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\title{Source-storage-transmission planning method considering carbon emission
responsibility allocation}



\author[1]{xiuyu yang}%
\author[1]{Kebing Su}%
\author[2]{Jian Peng}%
\author[2]{Gang Miu}%
\author[2]{ZhengYin Zhu}%
\affil[1]{Northeast Electric Power University}%
\affil[2]{urumqi power supply company}%


\vspace{-1em}



  
  \date{April 25, 2026}


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\selectlanguage{english}
\begin{abstract}
Equitable carbon responsibility distribution is pivotal for the
low-carbon transformation of the power system and the realization of
dual-carbon goals, fostering fair benefits and balanced development for
all entities within the system. Addressing the current practice of a
fixed ratio sharing between generation and load sources, which deviates
from the principle of ``the polluter pays'', this paper proposes a
coordinated planning method for generation, storage, and transmission,
considering carbon responsibility allocation from a planning
perspective. Firstly, a adhering to the fundamental principle of '' who
causes, who bears, '' the various stakeholders are classified and held
accountable, and the reasonable and fair sharing principle and reward
and punishment index are established. Then, on this basis, a two-layer
carbon responsibility cost allocation rule for power system power
balance and power balance is established. Secondly, a
source-storage-network joint planning model considering the investment
cost of conventional thermal power installation, energy storage
investment cost, wind curtailment penalty cost, transmission line
expansion cost and carbon emission responsibility cost is constructed.
Finally, the effectiveness of the proposed method is verified by an
example of a regional power grid transmission project system in
Northeast China, and compared with the source-storage-transmission
planning method without considering carbon responsibility allocation,
the necessity of considering carbon responsibility allocation is further
explained.%
\end{abstract}%



\sloppy


\textbf{1 INTRODUCTION}

In response to today's climate change and energy crisis, low-carbon
development is the only way for social sustainable development. In 2021,
the Central Committee of the Communist Party of China and the State
Council clearly put forward the ``dual-carbon targets'' of striving to
achieve carbon peak by 2030 and carbon neutrality by
2060\textsuperscript{{[}1{]}}. As one of the main sources of carbon
emissions, the carbon emissions of China's power industry account for 40
\% of the total energy-related carbon emissions of various
industries\textsuperscript{{[}2-4{]}}.There is a long way to go for the
low-carbon transformation of power systems. However, most of the current
power system planning methods are still based on the ``electric
perspective'', ignoring the carbon responsibility and carbon benefits of
each part of the power system, which will not be applicable to the high
proportion of renewable energy access in the future. Therefore, it is
very important to study the power system planning method that
effectively balances the ``carbon perspective ''and the ``electric
perspective'' fair carbon responsibility allocation for the new power
system with new energy as the main body in the future. Therefore, it is
very important to study the power system planning method that
effectively balances the ``carbon perspective'' and the ``electric
perspective'' fair carbon responsibility allocation for the new power
system with new energy as the main body in the future.

In recent years, in order to promote the realization of carbon emission
reduction targets and the sustainable development of low-carbon economy,
the research on carbon emission responsibility sharing has received
extensive attention. Many scholars have focused on the optimal operation
of new power systems from a ``carbon
perspective''\textsuperscript{{[}5{]}}. References {[}6-7{]}
preliminarily constructed the theoretical framework of power system
carbon emission flow analysis, and established the basic calculation
method of power system carbon emission flow based on the theory of
carbon emission flow. The original low-carbon research of power system
mostly focuses on the source side {[}8-9{]}. In order to reduce the
pressure on the source side, many scholars have shifted the research
focus from the power generation side to the demand
side\textsuperscript{{[}10-11{]}}. In
Reference\textsuperscript{{[}12{]}}, the carbon emissions of each load
are introduced into the Shapley value method into the carbon trading
model of the integrated energy system, and a two-layer scheduling model
of integrated energy based on price-based demand response is
constructed. In Reference {[}13{]}, a ``location fair'' user-side carbon
responsibility allocation method is proposed, and an ISO-load-side
demand response bi-level optimization model considering carbon
responsibility allocation is established. On the basis of Reference
{[}13{]}, Reference {[}14{]} proposed a step carbon price formulation
scheme and established a two-stage low-carbon optimal scheduling model
for power systems. According to the use of electric energy, Reference
{[}15{]} decomposes the carbon emission structure and proposes a model
for defining the distribution of carbon emission property rights in
power system. Aiming at the minimum carbon emissions in Reference
{[}16{]}, a day-ahead optimization model of integrated energy
distribution network is established, and the influence of load-side
demand response on system operation cost and carbon emissions is
analyzed.

The above research on the allocation of carbon emission responsibility
is based on the theory of carbon emission flow. Although the carbon
emission flow theory can better track the carbon emission path, it is
sometimes difficult to take into account the principle of ``who causes,
who bears, who governs, who benefits''. Considering fairness, carbon
responsibility should not be only allocated unilaterally by the power
generation side or the load side. References {[}17-18{]} proposed a
research method in which both sides of the source and load share carbon
responsibility. On the basis of carbon responsibility allocation between
source and load sides, Reference {[}19{]} established a robust energy
storage model of step-by-step carbon trading and time-of-use electricity
price. In reference {[}20{]}, considering the flexibility requirements
of the power system, the carbon emission responsibility is allocated to
both sides of the source and load, including new energy, and a
multi-level flexible resource planning method considering the carbon
emission responsibility of both sides of the source and load is
proposed.

In addition, in order to ensure the power balance of the power system,
absorb renewable energy as much as possible and reduce the comprehensive
cost, a large number of studies have coordinated power system planning
from the ``electric perspective''. On the basis of considering the cost
of carbon emissions, Reference {[}21{]} optimized the charging and
discharging strategies of various energy and energy storage devices in
the micro-energy network. Reference {[}22{]} analyzed the main factors
affecting the wind power acceptance capacity, and constructed a joint
planning model of energy storage and transmission network to improve the
wind power acceptance capacity. Reference {[}23{]} proposed that
long-term and short-term energy storage should cooperate with each other
to establish a source-storage-transmission joint planning model. In
order to cope with the safe and economic operation requirements of power
system under high wind power penetration in the future, Reference
{[}24{]} carried out a series of studies on source-storage-network
planning considering the flexibility requirements of power system. In
{[}25{]}, from the perspective of time-sharing multiplexing of energy
storage, the problem of wind curtailment is solved while configuring
energy storage, and a joint planning method of source-storage-network
considering the coupling relationship of wind curtailment events is
proposed. The above research lacks the overall consideration of
``electric perspective'' and ``carbon perspective'' in the planning
process, and it is difficult to observe the coupling relationship
between ' electricity ' and ' carbon ' behaviors in each link of the
planning process.

To sum up, most of the research on the new power system planning is the
separation of ``electricity'' and ``carbon'', and the research on the
allocation of carbon emission responsibility mostly focuses on the
bilateral allocation of source and load. The carbon emission
responsibility caused by the abandonment of renewable energy can not be
clearly defined, so there is little research on the allocation of carbon
responsibility by all stakeholders. Therefore, this paper proposes a
source-storage-transmission planning method considering carbon emission
responsibility allocation from the perspective of
``electricity-carbon''. Firstly, the double-layer carbon responsibility
allocation rule under the balance of electricity and power is
constructed. Then, the carbon responsibility cost is incorporated into
the objective function of the planning model, and a
source-storage-network joint planning model considering the conventional
thermal power installation investment cost, energy storage investment
cost, wind curtailment penalty cost, transmission line expansion cost
and carbon responsibility cost is constructed, and the iterative
solution algorithm of the model is designed. Finally, the effectiveness
and feasibility of the proposed method are verified by the standard
Garver-6 node engineering system.

\textbf{1 DOUBLE-LAYER ALLOCATION RULES OF CARBON EMISSION
RESPONSIBILITY}

To account for the responsibility of carbon emissions, it is necessary
to design a reasonable allocation of carbon emission quotas. At present,
the power industry mainly uses the method of free allocation to allocate
the initial carbon emission quota, and obtains the initial carbon
emission quota of free allocation according to the power generation of
thermal power units\textsuperscript{{[}26{]}}. The calculation formula
is as follows :

Where \emph{C} \textsubscript{total} is the total carbon emissions
;\emph{C} \textsubscript{unfree} is the paid carbon emission quota of
the system ; \emph{C} \textsubscript{free} is the system's free carbon
emission quota ; \emph{Q} \textsubscript{free} is the free quota
allocation coefficient. This paper refers to the EU's four-stage carbon
quota allocation method, and sets the free quota allocation coefficient
as 80\%. \selectlanguage{greek}\emph{μ} \selectlanguage{english}\textsubscript{coal} is the conversion coefficient of
energy carbon emissions ; \emph{P} \textsubscript{G} is the power
generation of thermal power units.

The paid carbon emission quota and the paid carbon emission liability
cost are obtained by the difference between the total carbon emission of
the system and the unpaid carbon emission quota.

In the formula, \emph{F} \textsubscript{unfree} is the paid carbon
emission responsibility cost of the system ;\emph{F}
\textsubscript{total} is the total cost of carbon emissions ;\emph{F}
\textsubscript{free}is the cost of free carbon emissions ;\selectlanguage{greek}\emph{λ}
\selectlanguage{english}\textsubscript{y}\textsuperscript{carbon} is the unit price of carbon
tax in that year.

\textbf{1.1 The initial allocation of carbon emission responsibility
under power balance}

Ignoring the real-time power balance constraints, only considering the
balance of power supply and demand in the power system, carbon emissions
are from thermal power units, that is, carbon emissions generated to
meet net load demand. At this time, following the principle of ``who
causes, who is responsible'', a scheme for thermal power units and load
sides to jointly assume carbon responsibility is
proposed\textsuperscript{{[}19{]}}. The calculation formula of the
carbon emission and system carbon emission responsibility cost of the
thermal power unit is as follows:

Where \emph{F} \textsubscript{p\_load} is the carbon emission cost
caused by net load demand, which can be expressed as the total carbon
emission cost of the system. \emph{F} \textsubscript{G} is the
responsibility cost of carbon emissions for thermal power units
;\selectlanguage{greek}\emph{ζ} \selectlanguage{english}\textsubscript{F-1}is the carbon responsibility factor of
thermal power unit, and \selectlanguage{greek}\emph{ζ} \selectlanguage{english}\textsubscript{F-1}is 0.5.\emph{P}
\textsubscript{p\_load} is the net load demand electricity ;\emph{F} * C
is the responsibility cost of system carbon emissions under power
balance.

\textbf{1.2 Secondary allocation of carbon emission responsibility under
power balance}

1.2.1 Responsibility sharing of carbon emissions caused by power
imbalance abandonment

Due to the volatility and uncertainty of renewable energy power, there
may be insufficient peak shaving and transmission congestion during
system operation, resulting in renewable energy curtailment. This part
of the abandoned electricity will increase the additional carbon
emissions on the basis of the electricity balance allocation. The
following is the secondary allocation of carbon emission responsibility
in the case of power abandonment. Here, renewable energy takes wind
power as an example, and its transmission congestion wind abandonment,
peak shaving insufficient wind abandonment, and total wind abandonment
after coupling. The detailed formula is shown in Appendix A Formula
A1-A4. The total wind curtailment diagram formed by each wind
curtailment sequence and coupling is shown in Appendix A, Figs.A1-A2.

By coupling the abandoned wind power after coupling, the total abandoned
wind carbon emission expression can be obtained as follows :

Where \emph{C} \textsubscript{w} is the carbon emission caused by
abandoned wind after coupling ; \emph{C} \textsubscript{w-Tf} is the
total amount of carbon emissions caused by insufficient peak shaving in
the total abandoned wind after coupling ; \emph{P}
\textsubscript{LW-i}is the wind curtailment at time \emph{t} in
scheduling day \emph{i} ;\emph{C} \textsubscript{w-Zs} is the carbon
emission caused by transmission blocking abandoned wind in the total
abandoned wind after coupling ; \emph{C} \textsubscript{eq} is the wind
curtailment of the same part of the total wind curtailment and the peak
wind curtailment and the transmission congestion wind curtailment after
coupling ;\emph{P} \textsubscript{e-i}(\emph{t} ) is the curtailed wind
power absorbed by the energy storage at time \emph{t} in the scheduling
day\emph{i} .

The reason for the wind curtailment of transmission congestion is that
the construction of the power grid is lagging behind, resulting in
additional carbon emissions. According to the principle of ``who causes,
who bears'' and , the carbon responsibility of this part of the wind
curtailment is borne by the grid side. The reason for the lack of peak
shaving and wind abandonment is the lack of peak shaving capacity of
conventional units. The carbon responsibility for this part of wind
abandonment is borne by both the source and load sides. There is an
overlap between the two kinds of abandoned wind, and this part of carbon
emissions is shared by the thermal power unit and the grid side. The
carbon emission expressions of the two abandoned winds and the total
abandoned winds after treatment are as follows :

Where \emph{C} \textsubscript{eq1} is the carbon emission caused by
insufficient wind curtailment after peak load regulation ;\emph{C}
\textsubscript{eq2} is the carbon emission caused by wind curtailment
due to transmission congestion after sharing responsibility.

The expression of carbon emission cost caused by wind curtailment is :

Where \emph{F} \textsubscript{w} is the carbon emission cost caused by
total abandoned wind ; \emph{F} \textsubscript{eq1} is the carbon
emission cost caused by insufficient peak shaving and wind abandonment
;\emph{F} \textsubscript{eq2} is the cost of carbon emissions caused by
wind curtailment due to transmission congestion.

1.2.2 The impact of energy storage configuration on carbon emission
responsibility sharing

Configuring energy storage can promote renewable energy consumption and
reduce system carbon emissions. Therefore, a certain auxiliary reward
should be applied to the carbon emissions reduced by wind curtailment
consumed by energy storage. The specific expression is :

Where \emph{F} \textsubscript{e} is the auxiliary reward for energy
storage to absorb wind curtailment ; \emph{P} \textsubscript{E-w} is
energy storage to absorb wind power.

\textbf{1.3 Analysis of the impact of carbon emission responsibility
sharing cost on each element}

By incorporating the carbon emission responsibility cost that each
stakeholder needs to bear into the unit price of each subject, the
quantification of carbon emission responsibility cost in the objective
function can be realized, and the impact of carbon emission
responsibility on each link in the planning can be observed more
intuitively.

1) Analysis of the impact of carbon emission responsibility cost on the
construction of thermal power units

The construction cost of thermal power unit is calculated by the ratio
of the construction cost of thermal power unit to the capacity of new
thermal power unit after considering the responsibility cost of carbon
emission. The expression is as follows :

Where \emph{P} \textsubscript{g} is the capacity of the new thermal
power unit ; \selectlanguage{greek}\emph{β} \selectlanguage{english}is the cost coefficient of carbon responsibility
of new thermal power units. (Calculated by the ratio of the total amount
of new units to thermal power units ); \selectlanguage{greek}\emph{σ} \selectlanguage{english}\textsubscript{g} is the
construction cost of the original unit thermal power unit of the system
; \selectlanguage{greek}Δ\selectlanguage{english}\selectlanguage{greek}\emph{σ} \selectlanguage{english}\textsubscript{g} is the construction cost of unit thermal
power unit after incorporating carbon responsibility cost.

It is set that the grid side is planned according to the installed
capacity of wind power, and there is no transmission congestion. The
unit price change of thermal power units after the integration of system
carbon emission responsibility cost is analyzed, as shown in Fig 1.

\textbf{FIGURE 1 Trend of unit price of thermal power unit construction}

The black curve in Fig 1 is the change trend of the unit price of
thermal power unit construction, showing a decreasing curve, and the red
straight line is the original unit price of thermal power unit
construction. It can be seen that with the decrease of the installed
capacity of the thermal motor group, the shortage of peak shaving and
the abandonment of wind are reduced, while the unit price of the thermal
power unit construction is reduced and gradually close to the original
construction cost.

2) Analysis of the impact of carbon emission responsibility cost on
transmission channel construction

The investment per unit length of the line is calculated by the ratio of
the total investment cost of the line to the length of the line after
considering the responsibility cost of carbon emissions. The expression
is :

Where \emph{C\textsubscript{l}} is the unit price per unit length of the
original line \emph{l} of the system ; \emph{n\textsubscript{l}} is the
number of construction rounds of line \emph{l}
;\emph{L\textsubscript{l}} is the length of line \emph{l}
.\emph{Z\textsubscript{l}} is the 0-1 decision variable of line \emph{l}
investment ; \selectlanguage{greek}Ω\selectlanguage{english}\textsubscript{l\emph{ine}} is the set of lines to be
selected ; \selectlanguage{greek}Δ\selectlanguage{english}\emph{C\textsubscript{l}} is the unit price per unit length
of line l after incorporating carbon responsibility
cost.\emph{K\textsubscript{line}} is the unit power cost per unit length
of line ; \emph{P\textsubscript{line}} \textsubscript{-\emph{l}} is the
transmission capacity of line \emph{l} .

The system flexibility is set to be sufficient, and there is no shortage
of peak shaving. The unit investment change of the transmission channel
after the system carbon emission responsibility cost is incorporated is
analyzed, as shown in Fig2.

\textbf{FIGURE 2 Transmission channel unit investment}

The black curve in figure 2 is the change trend of unit construction
cost of transmission line, showing a curve that gradually approaches a
numerical value after decreasing. The red straight line is the original
construction unit price of the transmission line. It can be seen that
with the increase of transmission channel capacity, the abandoned wind
of transmission congestion gradually decreases, and the investment cost
of unit transmission line decreases.

3) Analysis of the impact of carbon emission liability cost on the unit
price of energy storage

The energy storage unit capacity purchase cost is calculated by the
ratio of the energy storage construction cost to the energy storage
capacity after considering the carbon emission responsibility cost. The
expression is as follows :

Where \emph{Eess} is the configured energy storage capacity ;\selectlanguage{greek}\emph{σ}
\selectlanguage{english}\textsubscript{Eess} is the purchase cost of the original energy storage
unit capacity of the system ; \selectlanguage{greek}Δ\selectlanguage{english}\selectlanguage{greek}\emph{σ} \selectlanguage{english}\textsubscript{Eess} is the
purchase cost of energy storage unit capacity incorporated into carbon
responsibility cost.

Control the capacity construction of fire motor assembly and
transmission channel unchanged, and analyze the unit price change trend
of energy storage after the system carbon emission responsibility cost
is incorporated, as shown in Fig 3.

\textbf{FIGURE 3 Change trend of unit construction cost of energy
storage capacity}

The red curve in Figure 3 shows the trend of unit construction cost of
energy storage capacity, which is an increasing curve, but less than the
original unit cost of 600,000 yuan. It can be seen that with the change
of energy storage capacity configuration, the smaller the wind
curtailment of energy storage is, the smaller the energy storage reward
is, and the unit construction cost of energy storage capacity increases.

\textbf{2 Joint planning model of source-storage-transmission
considering carbon responsibility allocation}

\textbf{2.1 objective function}

From the ``carbon perspective'', this paper establishes the accounting
rules of carbon responsibility allocation in power system on the basis
of considering the allocation of carbon emission responsibility. Based
on the source-storage-transmission joint planning model, the carbon
responsibility sharing cost is converted into the construction unit
price of each subject, and embedded in the model objective function.
First, the basic model is modified, as shown in Equation (11).

Where \selectlanguage{greek}Δ\selectlanguage{english}\emph{I\textsubscript{g}} is the investment of thermal power
units after considering the cost sharing of carbon emission
responsibility ; \selectlanguage{greek}Δ\selectlanguage{english}\emph{I\textsubscript{e}} is the investment of energy
storage equipment after considering the cost sharing of carbon emission
responsibility ; \emph{C\textsubscript{T}} is wind abandonment penalty
cost ; \selectlanguage{greek}Δ\selectlanguage{english}\emph{I} \textsubscript{line} is the investment of transmission
line expansion after considering the cost sharing of carbon emission
responsibility. The specific calculation formulas are as follows.

In the formula : \emph{P} \textsubscript{ess} for the configuration of
energy storage power ; \selectlanguage{greek}\emph{σ} \selectlanguage{english}\textsubscript{pess} and\selectlanguage{greek}\emph{σ}
\selectlanguage{english}\textsubscript{T} are the purchase cost of unit power converter and the
penalty of unit wind curtailment respectively ;\emph{T}
\textsubscript{s} is the planning cycle.

\textbf{2.2 constraint condition}

1) Node power balance constraint

Where \emph{P} \textsubscript{g,h,m}(\emph{t} ) is the output power of
the node of the thermal power unit \emph{h} at the time \emph{t}
;\emph{P} \textsubscript{w,j,m}(\emph{t} ) is the output power of the
wind turbine \emph{j} at the node of time \emph{t} ; \selectlanguage{greek}Δ\selectlanguage{english}\emph{P}
\textsubscript{w,j,m}(\emph{t} ) is the abandoned wind power of the wind
turbine \emph{j} node at time \emph{t} ;\emph{P}
\textsubscript{e,m}(\emph{t} ) is the output power of the node of the
energy storage device at time \emph{t} ;\emph{P}
\textsubscript{L,m}(\emph{t} ) is the active load of node\emph{m} at
time \emph{t} .

2) Power balance constraint

Where [?]\emph{P} \textsubscript{g,h}(\selectlanguage{greek}Δ\selectlanguage{english}\emph{t} ) is the power of the
thermal power unit h in the \selectlanguage{greek}Δ\selectlanguage{english}\emph{t} period ;\emph{W}
\textsubscript{w}(\selectlanguage{greek}Δ\selectlanguage{english}\emph{t} ) is the amount of electricity of the wind
turbine during the \selectlanguage{greek}Δ\selectlanguage{english}\emph{t} period ;\emph{W}
\textsubscript{e}(\selectlanguage{greek}Δ\selectlanguage{english}\emph{t} ) is the power of the energy storage device
during the \selectlanguage{greek}Δ\selectlanguage{english}t period ; \emph{W} \textsubscript{Q}(\selectlanguage{greek}Δ\selectlanguage{english}\emph{t} ) is the
abandoned wind power of the wind farm during the \selectlanguage{greek}Δ\selectlanguage{english}\emph{t} period
;\emph{W} \textsubscript{L}(\selectlanguage{greek}Δ\selectlanguage{english}\emph{t} ) is the load power in \selectlanguage{greek}Δ\selectlanguage{english}\emph{t}
period.

3) Thermal power unit output constraint

Where \emph{P} \textsubscript{g}\textsuperscript{min} and\emph{P}
\textsubscript{g}\textsuperscript{min} are the minimum and maximum
output of thermal power units respectively ;\emph{P}
\textsubscript{g}(\emph{t} ) is the output of the thermal power unit
under normal operation at time \emph{t} .

4) DC power flow constraints

Where \emph{B} is the admittance matrix of the system node ;\selectlanguage{greek}\emph{θ}
\selectlanguage{english}(\emph{t} ) is the node voltage phase angle vector at time \emph{t} ;
\emph{P} \textsubscript{g}(\emph{t} ) is the output power vector of the
thermal power unit at time \emph{t} ;\emph{P} \textsubscript{w}(\emph{t}
) is the wind turbine output power vector at time \emph{t} ;\emph{P}
\textsubscript{e}(\emph{t} ) is the energy storage output power vector
at time \emph{t} ;\emph{P} \textsubscript{L}(\emph{t} ) is the load
power vector at time \emph{t} .

5) Energy storage capacity and power constraints

Where \emph{P} \textsubscript{e}\textsuperscript{min} and\emph{P}
\textsubscript{e}\textsuperscript{max} are the minimum and maximum power
of energy storage equipment respectively ;\emph{E}
\textsubscript{e}\textsuperscript{min} and\emph{E}
\textsubscript{e}\textsuperscript{max} are the minimum and maximum
capacity of energy storage equipment, respectively.\emph{P}
\textsubscript{e}(\emph{t} ) is the actual power of the energy storage
device at time \emph{t} ; \emph{E} \textsubscript{e}(\selectlanguage{greek}Δ\selectlanguage{english}\emph{t} ) is the
actual capacity of the energy storage device during the period of
\selectlanguage{greek}Δ\selectlanguage{english}\emph{t} ; \emph{P} \textsubscript{e,char}(t),\emph{P}
\textsubscript{e,dis}(t) are the charge and discharge power of energy
storage at time \emph{t} ; \selectlanguage{greek}\emph{η} \selectlanguage{english}\textsubscript{char} and\selectlanguage{greek}\emph{η}
\selectlanguage{english}\textsubscript{dis} are the charge and discharge efficiency of energy
storage.

6)spinning reserve constraint

Where \emph{P} \textsubscript{g,\emph{h}} (\emph{t} ) is the output
power of thermal power unit \emph{h} at time \emph{t} ;\emph{P}
\textsubscript{w,\emph{j}} (\emph{t} ) is the output power of wind farm
\emph{j} at time \emph{t} ;\emph{P} \textsubscript{e,\emph{k}} (\emph{t}
) energy storage device\emph{k} charging power at time \emph{t} ;
\selectlanguage{greek}Ω\selectlanguage{english}\textsubscript{g} is the set of thermal power units ;
\selectlanguage{greek}Ω\selectlanguage{english}\textsubscript{w} is the set of wind farms ; \selectlanguage{greek}Ω\selectlanguage{english}\textsubscript{e} is a
collection of energy storage devices ; \selectlanguage{greek}Ω\selectlanguage{english}\textsubscript{L} is the set of
load nodes ;\emph{R} \textsubscript{max} is the maximum reserve capacity
of the system.

7)Daily clearing constraint of state of charge of energy storage system

Where \selectlanguage{greek}\emph{δ} \selectlanguage{english}\textsubscript{SOC}(0) and \selectlanguage{greek}\emph{δ}
\selectlanguage{english}\textsubscript{SOC}(24) represent the state of charge at the initial and
final moments, respectively.

8) New line constraints

Where \selectlanguage{greek}\emph{ω\textsubscript{m}}\selectlanguage{english} is the number of new transmission lines
connected to node \emph{m} ;\emph{N\textsubscript{m}}
\textsubscript{,max} is the maximum number of new transmission lines.

9)Transmission line power transmission constraints

Where \emph{P\textsubscript{ab}} and\emph{P\textsubscript{ab}}
\textsuperscript{max} are the actual transmission power and the maximum
capacity of the line (\emph{a,b} ) respectively ;
\emph{x\textsubscript{ab}}
and\emph{x\textsubscript{ab}\textsuperscript{new}} are the number of
existing direct connected lines and new lines of node \emph{a} and
node\emph{b} , respectively.



\textbf{FIGURE 4 Model solving flowchart}

Step 6 : In the feasible region of thermal power installation and wind
power grid-connected point transmission capacity, considering the
transmission line expansion constraints, power transmission constraints
and conventional unit output constraints, the wind power grid-connected
point boundary and conventional power window capacity are traversed, and
the second step to the fifth step are repeated until the optimal joint
planning scheme of system source-storage-network is finally obtained.
The specific process is shown in Figure 4.

\textbf{3 example analysis}

\textbf{3.1 base data}

In this paper, a regional power grid transmission project in Northeast
China is analyzed. The network topology of the project is shown in
Appendix A, and the annual load change is shown in Appendix A. The
specific parameters used in the example are shown in Table 1.

\textbf{TABLE 1} Example calculation basic parameters\selectlanguage{english}
\begin{longtable}[]{@{}ll@{}}
\toprule
\textbf{parameter name} & \textbf{numerical value}\tabularnewline
\midrule
\endhead
Construction cost of thermal power unit /( million /MW) &
500\tabularnewline
Wind power base installed capacity /MW & 2000\tabularnewline
Maximum value of wind power /MW & 1371.5\tabularnewline
The maximum load on the network side /MW & 3769\tabularnewline
Outgoing transmission channel voltage level /kV & 220\tabularnewline
The length of outgoing transmission channel line /km &
200\tabularnewline
Unit capacity of thermal power unit /MW & 60\tabularnewline
Coal cost of thermal power unit / million /(MW[?]h)) &
0.061\tabularnewline
wind power curtailment penalty cost /( million /(MW[?]h)) &
0.1\tabularnewline
Energy storage unit capacity cost /( million /(MW[?]h)) &
60\tabularnewline
Converter unit power cost / million /MW) & 10\tabularnewline
Unit single circuit line construction cost / million /(MW\selectlanguage{ngerman}·km)) &
1\tabularnewline
planning cycle /year & 20\tabularnewline
Carbon emissions per unit of electricity /( ton /(MW[?]h)) &
1\tabularnewline
PSO /( million / ton) & 0.0415\tabularnewline
\bottomrule
\end{longtable}

\textbf{3.2 Carbon responsibility allocation and planning results
analysis}

In order to verify the effectiveness of the source-storage-network
planning method considering carbon responsibility allocation proposed in
this paper, A and B planning methods are used for comparative analysis.

Method A : Carry out source-storage-network planning for the system
without considering carbon responsibility allocation.

Method B : Considering the allocation of carbon responsibility, the
source-storage-network planning of the system is carried out.

The planning comparison results are shown in Table 2.

\textbf{TABLE 2} Planning results of method A and B\selectlanguage{english}
\begin{longtable}[]{@{}lllll@{}}
\toprule
\textbf{name} & \textbf{Method A} \textbf{Configuration results} &
\textbf{Method A investment / billion} & \textbf{Method B}
\textbf{Configuration results} & \textbf{Method B investment /
billion}\tabularnewline
\midrule
\endhead
new generating capacity & 1936MW & 96.8 & 1936MW & 103.63\tabularnewline
capacity expanding of lines & 1200MW & 24 & 1100MW & 22.2\tabularnewline
Total abandon wind & 3.71\selectlanguage{ngerman}×10\textsuperscript{4}MW.h & 7.42 &
3.65\selectlanguage{ngerman}×10\textsuperscript{4}MW.h & 7.29\tabularnewline
energy storage capacity & 1391.3MW.h & 8.35 & 1748.2MW.h &
9.76\tabularnewline
Converter power & 376.56MW & 0.38 & 485.634MW & 0.45\tabularnewline
Coal-fired thermal power units & 1.97\selectlanguage{ngerman}×10\textsuperscript{7}MW.h &
2370.44 & 1.97\selectlanguage{ngerman}×10\textsuperscript{7}MW.h & 2370.44\tabularnewline
gross investment & 2507.38 billion & 2513.78 billion & &\tabularnewline
\bottomrule
\end{longtable}

The planning results of method A are shown in the second and third
columns of Table 2, and the planning results of method B are shown in
the fourth and fifth columns of Table 2. Comparing method A, it can be
seen that the total wind curtailment of method B is smaller. Compared
with method A, this method reduces the abandoned wind power by 0.633 \selectlanguage{ngerman}×
104MW · h, reduces the abandoned wind loss by 0.13 billion yuan, reduces
the additional carbon emission cost caused by abandoned wind, reduces
the transmission channel capacity by 100 MW, saves the transmission
investment by 180 million yuan, and the energy storage capacity is
configured by 356.9MW·h, the energy storage power is configured by
109.074 MW, and the system flexibility is significantly improved.

The unit price and carbon responsibility cost of each subject of method
B after planning are shown in table 3. The coordinated optimization
process is shown in Fig.5.

not-yet-known
      not-yet-known
    
    
      not-yet-known
      
      
        unknown
      
    
  
  
    Table 3 Impact of carbon emission responsibility on subjects

not-yet-known not-yet-known not-yet-known unknown\selectlanguage{english}
\begin{longtable}[]{@{}lll@{}}
\toprule
name & unit price & Carbon emissions responsibility cost\tabularnewline
\midrule
\endhead
new generating capacity & 535.26MW & 6.83\begin{CJK}{UTF8}{gbsn}亿元\end{CJK}\selectlanguage{english}\tabularnewline
capacity expanding of lines & 201.80MW & 1980\begin{CJK}{UTF8}{gbsn}万元\end{CJK}\selectlanguage{english}\tabularnewline
energy storage capacity & 55.85MW.h & -7262.72\begin{CJK}{UTF8}{gbsn}万元\end{CJK}\selectlanguage{english}\tabularnewline
Converter power & 9.31MW & -336.25\begin{CJK}{UTF8}{gbsn}万元\end{CJK}\selectlanguage{english}\tabularnewline
Total cost of carbon emissions & 7.784 billion &\tabularnewline
\bottomrule
\end{longtable}

The second column in Table 3 is the construction unit price of each
subject after considering the responsibility cost of carbon emissions.
After the second apportionment of carbon emission responsibility, the
cost of carbon emission responsibility borne by each part is calculated
by the new part and unit price increment of each subject. In the
planning process, the configuration of energy storage participates in
the consumption of carbon emissions and gives certain auxiliary rewards,
so the carbon emission responsibility cost of energy storage
configuration is negative.

It can be seen from Table 3 that due to the lack of peak regulation of
thermal power units and the congestion of transmission channels, thermal
power units and transmission lines have assumed certain carbon emission
responsibilities, so the unit price of construction has risen. And in
the final planning results, the transmission channel capacity is
reduced. However, because the thermal power unit needs to meet the
balance of supply and demand and undertake the task of power generation,
the construction has not been reduced. The energy storage system is
configured to absorb the wind curtailment of the system, and the energy
storage system is rewarded. Therefore, the unit price of energy storage
construction is reduced to a certain extent, and the construction of
energy storage system is increased in the planning results.

\textbf{FIGURE 5 Results of coordination and optimization of thermal
power unit installed capacity and wind power planning boundary}

\textbf{FIGURE 6} Planning the optimal solution profile

In figure 5, the pentagram is marked as the optimal solution position of
the source-storage-network joint planning, and the optimal solution
section is the black line part in figure 6(a) and figure 6(b).

Figure 6(a) curve shows the optimization curve between the installed
capacity of thermal power units and the total cost, which is shown as a
concave curve. The reduction of the installed capacity of thermal power
units reduces the cost of insufficient peak shaving, wind abandonment
and carbon responsibility. At this time, the total cost decreases with
the decrease of the installed capacity of thermal power units. When the
installed capacity is reduced to the situation where the power balance
constraint cannot be satisfied, the energy storage configuration begins
to increase. At this time, the energy storage cost becomes the dominant
factor of the total cost ratio, so the total investment cost gradually
increases.

Figure 6(b) shows the relationship between the transmission channel
capacity and the total cost, which is shown as a concave curve. In the
process of transmission channel capacity planning changing from large to
small, the investment cost of transmission line decreases, and the total
cost decreases with the dominant factor in the early stage. As the
transmission channel capacity continues to decrease, the transmission
congestion wind abandonment increases, and the energy storage
configuration needs to be carried out. At this time, the energy storage
construction cost and the wind abandonment penalty cost are the dominant
factors of the total cost. The total cost decreases first and then
increases with the change of the transmission line channel capacity.

The above results show that the planning method proposed in this paper
can effectively reduce the carbon emissions of the system, and the
configuration of the energy storage system improves the flexibility of
the system.

\textbf{4 CONCLUSION}

This paper analyzes the carbon emissions caused by the behavior of each
subject in the power system from the ``carbon perspective'', constructs
a two-layer carbon responsibility allocation rule based on the balance
of electricity and power, and proposes a source-storage-network planning
method considering carbon responsibility allocation. The main
conclusions are as follows :

1)According to the principle of ``who causes,who bears'', a
double-layer allocation rule of carbon responsibility is constructed
from the perspective of electricity and electricity balance, which
realizes the fair allocation of responsibility and effective rewards and
punishments for additional carbon emissions generated by unpaid and paid
carbon quotas and real-time imbalance of electricity ;

2)A source-storage-network planning method considering carbon
responsibility allocation is proposed, which realizes the integration of
``electricity-carbon'' perspective, gives certain rewards and
punishments from the perspective of carbon emission cost, promotes
energy storage investment, reduces abandoned electricity, and reduces
carbon emissions. Compared with method A, this method reduces the
abandoned wind power by 0.633 \selectlanguage{ngerman}× 104MW · h, improves the utilization rate
of wind power, reduces carbon emissions, and reduces the cost of carbon
emissions.

With the continuous advancement of the dual-carbon strategy, the
research content of this paper can provide a more feasible reference for
the planning of new power systems.

REFERENCES

\begin{enumerate}
\tightlist
\item
  Hongli JIANG, Yuxi LIU, Yiming FENG, et al. Analysis of Power
  Generation Technology Trend in 14th Five-Year Plan Under the
  Background of Carbon Peak and Carbon Neutrality{[}J{]}. Power
  Generation Technology, 2022, 43(1): 54-64.
\item
  PAN Xiao, ZHANG Mingli, HAN Zhentao, et al. Energy Internet-oriented
  Optimization Planning Method for Intelligent Sensing Equipment of
  Zero-Carbon Park{[}J{]}. ELECTRIC POWER CONSTRUCTION, 2022, 43(12):
  47-55.
\item
  ZHAO Guotao, DING Quan, FU Junhua, et al. Research on the Low-Carbon
  Implementation Path of Regional Energy System Relying on the Linkage
  Mechanism of Multi-markets{[}J{]}. ELECTRIC POWER CONSTRUCTION, 2021,
  42(3): 19-26.
\item
  LIU Tianwei, BIAN Xiaoyan, WU Shan, et al. Overview and prospect of
  carbon emission accounting in electric power systems{[}J{]}. Power
  System Protection and Control, 2024, 52(4): 176-187.
\item
  KANG Chongqing, DU Ershun, LI Yaowang, et al. Key Scientific Problems
  and Research Framework for Carbon Perspective Research of New Power
  Systems{[}J{]}. Power System Technology, 2022, 46(03): 821-833.
\item
  ZHOU Tianrui, KANG Chongqing, XU Qianyao, et al. Preliminary
  Theoretical Investigation on Power System Carbon Emission Flow{[}J{]}.
  Automation of Electric Power Systems, 2012, 36(7): 38-43.
\item
  ZHOU Tianrui, KANG Chongqing, XU Qianyao, et al. Preliminary
  Investigation on a Method for Carbon Emission Flow Calculation of
  Power System{[}J{]}. Automation of Electric Power Systems, 2012,
  36(11): 44-49.
\item
  Li J, Wen J, Han X. Low-carbon unit commitment with intensive wind
  power generation and carbon capture power plant{[}J{]}. Journal of
  Modern Power Systems and Clean Energy, 2015, 3: 63-71.
\item
  J, Xue F, Song X. Simulation analysis on policy interaction effects
  between emission trading and renewable energy subsidy{[}J{]}. Journal
  of modern power systems and clean energy, 2013, 1(2): 195-201.
\item
  ZHOU Quan, FENG Donghan, XU Changbao, et al. Methods for Allocating
  Carbon Obligation in Demand Side: a Comparative Study{[}J{]}.
  Automation of Electric Power Systems, 2015, 39(17): 153-159.
\item
  Li B, Song Y, Hu Z. Carbon flow tracing method for assessment of
  demand side carbon emissions obligation{[}J{]}. IEEE Transactions on
  Sustainable Energy, 2013, 4(4): 1100-1107.
\item
  LIU Zheyuan, XING Haijun, CHENG Haozhong, YE Yujing.~Bi-level Optimal
  Scheduling of Integrated Energy System Considering Carbon Emission
  Flow and Demand Response.~High Voltage Engineering. 2023, 49(1):
  169-178.
\item
  CHEN Zhimeng, LEI Shuya, WEI Renjie, et al. Research on
  ''Location-Fair'' Approach for User-Side Carbon Responsibility
  Allocation in the Context of Dual Carbon Goals{[}J/OL{]}. Power System
  Technology: 1-10{[}2024-07-08{]}.
\item
  CHEN Houhe, MAO Wenling, ZHANG Rufeng, et al. Low-carbon optimal
  scheduling of a power system source-load considering coordination
  based on carbon emission flow theory{[}J{]}. Power System Protection
  and Control, 2021, 49(10): 1-11.
\item
  YUAN Shulin, MA Rui. A Research on the Allocation Model of Carbon
  Emission in Power System Based on Carbon Emission Flow
  Theory{[}J{]}.~Modern Electric Power, 2014, 31(6): 70-75.
\item
  YANG Mingjie, HU Yangyu, QIAN Haixia, et al. Optimization of day-ahead
  and intra-day multi-time scale scheduling for integratedpower-gas
  energy system considering carbon emission{[}J{]}. Power System
  Protection and Control, 2023, 51(5): 96-106.
\item
  LI Jiang, FAN Yuanzheng, LIU Bo. A Source-load Low Carbon Optimization
  Methodology Considering Carbon Responsibility for Direct Carbon
  Emissions from Cement Plants{[}J/OL{]}. Electric Power:
  1-12{[}2024-07-08{]}.
\item
  CHEN Lixia, SUN Tao, ZHOU Yun, et al. Method of Carbon Obligation
  Allocation Between Generation Side and Demand Side in Power
  System{[}J{]}. Automation of Electric Power Systems, 2018, 42(19):
  106-111.
\item
  HAO Ting, FAN Xiaochao, WANG Weiqing, et al. Optimal configuration of
  energy storage considering the source-load uncertainty under
  ladder-type carbon trading{[}J{]}. Power System Protection and
  Control, 2023, 51(1): 101-112.
\item
  BIAN\begin{CJK}{UTF8}{gbsn}　\end{CJK}\selectlanguage{english}Xiaoyan, WU\begin{CJK}{UTF8}{gbsn}　\end{CJK}\selectlanguage{english}Shan, ZHAO\begin{CJK}{UTF8}{gbsn}　\end{CJK}\selectlanguage{english}Jian, et al. Multi-level flexible
  resource planning of new power system considering source-load carbon
  responsibility allocation{[}J{]}. Electric Power Automation Equipment.
  2024, 44(02): 155-164.
\item
  FENG Yi, YING Zhanfeng, YAN Jianhu. Optimized operation of energy
  storage in a multi-energy complementary micro-energy network
  considering carbon emission cost{[}J{]}. Power System Protection and
  Control, 2021, 49(8): 92-99.
\item
  HUANG Ying, LIU Baozhu, WANG Kunyu, et al. Joint Planning of Energy
  Storage and Transmission Network Considering Wind Power Accommodation
  Capability{[}J{]}. Power System Technology, 2018, 42(05): 1480-1489.
\item
  ZHENG Yangwei, JIANG Yuewen, ZHANG Jinhui. Joint planning optimization
  of source-storage-transportation considering long-and short-term
  energy storage under high proportion of wind power penetration{[}J{]}.
  Electric Power Automation Equipment, 2023, 43(3): 2023, 43(03): 63-71.
\item
  YANG Xiuyu, MU Gang, CHAI Guofeng, et al. Source-storage-grid
  Integrated Planning Considering Flexible Supply-demand Balance{[}J{]}.
  Power System Technology, 2020, 44(09): 3238-3246.
\item
  YANG Xiuyu, GUO Qi, LIU Xueyuan, et al. Source-Storage-Grid Joint
  Planning Method Considering Coupling Relationship of Wind Power
  Curtailment Events{[}J{]}. Automation of Electric Power Systems, 2023,
  47(02): 53-60.
\item
  PAN Xianxian, YU Mengze, SUI Yu, et al. Allocation Scheme of Carbon
  Emission Rights for Power Industry Considering Multiple Correlated
  Factors{[}J{]}. Automation of Electric Power Systems, 2020,
  44(1):35-42.
\end{enumerate}



\textbf{APPENDIX A}

(1)Peak shaving is insufficient to abandon wind

Assuming that the transmission capacity of the system is sufficient and
there is no transmission congestion problem, the wind curtailment event
caused by the insufficient peak regulation of the system is the wind
curtailment caused by the insufficient peak regulation of the system.
The expression is :

A1

In the formula, \emph{P} \textsubscript{LG-\emph{i}} (\emph{t} ) is the
abandoned wind power caused by insufficient peak regulation at
time\emph{t} in the scheduling day \emph{i} ;\emph{P}
\textsubscript{W-\emph{i}} (\emph{t} )is the wind power at time\emph{t}
in scheduling day \emph{i} ;\emph{P} \textsubscript{FR-\emph{i}}
(\emph{t} ) is the acceptable wind power of the system at time \emph{t}
in the scheduling day \emph{i} .

(2)Transmission congestion wind curtailment

It is assumed that the system has sufficient flexibility, no peak
regulation and insufficient wind curtailment. The wind curtailment event
caused by the delay of wind power transmission due to the lag of power
grid construction is peak regulation and insufficient wind curtailment.
The expression is as follows :

A2

In the formula, \emph{P} \textsubscript{LT-\emph{i}} (\emph{t} ) is the
curtailed wind power caused by transmission congestion at time \emph{t}
in scheduling day \emph{i} ;\emph{P} \textsubscript{W-\emph{i}}
(\emph{t} ) is the wind power at time\emph{t} in scheduling day \emph{i}
; \emph{P} \textsubscript{L} is the maximum transmission capacity of
wind power grid-connected point.

(3)Total abandoned wind after coupling

The total wind curtailment of the system can be obtained by coupling the
above-mentioned peak-shaving insufficient wind curtailment event with
the transmission congestion wind curtailment event. The union of the two
wind curtailment events is taken, and the calculation formula is as
follows :

A3

In the formula, \emph{P} \textsubscript{LW-\emph{i}} (\emph{t} )is the
total abandoned wind power at time \emph{t} in scheduling day \emph{i} .

The total abandoned wind formula ( A4 ) of the comprehensive formula (
A1 ) and the formula ( A2 ) system can be expressed as follows :

A4

\begin{CJK}{UTF8}{gbsn}\textbf{FIGURE A1　 Generation of wind curtailment due to insufficient
peak shaving and transmission congestion}\end{CJK}\selectlanguage{english}

\begin{CJK}{UTF8}{gbsn}\textbf{FIGURE A2　Coupling leads to total abandoning wind}\end{CJK}\selectlanguage{english}

\begin{CJK}{UTF8}{gbsn}\textbf{FIGURE A3　Detailed explanation of steps 1 and 2 in the model
solving flowchart}\end{CJK}\selectlanguage{english}

\textbf{FIGURE A4 1-5 node load and 6 node wind power data}

\selectlanguage{english}
\FloatBarrier
\end{CJK}\end{document}

