Impact of PHEV on Reserve Scheduling: A MILP-SCUC Method

Ibrahim Krad Department of Electrical and Computer Engineering

University of Denver Denver, Colorado

ibrahim.krad@du.edu

David Wenzhong Gao Department of Electrical and Computer Engineering

University of Denver Denver, Colorado

Wenzhong.Gao@du.edu

Abstract— The electric power system is under rapid development under the context of smart grid. As electric demand evolves, the power system must evolve too. New loads in the system are changing the ways system operators ensure system security. One such load recently attracting attention are plug-in hybrid electric vehicles (PHEVs). Seen as the stepping stone to an all electric transportation sector, PHEVs are expected to significantly penetrate the distribution system in the foreseeable future. PHEVs offer unique challenges to system operators. Not only are they additional loads on the system, but PHEVs with vehicle to grid functionality can also behave as distributed generators. PHEVs can potentially offer ancillary services such as contingency reserves for the system operator. This paper will investigate the potential of PHEVs in providing contingency reserves. Analysis will be completed using mixed integer programming solved via the commercially available software AIMMS.

Index Terms— Security Constrained Unit Commitment (SCUC), plug-in hybrid electric vehicle (PHEV), vehicle to grid (V2G), ancillary services

I. INTRODUCTION The electric power system is undergoing a significant

paradigm shift. New technologies and social pressures are reshaping traditional power system operation. One of these new technologies is the plug-in hybrid electric vehicle. Of the current approximate 250 million cars in the United States, if only 10% of them are replaced by PHEVs, the excess demand would pose a serious threat to the current power infrastructure. Under level 1 and level 2 charging standards, a single PHEV load amounts approximately to the load of an average household. Thus serious research on the implications of PHEVs on the distribution system must be conducted that includes low-level analysis. The authors of [1] used a Dynamic Network Assignment-Simulation Model for Advanced Road Telematics, or DYNASMART, to determine vehicle driving patterns, parking patterns, vehicle density at any given point in the system, and typical trip distances. They proposed a framework for studying the impact of PHEVs on a network that physically changes over time, e.g. the movement of the PHEVs throughout the network [1].

The charging and discharging of PHEVs all at once could potentially cause blackout and price spikes if they are not

properly planned for. One of the potential benefits of PHEVs that is currently being researched is their application in facilitating renewable generating units. For example, PHEVs could theoretically absorb excess wind generation over night and thus help avoid curtailing the wind generation output. In order to study the impact of PHEVs, the number of PHEVs in a system, their battery size, their all-electric range, driving patterns, and charge rate limits must be known. The authors of [2] developed a stochastic unit commitment study on PHEVs to determine their impacts on power system operation and scheduling [2].

The introduction of PHEVs into the distribution system must be carefully studied because the increased loading due to PHEVs could very well overload current transformers. The authors of [3] model different types of electric vehicle loads based on three types of vehicles, group vehicles like public transportation, social vehicles like taxis, and personal vehicles. They itemized the important factors required to model EV loads including battery capacity, charging/discharging power, user behavior, and initial state of charge of the battery pack. They have divided the charging time into two time periods, during the work day and from when a consumer arrives home in the evening until he must return to work the next day. The authors investigate the impact of EVs on the overall grid load curve and their impact on peaks and valleys [3].

One of the major differences between conventional energy storage systems and the use of PHEVs as distributed energy storage systems is that the location of PHEVs in the system will change throughout the day. The amount of energy available in a PHEV at any time is a direct function of the state of charge of the onboard battery pack. In order to model the stochastic nature of the PHEVs in the system, the authors of [4] modeled them as truncated normal distribution functions. The final solution is obtained via Monte Carlo simulations. Their conclusion is that PHEVs are able to provide alternative paths of power flow throughout the system independent of system branch flow constraints. They also conclude that PHEVs can decrease the cost of renewable energy integration by minimizing renewable power generation curtailment. They also conclude that the impact of PHEVs on assisting system operation will depend on the consumer’s level of participation in such a system [4].

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PHEVs have substantial potential in applications for power systems. Personal PHEVs are only used approximately 4% of the day for transportation and are theoretically available for the rest. Currently, the power grid does not have any practical means of storing energy outside of the approximate 2% of pumped hydro storage. PHEVs may be able to provide distributed storage. There is also potential to provide ancillary services. Since PHEVs have low durability due to their relatively low operating lifetimes and relatively high cost per kWh of energy, they are ideal for high value, short duration ancillary services such as reserves, regulation, and lowering peak demand. Providing spinning reserves is especially attractive since traditionally, generators are paid to be available for their reserve capacities in the form of capacity credits as well as for the power they actually provide. Thus, it is natural to incentivize PHEV owners to be plugged in and available. Data from the California Independent System Operator show that PHEVs would typically only need to provide approximately 8% of their contracted power [5].

The rest of this paper is organized as follows: section II

formulates the problem and derives the mixed integer programming formulation. Section III discusses the simulation results. Section IV concludes the paper.

II. PROBLEM FORMULATION The problem will be formulated using mixed integer linear

programming. Mixed integer programming conveniently lends itself for solving multi-variable optimization problems. The problem is solved using the commercially available software AIMMS which is also available free of charge for academic use. The security constrained unit commitment problem is solved for a 24 hour horizon. The objective function is a minimization of the total cost of the system given below in equation 1. min ∑ ∑ , , , , , (1) The function Fi is the cost function of generator i. This function is determined by performing a piecewise linearization of the generator cost curve. The total cost of the generator is a function of the power output of the generator as well as the commitment status of that generator in any given time period. Pi,t is the power generation output of generator i during time period t. Ii,t is the unit commitment status of generator i during time period t. This is a binary variable. A value of 1 means that the generator is committed and a value of 0 means that the generator is not committed. SUi,t is the startup cost of generator i. In this formulation, the startup cost of each generator will be assumed constant regardless of generator off time. The shut down cost of each generator is assumed to be zero. RP is a reserve penalty term in order to capture the value of insufficient reserves. The cost function of each generator is given below in equation 2. , · , ∑ , · , (2)

In equation 2, Fmin,i is the minimum no load cost of generator i. IFi,j is the incremental cost of generation for generator i. This cost is determined by the piecewise linearization of the generator cost curves. The subscript k represents the number of parts of the piecewise linearization of the generator cost curve. The variable PXi,j represents the amount of generation occurring in each region of the piecewise linearized cost curve. A sample linearized cost curve is shown in Figure 1 where F and P represent arbitrary breakpoints of the power-cost curve. Note Pmin is equivalent to P0.

Fig. 1. Piecewise linearized cost curve of a sample generator

The constraints for the optimization problem are required in order to ensure that system security is not compromised. The constraint shown in equation 3 is known as the generation capacity constraint. , · , , , , · , (3) Pmin,i and Pmax,i are the minimum and maximum generating limits of generator i at any given time period t respectively and Ri,t is the unit reserve schedule. Equations 3 through 5 describe the output of each generating unit. , , , · , ∑ , (3)

, (4) (5) The binary variable δ represents in which region the generation is occurring based on the piecewise linearized model. The subscript j refers to each region of the linearized model. Equation 6 represents the load balance constraint. ∑ , · , (6) Dt is the total system load at any given time period t. This constraint must be satisfied for all simulated time periods. Load curtailment is not an option. Equation 7 represents the system reserve constraint. ∑ , , (7)

Ri,t is the generator reserve schedule and RTOT,t is the total reserve requirement at any given time period t. This constraint must also be satisfied for all time periods. In order to model the start up costs, the minimum ON time constraints, minimum OFF time constraints, generator ramp up constraints, and generator ramp down constraints, intermediate variables must be introduced. These intermediate variables are known as the start up and shut down indicators. Equations 8 and 9 are used to model these indicators. , , , , (8) , , 1 (9) The binary variable yi,t is the start up indicator. If this variable is 1, then generator i is being turned on at time period t. If this variable is 0, then generator i is not being turned on. The binary variable zi,t is the shut down indicator. If it is 1, then generator i is being turned off at time period t. If it is 0, then the generator is not being turned off. Equation 8 links these variables to the current and previous commitment status of generator i. This equation determines whether a unit is being turned on or turned off. Equation 9 insures that no generating unit is being turned on and turned off at the same time. With these indicators defined, the constant start up costs can be modeled easily as shown in equation 10. , · , (10) This model calculates the cost of starting up a generator simply by multiplying the start up cost of generator i with the start up indicator of generator i at time period t. The minimum on time constraint is modeled via equations 11, 12, and 13. , 1 1,2, … , (11)

∑ , , · ,, (12)

∑ , 1 ,, (13) uTi is the number of time periods that generator i must remain on at the beginning of the study period. Ton,i is the minimum ON time requirement for generator i. NT is the number of time periods considered in the problem. The minimum off time constraint is modeled via equations 14, 15, and 16. , 0 1,2, … , (14)

∑ , , · 1 ,, (15)

∑ , 1 1 ,, (16) dTi is the number of time periods that generator i must remain off at the beginning of the study period. Toff,i is the minimum OFF time requirement for generator i. Individual

generator unit ramping constraints are modeling using equations 17 and 18. , , 1 , , · , (17)

, , 1 , , · , (18) Equation 17 is the generator ramp up constraint. This constraint is to ensure that generators are not allowed to change their outputs beyond safe operating regions in between any two time periods. URi is the ramping up rate of generator i. Psu,i is the maximum output power possible after generator i is started. In this simulation, this power is taken as the minimum output power of the generator. Equation 18 is the generator ramp down constraint. This constraint is to ensure that generators are not allowed to change their outputs beyond safe operating regions in between any two time periods. DRi is the ramp down rate of generator i. Psd,i is the maximum output power before a generator is shut down. In this simulation, this value is taken as the minimum output power of the generator. Next, the system flow constraints are established. The flow constraints are necessary to ensure that no lines in the system are overloaded. These constraints are implemented via the DC power flow equations. The DC power flow constraints are shown in equations 19, 20, and 21. · (19) · · (20) | | (21) Equation 19 describes the power flow on a line as a function of the net power injection at the buses in the system and the system shift factors. sf is an m x n matrix. It is a function of the system configuration as well as the impedances of the lines. m is the number of branches in the system. n is the number of buses in the system. Pinj is an n x 1 vector that contains the net power injection at each bus in the system. The result of this product is an m x 1 vector that contains the power flows on each line in the system. Equation 20 is the net DC power injection at each bus where Kp and KD are generator and load incidence matrices respectively. Equation 21 is the enforcing of the line flow limits. The absolute value of the line flow is necessary to ensure that the flow limit is not violated in either the positive or the negative direction. Equations 22 through 30 represent the constraints governing the PHEVs derived from [4]. , · , · , , · , · (22) , · , · , , · , · (23) , , · , (24) , , , (25) , (26) , , 1 (27) · · (28) · · (29)

PEV, ∑ R , RTOT, (30) where ICH and IDCH are the status charging and discharging variables respectively, PCH and PDCH are the charging and discharging powers respectively, ECH and EDCH are the charging and discharging energies respectively. ENET is the net energy exchanged with the battery, η is the charging efficiency of the battery, N is the number of PHEVs being considered, PEV is the amount of power available in the battery, and E is the amount of energy available in the battery. Equations 22 and 23 set the limits on the battery charging and discharging powers. Equation 24 describes the net exchange of energy with the batteries. Equation 25 describes the amount of power available in the battery. Equation 26 describes how much energy is in the batteries at time t. Equation 27 ensures that the battery is not charging and discharging at the same time. Equation 28 enforces the energy limits on the batteries. Equation 29 enforces a minimum state of charge at the end of the optimization horizon. Equation 30 incorporates the PHEVs into the reserve scheduling constraint.

III. SIMULATION RESULTS The above optimization problem was enforced on a system

based on the IEEE 9 bus system. This was chosen to demonstrate the ability of PHEVs to help in supplying a distributed reserve requirement for small power systems. The PHEV battery data is based on [4]. The system information is taken from the MATPOWER toolbox [6]. The line resistances are assumed to be sufficiently small so as to be negligible with respect to the system solution. The generator data is based on [7]. The system data is summarized in tables I, II, III, and IV.

Table I – System Line Data

From Bus To Bus X (pu) Max (kW) 1 4 0.0576 250 4 5 0.092 250 5 6 0.17 150 3 6 0.0586 300 6 7 0.1008 150 7 8 0.072 250 8 2 0.0625 250 8 9 0.161 250 9 4 0.085 250

Table II – Generator Data

Unit 1 Unit 2 Unit 3 A ($/h) 1000 700 450

B ($/kWh) 16.19 16.6 19.7 C ($/kW2h) 0.00048 0.002 0.00398 Pmin (kw) 80 20 25 Pmax (Kw) 455 130 162

Ramp Up Rate (kW/h) 100 80 50 Ramp Down Rate (kW/h) 60 30 40

Minimum On Time (h) 8 5 6 Minimum Off Time (h) 8 5 6

Start Up Cost ($) 4500 550 900

Table III – Load Data

Bus Load (% of System) Load 1 9 30 Load 2 7 30 Load 3 5 40

Table IV – PHEV data

Value/PHEV A ($/kW2) 0.41 B ($/kW) 8.21 C ($/h) 0

Max Charge (kW) 7.29 Min Charge (W) 7.3

Max Discharge (kW) 6.2 Min Discharge (W) 6.2

Max Capacity (kWh) 27.4 Min Capacity (kWh) 5.48

There are several different methods in determining the

amount of spinning reserves required by a system. For example, the North American Electric Reliability Corporation’s BAL-002 standard says that a balancing authority or reserve sharing group must have enough reserve to cover the most severe single contingency. The Western Electric Coordinating Council says that an operator must schedule the maximum of the most severe single contingency or 5% of the hydro generation and 7% of the thermal generation. The Union for Coordination of Transmission of Electricity in Europe requires enough reserve to cover the maximum instantaneous power deviation of the synchronous system [8]. Three reserve scheduling scenarios were simulated. Scenario 1 requires scheduling enough reserve to cover the most severe single contingency, in this case the loss of generator 1. Scenario 2 requires enough reserve to be scheduled to equal to the magnitude of peak load. Scenario 3 requires scheduling enough reserve to cover 7% of total generation. Each scenario is simulated without PHEVs to obtain a base result, and then re-simulated with PHEVs to obtain their impact. The impact of the PHEVs on the production costs of the three scenarios is presented in Table V.

Table V – Total system costs for 3 reserve scenarios

Scenario 1 without PHEVs $ 968,430.34 Scenario 1 with 20 PHEVs $ 297,047.79 Scenario 2 without PHEVs $ 251,889.42 Scenario 2 with 20 PHEVs $ 239,724.50 Scenario 3 without PHEVs $ 111,499.37 Scenario 3 with 20 PHEVs $ 109,383.37

The results from table V show that by incorporating PHEVs

into the reserve scheduling algorithm, significant savings can be made in terms of total system production costs. The particularly interesting result is for scenario 1. Since this is a small system, its own generators were not enough to meet the

system load while scheduling enough reserve to cover the loss of generator 1. As a result, the system operator had to import reserve from outside the system and as a result was penalized. By incorporating the PHEVs into the reserve scheduling algorithm, the operator would have been able to avoid importing reserve and thus reaps significant costs savings. Another important trend from these results is that the magnitude of the benefit afforded by PHEVs significantly increases as the amount of required reserves increases. The inclusion of PHEVs into the reserve scheduling process may also allow more expensive units to be turned off and cheaper units can be turned on. This result is verified via the commitment schedule of the units if the reserve requirement requires enough reserve to cover 50% of system load as shown in table VI.

Table VI – Unit commitment schedules and total system cost

50% Reserve with no PHEVs Cost: $134,026.16 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10 0 0 0 0 0 0 0 0 0 1 1 1 1 1 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0

50% Reserve with 20 PHEVs Cost: $130,332.38 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 00 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 10 0 0 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Table VI shows that the PHEVs were enough to turn off the

more expensive unit (generator 1) and allow the other cheaper units to turn on to supply the load. This translates into a reduction in the total system cost for one day, in this case $3,693.78.

System locational marginal prices (LMPs) for the 24 hour

simulation are shown below in figure 2.

Fig. 2. System LMPs

The blue curve represents the LMPs for the system without

PHEVs while the red curve represents the system LMPs with 20 PHEVs. Since the size of this system is relatively small, there is no significant congestion throughout the network. As a result, all buses share the same LMP. The PHEVs do reduce

the LMPs at certain points throughout the day. Figure 3 shows the impact of the number of PHEVs on the depth of discharge of their collective batteries.

Fig. 3. Depth of Discharge

Figure 3 provides an interesting result. It can be seen that

until a certain number of PHEVs are connected to the system, the benefit they provide severely discharges the batteries. This may offset the benefit they provide by severely decreasing the operational lifetime of the battery. The number of PHEVs required to begin to mitigate the impact on battery depth of discharge is the critical number of PHEVs. This critical number of PHEVs represents the minimum number of PHEVs required such that their reserve schedule does not consume their entire schedulable energy. For this simulation, the reserve requirement was taken as 7% of the entire system load. By connecting less than 11 PHEVs, the entire available schedulable energy of the batteries is used. However, by increasing the number of PHEVs beyond this point, the impact on the depth of discharge of the batteries can be mitigated.

IV. CONCLUSION PHEVs are likely to be dominant in the future

transportation sector and PHEVs with vehicle-to-grid functionality can provide significant benefits to the power system. This paper explored the potential benefit afforded by including PHEVs into the spinning reserve scheduling process. The paper developed a mixed integer, linear programming security constrained unit commitment formulation that incorporates the PHEVs into the reserve scheduling process. Different reserve scheduling practices were simulated and the impacts of PHEVs on these techniques were presented. PHEVs can decrease the overall system operating cost. They can provide significant savings if their inclusion curtails the reserve imports from outside the network. They can decrease system LMPs at certain times by curbing the generation schedules of more expensive units. This paper showed the critical number of PHEVs required to satisfy system reserve requirements for a test system while beginning to mitigate the impact on battery depth of discharge. This paper investigated the impacts of PHEVs on small power systems. Future work should consider their impact on larger power systems, larger PHEV penetration

levels, and their potential benefit in other ancillary services such as regulation reserve.

V. ACKNOWLEDGEMENT This work was supported in part by NSF Grant 0844707.

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