# Unit Commitment Considering Electric Vehicles and Renewable Energy Integration—A CMAES Approach

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## Abstract

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## 1. Introduction

- A new discrete mapping operator is designed and compared with eight popular mapping operators. This new operator allows the CMAES to become applicable to solving discrete optimization problems;
- The discrete CMAES method is applied to large-scale UC problems for the first time;
- Two different test systems consisting of 10- and 54-unit power networks are tested in order to evaluate the searching capability of the proposed algorithm in test cases of different scales, achieving operating costs reduction of 1.92% and 1.13%, respectively;
- The elite reservation strategy and restart strategy are adopted to strengthen the global search capability of the algorithm and achieve population adaptation.

## 2. Problem Formulation

#### 2.1. Unit Commitment Problem with Electric Vehicles

#### Charging and Discharge Mode of Electric Vehicle

- Objective functionThe Unit Commitment with Electric Vehicles (UCEV) problem model is adapted from the basic UC problem model. Its objective function is similar to that of the fundamental UC problem, but the constraints are different. The objective function of the UCEV problem is given in Equation (1):$$min{F}^{UCEV}=\sum _{t=1}^{T}\sum _{i=1}^{N}\left[{F}_{FC,i}+{F}_{SC,i}\left(1-{U}_{i}(t-1)\right)\right]{U}_{i}\left(t\right)$$When the objective function considers emissions, Equation (1) can be rewritten as follows:$$min{F}^{UCEV}=\sum _{t=1}^{T}\sum _{i=1}^{N}\left[{\phi}_{c}\left({F}_{FC,i}+{F}_{SC,i}\left(1-{U}_{i}(t-1)\right)\right)+{\phi}_{e}{F}_{em,i}\right]{U}_{i}\left(t\right)$$In this objective function, the cost of the electric vehicle is neglected. The model uses two quadratic cost functions. In addition to the fuel cost of the basic UC problem, the emission cost is also considered. In Equation (3), ${F}_{em,i}$ is the emission target, and its quadratic function unit power generation is as follows:$${F}_{em,i}={\alpha}_{i}+{\beta}_{i}{P}_{u,i}\left(t\right)+{\gamma}_{i}\left({P}_{u,i}\left(t\right)\right)$$
- Units ConstraintsThe constraint conditions have also significantly changed, mainly in terms of the power balance and spinning reserve constraints. Some constraints of the electric vehicle itself, the load capacity constraint of the electric vehicle, the balance constraint of the electric vehicle, and the battery capacity balance constraint, are also added.The uncertain power output from the EVs and the output from the thermal power units must meet the load demand, as defined below:$$\sum _{i=1}^{N}{P}_{u,i}\left(t\right){U}_{i}\left(t\right)+{P}_{c}\left(t\right)={P}_{d}\left(t\right)$$The power output from the electric vehicles can be calculated as follows:$${P}_{c}\left(t\right)={N}_{EV}\left(t\right)\times P{V}_{av}\times {\eta}_{EV}\times \delta $$For reliable operation, the spinning reserve needs to be constrained as follows:$$\sum _{i=1}^{N}{P}_{u,i}^{max}{U}_{i}\left(t\right)+{P}_{c,max}\left(t\right)>=Pd\left(t\right)\times (1+SR)$$The maximum power output of the electric vehicle at time t. ${P}_{c,max}\left(t\right)$ can be obtained by the following equation:$${P}_{c,max}\left(t\right)={N}_{EV}\left(t\right)\times P{V}_{max}\times {\eta}_{EV}\times \delta $$The $P{V}_{max}$ represents the maximum battery capacity of the electric vehicle;
- Electric vehicle constraintsLoad capacity limitation of electric vehicles The power supply connected to the grid is limited by the capacity of the interface in the parking base area, as given below:$${N}_{EV}^{min}\left(t\right)\le {N}_{EV}\left(t\right)\le {N}_{EV}^{max}\left(t\right)$$Balance constraint of electric vehicle. The number of electric vehicles registered on the grid within a day is fixed, and all-electric vehicles connected to the grid must meet the following constraints:$$\sum _{t=1}^{T}{N}_{EV}\left(t\right)={N}_{EV}^{\mathrm{total}}$$Battery power balance. For the V2G/G2V mode of the electric vehicles, the charging capacity and discharge capacity of the battery must be limited by the balance of battery power, which can be expressed as follows:$$\sum _{{t}_{1}=1}^{{T}_{1}}{N}_{EV}^{G2V}\left(t\right)=\sum _{{t}_{2}=1}^{{T}_{2}}{N}_{EV}^{V2G}\left(t\right)$$

#### 2.2. Unit Commitment Problem with Electric Vehicles and Renewable Energy

#### 2.2.1. Mathematical Model of UC Problem with Electric Vehicles and Renewable Energy

- Objective functionThe model for the Unit Commitment with Electric Vehicles and Renewable Energy (UCEVR) problem is a more complex model based on UCEV. The UCEVR objective function is exactly the same as the UCEV objective function. These renewable energy sources do not affect the change in the model objective function, as shown below:$$min{F}^{UCEVR}=\sum _{i=1}^{T}\sum _{i=1}^{N}\left[{\phi}_{c}\left({F}_{fc,i}+{F}_{sc,i}\left(1-{U}_{i}(t-1)\right)\right)+{\phi}_{e}{F}_{em.i}\right]{U}_{i}^{\left(t\right)}$$
- Units ConstraintsThe UCEVR model is based on the UCEV model. For the constraints, the original power-balance conditions and spinning reserve constraints are changed. Equations (12) and (13) have changed as follows:$$\sum _{i=1}^{N}{P}_{u,i}\left(t\right){U}_{i}\left(t\right)+{P}_{w}\left(t\right)+{P}_{s}\left(t\right)+{P}_{c}\left(t\right)={P}_{d}\left(t\right)$$$$\sum _{i=1}^{N}{P}_{u,i}^{max}{U}_{i}\left(t\right)+{\eta}_{R}\left({P}_{w}\left(t\right)+{P}_{s}\left(t\right)\right)+{P}_{c,max}\left(t\right)>=Pd\left(t\right).(1+SR)$$
- Renewable energy constraintsRenewable energy has the feature of being unpredictable. Hence, we will only use a portion of the predicted power of renewable energy for power system scheduling. Especially when it comes to the constraints of spinning reserves, we need to consider the prediction error of renewable energy.

#### 2.2.2. Prediction of Renewable Energy

## 3. Binary Covariance Matrix Adaptation Evolution Strategy

#### 3.1. Covariance Matrix Adaptation Evolution Strategy

#### 3.2. Binary Adaptive Matrix Covariance Evolution Strategy

#### 3.2.1. Variable Discretization

#### 3.2.2. The Main Steps of the CMAES Algorithm

- Sampling.In the CMA evolution strategy, a set of new search points with algebras of $g=0,1,2,\dots $ are generated by sampling the multivariate normal distribution. The basic formula of sampling is:$${x}_{k}^{(g+1)}\sim {m}^{\left(g\right)}+{\sigma}^{\left(g\right)}N\left(0,{C}^{\left(g\right)}\right)\phantom{\rule{4.pt}{0ex}}\mathrm{for}\phantom{\rule{4.pt}{0ex}}k=1,\dots ,\lambda $$$N(0,{C}^{\left(g\right)})$ is a multivariate normal distribution with zero mean and covariance matrix ${C}^{g}$, ${x}_{k}^{(g+1)}\in {R}^{n}$ is the kth offspring (individual, search point) from the $g+1$ generation, ${m}^{g}$ is the average of the gth generation search distribution, and ${\sigma}^{\left(g\right)}\in {R}_{+}$ is the overall standard deviation in the gth generation, namely step size;
- Selection and recombination.The new mean ${m}^{g+1}$ is updated by the weighted mean of the sample data ${x}_{1}^{(g+1)},\dots ,{x}_{\lambda}^{(g+1)}$:$${m}^{(g+1)}=\sum _{i=1}^{\mu}{\omega}_{i}{x}_{i:\lambda}^{(g+1)}$$$$\sum _{i=1}^{\mu}{\omega}_{i}=1,\phantom{\rule{1.em}{0ex}}{\omega}_{1}\ge {\omega}_{2}\ge \dots \ge {\omega}_{\mu}>0$$
- Update of covariance matrix and step size.The update formula of covariance matrix is$${C}^{(g+1)}=\left(1-{c}_{1}-{c}_{\mu}\right){C}^{\left(g\right)}+{c}_{1}{p}_{c}^{(g+1)}{\left({p}_{c}^{(g+1)}\right)}^{T}+{c}_{\mu}\sum _{i=1}^{\mu}{\omega}_{i}{y}_{i:\lambda}^{(g+1)}{\left({y}_{i:\lambda}^{(g+1)}\right)}^{T}$$The update formula for the step size is$${\sigma}^{\mathrm{g}+1}={\sigma}^{g}+exp\left(\frac{{c}_{\sigma}}{{d}_{\sigma}}\left(\frac{\u2225{p}_{\sigma}^{g+1}\u2225}{E\parallel N(0,I)\parallel}\right)\right)$$

#### 3.2.3. Elite Retention Strategy

#### 3.2.4. Restart Strategy

- If the optimal function value of the last $10+[30n/\lambda ]$ generations is 0 or the absolute difference between the latest function value and the previous function value is less than the given number 10–12;
- If the standard deviation of the normal distribution is less than in all coordinates and ${p}_{\sigma}$ (the evolutionary path) is less than ${10}^{-12}$ in all components;
- If a standard deviation of 0.1 is added in the direction of the principal axis of ${C}^{\left(g\right)}$, the vector ${x}_{k}^{\left(g\right)}$ does not change;
- If a standard deviation of 0.2 is added to each coordinate, ${x}_{k}^{\left(g\right)}$ does not change;
- If the condition number of the covariance matrix exceeds ${10}^{14}$.

## 4. Implementation of BCMAES in the UC Problem

#### 4.1. Algorithm Procedure

#### 4.2. Encoding of the Solution

- Basic UC problem$$pop=\left[{U}_{11},{U}_{12},\dots ,{U}_{1T},\dots ,{U}_{NT}\right]$$
- UCEV problem$$pop=\left[{U}_{11},{U}_{12},\dots ,{U}_{1T},\dots {U}_{NT},{P}_{c1},\dots ,{P}_{cT}\right]$$
- UCEVR problem$$pop=\left[{U}_{11},{U}_{12},\dots ,{U}_{1T},\dots {U}_{NT},{P}_{c1},\dots ,{P}_{cT}\right]$$

#### 4.3. Constraint Processing

#### 4.3.1. Constraint Handling

- Minimum start-stop time constraint of unitBecause the state of each unit at the characteristic time point in a day is affected by the state of the previous time point or even the state of the unit at several time points, they affect each other and couple with each other. Therefore, it is necessary to adjust the unit’s start-stop state to meet its minimum start-stop constraint;
- Unit spinning reserve constraintAfter the minimum start-stop constraint of the unit is completed, the spinning reserve constraint of the unit should be carried out to ensure safe and stable operation. The core steps of adjusting the spinning reserve constraint can be divided into the following:
- Minimize the number of boot constraintsThe system may have redundant startup units when the spinning reserve constraint is adjusted. Therefore, it is necessary to minimize the operation of redundant units and reduce the operation costs of units while maintaining the stable operation of the power system;
- Power-balance constraintsWhen the above constraints are adjusted, the unit state is also determined. At this time, it is necessary to allocate the unit output power of each period to meet the power-balance constraint, which is the famous economic load dispatch problem. There are many mature and effective ways to solve this problem. The BCMAES algorithm adopts the traditional mathematical method, the Lambda iteration method, to solve this problem, which is convenient and fast.

#### 4.3.2. Constraint Handling in Electric Vehicle Discharge Mode

- Electric vehicle number constraint.When the BCMAES algorithm is randomly initialized, ${N}_{EV}\left(t\right)$, the balance constraint may not be met. The number of electric vehicles at each moment can be considered a random adjustment process. The number of electric vehicles at one moment is randomly selected. Then the sum of the number of electric vehicles at all moments is adjusted, and the number difference is calculated. The number of electric vehicles is repeated to meet the number of electric vehicles needed to meet the number constraint of electric vehicles;
- Electric vehicle load power constraints.The output power of electric vehicles in the model needs to meet certain restrictions. In particular, in the process of adjusting to meet the number constraints of electric vehicles, this process may generate new electric vehicle output that does not meet the load power constraints of electric vehicles. As with the general boundary treatment method, the endpoint method is used here to obtain the boundary value of the variable that crosses the boundary;
- Power-balance constraint and spinning reserve constraint.The V2G mode of electric vehicles is mainly based on the basic UC problem model, which mainly increases the charging of electric vehicles. This violates the original power-balance constraint and spinning reserve constraint. The original power-balance constraint and spinning reserve constraint are changed as follows:$$\left\{\begin{array}{c}{\displaystyle \sum _{i=1}^{N}}{P}_{\mathrm{u},i}\left(t\right){U}_{i}\left(t\right)=Pd\left(t\right)\hfill \\ {\displaystyle \sum _{i=1}^{N}}{P}_{u,i}^{\mathrm{max}}>=Pd\left(t\right)\times (1+SR)\hfill \end{array}\to \left\{\begin{array}{c}{\displaystyle \sum _{i=1}^{N}}{P}_{\mathrm{u},i}\left(t\right){U}_{i}\left(t\right)+{P}_{c}\left(t\right)=Pd\left(t\right)\hfill \\ {\displaystyle \sum _{i=1}^{N}}{P}_{u,i}^{max}+{P}_{c,max}\left(t\right)>=Pd\left(t\right)\times (1+SR)\hfill \end{array}\right.\right.$$

#### 4.3.3. Constraint Handling in Charging and Discharging Mode of the Electric Vehicle

#### 4.3.4. Renewable Energy Constraint Handling

## 5. Analysis of Simulation Results

#### 5.1. Ten Fundamental UC Problems

#### 5.2. Basic UC Problem of High-Dimensional Unit

#### 5.3. IEEE 118-Bus System with 54 Units Problems

Type | Minimum Operating Costs (USD) | ||||
---|---|---|---|---|---|

20 Units | 40 Units | 60 Units | 80 Units | 100 Units | |

GA | 1,126,243 | 2,251,911 | 3,376,625 | 4,504,933 | 5,627,437 |

EP | 1,127,257 | 2,252,612 | 3,376,255 | 4,505,536 | 5,633,800 |

SA [28] | 1,126,251 | 2,250,063 | – | 4,498,076 | 5,617,876 |

BCGA | 1,130,291 | 2,256,590 | 3,382,913 | 4,511,438 | 5,637,930 |

FPGA [36] | 1,124,998 | 2,248,235 | 3,368,375 | 4,491,169 | 5,614,357 |

ICGA | 1,127,244 | 2,254,123 | 3,378,108 | 4,498,943 | 5,630,838 |

MRCGA [37] | 1,127,244 | 2,254,123 | 3,378,108 | 4,498,943 | 5,630,838 |

LR | 1,130,660 | 2,258,503 | 3,394,066 | 4,526,022 | 5,657,277 |

PSOLR | 1,128,072 | 2,251,116 | 3,376,407 | 4,496,717 | 5,623,607 |

QEA [38] | 1,123,607 | 2,245,557 | 3,366,676 | 4,488,470 | 5,609,550 |

IPSO [39] | 1,125,279 | 2,248,163 | 3,370,979 | 4,495,032 | 5,619,284 |

IBPSO [38] | 1,125,276 | 2,248,581 | 3,367,865 | 4,491,083 | 5,610,293 |

HS | 1,132,029 | 2,271,188 | 3,410,737 | 4,553,929 | 5,697,561 |

TLBO | 1,131,247 | 2,286,549 | 3,425,802 | 4,587,544 | 5,747,395 |

BPSO | 1,130,597 | 2,271,170 | 3,413,645 | 4,579,435 | 5,717,184 |

BGOA [40] | 1,120,470 | 2,240,277 | 3,356,574 | 4,475,407 | 5,596,414 |

ABFMO [41] | 1,131,551 | 2,265,867 | 3,397,162 | 4,531,605 | 5,660,087 |

LS-MFA [31] | 1,123,297 | 2,240,277 | 3,363,491 | 4,475,407 | 5,604,146 |

BSLPSO [26] | 1,124,389 | 2,246,837 | 3,367,349 | 4,491,179 | 5,611,494 |

BCMAES | 1,124,202 | 2,246,621 | 3,365,137 | 4,487,337 | 5,607,082 |

Methods | Total Costs/USD | FES |
---|---|---|

BB-IPM [35] | 1,643,750.0 | 40,000 |

PSO [42] | 1,635,395.3 | 40,000 |

GWO [42] | 1,643,852.1 | 40,000 |

HGWO-PSO [42] | 1,619,385.9 | 40,000 |

ABSSA [34] | 1,636,381.0 | 40,000 |

SDP | 1,645,445.0 | 40,000 |

ABC-LR | 1,644,269.7 | 40,000 |

BRCFF | 1,644,141.0 | 40,000 |

GA [43] | 1,644,336.8 | 40,000 |

ACS [43] | 1,643,968.3 | 40,000 |

HTACS [43] | 1,643,840.4 | 40,000 |

BCMAES | 1,624,873.60 | 40,000 |

#### 5.4. Unit Commitment Problem with Electric Vehicle Discharge (V2G)

#### 5.4.1. Unit Commitment Problem with Electric Vehicle Discharge (V2G) without Considering Emissions

#### 5.4.2. Unit Commitment Problem with Electric Vehicle Discharge (V2G) Also Considering Emissions

#### 5.5. Unit Commitment Problem with Electric Vehicle Charging and Discharging (V2G/G2V)

#### 5.5.1. Unit Commitment Problem with Electric Vehicle Charging and Discharging (V2G/G2V) without Considering Emissions

#### 5.5.2. Unit Commitment Problem with Electric Vehicle Charging and Discharging (V2G/G2V) Considering Emissions

#### 5.6. Unit Commitment Problem with Electric Vehicles and Renewable Energy

## 6. Conclusions

- The CMAES algorithm has been extended to the binary domain by introducing the signal function to map the variables;
- The elite and restart strategies have been introduced to strengthen the algorithm’s global search capability and realize its population adaptation;
- The proposed BCMAES algorithm has been tested on power systems with 10 and 54 units and the simulation results confirm its efficacy and robustness in comparison with several popular UC approaches, achieving more than a 1% operation cost reduction in most cases;
- With the proposed algorithm, the influence of renewable energy integration and EV grid connection modes on the whole system UC is analyzed. It is found that V2G and integration of renewable energy can significantly reduce both the operation costs and emissions by 5.57% and 13.71%, respectively.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**Schematic diagram of the unit commitment considering electric vehicles and renewable energy.

time (h) | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |

solar (MW) | 0 | 0 | 0 | 0 | 0 | 0 | 0.09 | 17.46 |

wind (MW) | 44 | 70.2 | 76 | 82 | 84 | 84 | 100 | 100 |

time (h) | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |

solar (MW) | 31.45 | 36.01 | 38.06 | 35.93 | 36.78 | 31.59 | 9.7 | 12.92 |

wind (MW) | 78 | 64 | 100 | 92 | 84 | 80 | 78 | 32 |

time (h) | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |

solar (MW) | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

wind (MW) | 4 | 8 | 10 | 5 | 6 | 56 | 82 | 52 |

Scenario | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |

possibility | 0.123 | 0.089 | 0.072 | 0.056 | 0.166 | 0.077 | 0.141 | 0.13 | 0.093 | 0.056 |

Binary Symmetric Particle Swarm Optimization Family | |
---|---|

Name | Transfer Function |

BCMAES1 | $T\left(x\right)=\frac{1}{1+{e}^{-2x}}$ |

BCMAES2 | $T\left(x\right)=\frac{1}{1+{e}^{-x}}$ a |

BCMAES3 | $T\left(x\right)=\frac{1}{1+{e}^{(-1/2x)}}$ |

BCMAES4 | $T\left(x\right)=\frac{1}{1+{e}^{(-1/3x)}}$ |

BCMAES5 | $T\left(x\right)=|erf\left(\frac{\sqrt{\pi}}{2}x\right)|=|\frac{\sqrt{2}}{\pi}{\int}_{0}^{(\sqrt{\pi}/2)x}{e}^{-{t}^{2}}dt|$ |

BCMAES6 | $T\left(x\right)=|tanh(x\left)\right|$ |

BCMAES7 | $T\left(x\right)=\left|\left(x\right)/\sqrt{1+{x}^{2}}\right|$ |

BCMAES8 | $T\left(x\right)=\left|\frac{2}{\pi}arctan\left(\frac{\pi}{2}x\right)\right|$ |

BCMAES9 | $T\left(x\right)=x<0$ |

20 units | 40 units | |||||

Min | Avg | Max | Min | Avg | Max | |

P1 | 1.123221 | 1.12388 | 1.124417 | 2.243555 | 2.245358 | 2.246763 |

P2 | 1.123977 | 1.124316 | 1.124769 | 2.245769 | 2.24592 | 2.246111 |

P3 | 1.123648 | 1.124027 | 1.124217 | 2.245177 | 2.246111 | 2.247369 |

P4 | 1.123206 | 1.123886 | 1.124233 | 2.245596 | 2.245699 | 2.24588 |

P5 | 1.126278 | 1.126411 | 1.126614 | 2.263263 | 2.263433 | 2.26362 |

P6 | 1.12635 | 1.126357 | 1.126371 | 2.262673 | 2.263645 | 2.264279 |

P7 | 1.126382 | 1.126395 | 1.126422 | 2.264021 | 2.264067 | 2.264091 |

P8 | 1.126309 | 1.126694 | 1.127319 | 2.265278 | 2.266509 | 2.268025 |

P9 | 1.123206 | 1.123933 | 1.124379 | 2.243815 | 2.244699 | 2.245697 |

60 units | 100 units | |||||

Min | Avg | Max | Min | Avg | Max | |

P1 | 3.364839 | 3.365072 | 3.365532 | 5.608112 | 5.612727 | 5.615718 |

P2 | 3.364664 | 3.365765 | 3.367682 | 5.608446 | 5.610708 | 5.61394 |

P3 | 3.364791 | 3.365063 | 3.365276 | 5.606325 | 5.610009 | 5.614433 |

P4 | 3.364981 | 3.365393 | 3.365878 | 5.615403 | 5.61664 | 5.617814 |

P5 | 3.384527 | 3.384724 | 3.384929 | 5.668662 | 5.669071 | 5.669827 |

P6 | 3.383945 | 3.384454 | 3.384881 | 5.668573 | 5.669215 | 5.670004 |

P7 | 3.386345 | 3.386472 | 3.386562 | 5.673508 | 5.674349 | 5.674773 |

P8 | 3.393635 | 3.395331 | 3.397049 | 5.698824 | 5.705164 | 5.710726 |

P9 | 3.363243 | 3.364866 | 3.366701 | 5.605761 | 5.611051 | 5.612635 |

Minimum Cost (USD) | Average Cost (USD) | Maximum Cost (USD) | Standard Deviation | |
---|---|---|---|---|

GA | 565,825 | - | 570,032 | - |

EP | 564,554 | - | 566,231 | - |

SA | 565,828 | 565,988 | 566,260 | - |

BCGA | 567,367 | - | - | - |

FPGA | 564,094 | 566,675 | 569,237 | - |

ICGA | 566,404 | - | - | - |

MRCGA | 564,244 | 564,467 | 565,756 | - |

LR | 565,825 | - | - | - |

PSOLR | 565,869 | - | 566,793 | - |

QEA | 563,938 | 564,672 | 563,969 | - |

IQEA | 563,977 | 563,977 | 563,977 | 0 |

IPSO | 563,954 | 564,162 | 564,579 | - |

IBPSO | 563,977 | 564,155 | 565,312 | 143 |

QBPSO | 563,977 | 563,977 | 563,977 | 0 |

ATHS | 563,938 | - | - | - |

HHS | 563,937 | 563,965 | 563,995 | - |

NBPSO | 563,937 | 563,962 | 563,977 | - |

BCSO | 563,937 | 563,937 | 563,937 | 0 |

HS | 568,685 | 569,029 | 569,296 | 175 |

TLBO | 566,779 | 567,017 | 567,173 | 258 |

BPSO | 563,975 | 564,129 | 564,618 | 274 |

BCMAES | 563,937 | 563,937 | 563,937 | 0 |

Time | Unit Output | Start-Up Cost/USD | |||||||||
---|---|---|---|---|---|---|---|---|---|---|---|

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

1 | 455 | 245 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

2 | 455 | 295 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

3 | 455 | 370 | 0 | 0 | 25 | 0 | 0 | 0 | 0 | 0 | 900 |

4 | 455 | 455 | 0 | 0 | 40 | 0 | 0 | 0 | 0 | 0 | 0 |

5 | 455 | 390 | 0 | 130 | 25 | 0 | 0 | 0 | 0 | 0 | 560 |

6 | 455 | 360 | 130 | 130 | 25 | 0 | 0 | 0 | 0 | 0 | 1100 |

7 | 455 | 410 | 130 | 130 | 25 | 0 | 0 | 0 | 0 | 0 | 0 |

8 | 455 | 455 | 130 | 130 | 30 | 0 | 0 | 0 | 0 | 0 | 0 |

9 | 455 | 455 | 130 | 130 | 85 | 20 | 25 | 0 | 0 | 0 | 860 |

10 | 455 | 455 | 130 | 130 | 162 | 33 | 25 | 10 | 0 | 0 | 60 |

11 | 455 | 455 | 130 | 130 | 162 | 73 | 25 | 10 | 0 | 0 | 60 |

12 | 455 | 455 | 130 | 130 | 162 | 80 | 25 | 43 | 10 | 10 | 60 |

13 | 455 | 455 | 130 | 130 | 162 | 33 | 25 | 10 | 0 | 0 | 0 |

14 | 455 | 455 | 130 | 130 | 85 | 20 | 25 | 0 | 0 | 0 | 0 |

15 | 455 | 455 | 130 | 130 | 30 | 0 | 0 | 0 | 0 | 0 | 0 |

16 | 455 | 310 | 130 | 130 | 25 | 0 | 0 | 0 | 0 | 0 | 0 |

17 | 455 | 260 | 130 | 130 | 25 | 0 | 0 | 0 | 0 | 0 | 0 |

18 | 455 | 360 | 130 | 130 | 25 | 0 | 0 | 0 | 0 | 0 | 0 |

19 | 455 | 455 | 130 | 130 | 30 | 0 | 0 | 0 | 0 | 0 | 0 |

20 | 455 | 455 | 130 | 130 | 162 | 33 | 25 | 10 | 0 | 0 | 490 |

21 | 455 | 455 | 130 | 130 | 85 | 20 | 25 | 0 | 0 | 0 | 0 |

22 | 455 | 455 | 0 | 0 | 145 | 20 | 25 | 0 | 0 | 0 | 0 |

23 | 455 | 420 | 0 | 0 | 0 | 20 | 0 | 0 | 0 | 0 | 0 |

24 | 455 | 345 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

Total cost: USD 563,937 |

Name | Value |
---|---|

The average battery capacity of electric vehicles, av PV (MW) | 0.015 |

The maximum battery capacity of an electric vehicle, max PV (MW) | 0.025 |

The minimum battery capacity of an electric vehicle, min PV (MW) | 0.01 |

The average percentage of batteries that need to be charged for electric vehicles | 50% |

Total efficiency, EV | 85% |

Hour | N min (t) | Hour | N min (t) | Hour | N min (t) | Hour | N min (t) |
---|---|---|---|---|---|---|---|

1 | 0 | 7 | 0 | 13 | 3400 | 19 | 0 |

2 | 0 | 8 | 0 | 14 | 1500 | 20 | 0 |

3 | 2000 | 9 | 1500 | 15 | 0 | 21 | 0 |

4 | 0 | 10 | 3400 | 16 | 0 | 22 | 0 |

5 | 2200 | 11 | 3400 | 17 | 0 | 23 | 0 |

6 | 0 | 12 | 3400 | 18 | 0 | 24 | 0 |

Algorithms | Without Emissions | With Emissions | ||||
---|---|---|---|---|---|---|

Function | Cost (USD) | Emissions (t) | Function | Cost (USD) | Emissions (t) | |

PSO [42] | 554,509 | 554,509 | - | 825,392 | 565,326 | 260,066 |

GA-LR [9] | 552,427 | 552,427 | - | - | - | - |

GA | 556,420 | 556,420 | - | 798,183 | 561,196 | 236,987 |

LR | 558,389 | 558,389 | - | 812,392 | 559,822 | 252,570 |

BCMAES | 551,784 | 551,784 | - | 760,670 | 581,335 | 179,335 |

Algorithms | Basic UC | V2G | ||||
---|---|---|---|---|---|---|

Minimum | Mean | Maximum | Minimum | Mean | Maximum | |

PSO [42] | 564,714 | 554,743 | 565,443 | 554,509 | 557,584 | 559,987 |

GA-LR [9] | 564,703 | - | - | 552,427 | 552,965 | 553,765 |

GA | 565,825 | - | 570,032 | 556,420 | 558,635 | 560,720 |

LR | 565,825 | - | - | 558,339 | 560,034 | 562,572 |

BCMAES | 563,937 | 563,937 | 563,937 | 551,784 | 552,277 | 552,745 |

**Table 13.**The comparison of the results of different algorithms on solving the UCEV problem in different modes.

Algorithms | V2G | V2G/G2V | ||||
---|---|---|---|---|---|---|

Minimum | Mean | Maximum | Minimum | Mean | Maximum | |

PSO [42] | 554,509 | 557,584 | 559,987 | - | - | - |

GA-LR [9] | 552,427 | 552,965 | 553,765 | 561,821 | 564,049 | 566,281 |

GA | 556,420 | 558,635 | 560,720 | 562,301 | 565,577 | 568,804 |

LR | 558,339 | 560,034 | 562,572 | 564,795 | 567,020 | 568,138 |

BCMAES | 551,784 | 552,277 | 552,745 | 558,790 | 559,190 | 559,845 |

Algorithms | Without Emission | Emission | ||||
---|---|---|---|---|---|---|

Function | Cost (USD) | Emission (t) | Function | Cost (USD) | Emission (t) | |

PSO [42] | - | - | - | - | - | - |

GA-LR [9] | 561,821 | 561,821 | - | - | - | - |

GA | 563,361 | 563,361 | - | 806,485 | 566,939 | 239,546 |

LR | 564,795 | 564,795 | - | 801,484 | 570,265 | 231,219 |

BCMAES | 558,790 | 558,790 | - | 769,187 | 585,144 | 184,043 |

Algorithms | Without Emission | Emission | ||||
---|---|---|---|---|---|---|

Function | Cost (USD) | Emission (t) | Function | Cost (USD) | Emission (t) | |

PSO [42] | 825,392 | 565,326 | 260,066 | - | - | - |

GA-LR [9] | - | - | - | - | - | - |

GA | 798,183 | 561,196 | 236,987 | 806,485 | 566,939 | 239,546 |

LR | 812,392 | 559,822 | 252,570 | 801,484 | 570,265 | 231,219 |

BCMAES | 759,346 | 589,709 | 169,637 | 769,187 | 585,144 | 184,043 |

Model | Scene | Cost | Emission | Index 1 | Index 2 | Sce |
---|---|---|---|---|---|---|

discharge | 1 | 543,942 | 150,849 | 0.09996 | 0.09902 | 0.6181 |

2 | 542,971 | 150,901 | 0.09983 | 0.10015 | 0.445 | |

3 | 540,552 | 154,201 | 0.09996 | 0.1017 | 0.357 | |

4 | 542,525 | 151,427 | 0.09984 | 0.09824 | 0.2802 | |

5 | 542,633 | 153,297 | 0.10012 | 0.09932 | 0.8298 | |

6 | 545,941 | 150,218 | 0.10016 | 0.09967 | 0.3828 | |

7 | 540,347 | 154,295 | 0.09994 | 0.10088 | 0.7021 | |

8 | 541,260 | 153,444 | 0.09995 | 0.10087 | 0.6449 | |

9 | 544,800 | 151,161 | 0.10013 | 0.10038 | 0.4638 | |

10 | 540,427 | 155,466 | 0.10012 | 0.09972 | 0.2752 | |

charge | 1 | 548,044 | 165,029 | 0.1002 | 0.09902 | 0.6174 |

2 | 550,253 | 162,764 | 0.10019 | 0.10015 | 0.4442 | |

3 | 550,035 | 162,083 | 0.10007 | 0.1017 | 0.3568 | |

4 | 553,040 | 159,041 | 0.10006 | 0.09824 | 0.2824 | |

5 | 552,578 | 158,816 | 0.09997 | 0.09932 | 0.8326 | |

6 | 551,092 | 159,438 | 0.09984 | 0.09967 | 0.3859 | |

7 | 554,306 | 156,440 | 0.09988 | 0.10088 | 0.7023 | |

8 | 552,564 | 159,050 | 0.10000 | 0.10087 | 0.6472 | |

9 | 553,382 | 157,813 | 0.09993 | 0.10038 | 0.4642 | |

10 | 551,809 | 158,732 | 0.09984 | 0.09972 | 0.2806 |

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## Share and Cite

**MDPI and ACS Style**

Niu, Q.; Tang, L.; Yu, L.; Wang, H.; Yang, Z.
Unit Commitment Considering Electric Vehicles and Renewable Energy Integration—A CMAES Approach. *Sustainability* **2024**, *16*, 1019.
https://doi.org/10.3390/su16031019

**AMA Style**

Niu Q, Tang L, Yu L, Wang H, Yang Z.
Unit Commitment Considering Electric Vehicles and Renewable Energy Integration—A CMAES Approach. *Sustainability*. 2024; 16(3):1019.
https://doi.org/10.3390/su16031019

**Chicago/Turabian Style**

Niu, Qun, Lipeng Tang, Litao Yu, Han Wang, and Zhile Yang.
2024. "Unit Commitment Considering Electric Vehicles and Renewable Energy Integration—A CMAES Approach" *Sustainability* 16, no. 3: 1019.
https://doi.org/10.3390/su16031019