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Wind and solar (photovoltaic) power generations have rapidly evolved over the recent decades. Efficient and reliable planning of power system with significant penetration of these resources brings challenges due to their fluctuating and uncertain characteristics. In this paper, incorporation of both PV and wind units in the unit commitment of power system is investigated and a risk-constrained solution to this problem is presented. Considering the contribution of PV and wind units, the aim is to determine the start-up/shut-down status as well as the amount of generating power for all thermal units at minimum operating cost during the scheduling horizon, subject to the system and unit operational constraints. Using the probabilistic method of confidence interval, the uncertainties associated with wind and PV generation are modeled by analyzing the error in the forecasted wind speed and solar irradiation data. Differential evolution algorithm is proposed to solve the two-stage mixed-integer nonlinear optimization problem. Numerical results indicate that with indeterminate information about the wind and PV generation, a reliable day-ahead scheduling of other units is achieved by considering the estimated dependable generation of PV and wind units.

Nowadays, researches and applications of renewable energy sources, such as solar and wind is growing rapidly. Technological and economical progress of efficient and reliable wind turbines and photovoltaic (PV) panels as well as the concerns about environmental issues has contributed to large penetration of wind and solar energy in the power system. The exploitation level of wind energy in several countries in Europe has been reported to be up to 20% of the total annual demand [

One of the most prominent issues regarding power system operation is optimal scheduling of the units or the unit commitment (UC) problem. The problem is referred to as a nonlinear, nonconvex, large-scale, mixed integer, and combinatorial problem [

The literature on the UC problem is vast. Various solution methods including both classic and heuristic methods have so far been investigated and reported [

Some studies have focused on the integration of wind power into the unit commitment problem. In [

In the remainder of this paper, we present a simple method based on the probabilistic confidence interval accompanied with the differential evolution algorithm to form a risk-constrained solution to the unit commitment incorporating the uncertainties of PV and wind turbine generation (WTG) in power system. The effectiveness of the method is illustrated by application results to a test system.

The aim of solving the UC problem is to determine when to start up and shut down thermal units so that the total operating cost is minimized during the scheduling horizon, while the system and the generator constraints are satisfied. The generation costs of PV and WTG from the public utility are the cheapest because they need no fuel. Accordingly, the fuel cost is the significant component of the total operation cost, normally modeled by a quadratic input/output curve, written as

The constraints in the optimization process are explained as follows.

the unit initial operation status (must run, fixed power, unavailable/available);

the rated range of generation capacity:

ramp up/down rates:

the minimum up/down time limits of the units.

This constraint represents the minimum time for which a unit must remain on/off before it can be shut down or restarted, respectively:

As mentioned before, the scheduling of power system in the presence of PV and WTG units requires estimation of their available power over the scheduling period. Nevertheless, even the most precise prediction methods reveal errors compared to actual data. From the viewpoint of secure operation scheduling of power system, the important factor is to confine the generation risks and uncertainties to a definite level and ensure a level of confidence about the intermittent power. The maximum power at risk will be calculated based on the desired level of confidence (LC) defined by the operator. The risk constraint is written as follows:

the system hourly power balance:

the spinning reserve (10-min) requirements;

The overall fitness function is written as:

The day-ahead prediction is generally used for power plant scheduling and electricity trading [

The MLP network is trained using levenberg-marquardt technique which is fast for practical problems compared with other back-propagation algorithms such as gradient decent. Two independent networks are trained for solar and wind power prediction. The appropriate number of hidden neurons of each network determined using a forward heuristic simulation [

(a) Actual and estimated wind power. (b) Distribution of wind power forecast error from the applied NN model.

(a) Actual and estimated solar power. (b) Distribution of solar power forecast error from the applied NN model.

Models that consider the generation from wind and solar units completely deterministic ignore the additional problems that forecast uncertainty embeds in the system, while those that do not include meteorological forecasts may overvalue the costs. Because of the stochastic nature of the renewable, particularly wind power, accurate forecast is very difficult. Hence, the effort is made to minimize the effects of forecast errors and obtain a reliable data about the renewable power to be applied to the UC.

In order to model the uncertainty of the renewable power forecast, the dependable generation should be calculated and considered in the scheduling decisions. The forecast error of wind and solar power is likely normally distributed especially for a long-term operation [

The minimum error value (

Computation of the confidence interval using the forecast error PDF.

Differential evolution algorithm, introduced by Price et al. [

A mutant vector for each target vector (

The crossover operator generates a new vector, called trial vector. The trial vector takes the elements of the target vector (

Each individual of the new population is compared to the corresponding individual of the previous population, and the best of them is selected as a member of the population in the next generation (elitism). The resultant individuals

Flowchart of DE Algorithm.

Each individual vector in DE consists of a sequence of integers representing on/off status of generation units in the operating cycles during the planning period. Therefore, each solution is a vector of

The minimum up- and down-time constraints are satisfied with no need to penalty functions, as described in [

The case study is implemented on conventional 10-unit test system for the UC. The data for load and units of this system are presented in Tables

Load demand for 24 hours.

Hour [h] | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
---|---|---|---|---|---|---|---|---|---|---|---|---|

Demand [MW] | 700 | 750 | 850 | 950 | 1000 | 1100 | 1150 | 1200 | 1300 | 1400 | 1450 | 1500 |

Hour [h] | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |

Demand [MW] | 1400 | 1300 | 1200 | 1050 | 1000 | 1100 | 1200 | 1400 | 1300 | 1100 | 900 | 800 |

Operator data for ten thermal units in the system.

Unit 1 | Unit 2 | Unit 3 | Unit 4 | Unit 5 | Unit 6 | Unit 7 | Unit 8 | Unit 9 | Unit 10 | |
---|---|---|---|---|---|---|---|---|---|---|

455 | 455 | 130 | 130 | 162 | 80 | 85 | 55 | 55 | 55 | |

150 | 150 | 20 | 20 | 25 | 20 | 25 | 10 | 10 | 10 | |

_{i} | 1000 | 970 | 700 | 680 | 450 | 370 | 480 | 660 | 665 | 670 |

_{i} | 16.19 | 17.26 | 16.60 | 16.50 | 19.70 | 22.26 | 27.74 | 25.92 | 27.27 | 27.79 |

_{i} | 0.00048 | 0.00031 | 0.002 | 0.00211 | 0.00398 | 0.00712 | 0.00079 | 0.00413 | 0.00222 | 0.00173 |

MU_{i} | 8 | 8 | 5 | 5 | 6 | 3 | 3 | 1 | 1 | 1 |

MD_{i} | 8 | 8 | 5 | 5 | 6 | 3 | 3 | 1 | 1 | 1 |

HS_{i} | 4500 | 5000 | 550 | 560 | 900 | 170 | 260 | 30 | 30 | 30 |

CS_{i} | 9000 | 10000 | 1100 | 1120 | 1800 | 340 | 520 | 60 | 60 | 60 |

CSH_{i} | 5 | 5 | 4 | 4 | 4 | 2 | 2 | 0 | 0 | 0 |

Init. state | 8 | 8 | −5 | −5 | −6 | −3 | −3 | −1 | −1 | −1 |

Unit schedule in 24 hours and operation costs.

Power generation of units (MW) | Generation cost ($) | Start up cost ($) | ||||||||||||

Hour | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | ||

1 | 403.83 | 150 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 146.164 | 0 | 11182.36 | 0 |

2 | 455 | 164.484 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 130.515 | 0 | 12283.21 | 0 |

3 | 455 | 246.849 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 148.150 | 0 | 13715.33 | 0 |

4 | 455 | 335.784 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 159.215 | 0 | 15266.41 | 0 |

5 | 455 | 392.241 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 152.758 | 0 | 16253.61 | 0 |

6 | 455 | 377.552 | 130 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 137.447 | 0 | 18888.36 | 1100 |

7 | 455 | 421.606 | 130 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 143.393 | 0 | 19659.66 | 0 |

8 | 455 | 451.134 | 130 | 0 | 0 | 20 | 0 | 0 | 0 | 0 | 140.825 | 3.04 | 20995.35 | 340 |

9 | 455 | 455 | 130 | 0 | 0 | 80 | 0 | 12.437 | 0 | 0 | 150.843 | 16.72 | 23424.47 | 60 |

10 | 455 | 455 | 130 | 130 | 0 | 65.287 | 0 | 0 | 0 | 0 | 138.672 | 26.04 | 24959.4 | 1120 |

11 | 455 | 455 | 130 | 130 | 0 | 74.301 | 25 | 0 | 0 | 10 | 137.778 | 32.92 | 27291.08 | 580 |

12 | 455 | 455 | 130 | 130 | 0 | 80 | 54.857 | 0 | 0 | 0 | 157.063 | 38.08 | 27306.24 | 0 |

13 | 455 | 455 | 130 | 130 | 0 | 0 | 26.978 | 0 | 0 | 10 | 153.581 | 39.44 | 25282.8 | 60 |

14 | 455 | 408.662 | 130 | 130 | 0 | 0 | 0 | 0 | 0 | 0 | 139.257 | 37.08 | 22293.57 | 0 |

15 | 455 | 453.295 | 0 | 130 | 0 | 0 | 0 | 10 | 0 | 0 | 120.384 | 31.32 | 21103.68 | 60 |

16 | 455 | 313.709 | 0 | 130 | 0 | 0 | 0 | 0 | 0 | 0 | 128.330 | 22.96 | 17741.61 | 0 |

17 | 455 | 261.078 | 0 | 130 | 0 | 0 | 0 | 0 | 0 | 0 | 141.441 | 12.48 | 16823.82 | 0 |

18 | 455 | 358.129 | 0 | 130 | 0 | 0 | 0 | 0 | 0 | 0 | 156.230 | 0.64 | 18517.56 | 0 |

19 | 455 | 434.034 | 0 | 130 | 25 | 0 | 0 | 0 | 0 | 0 | 155.965 | 0 | 20791.31 | 1800 |

20 | 455 | 455 | 130 | 130 | 74.0957 | 0 | 0 | 0 | 0 | 0 | 155.904 | 0 | 25037.3 | 1100 |

21 | 455 | 455 | 130 | 0 | 106.744 | 0 | 0 | 0 | 0 | 0 | 153.255 | 0 | 22843.32 | 0 |

22 | 455 | 330.949 | 130 | 0 | 25 | 0 | 0 | 0 | 0 | 0 | 159.050 | 0 | 19018.76 | 0 |

23 | 455 | 0 | 130 | 0 | 159.261 | 0 | 0 | 0 | 0 | 0 | 155.738 | 0 | 15046.02 | 0 |

24 | 455 | 0 | 130 | 0 | 58.1027 | 0 | 0 | 0 | 0 | 0 | 156.897 | 0 | 12965.68 | 0 |

Total | 468690 | 6620 |

To show the effectiveness of DE, GA [

Comparison of best result of DE with GA in thermal and renewable integrated systems.

Method | Total operation cost ($) | |

With renewable integration | Without renewable integration | |

GA | 509320 | 565825 |

DE | 475310 | 564735 |

The risk constraint of renewable power has been implemented considering the LC to be 90%. The forecast error distribution of wind and solar power was shown in Figures

Estimated renewable power and applied power into UC with 90% and 95% confidence level.

Ever increasing penetration of intermittent renewable generations into the existing power systems reveals new reliability and security issues to the power system planners and operators. In this paper, the impact of the uncertain nature of solar and wind power on planning and dispatch of the thermal power system is examined. A class of MLP is used to estimate the renewable generation level. Although deterministic approaches use a point forecast of the power output, the risk associated with wind and solar power is derived from the mismatch between the historical predicted data and the measured data. On this basis, the hourly dependable generation of solar and wind power is input to the UC problem to satisfy the reliability needs of the power system operator. The resultant risk constraint is considered to reach a compromise between system security and total operation cost. By this approach, the need to evaluate different stochastic scenarios for the wind and solar power in the optimization process is also eliminated and the computational burden is reduced. The risk-constrained UC problem is solved using differential evolution algorithm and the optimal day ahead scheduling of the dispatchable units is obtained. Simulation results indicate the effectiveness of the method for the integration of PV and wind power in the UC problem.

Minimum output power of

Maximum output power of

Minimum rated generation level of unit

Maximum rated generation capacity of unit

Output power of

The UC time step, equals 60 min

Ramp-down rate of unit

Ramp-up rate of unit

The period during which the

The period during which the

Maximum up-time limit of unit

Minimum down-time limit of unit

Operation status of unit

The confident level of power available from PV and wind units at hour

System load demand at hour

System reserve at hour

The fuel cost function coefficients

Cold start hour of unit

Hot start cost of unit

Cold start cost of unit

Start-up cost for unit

Shutdown cost for unit

Unit ramp function

The value at risk of the estimated

Mean value of the data forecast error

Standard deviation of the forecasted data.