2.1. Analysis of the Response of Car owners to Charging Fees.
Adjustment of charging fees can influence the charging behaviors of car owners. Thus, the charging power at each period changes. When implementing the policy of real-time charging fees, car owners will respond to the change of charging fees:
where
is the column vector of rate of change of charging power at each period,
.
is the column vector of rate of change of charging fees at each period,
.
is the elastic coefficient matrix between charging fees and charging power,
,
,
is the different period.
and
are the variation in charging power and the variation in charging fees at
period.
is the charging power at
period.
and
are the charging fees at
and
period.
By setting reasonable real-time charging fees at each time period, according to the known elastic coefficient matrix, the variation in charging power at each period can be obtained. Due to the charging fees, owners will not have their cars charged at the peak load times, thus, the charging load is transferred to other periods to prevent congestion happening in the distribution network.
2.2. Adjustment Strategy for Line Congestion
Operators, as market participants, need to check charging plans to avoid congestion in the distribution network. If the charging plans cause congestion in the network, operators will adjust charging fees to guide the charging behaviors of the car owners and solve congestion problem in distribution network.
The “line power needed to be cut” is defined as the basis of judging the degree of line congestion:
where
is the power needed to be cut of line
l at period
t,
is the upper limit of active power of line
l,
is the active power of line
l at period
t, and this can be represented by Equation (3):
where
,
are the voltage amplitude of node
and node
at period
t,
and
are the conductance and susceptance of line
and line
.
is the difference in voltage phase angle of node
and node
at period
t.
In the electric vehicle free charging mode, operators need to verify the charging plans of car owners. Through the power flow calculation, the power flow of each line at each time period can be obtained. Thus, the time period that the congestion occurs and the line number can be obtained.
To reflect the correlation between the charging power of charging stations at different nodes and power lines, the following definitions are given:
Let be the set of all charging station nodes in the specified area for any subset and its complement is . If there is a power line , its power flow is related to the charging power of the charging station at , and is not related to the charging power of the charging station at . In this paper, the line is the related line of all the charging stations at , and all the charging stations at are related to the power line .
A set of lines that meet the above definition is denoted as
. If a line in the set is congested at period t, congestion can be solved by reducing the charging power of the charging stations that are related to the line. In order to ensure that all lines in the set are not congested after the adjustment, the reduction of line’s power should be not less than the maximum value of the “line power needed to be cut” in the set, as shown in Equation (4):
where
is the reduction of charging power of charging station at node
at period
t (in this paper,
is considered to be negative). The active power loss in the line is ignored in this paper.
The charging power that needs to be cut in the congested period is transferred to other non-congested periods. After the transfer, in order to ensure that new congestion does not occur in the non-congested period, the margin of line power for congestion needs to be considered.
The “margin of line power for congestion” is defined as:
where
is the margin of line power for congestion of line
l at period
, which represents the maximum active power increase that line
l can bear without congestion.
In order to ensure all lines which are related to
do not have new congestion after adjustment, the transferred charging power should meet the following requirements as shown in Equation (6). The charging power is accepted by each charging station at
and in a non-congested period:
where
is the charging power increase of charging station at node
and non-congested period
.
The owners’ response to the adjustment in charging fees is taken into account by the operators. Operators formulate real-time charging fees for each charging station according to the charging power. The charging power needs to be adjusted at each period, as shown in Equation (7).
In the equation, there is a total of charging stations in the area. is the charging power of the charging station at node and period t before the implementation of the real-time charging fees policy. is the charging power variation of the charging station at node and period t before and after the implementation of the real-time charging fees policy. Depending on the line congestion state, when the charging station at node needs to cut the charging power at period t, is . When the charging station at node needs to accept the transferred charging power at period , is . is the charging fees of the charging station at node and period t before the implementation of the real-time charging fees policy. is the charging fees variation of charging station at node and period t before and after the implementation of the real-time charging fees policy. is the elastic coefficient matrix between charging fees and charging power.