An optimal solution to unit commitment problem of realistic integrated power system involving wind and electric vehicles using chaotic slime mould optimizer

Abstract

Plug-in electric vehicles (PEVs) could be integrated into power networks to meet rising demand as well as provide mobile storage to help the electric grid operate more efficiently. The most efficient charging and discharging of PEVs are required for the effective utilization of this potential. PEVs with poor charging management may see a spike in peak demand, resulting in increased generation. To take advantage of off-peak charging benefits and avoid load shedding, PEVs charging and discharging must be intelligently scheduled. This paper offers a solution to optimal generation scheduling and the impact of vehicle to grid (V2G) operation in the presence of wind as a renewable energy source using the chaotic slime mould algorithm (CSMA). Further, the effectiveness of the proposed simulation results for a 10-unit system incorporating V2G operation has been compared with other well-known optimization techniques such as harmony search algorithm (HAS), chemical reaction optimization(CRO), genetic algorithm and artificial neural network(GA-ANN), particle swarm optimization (PSO), and cuckoo search (CS). The comparative analysis of the results reveals a significant cost savings in power generation.

Background

The majority of existing generation and transportation systems rely solely on fossil fuels, resulting in massive pollution and adverse impacts on the atmosphere. To ensure the long-term viability of these finite energy sources, it is essential to use them very precisely and economically. The incorporation of electric vehicles (EVs) has resulted in a decrease in the use of conventional petroleum-based transportation systems during the last few years. The main sources of battery charging are electric power utilities. A well-coordinated charging and discharging cycle, on the other hand, could help to reduce overall fossil fuel usage and pollutant emissions. Meanwhile, due to progress in power electronics, battery technology, and controller topologies, surplus power stored in batteries might be sent back to utilities via a convertor plant at the consumer's location. V2G technology has various advantages, including (i) alternative energy sources, (ii) energy diversification, (iii) pollution reduction, and (iv) increased performance and efficiencies. It also provides voltage regulation, harmonic filtering, and primary frequency control.

Overview of wind power and electric vehicles

Power developed by a wind turbine depends upon wind speed. As wind velocity continuously changes, power generated is always fluctuating. A large number of methods are available for predicting the uncertainties associated with wind power. In this study, Weibull function [1] is used for evaluating uncertainties in wind and mathematically represented as,

$$pdk_{1} (c,k1,\lambda )\, = \frac{{k_{1} }}{\lambda }\,\left( {\frac{c}{\lambda }} \right)^{{k_{1} - 1}} \,\exp \left[ { - \left( {\frac{c}{{k_{1} }}} \right)^{{k_{1} }} } \right]\,\,\,\,\,$$

(1)

As the power generated by wind is uncertain, variable due to randomness of wind velocity expressed as,

$$Pw\, = \,\left\{ {\begin{array}{*{20}c} {0\,\,\,\,\,\,\,\,\,\,(c^{h} \, \le \,\,c{\text{in}}\,\,or\,\,\,c^{h} \,\, \ge \,c_{{{\text{out}}}} )\,} \\ {Pwr\,\,\,\,\,\,\,\,\,\,\,(c_{r} \, \le \,\,\,\,c^{h} \,\, \ge \,\,c_{{{\text{out}}}} )\,\,\,\,\,\,\,\,\,\,\,\,\,} \\ {\frac{{\left( {c - c{\text{in}}} \right)}}{{cr - c{\text{in}}}}\,\,\,\,\,(c_{{{\text{in}}}} \, \le \,\,\,\,c^{h} \,\, \ge \,\,c_{r} )} \\ \end{array} } \right.$$

(2)

From Eq. (2), when wind speed $c^{h}$ is less than or equal to minimum rated velocity, wind power is zero. Wind power is equal to the rated wind power, when wind speed is greater than rated speed. So, this shows that wind power is a discrete variable. The probability of wind power being 0,$P_{wr}$ is calculated as per Eqs. (3) & (4), respectively, and described below:

$$\begin{aligned} P_{r} (P_{w} = 0)\, & = \,{\text{d}}f(c_{{{\text{in}}}} )\, + \left[ {1 - {\text{d}}f(c_{{{\text{out}}}} )} \right]\,\, \\ {\text{For}}\,\,Pw\, = 0,\,\Pr & \, = \left[ {1 - \exp - \left( {\frac{{c_{{{\text{in}}}} }}{\lambda }} \right)^{{k_{1} }} } \right]\, + \,\exp \left[ { - \left( {\frac{{c_{{{\text{out}}}} }}{\lambda }} \right)^{{k_{1} }} } \right]\,\,\,\, \\ \end{aligned}$$

(3)

The probability density function depends upon $v_{in\,\,} {\text{and}}\,v_{r}$ as the wind power is a continuous variable and it can be written as,

$$pdf(P_{w} )\, = \frac{{KLv_{{{\text{in}}}} }}{{\left( {P_{wT} } \right)^{2} }}\,\left[ {\frac{{1 + \left( {{\raise0.7ex\hbox{${LP_{w} }$} \!\mathord{\left/ {\vphantom {{LP_{w} } {P_{{{\text{WR}}}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${P_{{{\text{WR}}}} }$}}} \right)c_{{{\text{in}}}} }}{\lambda }} \right]\, \times \,\exp \left[ { - \left( {\frac{{1 + \left( {{\raise0.7ex\hbox{${LP_{w} }$} \!\mathord{\left/ {\vphantom {{LP_{w} } {P_{{{\text{WR}}}} }}}\right.\kern-0pt} \!\lower0.7ex\hbox{${P_{{{\text{WR}}}} }$}}} \right)c_{{{\text{in}}}} }}{\lambda }} \right)^{k} } \right]\,\,\,\,\,\,\,\,\,\,\,$$

(4)

The facility of the spinning reserve to meet the sudden demand may be fulfilled by the empirical formulas shown in Eq. (4). The base section of the load curve is considered for maximum wind power generation. A typical load pattern for maximum wind power supplied is plotted for a 24-hour duration as shown in Fig. 1.

Fig. 1

Wind variation cycle [2]

EVs operate by consuming the stored energy in batteries and act as an excess load on existing system [3]. EVs may be broadly classified as: battery operated vehicles, PEVs and hybrid electric vehicles. With the advancement in battery technologies, a large variety of EVs are being recently manufactured on a large scale. Some of the electrochemical battery categories are given in Table 1. In [4], a systematic approach towards V2G planning is explored for cost minimization. Further, availability of large number of charging facilities either while transportation or during parking bounds huge attraction of consumers. A typical charging/discharging pattern is selected as shown in Fig. 2

Table 1 Types of batteries [5]

Fig. 2

EV- Charging/discharging pattern [6]

Overview of vehicle to grid operation

EVs can store or generate 4 KW to 80 KW-Hr on average, and if a well-coordinated system is available, widespread use of these vehicles may be viable. The unplanned charging and discharging of such a huge number of EVs could disturb the power system's dynamics and stability. However, a common power aggregator that can bring together a group of EVs and present the entire system to the grid as a single system could result in significant power contribution. The power aggregator should keep a keen watch on performance so that a large enough number of vehicles may engage in V2G operations. Figure 3 depicts a simplified model that explains the various operations that fall under the V2G framework [7].

Fig. 3

Schematic representation of V2G operation

Optimization approaches for UC-V2G

The concept of smart grid technology enables a large number of consumers to take participate in energy conservation by selling back excessive power to grid. Advancement in battery technology enables to design desired sizing and providing efficient facilities for controlled charging and discharging. The UC problem becomes rather more complex by this increased power injection. Thus, it becomes necessary to have proper co-ordination of UC-V2G operation by fixing various UC and V2G constraints. The complexities of intermittent nature of wind energy and electric vehicles are coordinated, and unit commitment problem is resolved using mixed integer linear programming [8]. A power dispatch with 15 conventional units and 3 wind farms along PEV is incorporated in shifting of EV and wind power injection effectively to reduce the generation cost. Chemical reaction optimization technique is employed for economic generation scheduling incorporating V2G operation [9]. The charging and discharging patterns of electric vehicles were correctly formulated for cost minimization and enhancing system reliability by using genetic algorithm [10]. Virtual power of parking lot is fed back to grid using GA-ANN method for removing additional cost of small units required for reserve [11]. Complexities in conventional UC due to large number of grid-able electric vehicles were effectively resolved by using particle swarm optimizer algorithm. PSO enables to provide solution for cost minimization and low emission [12].The subsequent section presents construction of unit commitment problem using proposed CSMA algorithm.

Construction of unit commitment problem

Mathematical formulation

The generation schedule must be planned well in advance such that sufficient power is always available to meet forecasted load demand with reliability. This could be more effective if a sufficient amount of power is contributed by renewable energy sources. Various mathematical equations satisfying system constraints are formulated to meet load demand including the cost of fuel, starting cost, and shunt down cost. The total fuel cost (F_T) is determined by summing up generation cost of each individual unit for a defined time interval. It can be mathematically represented as:

$$F_{T} \, = \sum\limits_{i = 1}^{H} {\,\left[ {\sum\limits_{i = 1}^{N} {\left( {a_{i} \,P_{i,h}^{2} + \,b_{i} \,P_{i,h} + c_{i} } \right)U_{i,h} \, + \,ST_{c(i)} (1 - U_{i(h - 1)} )\,U_{i,h} } } \right]} \,\,\,\,\$ /hr\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$

(5)

where $a_{i} \,b_{i} \,{\text{and }}\,c_{i}$ are the fuel cost function expressed in $\$ /{\text{h}}\,,\,\$ /{\text{MWh}}\,,\,\,{\text{and}}\,\,\,\$ /{\text{MWh}}^{2} \,$, respectively.

Mathematically, start-up cost $ST_{c(i)}$ can be expressed as the sum of cold start-up $({\text{CSch}}(i))$ and hot start-up cost $({\text{HSch}})$ of ith unit, respectively.

$${\text{ST}}_{c(i)} = \,\left\{ {\begin{array}{*{20}c} {{\text{HSch}}(i);} & {{\text{MD}}t(i)\, \le \,T_{{{\text{h}}i}}^{{{\text{OFF}}}} \,\, \le \,\,(\,{\text{MD}}t(i\,) + \,{\text{CSh}}(i))} \\ {{\text{CSch}}(i);} & {T_{{{\text{h}}(i)}}^{{{\text{OFF}}}} \,\rangle \,\left( {{\text{MD}}t(i\,) + \,{\text{CSh}}(i)} \right)\,\,\,\,\,\,\,\,\,\,\,\,} \\ \end{array} } \right.\begin{array}{*{20}c} {\,(i \in \,N;{\text{h}} = 1,2,3,.....,H)\,\,\,\,\,\,\,\,\,\,\,\,\,} & {} \\ \end{array}$$

(6)

Unit commitment problem needs to provide optimum solution within certain constraints. The major constraints involved in UC problem are:

• (i) Operating limit constraints

• (ii) Load balance constraints

• (iii) V2G constraints

• (iv) Spinning reserve constraints

Operating limits constraints

There is a limit below which power generation is not economical due to some technical limitations. Similarly, power generation should not be more maximum power generation limit. These power generation limits for a particular unit are calculated from the heat rate curve and fuel cost coefficient limits.

$$P_{g\min (i)\,} \le \,P_{g(i)} \, \le \,P_{g\max )(i)} \,\,(i \in 1,2,....,N\,\,\,;\,\,{\text{h}} \in 1,2,....,{\text{H}})\,\,$$

(7)

Load balance constraints

The load demand is found to never remain constant, and it continuously changes over the entire span of the considered time interval. It is desired that the overall power generated by all the committed units (N) for a particular duration (h) should always satisfy the connected load demand (DL). Therefore, at any instant of time, the power supplied by thermal unit and additional wind power should always be equal to power demand.

$$\sum\limits_{i = 1}^{N} {P_{g(i)} U_{i,h\,} + P_{g}^{w} } = D_{L} \,\,\,\,\,\,\,\,\,\,\,\,(i = 1,2,.....,N)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$

(8)

Case-1: During charging of vehicle (grid to vehicle)

$$\sum\limits_{i = 1}^{N} {P_{g(i)} U_{i,h\,} + P_{g}^{w} } = D_{L} + D_{h}^{V} \,\,\,\,\,\,\,\,\,\,\,\,(i = 1,2,.....,N)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$

(9)

Case-2: During discharging (vehicle to grid)

$$\sum\limits_{i = 1}^{N} {P_{g(i)} U_{i,h\,} + P_{g}^{w} } + D_{h}^{V} = D_{L} \,\,\,\,\,\,\,\,\,\,\,\,(i = 1,2,.....,N)\,\,\,\,\,\,\,\,$$

(10)

The power outputs of the NG generating units at a particular time period have to satisfy the forecasted load. For arbitrary free unit power outputs Phi, (i=1, 2, NG), it is assumed that the Rth reference unit power output is constrained by the power balance equation as:

$$P_{Rh} = D_{L} \, - \sum\limits_{i = 1}^{NG} {P_{g(i)} U_{i,h\,} + P_{g}^{w} } \,\,\,\,\,\,\,\,\,\,\,(i = 1,2,.....,N)\,\,\,\,\,\,\,$$

(11)

Case-1: During charging of vehicle

$$P_{Rh} = \left( {D_{L} \, - \,\sum\limits_{i = 1}^{N} {\,\left( {P_{g(i)} \,\,U_{i,h\,} + \,\,P_{g}^{w} } \right)} \, - \,\,D_{h}^{V} } \right)\,\,\,\,\,\,\,\,\,(i = 1,2,.....,N)\,\,\,\,$$

(12)

Case-2: During discharging

$$P_{Rh} = \left( {D_{L} \, - \,\sum\limits_{i = 1}^{N} {\left( {P_{g(i)} U_{i,h\,} + P_{g}^{w} } \right)} \, - D_{h}^{V} } \right)\,\,\,\,\,\,\,\,\,(i = 1,2,.....,N)\,\,\,$$

(13)

V2G constraint

V2G technology enables a fixed number of registered vehicle to participate in UC. EVs are assumed to be charged during off-load period by utility grid or from renewable energy sources. Charging–discharging duration depends upon battery size and charging facilities. It is assumed that all vehicles charged by stand-alone system available at the parking slot.

$$\sum\limits_{t = 1}^{H} {N_{V2G} } \,(t) = \,N_{V2G}^{{{\text{Max}}}} (t)$$

(14)

Spinning reserve constraints

Unpredictable disturbances, such as sudden load demand or unexpected tripping of lines or generators, necessitate the availability of additional generation capacity. Spinning reserve is the term given to this additional generation capability. To meet demand while maintaining an adequate reserve margin, optimal generation allocation must be planned ahead of time. Wind penetration adds additional electricity, which assists to contribute towards total power generation. As a result of the additional power provided by wind energy, the load on thermal units may be reduced. Mathematically, spinning reserve is given as:

$$\sum\limits_{i = 1}^{N} {P_{g\max (i)} U_{{i,{\text{h}}\,}} + P_{{g({\text{h}})}}^{W} } \ge D_{{L({\text{h}})}} + {\text{SP}}_{{R({\text{h}})}} \,\,\,\,\,\,\,\,\,\,\,\,({\text{h}} = 1,2,.....,H)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$

(15)

Grid to vehicle

$$\sum\limits_{i = 1}^{N} {P_{g\max (i)} U_{{i,{\text{h}}\,}} + P_{{g({\text{h}})}}^{W} } \ge D_{{L({\text{h}})}} + {\text{SP}}_{{R({\text{h}})}} + \,D_{{\text{h}}}^{V} \,\,\,\,\,\,\,\,\,\,\,({\text{h}} = 1,2,.....,H)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$

(16)

Vehicle to grid

$$\sum\limits_{i = 1}^{N} {P_{g\max (i)} U_{{i,{\text{h}}\,}} + P_{{g({\text{h}})}}^{W} } \ge D_{{L({\text{h}})}} + {\text{SP}}_{{R({\text{h}})}} - \,D_{h}^{V} \,\,\,\,\,\,\,\,\,\,\,({\text{h}} = 1,2,.....,H)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$

(17)

CSMA mathematical formulation

Slime moulds have received a level of admiration in recent times. The slime mould mentioned in this article is usually Physarum polycephalum. Typically, the plasmodium forms a network of protoplasmic tubes connecting the masses of protoplasm at the food sources, which is efficient in terms of network length and elasticity [13]. The slime mould even flows vibrantly in the situation of food scarcity, which aids in comprehending how slime mould search, move, and connect food in a changing environment. It can judge positive and negative feedback, when a secretion approaches the target and determines the most effective approach to capture food. While foraging, slime mould uses empirical principles based on currently available insufficient data to decide whether to start a fresh search and leave the existing place.

Mould may divide its biomass to exploit other resources on the information of some other rich high-quality food information, even if a food source is abundant. It may modify their search patterns dynamically depending on the quality of food sources [14].The concept of probability distribution is captured by lot of meta-heuristics algorithms to gain randomness. Chaotic maps could be beneficial if randomness due to ergodicity, idleness and randomness properties are properly utilized. These chaotic criteria’s are fulfilled by Eq. (18).

$$O_{k + 1} \, = \,f(O_{k} )$$

(18)

In Eq. (1), $O_{k + 1} \,\& f(O_{k} )$ are the $(\,k + 1){\text{th}}\,\,\& \,k{\text{th}}$ chaotic number, respectively. The action of chaotic function is dependent on initial value $O_{0}$. In the proposed work, from the 10 most commonly used chaotic strategies presented in Table 2, Tent chaotic function has been combined with basic CSMA algorithm to search space more enthusiastically and comprehensively.

Table 2 Chaotic functions [14]

The optimization procedure for the CSMA algorithm consists of the following eight steps:

Step 1:

Specify the input parameters required by SMA and random chaotic function to solve the optimization problem defined by Eq. (21). Moulds position, population size, maximum iteration and smell index associated food searching, random iteration, random variables r, mean position of moulds, upper bound and lower bound (Ub), (Lb) are according initiated.

Step 2:

Initialization of stochastic population (X_i = 1, 2, 3…..,N) and maximum iteration number is taken as ier_max.

Step 3:

Calculate the fitness of all slime mould and estimating the updated position of moulds.

$$\overrightarrow {{X\left( {t + 1} \right)}} = \left\{ {\begin{array}{*{20}c} {\overrightarrow {{X_{b} \left( t \right)}} + \overrightarrow {{v_{b} }} .\left( {\overrightarrow {{\text{W}}} .\overrightarrow {{X_{A} \left( t \right)}} - \overrightarrow {{X_{B} \left( t \right)}} } \right),} & {r < p} \\ {\overrightarrow {{v_{c} }} .\overrightarrow {X\left( t \right)} ,} & {r \ge p} \\ \end{array} } \right.$$

(19)

Step 4:

Enhancing the search process by clubbing chaotic strategy.

Step 5:

Calculating the

$$\overrightarrow {{{\text{W}}\left( {{\text{smell}}\,{\text{index}}\left( {\text{i}} \right)} \right)}} = \left\{ {\begin{array}{*{20}c} {1 + r.\log \left( {\frac{bF - S\left( i \right)}{{bF - wF}} + 1} \right),} & {{\text{condition}}} \\ {1 - r.\log \left( {\frac{bF - S\left( i \right)}{{bF - wF}} + 1} \right),} & {others} \\ \end{array} } \right.$$

(20)

Step 6:

For each search iteration using sinusoidal chaotic function, the positions of $p,vb, vc$ are updated

$$\begin{gathered} r_{o} = rand; \hfill \\ r_{o} \left( {t + 1} \right) = 2.3 \times r_{0}^{2} \times {\text{Sin}} \left( {Pi.r_{0} } \right) \hfill \\ r_{1} = r_{0} \left( {t + 1} \right); \hfill \\ \end{gathered}$$

(21)

Step 7:

The eqn. for upgrading the positions of agents (i.e. to wrap food) is given as:

$$\overrightarrow {{X^{*} }} = \left\{ {\begin{array}{*{20}l} {rand.\left( {UB - LB} \right) + LB,\,rand < z} \hfill \\ {\overrightarrow {{X_{b} \left( t \right)}} + \overrightarrow {{v_{b} }} .\left( {{\text{W}}.\overrightarrow {{X_{A} \left( t \right)}} - \overrightarrow {{X_{B} \left( t \right)}} ,\,r < p} \right)} \hfill \\ {\overrightarrow {{v_{c} }} .\overrightarrow {X\left( t \right)} ,\,r \ge p} \hfill \\ \end{array} } \right.$$

(22)

Step 8:

With the up gradation in the search process, the value of $\overrightarrow {{v_{b} }}$ vibrantly changes between [− a,a] and $\overrightarrow {{v_{c} }}$ varies between [− 1,1] and at last shrinks to zero. This is known to be as ‘grabbling of food’.

The flow chart for optimization procedure for the CSMA algorithm is shown in fig. 4.

Fig. 4

Flow chart of chaotic SMA

Implementation of proposed CSMA algorithm for unit commitment problem

The CSMA method is an innovative meta-heuristic algorithm that has an excellent ability of exploration and exploitation and effectively utilized to solve the unit commitment problem of a hybrid system. For a particular test system, the proposed algorithm selects an optimal generating schedule as a binary variable showing ON/OFF status. The following steps elucidate the procedure of a unit commitment problem [15].

Step 1:

The status of a unit for generation scheduling is expressed through their position. In this study, we define the status of a unit as a binary number: 0 indicates de-committed unit, and 1 is for committed unit. Once the generation schedule is for a particular load demand is selected, the data of units are stored in integer matrix $U_{NG}$ as,

$$U_{NG} = \left[ {\begin{array}{*{20}c} \begin{gathered} u_{1}^{1} \hfill \\ u_{2}^{1} \hfill \\ \vdots \hfill \\ u_{G}^{1} \hfill \\ \end{gathered} & \begin{gathered} u_{1}^{2} \hfill \\ u_{2}^{2} \hfill \\ \vdots \hfill \\ u_{G}^{2} \hfill \\ \end{gathered} & \begin{gathered} \cdots \hfill \\ \cdots \hfill \\ \vdots \hfill \\ \cdots \hfill \\ \end{gathered} & \begin{gathered} u_{1}^{H} \hfill \\ u_{2}^{H} \hfill \\ \vdots \hfill \\ u_{G}^{H} \hfill \\ \end{gathered} \\ \end{array} } \right]$$

Step 2:

Enter UCP input parameters, i.e. Maximum power limit, minimum power limit, fuel cost coefficient

Step 3:

Set iteration counter, i =0 and initialize random position of search agents.

Step 4:

Calculate the priority list of each search generator according to characteristics of each generating units.

Step 5:

Modify search agent position to satisfy reserve constraints.

Step 6:

Repair each search agent position for minimum Up/Down time violation.

Step 7:

Verify generator output power or else increment iteration count by 1 and go to step 5.

Constraints repair strategy

Typically unit commitment programmes are designed to represent the operations of a centrally dispatched power system that is the portfolio of generators all scheduled in a coordinated way to meet aggregated electricity demand. The goal is always to minimize the cost of doing this subjected to constraints. During the major scheduling by CSMA, there may be a possibility that CSMA may fail to fulfill essential constraints such as minimum up/downtime, and spinning reserve. So, deviations in these constraints are needed to be repaired. In this paper, the strategy adopted is a heuristic search to tackle the UC problem.

Constraints related to minimum up /minimum downtime

Once a unit is started, it should not be turned off immediately before reaching MUT. This is required to satisfy economic, mechanical, and design limitations. Similarly, any unit which is once de-committed should not put online immediately. These constraints are required to be calculated in advance by using the following recursive relation:

$$\begin{gathered} T_{g,on}^{i,j} = \left\{ {T_{g,on}^{i - 1} + 1;\begin{array}{*{20}c} {if\begin{array}{*{20}c} {u_{j}^{i} = 1} \\ \end{array} } \\ \end{array} } \right\} \hfill \\ T_{g,on}^{i,j} = 0\begin{array}{*{20}c} {if\begin{array}{*{20}c} {u_{j}^{i} } \\ \end{array} } \\ \end{array} = 0 \hfill \\ T_{g.off}^{i,j} = T_{g,off}^{i - 1} + 1;\begin{array}{*{20}c} {if} \\ \end{array} \begin{array}{*{20}c} {u_{j}^{i} } \\ \end{array} = 0 \hfill \\ T_{g,OFF}^{i,j} = 0\begin{array}{*{20}c} {;\begin{array}{*{20}c} {if\begin{array}{*{20}c} {u_{j}^{i} } \\ \end{array} } \\ \end{array} } \\ \end{array} = 0 \hfill \\ \end{gathered}$$

(22)

Handling of spinning reserve constraints

The CSMA algorithm may sometimes perform unenviably to satisfy spinning reserve constraint. This happens to handle minimum up/down constraint, and excessive spinning reserve is needed. Thus, this spinning reserve constraint requirement should be handled heuristically. The PSEUDO code is shown in appendix-1, and whole process to repair spinning reserve requirement is represented in Fig. 5

Fig. 5

Flow chart for spinning reserve repairing

De-committing of excess of units

During repair process of MDT/MUT and spinning reserve, some of the units may get unnecessarily ON. To avoid this situation that could result in excessive cost for running those units, some of the units need to be shut-down. The PSEUDO code is shown in appendix-2, and flow chart for de-committing of excessive units is shown in fig. 6.

Fig. 6

Flow chart for the decommitment of excessive generating units

Results & discussion for unit commitment problem

In this section, results of standard IEEE test system with conventional UC and UC-EV system are presented. The test systems are simulated MATLAB 2018a Windows 10, CPU@2.10Ghz-4GB RAM Core i5. To check the performance of the CSMA method for solving the unit commitment, standard test system of IEEE is taken into concern.

Overview of assumptions

• (i) It is assumed that system is considered as lossless.

• (ii) Operating cost of V2G is omitted in this study

• (iii) A fleet of 40,000 electric vehicles are taken into consideration. Out of which 8000 vehicles are assumed to wire for V2G operation at any instant.

• (iv) Wind power forecasting error cost is not considered as it is out of scope in the present research

• (v) Simulation with different wind penetration levels, capacity of thermal generation and participation of PEVs are kept fixed

A standard IEEE 10-unit system presented in Table 3 is considered for simulation study with 40000 PEVs. Spinning reserve requirement is assumed to be 10% of the hourly load demand in 24 hour scheduling time period. Parameters of PEV are depicted in Table 4. Table 5 shows unit allocation and active power scheduling for 10-unit system. Figure 7 shows convergence curve for 10 unit system with 10% SR.Table 6 illustrates unit allocation and active power scheduling for 10-unit system with wind. Figure 8 shows convergence curve for 10 unit system with 10% SR with wind using CSMA. Table 7 shows unit allocation and active power scheduling for 10-unit system with V2G penetration using CSMA. Figure 9 shows convergence curve for 10 units system with EV penetration. Figure 10 shows cost comparison for 10 unit system with EV penetration using CSMA method.Further, effectiveness of the proposed simulation results for a 10 unit system incorporating wind and V2G operation has been compared with other well-known optimization techniques such as HSA[8], CRO[8], GA-ANN[8], PSO[8] and CS[8]. The comparative analysis of the results shows a significant cost reduction for V2G operation using proposed CSMA method (Table 8).

Table 3 Standard IEEE 10-unit system [16]

Table 4 Parameters of PEVs [5]

Table 5 Unit allocation and active power schedule for 10-unit test system with 10% SR using CSMA

Fig. 7

Convergence curve for 10 units system

Table 6 Generation scheduling for 10-unit system with wind penetration using CSMA

Fig. 8

Scheduling for 10 units system with wind penetration

Table 7 Generation scheduling for 10-unit system with wind and EV penetration using CSMA

Fig. 9

Convergence curve for 10 units system with wind and EV penetration

Fig. 10

Cost comparison for 10 units system with EV penetration

Table 8 Comparison 10-unit system (10% SR) for thermal-V2G using CSMA with other algorithms

Conclusion

In this paper, standard IEEE 10 unit system has been simulated with and without V2G by applying CSMA method for minimizing the overall cost. Results revealed that proposed method is effective in solving economic despatch problem very precisely. To check the effectiveness of proposed algorithm, results are compared with other methods. The comparative analysis reveals that proposed method outperforms in all aspects. Thus, proposed method is a cost effective solution for solving UC problem with due effect of renewables and EV.

Appendix

(1) Pseudo code for satisfying minimum up and down using heuristic repair mechanism.

(2) PSEUDO code for spinning reserve repairing.