Table 3 DRE uncertainty planning model characteristics

Chance constrained

[108]

Annual total costs; risk in REN

Chance constraints of power, voltage; correlations;

DRE investment

The probability that the constraint holds is not less than a certain confidence level, which can be set artificially

[120]

Power losses; voltage quality

Chance constraints of power, voltage; PV capacity and number

Two-stage

[111, 112]

First: DRE investment costs

Second: operation and maintenance costs

Power; DRE size; generation;

investment; expected energy not served (EENS)

The first stage: before the realization of random variables, independent of decision variables;

The second stage: the objective function is improved based on decision variables.

[113]

First: DRE investments costs

Second: Operation costs

Power; reliability;

the operation of DRE unit

[114]

First: installation costs

Second: power losses

Power; PV placement and size

Multi-stage

[115]

Different costs per stage

Power; generation; investment;

reliability; EENS; DRE penetration;

Two-stage expansion;

complex calculations

Distribute robust

[102]

DRE capacity meeting the risk level in the case of the worst probability distribution

Power; DRE output; the risk level δ

The model combines uncertainty planning and robust optimization, and considers the optimization under the worst distribution.

Multi-objective

[99]

DRE costs and profit; technical issues; pollutant gas emissions

Power; critical transmitted power; DRE capacity; DRE cost and investment

More than two conflicting targets, and generally turn them into single target through weighting method to solve.

[100]

Restore the critical loads; EENS

Power; DRE capacity and location

[103]

Power losses; operating costs;

voltage quality

Power; DRE capacity

[109]

Operational risk; costs and profit

Power; DRE power; reverse power flow

[116]

Reliable power supply; costs and profit

Power; DRE power; load shed

[150]

Power losses; voltage stability

Power; DRE size and capacity

Bi-level

[104, 105]

Upper: Annual total costs

Lower: Power losses

Upper: Power; capacities of devices

Lower: Power; switching number of capacitor bank; regulation ranges of devices

The upper and lower planning have some independent decision variables to optimize their respective objective functions, and they interact with each other. Generally, the lower level makes decisions on the basis of the upper level.

[107]

Upper: Annual total costs; voltage quality

Lower: Annual DRE costs and generation; power losses; voltage quality

Power; DRE capacity