REVIEW ON: Markov Chain Monte Carlo Simulation of Electric Vehicle Use for Network Integration Studies

**Source**: [1] Y. Wang, D. Infield, Markov Chain Monte Carlo simulation of electric vehicle use for network integration studies, International Journal of Electrical Power & Energy Systems, Vol.99, 2018, Pages 85-94

- https://doi.org/10.1016/j.ijepes.2018.01.008.

Literature Review** **by Q.Dang [qiyun.dang@mail.mcgill.ca]

Edited by D.Wu [di.wu5@mail.mcgill.ca]

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#### 1. Paper Motivation

As the penetration of electric vehicles (EVs) increases, their patterns of use need to be well understood for future system planning and operating purposes. Using high resolution data by 10 minutes, accurate driving patterns were generated by a Markov Chain Monte Carlo (MCMC) simulation.

However, previous MCMC simulation works was not complete in the sense that model results were not subject to** verification** and **uncertainty analysis **for practical network assessment was not undertaken. The present paper includes both these important elements.

#### 2. Methods

**Method Name: **Time-inhomogeneous Markov Chain Monte Carlo (MCMC)
simulation

**Description:** The EV movement was simulated using a discrete-state,
discrete-time Markov chain to define the states of all the EV at each time step
of T minutes. It was assumed that, at every unit of time, one and only one
event from a set of a finite number of events can occur to a given EV.

Four events were considered: {D, H, W, C}, correspond to ‘driving’, ‘parking at home’, ‘parking at workplace’, and ‘parking at commercial areas’ respectively

Proposed Markov Chain Diagram:

Fig. 1. *Markov
Chain diagram of possible vehicle state transitions at time t*

From time step t-1
to t, the associated transition probability is given for each possible
transition at this specific time stamp. For instance, P^{t}_{H->D}
indicates the probability of the vehicle being ‘D’ at t given being ‘H’ at time
t-1.

#### 3. Paper structure

**1) Review Previous **Markov Chain Simulation of Electric Vehicle **→**

**2) Introduce** the survey **data**,
the 2000 UK Time of Use Survey (TUS) data **→**

3) A **matrix representation** of the transition
diagram at time t, Tt, is shown by Eq. (1) **→**

An example of the state transition matrix at 8:40 am (t = 29, t0=4am, 4am+29*10min=8:50am) is shown in Eq. (2),

**→** Verification of proposed MCMC method by **convergence analysis.** **→**

4) Distribution **grid case study** by OpenDSS software (Case
1 commercial, Case 2 residential).

Case 1: A University building at Strathclyde, accommodates up to 300 workers, and has a nominal parking availability for approximately 100 cars. This building is supplied by a dedicated 1000 kVA transformer.

Case 2: low-voltage single-phase domestic network that consists of 17 households.

Fig. 2. *Case 2 Single
phase distribution network layout*.

#### 3.Paper Results

Results Description: 24 hour Load (KVA) profile in grids, before and after EV connected.

Fig. 3. *(Upper)Aggregate demand of workplace EV charging. And (Lower) averaged voltage profile for Household 17 with 99% CI under full EV penetrations.*

**Notes:**

**Case 1 : An office building, approximately 100 cars, 100% EV penetration level, that is, 100 out of 100 cars are EV. This building is supplied by a 1000 kVA transformer.**

For Case 1, a 1000 kVA transformer would easily survive the extra EV load for both standard and fast charging cases. A more typical transformer for this building with rating of nearer 500 kVA would, however, fail to supply the EV related load in the fast charging scenario.

**Case 2: low-voltage single-phase community consists of 17 households.**

For Case2, EV penetration in this case causes a severe voltage violation of the network (with specified tolerance of [−0.06 +1.10] p.u.,

#### 4. Summarization

1) Markov Chain Monte Carlo simulation, as
a numerical approach, can be used to **generate
different electricity load profiles** according to various EV charging
schemes.

2) The impact of the additional EV charging
loads on the local distribution network can be assessed by identifying the
expected value and associated uncertainty, as measured by the standard
deviation, for various grid operational metrics, such as **thermal loading, voltage profiles, transformer loss of life, energy
losses**, and harmonic distortion levels.

3) The uncertainty identification of these different metrics requires large number of trials from MCMC simulation to achieve convergence. These uncertainties could not be generated directly by sampling from the original TUS dataset due to its size limitation.

4) Also, the same steps of MCMC approach, as described in this work, can be applied to new data sets for extracting their own inherent statistical characteristics.

**5.
SUGGESTED FUTURE WORK**

The EV movement was simulated using a discrete-state, discrete-time Markov chain for four events {D, H, W, C}, correspond to ‘driving’, ‘parking at home’, ‘parking at workplace’, and ‘parking at commercial areas’ respectively

The model can be extending to EV Charging States, including V2G and G2V, and further implemented in reinforcement leaning problems.

**APPENDIX**

**Useful Datasets download link (1&2):**

1. National Household Travel Survey : http://nhts.ornl.gov/index.shtml

2. The United Kingdom 2000 Time Use Survey. National Statistics Technical Report; 2003.https://beta.ukdataservice.ac.uk/datacatalogue/studies/study?id=4504

Screenshot:

**Review of previous Markov Chain × EV works by author**

**Table 1. Summary of relevant literature works.**

A | B | C | D | E | F | |

[1]
| ✓ | ✓ | ✓ | ✓ | — | — |

[2]
| ✗ | ✓ | ✗ | ✗ | ✓ | ✗ |

[3]
| ✓ | ✗ | ✓ | ✓ | ✗ | ✗ |

[4]
| ✗ | ✓ | ✓ | ✗ | ✗ | ✗ |

[5]
| ✗ | ✓ | ✓ | ✓ | ✗ | ✗ |

[6]
| ✗ | — | — | — | ✓ | ✗ |

[7]
| ✗ | ✓ | ✗ | — | ✗ | — |

[8]
| ✗ | ✓ | ✗ | ✗ | — | — |

[9]
| ✗ | ✓ | ✗ | — | ✓ | ✗ |

[10]
| ✓ | ✓ | ✓ | ✗ | ✓ | ✗ |

This work | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ |

- A: Fine data resolution (less or equal to 10 min per step).
- B: Vehicle status definition.
- C: Vehicle movement simulation.
- D: Vehicle use pattern verification.
- E: Detailed network impact analyses considering charging location.
- F: Uncertainty analysis of detailed network impact.
- ✓: model feature is included in a suitable manner.
- ✗: model feature not included.
- —: not relevant.

### References

[1] T.-K. Lee, Z. Bareket, T. Gordon, Z.S. Filipi**Stochastic modeling for studies of real-world PHEV usage: driving schedule and daily temporal distributions** IEEE Trans Veh Technol, 61 (4) (May 2012), pp. 1493-1502

[2] F.J. Soares, J.P. Lopes, P.R. Almeida, C.L. Moreira, L. Seca**A stochastic model to simulate electric vehicles motion and quantify the energy required from the grid** PSCC, Stockholm, Sweden (2011)

[3] Iversen EB, Møller JK, Morales JM, Madsen H. Inhomogeneous Markov models for describing driving patterns. IEEE Trans Power Syst.

[4] A. Lojowska, D. Kurowicka, G. Papaefthymiou, L. van der Sluis **Stochastic modeling of power demand due to EVs using copula** IEEE Trans Power Syst, 27 (4) (2012), pp. 1960-1968

[5] A. Ashtari, E. Bibeau, S. Shahidinejad, T. Molinski**PEV charging profile prediction and analysis based on vehicle usage data** IEEE Trans Smart Grid, 3 (1) (2012), pp. 341-350

[6] A.D. Hilshey, P.D. Hines, P. Rezaei, J.R. Dowds**Estimating the impact of electric vehicle smart charging on distribution transformer aging** IEEE Trans Smart Grid, 4 (2) (2013), pp. 905-913

[7] F. Rassaei, W.S. Soh, K.C. Chua**Demand response for residential electric vehicles with random usage patterns in smart grids** IEEE Trans Sustain Energy, 6 (4) (2015), pp. 1367-1376

[8] Fluhr J, Ahlert KH, Weinhardt C. A stochastic model for simulating the availability of electric vehicles for services to the power grid. In: System Sciences (HICSS), 43rd Hawaii International Conference on. IEEE; 2010. p. 1–10.

[9] S. Shafiee, M. Fotuhi-Firuzabad, M. Rastegar**Investigating the impacts of plug-in hybrid electric vehicles on power distribution systems **IEEE Trans Smart Grid, 4 (3) (2013), pp. 1351-1360

[10] Wang Y, Huang S, Infield D. Investigation of the potential for electric vehicles to support the domestic peak load. In: Electric Vehicle Conference (IEVC), IEEE. Dec. 2014. p. 1–8.

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<*End of Review*>