Research on Carbon-Reduction-Oriented Demand Response Technology Based on Generalized Nodal Carbon Emission Flow Theory

Abstract

The decarbonization of power systems plays a great part in the carbon neutrality goal. Currently, researchers have explored reducing carbon in power systems in terms of the optimization of energy supply structure and operation strategies, but ignored the carbon reduction potential of users. To investigate the carbon reduction capability of users and further promote power system decarbonization through the active response of electricity loads, this paper proposes a carbon-reduction-oriented demand response (CRODR) technology based on generalized nodal carbon emission flow theory. First, the framework of the CRODR mechanism is established to provide an interaction baseline for users facing carbon reduction guiding signals. Secondly, the generalized nodal carbon emission flow theory is introduced to provide a calculation method for the guiding signals, considering dynamic electricity carbon emission factors with various spatiotemporal resolutions. Then, a matrix-based method is proposed to efficiently solve the carbon emission flow and obtain the guiding signals. On this basis, an optimal load-regulating model to help users meet their carbon reduction goals is built, and a carbon reduction benefit-evaluation method is proposed. Case studies on China’s national power system and a textile company verify that CRODR technology can realize efficient carbon reduction through load shifting while maintaining the total power consumption of users. The proposed CRODR technology is expected to provide a theoretical basis and guiding mechanism for promoting carbon reduction throughout the entire power system.

1. Introduction

As approximately 70% of global carbon emissions come from the energy sector, and the power industry accounts for over 40% of the energy sector [1,2], the decarbonization of power systems plays a great part in the carbon neutrality goal [3]. Facing the urgent demand for the low-carbon transition of power systems, scholars have carried out abundant research on low-carbon transition pathways and low-carbon optimal scheduling. For example, Ref. [4] elaborated on several possible pathways for China’s power sector to achieve the goals of carbon peaking and carbon neutrality. Ref. [5] proposed a long-term power-generation expansion planning model, incorporating integration costs for renewable energy penetration, and studied the most cost-effective low-carbon transition pathway for the power sector with a high penetration of renewable energy based on this model. Ref. [6] developed an energy system optimization model with high spatiotemporal resolution and explored transition pathways for power systems in the Guangdong–Hong Kong–Macao region of China under various decarbonization scenarios. Refs. [7,8] studied low-carbon economic optimization scheduling, considering uncertainties and carbon capture, respectively. It can be seen that existing studies are mainly focused on reducing carbon in power systems on the source side, which is mainly achieved by the optimal planning and scheduling of power-generation units. These studies have provided important references for the low-carbon transition of power supply structures and for generation unit regulation strategies, but they ignored the coupling effects on generation behavior resulting from the load demand of users on the source side, failing to utilize carbon reduction approaches on the demand side.

To address this problem, Refs. [9,10,11] studied optimal system scheduling, considering the regulation of users in market environments such as the carbon quota market and green power trading. Still, the above literature is mainly focused on source–load collaborative scheduling to achieve carbon reduction and does not specifically design a carbon reduction mechanism for the load side. Moreover, regarding the low-carbon transition of international power systems, Refs. [12,13] studied low-carbon and optimal economic operation under the conditions of high proportions of new energy grid connection and large-scale energy storage access, ignoring the carbon emission changes in users’ electricity consumption at different periods due to the high proportion of new energy access. Considering that power systems balance power generation and consumption in real time, the power consumption behavior of users will have a great effect on power-generation schedules, which in turn affects the carbon emission of power systems. Therefore, the impact of the load side on carbon emission reduction is of vital importance in studying low-carbon power technologies.

Some scholars have noticed effects of the load side on carbon emissions in power systems, and have considered the influence of electric customers in low-carbon planning and scheduling. Ref. [14] proposed a low-carbon planning method for distribution networks with economic and environmental objectives, taking into account the impact of carbon trading and demand response. However, carbon reduction was still mainly considered from the perspective of distribution network planning, and electricity consumption behavior was guided based on electricity prices. Refs. [15,16] considered the coordinated interaction between demand response and generation units, such as CCUS units and renewable energy power plants, to carry out the optimal scheduling of power systems in line with low-carbon and economical goals. However, they mainly focused on the consumption of renewable energy from the perspective of source–load interaction, and no guidance was provided to help users carry out load regulation specifically aimed at carbon reduction. Ref. [17] established a behavioral model of demand response and energy storage and proposed a low-carbon scheduling strategy for power systems based on this model and the clean development mechanism in China. In this study, the carbon reduction behavior of electricity users was achieved by reducing carbon costs through trading activities in the carbon market. However, there is currently no mature electric–carbon coupling market in China, and this technology is difficult to achieve practically.

The above studies researched the capabilities of demand-side resources, such as flexible load, to reduce carbon emissions in power systems, but they still focus on price incentives under the electricity demand response mechanism to guide the power consumption behavior of users. Thus, they all neglected a key incentive signal to guide users to reduce their carbon emissions actively: the carbon emission factor (CEF) of electricity consumption. The CEF of electricity consumption is a key signal that transmits the responsibility for carbon emissions from the generation side to the consumption side. Currently, users mainly obtain the carbon emission information corresponding to their electricity consumption behavior through the CEF. However, the most commonly used CEF in many areas, including China, is the average CES. The update time frequency of this measure is years, and its spatial resolution is calculated in terms of provinces or regions. Thus, the current CEF has the disadvantages of time lag and low spatiotemporal resolution [18], failing to allow users to perceive differences in carbon emissions due to power consumption during different periods or in different areas. Under this situation, users lack the basis and motivation to actively respond to carbon reduction goals.

To solve this problem, scholars have conducted extensive research on the indirect carbon emission characteristics of power systems utilizing the sensitivity analysis method, the cooperative game method, and the carbon emission flow method, respectively. The sensitivity analysis method is used to analyze changes in system carbon emissions caused by load changes in certain nodes. However, it is difficult to analyze the total amount of indirect carbon emissions resulting from the electricity consumption of users or clarify the transfer process of carbon emission responsibility [19]. The cooperative game method solves carbon emission responsibility allocation problem through cooperative game theory, transforming it into a cost-sharing problem [20]. But due to the high computational complexity of this method, it is not suitable for indirect carbon emission calculation in power systems with a large number of users. The carbon emission flow method is used to study the transfer of carbon emission responsibility from the source side to users through power grids. The carbon emission flow of the power system is defined as a virtual network flow that is attached to the power flow. Divided by different flow information, current carbon emission flow methods mainly include the carbon emission flow analysis method based on the principle of proportional sharing [21,22,23], the complex power method [24], and the grid power distribution method [25]. Among them, the carbon emission flow analysis method based on the principle of proportional sharing has attracted widespread attention from the industrial and academic communities due to its advantages such as simplicity, intuitiveness, and lower computational complexity. Still, this method relies on detailed node power-flow information, resulting in the poor privacy of power grid topology and power-flow information. Moreover, redundant calculation steps are required to determine the fairness of the carbon emission allocation results. Further enhancement is still needed to support the efficient calculation of a dynamic CEF, which will further support the implementation of carbon-reduction-oriented demand response technology.

To address the above issues, this paper proposes a carbon-reduction-oriented demand response technology. The main contributions are as follows:

(1) The carbon-reduction-oriented demand response technology was established to provide a framework between carbon reduction guidance and the power consumption behavior of users. This mechanism can be regarded as a derivative of the electricity demand response mechanism, but with a carbon reduction goal.

(2) A generalized nodal carbon emission flow theory and an efficient solution for regional power systems are introduced. This theory can realize dynamic power consumption carbon emission factor calculations at various spatiotemporal resolutions, which provides key guiding signals for users to regulate consumption behaviors towards carbon reduction goals.

(3) An optimal decision-making and carbon reduction benefit-evaluation method is proposed to support the active demand response of users. Case studies based on the national power system of China and an actual textile company are carried out to verify the effectiveness and the carbon reduction potential of the proposed theory.

The rest of this paper is organized as follows: Section 2 proposes the carbon-reduction-oriented demand response mechanism. Section 3 introduces the generalized nodal carbon emission flow theory and Section 4 provides the solution algorithm for generalized nodal carbon emission flow in regional power systems. Section 5 establishes the optimization model of carbon-reduction-oriented demand response behavior and the benefit-evaluation method of the proposed technology. Section 6 examines case studies. Section 7 concludes this paper.

2. The Carbon-Reduction-Oriented Demand Response Mechanism

Traditional demand response mechanisms incentivize users to change their electricity consumption behaviors by issuing electricity price signals, promoting the safe and economic operation of power systems [26]. In contrast, the carbon-reduction-oriented demand response (CRODR) mechanism guides users to shift their electricity consumption to low-carbon-emission periods by releasing dynamic carbon emission factors with high spatiotemporal resolution, thus reducing the overall carbon emissions of power systems and improving the consumption rate of renewable power generation.

In the CRODR mechanism, the carbon emission responsibility of users is mainly determined by the CEF, which is mainly used to reflect the carbon emissions of source-side units caused by users’ energy consumption. It is a bridge between direct carbon emissions from the generation side and indirect carbon emissions buried on the consumption side.

The CEF of electricity consumption used in the CRODR mechanism needs to possess the following characteristics:

(1) The CEF needs to be capable of reflecting the temporal variability of carbon emissions caused by the electricity consumption of users. To this end, the CEF of the CRODR mechanism should be time-varying during the day.

(2) In each period for a given area, the sum of indirect carbon emissions obtained from the CEFs of electricity consumption and network losses should be equal to the direct carbon emissions resulting from power generation.

A schematic diagram of the CRODR mechanism is shown in Figure 1. The realization of carbon reduction through the CRODR mechanism is carried out as per the following steps.

Step 1: Obtaining dynamic CEFs. Dynamic CEFs of users are calculated based on the power supply schemes of users in different periods. Carbon emission information including CEF curves and statistical carbon emissions from electricity consumption will be delivered to users.

Step 2: Obtaining the baseline load curve. The baseline load curve refers to the original load curve of the users before carrying out the CRODR regulation. According to the baseline load curve and the measured CEFs of electricity consumption, the original indirect carbon emission of users before carrying out the CRODR regulation can be calculated.

Step 3: Optimizing the electricity consumption behaviors of users. After sensing the time-varying characteristics of the CEFs of electricity consumption, users should formulate optimized load regulation or shift schedules according to their carbon emission reduction needs and historical carbon emissions to meet constraints or goals such as carbon quotas and carbon costs. By carrying out the CRODR regulation, users may reduce their carbon emissions without changing their total electricity consumption in one day.

Step 4: Based on the dynamic carbon emission factors of the day and the energy consumption before and after the user’s low-carbon demand response, the actual and original carbon emission responsibility of users’ electricity consumption can be obtained. Then, the carbon emission reduction benefit of the CRODR mechanism can be quantified.

To ensure the fairness and rationality of the CRODR mechanism, it is required to satisfy the following basic principles:

(1) Users need to be able to accurately perceive dynamic CEFs during different periods, including CEFs in the future, in real-time, and in historical periods. This is the basic requirement to enable users to evaluate their carbon emission responsibilities during different periods and make targeted load adjustment plans in advance.

(2) The CEFs of electricity consumption for different users in a certain region should be consistent under a given period to ensure reasonable fairness.

(3) The participation motivation and adjustment potential of users should mainly be incented by the spontaneous willingness of users and the transaction prices or caron information in the carbon market. Participating in the CRODR approach creates carbon emission benefits, which will be further transformed into economic profits in the carbon quota market through carbon transactions in certified emission reduction mechanisms.

(4) Information pertaining to the indirect carbon emissions of electricity consumption and carbon emission reductions generated by the CRODR mechanism needs to be measured, recorded, and certified to support the construction of a standardized incentive mechanism.

The above procedure and framework of the CRODR mechanism can be used by grid companies or other operators to guide regional electricity users to carry out the CRODR approach, including guiding signal calculation, guiding signal release, recommended load-shifting schedule release, and carbon reduction benefit evaluations.

3. The Generalized Nodal Carbon Emission Flow Theory

3.1. Analysis of the Transferring Process for the Generalized Node

Figure 2 shows a diagram of the generalized nodal carbon emission transfer process, adopting the modified IEEE 33-node system topology as an example. As shown in Figure 2, the carbon emission flow variables in any generalized node consist of the carbon emissions of external injected power, the carbon emissions of internal power generation, the carbon emissions of output power, and the carbon emissions of power consumed by the local load. Specifically, the carbon emissions of internal power generation come from the direct carbon emissions generated by power units, while the carbon emissions of external power, output power, and local power consumption are all indirect carbon emissions.

According to the carbon emission flow theory, the CEF of electricity consumption for a node is only related to the carbon emissions injected. Therefore, when calculating the CEF of electricity consumption for a generalized node, the carbon emission information of internal power generation and external injected power will be sufficient. The CEF of output power and power consumption remain the same.

$${\rho }_b=F_{\mathrm{area}}={\displaystyle \frac{{\displaystyle \sum _{a\in N^{+}}{P}_a}{\rho }_a}{{\displaystyle \sum _{a\in N^{+}}{P}_a}}},\forall b\in N^{-}.$$

(1)

In Equation (1), P_a is the active power of external injected power flow and the power generation of a given region; ρ_a is the carbon flow density of the power injected into branch a; a ∈ N⁺ and N⁺ are a set of power-injecting branches; P_b is the active power outflow from the given region and the power consumption of loads; ρ_b is the carbon flow density of power outflowing from branch b; b ∈ N⁻ and N⁻ are a set of power output branches; and F_area is the average CEF of the given region. According to carbon emission flow theory [21,22], ρ_b is equal to F_area.

It can be seen that the carbon flow density of power output branches is equal to the regional CEF, which is the proportional mixture of carbon emissions contained in the input power.

When calculating the CES of electricity consumption, the proposed method only requires total internal power generation and corresponding carbon emissions, total external power injection and corresponding carbon emissions, and total power consumption. The spatiotemporal resolution of the CEF can vary according to the actual data; thus, potential information security issues related to confidential grid topology and power-flow data are avoided. It can be seen that the generalized nodal carbon emission flow theory has the same calculating principle as the average carbon emission factor method that is currently adopted by most areas of China [21], except it has higher and more flexible spatiotemporal resolution in terms of carbon emission factors. This characteristic means that the generalized nodal carbon emission theory aligns well with current methods while realizing technical improvements.

3.2. Interregional Power Transmission Corridor Simplification

Figure 3 shows the process of interregional power transmission corridor simplification when calculating carbon emissions and CEFs.

According to the carbon emission flow theory, the CEFs of different powers flowing out of the same generalized node are equal. Therefore, in the process of carbon emission flow calculation, multiple power transmission corridors between two generalized nodes can be simplified to one output corridor and one input channel. The flow direction of active power in the simplified power corridor is the same as that in the original corridors, and the value of active power is equal to the sum of the values in all original corridors. After obtaining the CEF of the generalized nodes, the carbon emission transmitted by each corridor before simplification can be obtained according to the principle of proportional distribution. Through this simplification method, the branch data can be further reduced and the CEF solution process can be accelerated.

3.3. Key Indicators for the Generalized Nodal Carbon Emission Flow Theory

To express the process for calculating the carbon emissions produced from electricity consumption in regional power grids, this paper constructed the following indicators for the generalized nodal carbon emission flow theory [22,23].

(a) The direct carbon emissions of generalized nodes ($E_{\mathrm{in},\mathrm{Gen},i}^{\mathrm{GN}}$). The direct carbon emissions of generalized nodes only include direct carbon emissions generated by internal power-generation units:

$$E_{\mathrm{in},\mathrm{Gen}}^{\mathrm{GN}}=(E_{\mathrm{in},\mathrm{Gen},1}^{\mathrm{GN}},E_{\mathrm{in},\mathrm{Gen},2}^{\mathrm{GN}},\dots ,E_{\mathrm{in},\mathrm{Gen},i}^{\mathrm{GN}}\dots ,E_{\mathrm{in},\mathrm{Gen},I}^{\mathrm{GN}}{)}^{\mathrm{T}}.$$

(2)

where $E_{\mathrm{in},\mathrm{Gen},i}^{\mathrm{GN}}$ (i = 1, 2,..., I,) is the total carbon emissions generated by all power-generation units in generalized node I, and I is the number of generalized nodes. The subscript “in,Gen” represents the power-generation units corresponding to generalized node i. The subscript “i” represents the serial number of each generalized node. The superscript “GN” represents generalized nodes.

(b) The indirect carbon emissions of loads in generalized nodes ($E_{\mathrm{L}}^{\mathrm{GN}}$). This indicator reflects the indirect electricity consumption for each generalized node:

$$E_{\mathrm{L}}^{\mathrm{GN}}=(E_{\mathrm{L},1}^{\mathrm{GN}},E_{\mathrm{L},2}^{\mathrm{GN}},\dots ,E_{\mathrm{L},i}^{\mathrm{GN}}\dots ,E_{\mathrm{L},I}^{\mathrm{GN}}{)}^{\mathrm{T}}.$$

(3)

where the subscript “L” represents loads.

(c) The indirect carbon emissions of external power for generalized nodes ($E_{\mathrm{Cor},\mathrm{in}}^{\mathrm{GN}}$). This indicator represents the carbon content of the power injected into each generalized node from other generalized nodes:

$$E_{\mathrm{Cor},\mathrm{in}}^{\mathrm{GN}}={\left(E_{\mathrm{Cor},\mathrm{in},ij}^{\mathrm{GN}}\right)}_{I\times I}.$$

(4)

where $E_{\mathrm{Cor},\mathrm{in},ij}^{\mathrm{GN}}$ (i, j = 1, 2, ..., I) is the indirect carbon emission injected into generalized node j from generalized node i through branch ij. $E_{\mathrm{Cor},\mathrm{in}}^{\mathrm{GN}}$ takes the value of 0 when i = j. The subscript “ij” represents that the direction of active power is from the generalized node i to the generalized node ij. The subscript “Cor,in” represents the tor in which the power flows into the generalized node. The same is true below.

(d) The indirect carbon emissions of output power for generalized nodes ($E_{\mathrm{Cor},\mathrm{out}}^{\mathrm{GN}}$). The indirect carbon emissions of output power for generalized nodes represent the carbon content of the power sent out by each generalized node. The vector is as follows:

$$E_{\mathrm{Cor},\mathrm{out}}^{\mathrm{GN}}={\left(E_{\mathrm{Cor},\mathrm{out},ij}^{\mathrm{GN}}\right)}_{I\times I}.$$

(5)

where $E_{\mathrm{Cor},\mathrm{out},ij}^{\mathrm{GN}}$ (i, j = 1, 2, ..., I) is the indirect carbon emissions flowing out from generalized node i and flowing into generalized node j, and each element of the matrix $E_{\mathrm{Cor},\mathrm{out}}^{\mathrm{GN}}$ takes the value of 0 when i = j. In terms of the symbols, the subscript “ij” represents that the direction of active power is from the generalized node i to the generalized node j, and the subscript “Cor,out” represents the corridors injecting power into the corresponding generalized node.

(e) The indirect carbon emissions of network losses ($E_{\mathrm{Cor},\mathrm{Loss}}^{\mathrm{GN}}$). This represents the carbon emission responsibility corresponding to active power losses occurring on transmission lines:

$$E_{\mathrm{Cor},\mathrm{Loss}}^{\mathrm{GN}}={\left(E_{\mathrm{Cor},\mathrm{Loss},ij}^{\mathrm{GN}}\right)}_{I\times I}.$$

(6)

where $E_{\mathrm{Cor},\mathrm{Loss},ij}^{\mathrm{GN}}$ is the carbon emission responsibility corresponding to the active power loss on line ij. The subscript “Cor,Loss” represents the network loss of power lines.

(f) The CEF of electricity consumption for generalized nodes ($F^{\mathrm{GN}}$). This indicator directly reflects the carbon emission responsibility of unit electricity consumption for each generalized node:

$$F^{\mathrm{GN}}=(F_1^{\mathrm{GN}},F_2^{\mathrm{GN}},\dots ,F_i^{\mathrm{GN}}\dots ,F_I^{\mathrm{GN}}{)}^{\mathrm{T}}.$$

(7)

(g) The carbon flow rate between generalized nodes. This indicator is the carbon flow rate at the outlet of generalized nodes that send out power, indicating the transmission rate of carbon emissions out of generalized nodes. It includes the carbon flow rate of transmission lines and the carbon flow rate of network losses. The matrixes of the carbon flow rate of power lines ($R_{\mathrm{Cor},\mathrm{out}}^{\mathrm{GN}}$) and network losses ($R_{\mathrm{Cor},\mathrm{Loss}}^{\mathrm{GN}}$) are as follows:

$$R_{\mathrm{Cor},\mathrm{out}}^{\mathrm{GN}}={\left(R_{\mathrm{Cor},\mathrm{out},ij}^{\mathrm{GN}}\right)}_{I\times I},$$

(8)

$$R_{\mathrm{Cor},\mathrm{Loss}}^{\mathrm{GN}}={\left(R_{\mathrm{Cor},\mathrm{Loss},ij}^{\mathrm{GN}}\right)}_{I\times I}.$$

(9)

where $R_{\mathrm{Cor},\mathrm{out},ij}^{\mathrm{GN}}$ and $R_{\mathrm{Cor},\mathrm{Loss},ij}^{\mathrm{GN}}$ are the carbon flow rate of line ij and network losses occurring on line ij, respectively.

(h) The carbon flow density between generalized nodes (${\rho }_{\mathrm{B}}$). This represents the indirect carbon emissions of unit-transmitted electricity between generalized nodes:

$${\rho }_{\mathrm{B}}={({\rho }_{\mathrm{B},ij})}_{I\times I}.$$

(10)

where ρ_B,ij is the carbon flow density of line ij, in which the active power flows from generalized node i to j.

4. Method for Solving Generalized Nodal Carbon Emission Flow in Regional Power Systems

In the practical application of calculating the carbon emissions of regional power grids, generalized nodes will usually be replaced by areas in the above indicators, and the superscript “GN” will be replaced by “area” in the above variables to provide a clearer description of the relevant theory and calculation examples.

4.1. Relationship Analysis of Carbon Emission Indicators for Generalized Nodes

In this section, we take region i as the study object and illustrate the relationship between the main carbon emission indicators connected to region i.

The relationship between the carbon emission indicators of generalized nodes is shown in Figure 4. In Figure 4, $E_{\mathrm{Cor},\mathrm{in},ji}^{\mathrm{area}}$ (j ∈ S_i and S_i are a set of regions connected to region i) is the carbon emissions flowing out of region j being injected into region i, and $W_{\mathrm{Cor},\mathrm{in},ji}^{\mathrm{area}}$ is the corresponding electricity; $E_{\mathrm{in},\mathrm{Gen},i}^{\mathrm{area}}$ is the direct carbon emissions generated by generation units in region i and $W_{\mathrm{G},k,i}^{\mathrm{area}}$ (k ∈ Ω_i and Ω_i are a set of generation units in region i) is the corresponding electricity; $E_{\mathrm{L},i}^{\mathrm{area}}$ is the carbon emissions from the electricity consumption in region i, and $W_{\mathrm{L},i}^{\mathrm{area}}$ is the corresponding electricity; $E_{\mathrm{Cor},\mathrm{out},ij}^{\mathrm{area}}$ is the carbon emissions flowing out of region i, including $E_{\mathrm{Cor},\mathrm{in},ij}^{\mathrm{area}}$ (the carbon emissions flowing into region j) and $E_{\mathrm{Cor},\mathrm{Loss},ij}^{\mathrm{area}}$ (the carbon emissions of network loss on line ij); $R_{\mathrm{Cor},\mathrm{out},ij}^{\mathrm{area}}$ is the carbon flow rate at the outlet of region i, and $R_{\mathrm{Cor},\mathrm{Loss},ij}^{\mathrm{area}}$ is the carbon flow rate of network loss on line ij.

4.2. The Matrix Solution for Carbon Emissions Flow in Regional Power Grids

(a) Calculate regional direct carbon emission.

$$E_{\mathrm{in},\mathrm{Gen},i}^{\mathrm{area}}={\displaystyle \sum _{k\in {\Omega }_i}{F}_{\mathrm{G},k,i}^{\mathrm{area}}}{W}_{\mathrm{G},k,i}^{\mathrm{area}}.$$

(11)

where $F_{\mathrm{G},k,i}^{\mathrm{area}}$ is the fuel consumption emission factor of the kth generator in region i.

(b) Calculate the regional input power matrix. The regional input power includes the power generated by the generation units within the region and the power injected from other regions.

$$W_{\mathrm{in}}^{\mathrm{area}}=\mathrm{diag}\left(W_{\mathrm{in},1}^{\mathrm{area}},W_{\mathrm{in},2}^{\mathrm{area}},\dots ,W_{\mathrm{in},i}^{\mathrm{area}},\dots ,W_{\mathrm{in},I}^{\mathrm{area}}\right),$$

(12)

$$W_{\mathrm{in},i}^{\mathrm{area}}={\displaystyle \sum _{k\in {\Omega }_i}{W}_{\mathrm{G},k,i}^{\mathrm{area}}}+{\displaystyle \sum _{j\in S_i}{W}_{\mathrm{Cor},\mathrm{in},ji}^{\mathrm{area}}}.$$

(13)

(c) Calculate the regional carbon emission factor matrix.

$$F_i^{\mathrm{area}}=E_{\mathrm{in},i}^{\mathrm{area}}/W_{\mathrm{in},i}^{\mathrm{area}},$$

(14)

$$E_{\mathrm{in},i}^{\mathrm{area}}=E_{\mathrm{in},\mathrm{Gen},i}^{\mathrm{area}}+{\displaystyle \sum _{j\in S_i}{E}_{\mathrm{Cor},\mathrm{in},ji}^{\mathrm{area}}}.$$

(15)

where $E_{\mathrm{in},i}^{\mathrm{area}}$ is the carbon emissions flowing into region i, including the direct carbon emission of generation units within the region and the indirect carbon emissions injected into region i. Equation (15) can be expressed in matrix form as follows:

$$W_{\mathrm{in}}^{\mathrm{area}}{F}^{\mathrm{area}}={(W_{\mathrm{Cor},\mathrm{in}}^{\mathrm{area}})}^{\mathrm{T}}{F}^{\mathrm{area}}+E_{\mathrm{in},\mathrm{Gen}}^{\mathrm{area}},$$

(16)

$$W_{\mathrm{Cor},\mathrm{in}}^{\mathrm{area}}={\left(W_{\mathrm{Cor},\mathrm{in},ji}^{\mathrm{area}}\right)}_{I\times I},E_{\mathrm{in},\mathrm{Gen}}^{\mathrm{area}}={\left(E_{\mathrm{in},\mathrm{Gen},i}^{\mathrm{area}}\right)}_{I\times I}.$$

(17)

$$F^{\mathrm{area}}={\left(W_{\mathrm{in}}^{\mathrm{area}}-{(W_{\mathrm{Cor},\mathrm{in}}^{\mathrm{area}})}^{\mathrm{T}}\right)}^{-1}{E}_{\mathrm{in},\mathrm{Gen}}^{\mathrm{area}}.$$

(18)

where $W_{\mathrm{Cor},\mathrm{in}}^{\mathrm{area}}$ is the regional input electricity matrix; $E_{\mathrm{in},\mathrm{Gen}}^{\mathrm{area}}$ is the regional direct carbon emissions matrix.

(d) Calculate the indirect carbon emission of electricity consumption for regional loads.

$$E_{\mathrm{L}}^{\mathrm{area}}=W_{\mathrm{L}}^{\mathrm{area}}{F}^{\mathrm{area}},$$

(19)

$$W_{\mathrm{L}}^{\mathrm{area}}=\mathrm{diag}\left(W_{\mathrm{L},1}^{\mathrm{area}},W_{\mathrm{L},2}^{\mathrm{area}},\dots ,W_{\mathrm{L},i}^{\mathrm{area}}\dots ,W_{\mathrm{L},I}^{\mathrm{area}}\right).$$

(20)

where $W_{\mathrm{L}}^{\mathrm{area}}$ is the matrix of regional load electricity consumption

(e) Calculate the carbon emissions associated with power lines.

$${\rho }_{\mathrm{B}}=\mathrm{diag}(F_1^{\mathrm{area}},F_2^{\mathrm{area}},\dots ,F_i^{\mathrm{area}}\dots ,F_I^{\mathrm{area}})H.$$

(21)

where H is the relationship matrix of forward power flow in transmission corridors. The carbon flow rate matrixes of the corridors and network losses are calculated as follows:

$$R_{\mathrm{Cor},\mathrm{out}}^{\mathrm{area}}={\rho }_{\mathrm{B}}{W}_{\mathrm{Cor},\mathrm{out}}^{\mathrm{area}},$$

(22)

$$R_{\mathrm{Cor},\mathrm{Loss}}^{\mathrm{area}}={\rho }_{\mathrm{B}}{W}_{\mathrm{Loss},\mathrm{out}}^{\mathrm{area}},$$

(23)

$$W_{\mathrm{Cor},\mathrm{out}}^{\mathrm{area}}={\left(W_{\mathrm{Cor},\mathrm{out},ij}^{\mathrm{area}}\right)}_{I\times I},W_{\mathrm{Loss},\mathrm{out}}^{\mathrm{area}}={\left(W_{\mathrm{Loss},\mathrm{out},ij}^{\mathrm{area}}\right)}_{I\times I}.$$

(24)

where $W_{\mathrm{Cor},\mathrm{out}}^{\mathrm{area}}$ and $W_{\mathrm{Loss},\mathrm{out}}^{\mathrm{area}}$ are the output power-flow electricity matrix and network losses matrix of the corresponding corridor, respectively. The indirect carbon emissions matrixes for corridors and network losses are calculated as follows:

$$E_{\mathrm{Cor},\mathrm{out}}^{\mathrm{area}}=∆t{R}_{\mathrm{Cor},\mathrm{out}}^{\mathrm{area}}.$$

(25)

$$E_{\mathrm{Cor},\mathrm{Loss}}^{\mathrm{area}}=∆t{R}_{\mathrm{Cor},\mathrm{Loss}}^{\mathrm{area}}.$$

(26)

where Δt is the time of electricity delivery.

5. Optimal Load-Shifting Model and Benefit Evaluation of Carbon-Reduction-Oriented Demand Response Mechanism

The CRODR mechanism has impacts on both power users and generators. It can guide users to actively reduce carbon emissions through load shifting, thereby reducing their carbon emission responsibilities. In terms of the power system, users transfer more electricity load to periods with a higher proportion of clean energy, which can promote the consumption of renewable energy generation.

The carbon emission reduction benefit-evaluation procedure for the CRDR mechanism is as follows.

Step 1: Obtain the hourly operation data of the power system throughout the whole year, including power flow and unit output based on the panoramic time-sequence operation simulation technology of the power system [27].

Step 2: Obtain the dynamic CEFs of electricity consumption for users based on the generalized nodal carbon emission flow theory and the data obtained in step 1.

Step 3: Obtain the optimal load-shifting schemes of users. When users receive the forecast carbon emission factor curve released by the power grid a day ahead, they can adjust their electricity loads to minimize carbon emissions resulting from electricity consumption according to their flexible regulation capability. The daily optimal load-shifting optimization model is as follows:

(a)

Objective function

$$\max ∆E_{{\mathrm{CO}}_2,\mathrm{day}}={\displaystyle \sum _{t\in T_{\mathrm{D}}}(∆P_{\mathrm{L},t}^{-}-∆P_{\mathrm{L},t}^{+})∆t\cdot F_t}$$

(27)

where $∆E_{{\mathrm{CO}}_2,d}$ is the daily carbon emission reduction of users; T_D is the period number in one day; $∆t$ is the time resolution (1 h); and $∆P_{\mathrm{L},t}^{+}$ and $∆P_{\mathrm{L},t}^{-}$ are the increased load and decreased load of users in period t, respectively.

(b)

Constraints

Constraints (28)~(30) reflect the regulation capability of users: Equation (28) is the constraint of the maximum and minimum regulation capacity of users; Equation (29) is the constraint of load increase, which represents that the load of users cannot exceed the maximum-rated load; Equation (30) is the constraint of load decrease, which represents that the load of users cannot be lower than the baseline load.

$$\left\{\begin{array}{l}0\le ∆P_{\mathrm{L},t}^{+}\le u_{\mathrm{L},t}^{+}\cdot ∆{\overline{P}}_{\mathrm{L}}\\ 0\le ∆P_{\mathrm{L},t}^{-}\le u_{\mathrm{L},t}^{-}\cdot ∆{\overline{P}}_{\mathrm{L}}\end{array}\right.$$

(28)

$$P_{\mathrm{L},t}+∆P_{\mathrm{L},t}^{+}\le {\overline{P}}_L$$

(29)

$$∆P_{\mathrm{L},t}^{-}\le P_{\mathrm{L},t}$$

(30)

where $∆{\overline{P}}_L$ is the upper limit of loads that can be adjusted by users in each period. $u_{\mathrm{L},t}^{+}$ and $u_{\mathrm{L},t}^{-}$ are the variables of 0 and 1, indicating whether the user is in the state of load increasing or decreasing; $∆{\overline{Q}}_{\mathrm{L}}$ is the maximum load shifting for users in one day; and $P_{\mathrm{L},t}$ is the baseline load of period t.

Equation (31) is the daily load variation constraint, which indicates that the total load consumption of users remains nearly unchanged after participating in the CRODR approach.

$$\left|{\displaystyle \sum _{t\in T_{\mathrm{D}}}(∆P_{\mathrm{L},t}^{+}-∆P_{\mathrm{L},t}^{-})}\right|\le ∆{\overline{Q}}_{\mathrm{L}}$$

(31)

where $∆{\overline{Q}}_{\mathrm{L}}$ is the maximum variation in the electricity consumption of users in one day.

Equation (32) is the constraint of load-shifting state, which ensures that a user cannot be in a state of load increase and load decrease at the same time:

$$u_{\mathrm{L},t}^{+}+u_{\mathrm{L},t}^{-}\le 1$$

(32)

Step 4: Calculate the carbon emission reduction benefit. Based on the behavioral variation in user power consumption throughout the year, the annual carbon emission reduction of users under the CRODR mechanism and the carbon reduction benefit in the carbon market can be obtained via Equations (33) and (34).

$$∆E_{{\mathrm{CO}}_2,Y}={\displaystyle \sum _{t\in T_Y}(∆P_{\mathrm{L},t}^{+}-∆P_{\mathrm{L},t}^{-})∆t\cdot F_t}$$

(33)

$$R_{{\mathrm{CO}}_2,Y}=∆E_{{\mathrm{CO}}_2,Y}\cdot p_{{\mathrm{CO}}_2}$$

(34)

where $∆E_{{\mathrm{CO}}_2,Y}$ denotes the annual carbon reduction; $T_{\mathrm{Y}}$ denotes the total number of periods in a year.

6. Case Studies of China’s Power System Planning Scenarios

This section carries out carbon flow calculations and benefit evaluations of CRODR technology in relation to China’s future power systems to verify the carbon reduction potential of CRODR technology. The case studies are based on the systems’ optimal planning schemes and simulated operation schedules of China’s national power system for 2025–2040 to verify the effectiveness of the proposed methods. The planning schemes and operation schedules are obtained from Ref. [28].

6.1. Carbon Emission Flow Calculation Results

Based on the power-generation and power-flow data of 31 provinces in mainland China, the carbon emission flow data of the national power system from 2025 to 2040 on a scale of 8760 h throughout the whole year is solved. The provincial generalized nodes are listed below in

Table 1. Provincial generalized nodes.

No.	Province	No.	Province
1	Beijing	17	Hubei
2	Tianjin	18	Hunan
3	Hebei	19	Guangdong
4	Shanxi	20	Guangxi
5	Inner Mongolia	21	Hainan
6	Liaoning	22	Chongqing
7	Jilin	23	Sichuan
8	Heilongjiang	24	Guizhou
9	Shanghai	25	Yunnan
10	Jiangsu	26	Xizang
11	Zhejiang	27	Shaanxi
12	Anhui	28	Gansu
13	Fujian	29	Qinghai
14	Jiangxi	30	Ningxia
15	Shandong	31	Xinjiang
16	Henan

.

The monthly average carbon emission factors of each province in each scenario are shown in Figure 5. Figure 5 shows that the overall carbon content of electricity consumption decreases with the optimization of the energy supply structure. In Figure 5, when the color of a block is green, it indicates the CEF of corresponding node during this period is low, while red refers to higher CEF. The results in Figure 5 verify that the carbon emission flow theory proposed in this paper can realize the calculation of different nodes in the systems. As mentioned in Section 3, the spatial resolution of generalized nodes can vary between power system buses and power supply regions of different levels. Thus, this provides a solution to support the precise analysis of spatial differences when calculating the carbon emission characteristics of power systems.

Beijing’s dynamic carbon emission factor curves for 12 typical days in 2025 are presented in Figure 6 to show the capability of carbon flow theory to calculate the carbon emission characteristics of power consumption at a high time resolution. From Figure 6, it can be seen that the carbon content of power consumption varies over time.

Taking Beijing in 2025 as an example, the peak–valley difference in carbon emission factors is within the range of 0.128~0.269. The fluctuation in carbon emission factors accounts for 21.22~45.38%. Based on dynamic carbon emission factor curves, users can shift loads from high-carbon-emission periods to lower ones, thus reducing carbon emissions resulting from power consumption. With a maximum carbon emission factor peak–valley difference of 45.38%, one user can reduce nearly half of their daily carbon emissions in the most extreme case.

It can be concluded from Figure 5, Figure 6 and Figure 7 that the carbon emission flow theory can achieve high spatiotemporal resolution in the calculation of carbon emission parameters, thus enabling users to intuitively perceive differences in carbon emission responsibilities in terms of their electricity consumption across different regions and at different periods of the day. Then, users can perform spatiotemporal load transfer and reduce their carbon emissions. Considering that carbon emission factors are generally lower during periods with a higher proportion of clean energy generation, orienting load transfer behavior towards dynamic emission factors will also contribute to the consumption of renewable energy.

6.2. Carbon Emission Reduction Analysis

The carbon reduction benefit generated by CRODR from 2025 to 2040 is shown in Figure 7 for every province, assuming that 5% of the load in each province can participate in CRODR. The data labels refer to the carbon reduction data. As can be seen in Figure 7, from 2025 to 2040, the regions that profited most from the CRODR approach gradually shifted from the north to the southeast.

In addition, the increment of renewable power consumption is shown in Figure 8. Considering that the most prominent problem with renewable power consumption lies in the effective consumption of wind power and PV energy, we mainly study how the CRODR mechanism improves PV and wind power consumption in this study.

The regulation of users’ power consumption behavior will not only reduce the carbon emissions of power systems, but also improve the utilization level of clean energy. The simulation results in Figure 8 show that, through the low-carbon demand response technology, the amount of non-water new energy consumption in 2025, 2030, 2035, and 2040 will be increased by about 183.14 t kWh, 306.26 t kWh, 575.92 t kWh, and 612.59 t kWh, respectively.

Figure 9 shows the annual carbon emission reduction potential of the whole national power system under different maximum load response ratios. It is obvious that with the increase in the maximum ratio, the annual carbon emission reduction increases too. With more load participating in CRODR, the carbon emission reductions caused by load shifting will grow.

As the carbon emission reductions for 2025~2040 increase, according to

Table 2. Carbon reduction benefit of CRODR from 2025 to 2040. (a) Carbon emission reductions and annual total carbon emissions (unit: 10⁴ tCO₂); (b) carbon emission reduction ratio.

Maximum Load Response Ratio	2025	2030	2035	2040
(a)
1%	405.92	456.66	588.83	805.17
3%	1217.77	1369.97	1766.48	2408.82
5%	2029.62	2283.29	2944.13	4012.47
7%	2841.46	3196.61	4121.78	5616.12
9%	3653.31	4109.92	5299.43	7219.78
Annual Carbon Emissions	409,492.3	384,232.7	295,897.9	204,163.8
(b)
1%	0.10%	0.12%	0.20%	0.39%
3%	0.30%	0.36%	0.60%	1.18%
5%	0.50%	0.59%	0.99%	1.97%
7%	0.69%	0.83%	1.39%	2.75%
9%	0.89%	1.07%	1.79%	3.54%

, the annual total carbon emissions for 2025~2040 decrease, and the carbon emission reduction ratios increase. To explain this situation, we take the dynamic CEF curves of Beijing on a typical day in January as an example in Figure 10.

It can be seen that when the share of new energy generation in the system is low, fossil fuel generators will provide more power supply in the system, leading to a relatively stable CEF curve. Therefore, even if the load level is high and the flexible regulation ability of users is good, the carbon reduction capacity of CRODR technology is still limited. For example, it can be seen in Figure 7 that, in 2025, the carbon reduction in Shandong and Jiangsu with a high level of load regulation ability is lower than that in Inner Mongolia with a high level of new energy installation capacity.

If the penetration rate of renewable power generation grows too high, the CEF of the system will tend to remain at a low level the whole time. Then, the carbon reduction benefit of CRODR will still be limited. For example, with the increase in the installed capacity of wind and solar power, the carbon reduction in Inner Mongolia in Figure 7 from 2025 to 2040 has a decreasing trend. Moreover, western provinces of the Chinese mainland have higher levels of installed clean energy and low levels of CEF values, as well as low local loads. As a result, the carbon reduction through CRODR is lower compared with eastern regions whose load consumption demands are high.

In contrast, the central–eastern and southeastern regions are typical heavy-load areas, resulting in the considerable regulation potential of users. In addition, with the increasing proportion of new energy sources, such as photovoltaic power generation, the peak–valley differences in CEFs for power systems are more obvious. Therefore, in 2035 and 2040, provinces such as Shandong, Jiangsu, Anhui, and Guangdong will become the main carbon reduction provinces under the CRODR mechanism. As shown in Figure 8, Figure 9 and Figure 10 and Table 2, similar reasons have caused overall increments in carbon reduction, with the total emissions of systems decreasing from 2025 to 2040.

Thus, we can conclude that the carbon reduction capacity of the CRODR mechanism is mainly affected by two factors: (1) the fluctuation degree of dynamic CEFs represented by peak–valley differences; (2) the flexible response capacity of users.

7. Case Study of a Typical User in China

This section carries out a benefit evaluation of the carbon-reduction-oriented demand response technology considering a typical user: a textile company in Changzhou City, Jiangsu Province. The load profile and carbon emission factors are obtained based on actual data from a typical day in September 2021.

The dynamic carbon emission factors of Changzhou City on this day are shown in Figure 11. The studied company is equipped with an energy storage device with a capacity of 440 kW/3960 kWh, which enables this company to practice CRODR via flexible net load regulation. The optimized net load transfer scheme is solved based on the optimal model of Equations (27)–(34). Comparisons of netload curves and carbon emission conditions before and after the CRODR mechanism are shown in Figure 12 and Figure 13, respectively.

Figure 12 indicates that the dynamic carbon emission factor guides the company to transfer part of its netload to periods with lower carbon emission factors, reducing its carbon emission responsibility and power consumption. More specifically, the energy storage is used from 8:00 to 15:00, 17:00 to 18:00, and at 21:00, when carbon emission factors are relatively low. Then, when the carbon content of electrical power is higher, the system discharges and supports the load demand of the company. According to Figure 13, through the netload regulation based on CRODR, this company’s daily carbon emission of power consumption reduced from 8324.2 kg to 8244.3 kg, while the total power consumption remained the same (13,566.4 kWh).

8. Conclusions

Targeted at power system decarbonization through demand-side regulation, this paper proposed a carbon-reduction-oriented demand response (CRODR) technology based on generalized nodal carbon emission flow theory. First, the framework of the CRODR technology is established to provide the basic interaction principles of users in relation to dynamic carbon emission factors. Then, the generalized nodal carbon emission flow and its solution are proposed. On this basis, an optimization model of load-shifting schedules is built and the carbon reduction benefit-evaluation method is proposed. Case studies based on the future national power system of China and a textile company verified the effectiveness of the proposed theory. The results indicate that the CRODR mechanism proposed can guide users to reduce the carbon emission of power consumption through load regulation while keeping the total power consumption unchanged. Meanwhile, the fluctuation degree of dynamic carbon emission factors and the flexible response capacity of users are the two main factors influencing the carbon reduction benefit of the CRODR mechanism. The detailed findings are as follows:

(1) The generalized nodal carbon emission theory can realize CEF calculation at high spatiotemporal resolutions, providing an effective way to obtain the guiding signals of CRODR.

(2) From 2025 to 2040, the carbon reduction brought to the national power system of China by the CRODR mechanism will show an upward trend. It will also promote the consumption of new non-water energy at the same time.

(3) Regions with large load regulation potential and large peak-to-valley differences in carbon emission factors have better carbon reduction effects from CRODR. Under the CRODR mechanism, future carbon reduction effects in the southeastern region of China will be better than those in the northwestern region.

(4) The use the CRODR mechanism by individual users can guide users to regulate their power consumption behavior and realize carbon reduction while maintaining their original total power consumption.

In the market environment, trading activities such as electricity contracts and spot trading will have significant impacts on users’ carbon emission measurement results and optimization approaches. The improvement of carbon emission flow theory considering multi-type trading behaviors, as well as carbon-reduction guiding mechanisms and decision-making methods for users in the market environment will be key research points in the future.