm{c}}^{\mathrm{T}}\\ P_{\mathrm{h}}^{\mathrm{T}}\end{array}\right]}}=\underset{\mathrm{conversion\; coupling\; matrix}{C}^{\mathrm{T}}}{\underbrace{\left[\begin{array}{ll}{\beta }_{\mathrm{1}}& \gamma {\eta }_{\mathrm{M}\mathrm{T}}^{\mathrm{e}}\\ {\beta }_{\mathrm{2}}{\eta }_{\mathrm{A}\mathrm{C}}^{\mathrm{c}}& \delta {\eta }_{\mathrm{A}\mathrm{R}}^{\mathrm{c}}[\gamma {\eta }_{\mathrm{M}\mathrm{T}}^{\mathrm{h}}+(\mathrm{1}-\gamma ){\eta }_{\mathrm{G}\mathrm{B}}^{\mathrm{h}}]\\ {\beta }_{\mathrm{3}}{\eta }_{\mathrm{E}\mathrm{B}}^{\mathrm{h}}& (\mathrm{1}-\delta )[\gamma {\eta }_{\mathrm{M}\mathrm{T}}^{\mathrm{h}}+(\mathrm{1}-\gamma ){\eta }_{\mathrm{G}\mathrm{B}}^{\mathrm{h}}]\end{array}\right]}}\underset{\mathrm{conversion\; input\; matrix}{P}^{\mathrm{t}}}{\cdot \underbrace{\left[\begin{array}{l}{P}_{\mathrm{e}}^{\mathrm{t}}\\ P_{\mathrm{g}}^{\mathrm{t}}\end{array}\right]}},

(8)P^{\mathrm{T}}=C^{\mathrm{T}}{P}^{\mathrm{t}},

where P_{\mathrm{e}}^{\mathrm{T}}, P_{\mathrm{c}}^{\mathrm{T}}, and P_{\mathrm{h}}^{\mathrm{T}} are electric output, cooling output, and heating output of transformation module; β₁, β₂, and β₃ represent the distribution coefficients of power input P_{\mathrm{e}}^{\mathrm{t}} being distributed to electric load, electric refrigerator, and electric boiler, the sum of which is 1; γ means the proportion coefficient that the micro-gas turbine consumes natural gas input P_{\mathrm{g}}^1; δ indicates the proportion coefficient of the total heat consumption of the lithium bromide refrigerator; {\eta }_{\mathrm{A}\mathrm{C}}^{\mathrm{c}} signifies the refrigeration coefficient of the electric refrigerator; {\eta }_{\mathrm{A}\mathrm{R}}^{\mathrm{c}} is the refrigeration coefficient of the lithium bromide refrigerator; {\eta }_{\mathrm{E}\mathrm{B}}^{\mathrm{h}} denotes the heating coefficient of the electric boiler; {\eta }_{\mathrm{G}\mathrm{B}}^{\mathrm{h}} stands for the heating coefficient of the steam boiler; and {\eta }_{\mathrm{M}\mathrm{T}}^{\mathrm{e}} and {\eta }_{\mathrm{M}\mathrm{T}}^{\mathrm{h}} are the electrical efficiency and heating coefficient of micro-gas turbine. Please refer to Ref. [⁴] for various equipment models.

Mathematical description of storage module

In the storage module, the electric storage equipment and heat storage equipment are considered. The gas storage equipment is considered in the supply module. The energy relation is

(9)\underset{\mathrm{load\; matrix}L}{\underbrace{\left[\begin{array}{l}{L}_{\mathrm{e}}\\ L_{\mathrm{c}}\\ L_{\mathrm{h}}\end{array}\right]}}=\underset{P^{\mathrm{T}}}{\underbrace{\left[\begin{array}{l}{P}_{\mathrm{e}}^{\mathrm{T}}\\ P_{\mathrm{c}}^{\mathrm{T}}\\ P_{\mathrm{h}}^{\mathrm{T}}\end{array}\right]}}+\underset{\mathrm{energy\; storage\; matrix}S}{\underbrace{\left[\begin{array}{l}{P}_{\mathrm{e}}^{\mathrm{s}}\\ \mathrm{0}\\ P_{\mathrm{h}}^{\mathrm{s}}\end{array}\right]}},

(10)L=P^{\mathrm{T}}+S,

where L_e, L_c, and L_h respectively represent the electrical load, the cold load, and the heat load; and P_{\mathrm{e}}^{\mathrm{s}} represents the actual interaction value of the accumulator and P_{\mathrm{h}}^{\mathrm{s}} represents the actual interaction value of the thermal storage tank.

In this paper, an accumulator was adopted as the electric storage equipment. The charge-discharge power and current electric quantity are mainly considered, while the internal charge and discharge circuit process is ignored. The state of charge of the accumulator is

(11)Soc(t)=(\mathrm{1}-\vartheta )Soc(t-\mathrm{1})+{\displaystyle \frac{P_{\mathrm{e}}^{\mathrm{s}}}{E_{\mathrm{c}}}},

(12)P_{\mathrm{e}}^{\mathrm{s}}=[P_{\mathrm{e}}^{\mathrm{c}}{\eta }_{\mathrm{e}}^{\mathrm{c}}{\mu }_{\mathrm{e}}-{\displaystyle \frac{P_{\mathrm{e}}^{\mathrm{d}\mathrm{i}\mathrm{s}}}{{\eta }_{\mathrm{e}}^{\mathrm{d}\mathrm{i}\mathrm{s}}}}(\mathrm{1}-{\mu }_{\mathrm{e}})]\times t,

where Soc(t) is the state of charge of the accumulator at time t; \vartheta means the discharge rate of the accumulator; E_c indicates the rated capacity of the accumulator; P_{\mathrm{e}}^{\mathrm{c}} and P_{\mathrm{e}}^{\mathrm{d}\mathrm{i}\mathrm{s}} are the energies stored and released by the accumulator; {\eta }_{\mathrm{e}}^{\mathrm{c}} and {\eta }_{\mathrm{e}}^{\mathrm{d}\mathrm{i}\mathrm{s}} denote the electric storage and discharge efficiency respectively; and μ_e is a variable of 0 or 1, in which 1 and 0 indicate the charging state and discharging state respectively.

The energy relation of the equipment before and after heat storage and release of the thermal storage tank is

(13)W_{\mathrm{h}}(t)=W_{\mathrm{h}}(t-\mathrm{1})+P_{\mathrm{h}}^{\mathrm{s}},

(14)P_{\mathrm{h}}^{\mathrm{s}}=[P_{\mathrm{h}}^{\mathrm{c}}{\eta }_{\mathrm{h}}^{\mathrm{c}}{\mu }_{\mathrm{h}}-{\displaystyle \frac{P_{\mathrm{h}}^{\mathrm{d}\mathrm{i}\mathrm{s}}}{{\eta }_{\mathrm{h}}^{\mathrm{d}\mathrm{i}\mathrm{s}}}}(\mathrm{1}-{\mu }_{\mathrm{h}})]\times t,

where W_h(t–1) and W_h(t) are the energies stored of the equipment before and after heat storage or release; P_{\mathrm{h}}^{\mathrm{c}} and P_{\mathrm{h}}^{\mathrm{dis}} represent the energies stored or released by the thermal storage tank; {\eta }_{\mathrm{h}}^{\mathrm{c}}and {\eta }_{\mathrm{h}}^{\mathrm{dis}} denote the heat storage and release efficiency; and μ_h is a variable of 0 or1, in which 1 and 0 indicate the heat storage state and heat release state respectively.

Mathematical description of load module

The load module comprises cooling, heating and power loads. In this paper, the operating characteristics of different loads on user side are fully considered, and each type of load can be divided into rigid load and flexible load according to the elasticity of working time [¹⁵].

1) Rigid load: Without time elasticity, it should be supplied unconditionally once the user has a need. Such type of load can often meet people’s basic living needs, and therefore, it does not participate in optimal dispatch of the system.

2) Flexible load: With some time elasticity, the load is controllable within users’ acceptable range. Flexible load can be further divided into shiftable load, transferable load, and cuttable load. Cooling and heating loads are not as flexible as power load, and therefore, cooling and heating loads consider shiftable load and cuttable load only.

(15)\underset{\mathrm{load\; matrix}L}{\underbrace{\left[\begin{array}{l}{L}_{\mathrm{e}}\\ L_{\mathrm{c}}\\ L_{\mathrm{h}}\end{array}\right]}}=\underset{\mathrm{rigid\; load}{L}^{\mathrm{r}}}{\underbrace{\left[\begin{array}{l}{L}_{\mathrm{e}}^{\mathrm{r}}\\ L_{\mathrm{c}}^{\mathrm{r}}\\ L_{\mathrm{h}}^{\mathrm{r}}\end{array}\right]}}+\underset{\mathrm{flexible\; load}{L}^{\mathrm{f}}}{\underbrace{\left[\begin{array}{l}{L}_{\mathrm{e}}^{\mathrm{f}}\\ L_{\mathrm{c}}^{\mathrm{f}}\\ L_{\mathrm{h}}^{\mathrm{f}}\end{array}\right]}},

(16)L=L^{\mathrm{r}}+L^{\mathrm{f}},

where L_{\mathrm{e}}^{\mathrm{r}}, L_{\mathrm{c}}^{\mathrm{r}}, and L_{\mathrm{h}}^{\mathrm{r}} are rigid electrical, cold, and heat loads; L_{\mathrm{e}}^{\mathrm{f}}, L_{\mathrm{c}}^{\mathrm{f}},and L_{\mathrm{h}}^{\mathrm{f}} are flexible electrical, cold, and heat loads.

To sum up, by combining the supply module, transformation module, storage module, and load module, the energy relation expression matrix of energy hub can be obtained, which can be expressed as

(17)L^{\mathrm{r}}+L^{\mathrm{f}}=C^{\mathrm{T}}（P^{\mathrm{n}\mathrm{e}\mathrm{t}}+P^{\mathrm{i}\mathrm{n}}+P^{\mathrm{P}\mathrm{2}\mathrm{G}}）+S,

where P^net+Pⁱⁿ+P^P2G, C^T, S, and L^r + L^f are respectively the supply, transformation, storage, and load module in the universal energy hub.

According to the concept and series characteristic of energy hub, the two-port network of input-output described in Eq. (1) is expanded and the energy hub model is modularized in series to obtain the energy relation expression matrix of the energy hub in Eq. (17). The above energy hub modeling method is efficient and fast. For model establishment in different scenarios, it is just necessary to modify corresponding elements in the energy relation expression after the above modules are classified according to different models.

Optimal dispatch model of multi-energy system with P2G considering flexible load on user side

Based on the concept of energy hub, this paper established a multi-energy system, as shown in Fig. 1. Its optimal dispatch can be described as follows: optimize the flexible load on user side according to the data such as power, cooling and heating loads as well as new energy output predicted every hour by combining with the coupling relationship of energy hub within the dispatching cycle of one day; reduce the operating cost as much as possible; make energy distribution in the energy hub more reasonable.

Objective function

Optimization objectives of coordinated dispatch of multi-energy system are to reduce energy cost of the system as much as possible to reasonably dispatch the flexible load involved in interaction on user side, to reduce gaseous emission, to increase new energy output [²²], and to increase the conversion efficiency of P2G equipment, i.e.,

(18)\min {\displaystyle \sum _{t=\mathrm{1}}^{\mathrm{24}}{C}_{\mathrm{e}}(t)P_{\mathrm{e}}^{\mathrm{t}}(t)+}{C}_{\mathrm{g}}(t)P_{\mathrm{g}}^{\mathrm{t}}(t)+C_{\mathrm{em}}+C_{\mathrm{new}}+C_{\mathrm{P2G}}+C_{\mathrm{f}},

where C_e(t) and C_g(t) are the electricity price and natural gas price at time t, in which the electricity price includes purchase tariff and selling tariff; P_{\mathrm{e}}^{\mathrm{t}}(t) represents the grid switching power at time t, which is the interaction value between the energy hub and the power grid; P_{\mathrm{g}}^{\mathrm{t}}(t)represents the gas consumption volume at time t, which is the interaction value between the energy hub and the natural gas network; C_em, C_new, C_P2G, and C_f are penalty terms of gaseous emission, amount of abandoned new energy, P2G conversion loss, and flexible load compensation, which will be calculated in the objective function according to a certain proportion.

(19)C_{\mathrm{em}}={\displaystyle \sum _{t=\mathrm{1}}^{\mathrm{24}}({\alpha }_{\mathrm{1}}{P}_{\mathrm{e}}^{\mathrm{t}}(t)+}{\alpha }_2{P}_{\mathrm{g}}^{\mathrm{t}}(t)),

(20)C_{\mathrm{new}}={\displaystyle \sum _{t=\mathrm{1}}^{\mathrm{24}}{\alpha }_3(P_{\mathrm{new}}(t\mathrm{)-}}{P}_{\mathrm{e}}^{\mathrm{new}}(t)),

(21)C_{\mathrm{P}\mathrm{2}\mathrm{G}}={\alpha }_4{\displaystyle \sum _{t=\mathrm{1}}^{\mathrm{24}}（C_{\mathrm{e}}(t)P_{\mathrm{e}}^{\mathrm{P2G}}(t)-}{C}_{\mathrm{g}}(t)P_{\mathrm{g}}^{\mathrm{P2G}}(t)）,

(22)C_{\mathrm{f}}={\displaystyle \sum _{t=\mathrm{1}}^{\mathrm{24}}[C_{\mathrm{shift}}(t)+C_{\mathrm{tran}}(t)+C_{\mathrm{cut}}(t)]},

in which,

(23)\{\begin{array}{l}{C}_{\mathrm{shift}}(t)=C_{\mathrm{cost}}^{\mathrm{shift}}{P}_{\mathrm{shift}}(t)\cdot y(t)\\ C_{\mathrm{tran}}(t)=C_{\mathrm{cost}}^{\mathrm{tran}}[P_{\mathrm{tran}}^{*}(t)-P_{\mathrm{tran}}(t)]\cdot v(t)\\ C_{\mathrm{cut}}(t)=C_{\mathrm{fix}}+\rho C_{\mathrm{cost}}^{\mathrm{cut}}{P}_{\mathrm{cut}}^{*}(t)\cdot u(t)\end{array},

where α₁ to α₄ represent penalty factors; P_{\mathrm{new}}(t) and P_{\mathrm{e}}^{\mathrm{new}}(t) are the predicted electric power and actual electric power of new energy at time t; P_{\mathrm{e}}^{\mathrm{P2G}} and P_{\mathrm{g}}^{\mathrm{P2G}} denote the electrolysis power in P2G process and gas volume produced; C_shift, C_tran, and C_cut indicate the compensation fees of shiftable, transferable, and cuttable loads respectively; C_{\mathrm{cost}}^{\mathrm{shift}}, C_{\mathrm{cost}}^{\mathrm{tran}}, and C_{\mathrm{cost}}^{\mathrm{cut}} signify the unit power compensation prices of shiftable, transferable, and cuttable loads; P_shift and P_tran mean the powers after shiftable and cuttable loads participate in the dispatch; P_{\mathrm{tran}}^{*} and P_{\mathrm{cut}}^{*} are the powers before transferable and cuttable loads participate in the dispatch; and y(t), v(t), and u(t) represent the shiftable, transferable, and cuttable marks.

Constraint conditions

According to the series characteristic of energy hub, constraint conditions for optimal dispatch of multi-energy system can be divided into supply module constraint, transformation module constraint, energy storage module constraint, and load module constraint as well as coupling matrix constraint of energy hub.

Supply module constraint

The supply module constraint includes draft fan, the photovoltaic power constraint, and the rated capacity constraint of P2G equipment, as shown in Eqs. (24) – (26). For convenience, the gas storage tank constraint is described in the storage module.

(24)0\le P_{\mathrm{e}}^{\mathrm{wind}}\le P_{\mathrm{wind,max}},

(25)0\le P_{\mathrm{e}}^{\mathrm{solar}}\le P_{\mathrm{solar,max}},

(26)0\le P_{\mathrm{e}}^{\mathrm{P}\mathrm{2}\mathrm{G}}\le P_{\mathrm{e},\max }^{\mathrm{P}\mathrm{2}\mathrm{G}}.

Transformation module constraint

The transformation module constraint means the rated capacity constraint of various transformation modules, as shown in Eqs. (27) – (31).

(27)P_{\mathrm{MT}}\le P_{\mathrm{MTen}},

(28)Q_{\mathrm{AR}}\le Q_{\mathrm{ARen}},

(29)Q_{\mathrm{GB}}\le Q_{\mathrm{GBen}},

(30)Q_{\mathrm{AC}}\le Q_{\mathrm{ACen}},

(31)Q_{\mathrm{EB}}\le Q_{\mathrm{EBen}},

where P_MTen is the rated power of the micro-gas turbine; Q_ARen means the rated refrigerating capacity of the lithium bromide refrigerator; Q_GBen indicates the rated heating capacity of the gas-fired boiler; Q_ACen denotes the rated refrigerating capacity of the electric refrigerator; and Q_EBen signifies the rated heating capacity of the electric boiler.

Storage module constraint

The storage module constraint includes the constraint of the accumulator and the thermal storage tank as well as the constraint of the air tank in the supply module. Taking the accumulator as an example, the constraints of rated capacity and exchanging power should be satisfied at the same time [²¹].

1) Charge-discharge power constraint of the accumulator

(32)0\le P_{\mathrm{e}}^{\mathrm{c}}\le P_{\mathrm{e}.\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{c}}{\eta }_{\mathrm{e}}^{\mathrm{c}},

(33)0\le P_{\mathrm{e}}^{\mathrm{d}\mathrm{i}\mathrm{s}}\le P_{\mathrm{e}.\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{d}\mathrm{i}\mathrm{s}}/{\eta }_{\mathrm{e}}^{\mathrm{d}\mathrm{i}\mathrm{s}},

where P_{\mathrm{e}}^{\mathrm{c}} and P_{\mathrm{e}}^{\mathrm{d}\mathrm{i}\mathrm{s}} represent the energies stored or released by the accumulator; {\eta }_{\mathrm{e}}^{\mathrm{c}} and {\eta }_{\mathrm{e}}^{\mathrm{d}\mathrm{i}\mathrm{s}} are the accumulation and discharging efficiency; and P_{\mathrm{e}.\mathrm{m}\mathrm{a}\mathrm{x}}^{\mathrm{c}} and P_{\mathrm{e}.\mathrm{m}\mathrm{ax}}^{\mathrm{d}\mathrm{i}\mathrm{s}} represent the maximum energies stored or released by the accumulator.

2) Rated capacity constraint of the accumulator

(34)W_{\mathrm{e},\min }\le W_{\mathrm{e}}\le W_{\mathrm{e},\max },

where W_e,min and W_e,max are the maximum/minimum energy storage capacities of the accumulator.

3) Net exchanging power of the accumulator per day is 0 constraint

(35){\displaystyle \sum _{t=\mathrm{1}}^{\mathrm{24}}（P_{\mathrm{e}}^{\mathrm{c}}（t）+P_{\mathrm{e}}^{\mathrm{d}\mathrm{i}\mathrm{s}}(t)})\mathrm{=0}.

4) Number of daily charge-discharge times of the accumulator

The number of daily charge-discharge times should not exceed 8.

Load module constraint

This paper further divides the flexible load into shiftable load, transferable load, and cuttable load according to different adjustment modes. The load characteristics are as follows:

Shiftable load

Only monolithic translation can be conducted for shiftable load, and attention should be paid to the constraints of continuity of service and shifting time interval.

(1) Interval constraint of shiftable load

(36)t\in [t_{\mathrm{sh}–},t_{\mathrm{sh}+}],

(2) Dispatch constraint of shiftable load

The shiftable load has and only has two situations after the dispatch: no shifting; shifting to the acceptable time interval. Therefore, the constraint is

(37){\displaystyle \sum _{t\in [t_{\mathrm{sh-}},t_{\mathrm{sh}+}]}{y}_t=\mathrm{1}},{\displaystyle \sum _{t\in [t_{\mathrm{sh}-},t_{\mathrm{sh}+}]}{y}_t=\mathrm{0}},

where [t_sh–, t_sh+] is the acceptable shifting time interval; y means the load shifting mark, and the load is shifted when y = 1.

2) Transferable load

The total electricity consumption remains unchanged, but the electricity consumption in various periods can be adjusted flexibly. Constraints are imposed on the shifting power range, shifting period interval, minimum continuous duration of load, and constant total shifting load.

(1) Interval constraint of transferable load

(38)t\in [t_{\mathrm{sh}–},t_{\mathrm{sh}+}].

(2) Power range constraint of load

(39)

(3) Minimum duration constraint

(40){\displaystyle \sum _{t=\mathrm{1}}^{t+T_{\mathrm{tr},\min }-\mathrm{1}}{\nu }_t}\ge T_{\mathrm{tr},\min }({\nu }_t-{\nu }_{t-\mathrm{1}}).

(4) Constraint of constant total power

(41){\displaystyle \sum _{t\in [t_{\mathrm{sh}-},t_{\mathrm{sh}+}]}{P}_{\mathrm{tr}*}}={\displaystyle \sum _{t\in [t_{\mathrm{sh}-},t_{\mathrm{sh+}}]}{P}_{\mathrm{tr}}},

where [t_sh–, t_sh+] is the acceptable transfer time interval; v_{tmeans the load transfer mark, and the load is transferred when vt = 1; Ttr,min indicates the minimum duration; and Ptr* and Ptr represent the loads before and after the transfer.}

3) Cuttable load

Cuttable load can be partially or wholly cut according to the need, and the cutting duration and number of cutting times should be considered in the dispatch.

(1) Minimum duration constraint

(42){\displaystyle \sum _{t=\mathrm{1}}^{t+T_{\mathrm{cut},\min }-\mathrm{1}}{\mu }_t}\ge T_{\mathrm{cut},\min }({\mu }_t-{\mu }_{t-\mathrm{1}}).

(2) Maximum duration constraint

(43){\displaystyle \sum _{t=\mathrm{1}}^{T_{\mathrm{cut},\min }+\mathrm{1}}（\mathrm{1-}{\mu }_t}）\ge 1.

(3) Frequency constraint

(44){\displaystyle \sum _{t=\mathrm{1}}^T{\mu }_t}\le N_{\mathrm{cut},\max },

where μ_t means the load cutting mark, and the load is cut when μ_t = 1; T_cut,min indicates the minimum duration; T_cut,max denotes the maximum duration; and N_cut,max signifies the maximum number of cutting times.

Coupling matrix constraint of energy hub

The generic energy hub model is presented in Fig. 1, whose detailed mathematical model description is given in Section 2. Therefore, this will not be repeated here. The energy relation expression matrix of the energy hub can be treated as either the coupling matrix constraint of energy hub or the energy conservation constraint of supply and demand, as shown in Eq. (17).

Solving method

In this paper, the mixed integer linear programming method is used to solve the problem. There is a mature solving algorithm [²⁴]. The standard form for solving the model is

(45)\{\begin{array}{l}\min {\mathit{c}}^{\mathrm{T}}\mathit{x}+d^{\mathrm{T}}y,\\ s.t. \mathit{A}\mathit{x}+By\le \mathit{b},\\ Cx+Dy=e,\\ x\in D\subseteq {\Re }^n,y\in \{\mathrm{0},\mathrm{1}\},\end{array}

wherein, the decision variables include continuous variables and 0 or 1 variables. The continuous variables include the output of source equipment, input of conversion equipment, input and output of energy storage, power grid purchase, electricity sales, volume of gas purchased, and volume of gas sold; variables 0 or 1 include flexible load shiftable, transferable, cuttable, and energy storage charging and discharging flags. The equality constraint is the coupling matrix constraint of the energy hub constraint and the energy storage relation of the energy storage device, wherein in the energy storage relation of the energy storage device, such as Eqs. (6), (12), and (14), nonlinear terms are introduced, and judgment statements are used to conduct nonlinear processing; inequality constraints are the operating constraints of various devices, such as the charging and discharging power of batteries, the exchange power of power grids, and the output power of gas turbines, etc.

Aiming at the above model, this paper uses the Cplex solver in Yalmip toolbox to solve the model in a MATLAB environment.

Analysis of calculation example

Situations of load and energy price

In this paper, the multi-energy system shown in Fig. 1 is adopted, and the specific efficiency and coefficients of various devices are presented in Table A1 in Appendix. The typical daily load data of a certain community in summer in Ref. [²⁵] are adopted, and the daily load curve is depicted in Fig. A1 in Appendix. The maximum output of new energy is illustrated in Fig. A2 in Appendix.

The energy price covers electricity price and natural gas price, in which the electricity price includes the purchase tariff and selling tariff that are peak valley prices; the natural gas price considers the purchase price only and the fixed gas price is used, as demonstrated in Fig. A3 in Appendix.

Analysis of optimal dispatch result

The supply and demand balance of electricity, heat, cooling and gas, optimization result of flexible load on user side, and changes of energy output with time can be obtained from simulated analysis of MATLAB optimal dispatch (the dispatching cycle is 1 day). According to the energy output, the draft fan and photovoltaic outputs of the whole day are utilized, and as a result, the renewable energy source output is improved, as intended. The output change of power grid and gas network is influenced by the electricity price and actual output of new energy; the actual output of new energy has a greater influence. Please, refer to Figs. A4 and A5 in Appendix for more details.

Analysis on supply and demand balance of multi-energy system

Figure 2 shows the supply and demand balance of electricity, heat, cooling and gas. According to Fig. 2(a), the power load is mainly satisfied with the draft fan and micro-gas turbine output at valley electricity price (1:00 – 8:00), while grid electricity purchase seldom exists. In addition, there is a great difference between electricity price and gas price, and the P2G equipment is in operation. Hence, profits can be gained when the P2G equipment operates at valley electricity price. At peak electricity and flat price (9:00 – 24:00), the power load is mainly satisfied with the power grid, micro-gas turbine and photovoltaic output, and the draft fan will provide a few outputs for supplementation. During this period, the accumulator is charging at flat price (9:00 – 11:00, 17:00 – 19:00, and 23:00 – 24:00), and is discharging at peak electricity price (12:00 – 16:00 and 20:00 – 22:00), which can relieve the load in peak demand for electricity and guarantee the economic efficiency of cooperative dispatch. In addition, at peak electricity and flat price (9:00 – 24:00), due to the increase of cooling and heating loads, the electric equipment also begins to work accordingly. At 24:00, when micro-gas turbine and draft fan outputs can totally satisfy the power load, electricity is sold to the power grid for interests.

According to Fig. 2(b), the heating load is mainly satisfied with micro-gas turbine output, and a large amount of heat is used for refrigeration of the lithium bromide refrigerator. At valley electricity price, the need for heating load is relatively low and often satisfied with the micro-gas turbine output. At peak electricity and flat price, the heating load increases, the micro-gas turbine operates at full load, and the gas-fired boiler, the electric boiler, and the air tank provide support. At flat price, the electric boiler will offer supplementary output; at peak electricity price, the gas-fired boiler and the air tank will offer supplementary output. Here, selection of coupling equipment is realized on the basis of energy price difference, and its economic efficiency is presented.

According to Fig. 2(c), in terms of the cooling load, the lithium bromide refrigerator mainly undertakes the base-load function, and the electric refrigerator often plays a supplementary role.

According to Fig. 2(d), natural gas is mainly supplied by the natural gas network, whereas the P2G and gas storage tank have a regulating effect.

Analysis of optimization of flexible load on user side

Figure 3 shows the variation of load before and after electricity, heat and cooling load optimization. According to Fig. 3(a) and Fig. 3(b), the power load can be shifted from 18:00 – 20:00 to 6:00 – 8:00, i.e., from the original evening peak to daytime. According to Fig. 2(a), the output of the draft fan is abundant at daytime. Hence, when the load is shifted here, not only the power supply pressure can be relieved at evening peak, but also the draft fan output directly utilized at daytime. The load can be cut in peak period of electricity to meet various requirements, thus the peak clipping function is expressed. Transferable loads are originally distributed at 11:00 – 14:00, and divided into several segments in the transferable interval. Various segments will be maintained for at least two time sections, and the power distribution is more flexible.

According to Figs. 3(c–f), the cooling and heating loads are similar to the power load. The heating load is shifted to the off-peak period at evening peak, and the cooling load is also shifted to the constraint period from the peak at noon. In summer, to satisfy users’ demand, there is not much cuttable load in cooling load. The cuttable load of cooling and heating loads can cooperate with each other, which will further reduce the power load.

Optimal dispatch analysis in different scenarios

Optimal dispatch analysis for the system is conducted in the following scenarios (the dispatching cycle is 1 day). In different scenarios, modules in the energy hub are chosen and removed. The dispatching costs in four scenarios are listed in Table 1.

In Scenario 1, the energy hub contains conversion equipment of different energies only, so as to check the optimal dispatch of the energy hub.

In Scenario 2, the supply module is added based on Scenario 1, so as to check the absorption ability of the energy hub for new energy and the optimal dispatch of the system.

In Scenario 3, the storage module is added based on Scenario 2, so as to check the absorption ability of the energy hub for new energy, the economic efficiency of energy management, and the optimal dispatch of the system.

In Scenario 4, Scenario 4 is the system established in this paper. The energy hub includes the supply, transformation, storage and load modules. Highly coupled, it can check the absorption ability of the energy hub for new energy, the economic efficiency of energy management, the optimal dispatch of the system, and the demand response of flexible load on user side.

According to Table 1, the dispatching cost of Scenario 4 is the lowest, about 2.34% lower than that of Scenario 3, about 6.79% lower than that of Scenario 2, and about 21.22% lower than that of Scenario 2. Hence, the economic benefit of highly coupled multi-energy system considering flexible load on user side is quite considerable.

A simple analysis is made on the outputs of the power grid and natural gas network under different scenarios. According to Fig. 3, owing to the adding of the supply model in Scenarios 2 and 3, the output of the power grid is much lower than that of Scenario 1 as P2G and new energy absorption are added at valley electricity price under the optimum cost principle of collaborative dispatch model. The difference between Scenarios 2 and 3 is mainly reflected in the storage module which can accumulate energy at flat price and release energy at peak electricity price. The input of storage module further reduces the electricity consumption at electricity consumption peak. The difference between Scenarios 4 and 3 is mainly reflected in the load module. Scenario 4 considers the characteristic of flexible load on user side. The participation of shiftable load and transferable load in interaction leads to the peak moving phenomenon in the load curve. The participation of cuttable load further reduces the peak time, and the cooperation of cooling, heating and power loads plays a role of peak-load shifting.

According to Fig. 4, the difference among Scenarios 2, 3, and 1 is mainly reflected in the operation of the P2G equipment and the gas storage tank in the supply module. There is no great difference between Scenarios 3 and 2, which is only reflected in the utilization of the accumulator and the thermal storage tank in the gas storage module. Changes occur to Scenarios 4 and 3, as cutting, transfer and shifting of flexible load on user side are considered, and the power grid output is significantly reduced in peak period. In other periods, load compensation is offered to users.

The calculation results and the outputs of power grid and natural gas network indicate that the multi-energy system of Scenario 4 not only effectively reduces the cost of cooperative dispatch, but also decreases the energy consumption in peak period and plays a role of peak-load shifting. Besides, it also makes a contribution to absorption of new energy and power-gas transformation of the P2G equipment. In this way, the environmental benefit and economic benefit of multi-energy system with P2G are reflected.

Conclusions

In the multi-energy system, an efficient and fast modeling method is needed to establish the energy hub. First, based on the concept and series characteristic of the energy hub, this paper, the energy hub model was divided into supply, transformation, storage and consumption modules, and a generic multi-energy system model was proposed which not only dealt with modeling in different scenarios, but also considered the flexible load on user side and makes the flexible load on user side participate in optimal dispatch. Besides, an important analysis was made on the optimal dispatch results of the multi-energy system with P2G considering flexible load on user side. The calculating example demonstrated that this system was characterized by economic efficiency, environmental protection, safety and stability. Verification was conducted for the absorption ability of the energy hub for new energy, economic efficiency of energy management, optimal dispatch of the system, and demand response of flexible load on user side in several scenarios.

This paper mainly focuses on modeling and analysis of a single energy hub. The multi-zone multi-energy system will be further studied in the future, taking into consideration the complementarity of loads in different regions, so as to further improve the energy use efficiency and realize overall optimization.

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