3.2. Objective Function
The objective function is to measure and maximize the net income brought by grid-connected DG, considering the income items and investment items of DG, instead of the conventional simple minimization of indicators, like network loss, costs, etc. This is conducive in terms of not only quantifying the economic benefits, but also to focus on the impacts of one or several indicators on DG planning, so that all parties are able to make their own decisions on the planning scheme with their interested indicators. The involved income items include loss reduction, delaying the upgrade of lines, environmental protection, saving fuels, electricity trading and subsidies; and the investment item is the fixed investment and maintenance of DG.
(1) Loss reduction.
In Equation (3), CLoss is the cumulative income of loss reduction throughout the year; where c1 is the price of the lost electricity; NS is the number of typical daily load sequences; dk is the number of daily load sequences within typical daily load sequence k; NT is the number of the time-steps divided on the typical daily load sequence; ti is the duration of period i, NL is the number of branches in the distribution network; Ikil and I’kil are the electric current of branch l in period i on typical daily load sequence k before and after the connection of DG, respectively; and Rl is the resistance of branch l.
(2) Delaying the upgrade of lines.
In Equation (4), CUp is the income coming from delaying the upgrade of lines; where ei is a 0–1 variable; r is the annual interest rate; n1i and n2i are the number of years from the start of line i to the upgrade without and with DG, respectively; and CLi is the fixed investment of line i.
(3) Environmental protection. In general, the pollutants of traditional coal-fired power plants mainly include SO
2, NO
x, CO
2, CO, total suspended particulate (TSP), fly ash, slag,
etc. The development and utilization of DG can effectively reduce the emissions of these pollutants, so that the environment can be improved to a certain extent. The costs of environmental values caused by these pollutants from the production of each unit of electricity can be calculated using the data provided in [
26].
Table 1 shows the calculation results of traditional coal-fired power plants and some common DG.
Table 1.
Costs of environmental values of various pollutants (Chinese Yuan (CNY)/MWh).
Table 1.
Costs of environmental values of various pollutants (Chinese Yuan (CNY)/MWh).
Power generation methods | SO2 | NOx | CO2 | CO | TSP | Fly ash | Slag |
---|
Coal-fired power | 41.47 | 23.04 | 27.42 | 0.09 | 0.32 | 47.52 | 1.08 |
Wind power | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Photovoltaic power | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
Gas turbine | 0.01 | 9.92 | 17.69 | 0 | 0.10 | 0 | 0 |
Fuel cell | 0.01 | 7.75 | 13.82 | 0 | 0.08 | 0 | 0 |
The environmental benefits of DG can be expressed as follows:
where
CEnv is the income coming from environmental production;
ND is the number of grid-connected DG generators;
Qa is the annual power generation of the
a-th DG generator;
NP is the number of the types of pollutants;
CFPi and
CDPi are the cost of environmental values caused by pollutant
i from traditional coal-fired power plants and DG, respectively; and
Pakj is the active power in period
j on typical daily load sequence
k of the
a-th DG generator.
If only the interests of the DG owners are considered, pollution fines should be applied by the market regulator. In this case, the benefits of environmental values do not belong to the owner of DG. Equation (5) can be rewritten as:
where
DPi is the fine of pollutant
i.
(4) Saving fuels.
In Equation (8), CFuel is the income coming from saving fuels; where CF is the average cost of the fuels consumed by traditional coal-fired power plants per unit electricity produced; CDa is the average cost of the fuels consumed by the a-th DG generator when a unit of electricity is produced.
Similarly, if only the interests of the DG owners are considered, Equation (8) should be rewritten as:
(5) Electricity trading and subsidies. This income item exists only when only the interests of the DG owners are considered; otherwise, it does not exist.
where
CSasb is the income obtained by the owner of DG coming from electricity trading and subsidies;
CBuy is the purchase price of the electricity;
CSal is the sell price of the electricity;
CSub is the subsidy price of the electricity; and α and β are, respectively, the proportion of the electric quantity to buy and that to sell.
(6) The fixed investment and maintenance of DG.
where
CDG is the fixed investment and maintenance cost of DG converted to each year;
nDi is the economic life of the
i-th DG generator;
VDi is the fixed investment cost of the
i-th DG generator; and
WDi is the maintenance cost of the
i-th DG generator each year.
Based on the above analysis, the objective function in this paper can be expressed as:
As can be seen, when λ1 = λ2 = λ3 = λ4 = λ6 = 1 and λ5 = 0, Equation (13) is the maximum net income brought by DG. In addition, when different interest groups are making decisions on the planning scheme, they can adjust the corresponding weights according to their interested indicators so that their own benefits can be maximized.
3.3. Constraint Conditions
Constraints for the proposed planning model are listed as below:
where
PGi,
PDi and
PLi are, respectively, the active power of the generator, DG and load at node
i,
QGi,
QDi and
QLi are, respectively, the reactive power of the generator, DG and load at node
i,
Gij and
Bij are, respectively, the conductance and susceptance of branch
ij,
θij is the power angle between node
i and node
j,
,
and
are, respectively, the voltage and its upper and lower limits at node
i,
,
and
are, respectively, the active power and its upper and lower limits of the DG at node
i,
and
are, respectively, the upper and lower limits of the DG in the distribution network,
nL is the number of load points in the distribution network,
PDki is the active power of the DG whose type number is
k at node
i and
and
are, respectively, the upper and lower limits of the active power of the DG whose type number is
k in the distribution network.