Online Optimal Power Management Considering Electric Vehicles, Load Curtailment and Grid Trade in a Microgrid Energy Market Vivek Mohan, Reshma Suresh M P, Jai Govind Singh and Weerakorn Ongsakul Energy FoS, SERD, Asian Institute of Technology, Khlong Luang, Pathumthani, 12120, Thailand Email:
[email protected] Abstract—This paper proposes an online optimal power management problem for microgrid energy market considering electric vehicle (EV) charging/discharging, load curtailment and grid power transactions. Fuel and emission costs of conventional sources, hourly profits, incentives for load curtailment, revenue/cost of grid power trade and charging/discharging price of electric vehicles (EV) are considered by the microgrid central controller (MGCC) for the dispatch. A realistic model for EV is considered with its state of charge (SOC), age/life, charging/discharging rate limits, trip period and number of switching. Two different objectives of the MGCC viz. operational cost minimization and overall profit maximization are compared in the CIGRE LV benchmark microgrid in terms of revenue, expense, node voltage, curtailed load, EV power, grid trade and overall execution time. Particle swarm optimization with time varying acceleration co-efficient (PSO-TVAC) and modified backward forward sweep (BFS) based optimal power flow (OPF) method is used to optimize the benefits. Index Terms— Demand response, Electric vehicle, Microgrid, Optimization, Power market
I. INTRODUCTION An electrical system with loads and energy resources that is operated in parallel with the utility grid or as an electrical island is termed as a microgrid [1]. The growth of self-sustainable microgrids on a deregulated platform, with increasing load demand, encouraged the investigations on efficient economic and operational management techniques for low voltage systems. Nowadays, microgrids participate in local as well as in the upstream grid power market through aggregators. Environmental impacts and fluctuating oil prices have encouraged the exploitation of renewable energy sources in the microgrids. It is easy to add generation sources to low voltage (LV) feeders and convert them to a microgrid if their capacities are less than 100kW. This option leads to the growth of radial utility distribution microgrids having a variety of DERs. Online power management takes measured data of loads and renewable power for real/quasi real time or very short term horizon dispatches and thus demands high speed algorithms. The MGCC of the microgrid is assigned the duty of scheduling power to the sources, feeding loads, checking operational contracts and minimizing operational costs [2]. Energy management problems based on optimization were discussed in several literatures. Some of them considered only
Boddeti Kalyan Kumar Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai - 600036, Tamil Nadu, India Email:
[email protected] fuel cost as operational expense [3] whereas others considered emission costs as well [4]. The benefits of MGCC was optimized considering demand response and power market in [5]. The same problem was addressed using power world simulator in [6]. But, the effects of EVs in power market were not considered. Different EV charging strategies were analyzed to choose the best one based on network and economic benefits in [7]-[9]. But the formulation emphasized on monopolistic objectives only. This paper proposes a power management problem in a microgrid considering 1) charging, discharging and idle modes of EVs 2) battery and network constraints 3) load curtailment compensation bids 3) fuel and emission costs of non-renewable energy sources 4) grid power trade at open market price 5) two different strategies of the MGCC to maximize overall profit or minimize operational cost and 6) 24hrs measured data of renewable energy and demand. The proposed problem is solved using PSO-TVAC and BFS based OPF in a three feeder CIGRE LV benchmark microgrid, comparing the two different strategies of the MGCC. The reminder of the paper is organized as follows. Objective formulation is given in Section II. Operational constraints are discussed in Section III. The methodology of OPF is detailed in Section IV and the test system data, results and analyses are given in Section V. The paper is concluded in Section VI with the run-down of main points. II. OBJECTIVE FORMULATION In the microgrid energy market, the bids are submitted by the generators, curtailable loads and EVs prior to the actual dispatch period. The real time measured data includes load demand, renewable power generation and availability of charging and discharging EVs in the parking lots. Based on the bids and real time measured data, the MGCC decides the actual dispatch and sends it to the local controllers for implementation and possible alterations. A scheme for incentive based demand response enables the consumers to curtail their load. The incentive is represented as a fraction of grid power price so that it takes in to account, the peak and off-peak hour demands. Equation (1) represents the load bid. ܥܥܮሺܲ ሻ ൌ ߛ Ǥ ܥௗ Ǥ ܲ
(1)
ܲ is the load curtailment from݆th consumer (kW), ܥܥܮሺܲ ሻ is the expected load curtailment compensation submitted as bid, ߛ is the percentage of grid power price (ܥௗ ) given as compensation. Each curtailable load has its own compensation according to the criticality. Maximum curtailable power for ݆௧ ሺ௫ሻ . Equation (2) represents the generator load is limited to ܲ bid. ܾ݀݅݊݁ܩ൫ܲ ൯ ൌ ܥܫ Ǥ ܲ ܿ
(2)
ܥܫ for conventional power sources (FC, MT and DG) is the sum of incremental fuel and emission costs of the ݅ ௧ generator and ܿ is its expected hourly profit. Active power output of ݅ ௧ generator is ܲ (kW). For renewable energy sources, ܥܫ is annual depreciation for kWh output and ܿ is zero [6]. EV bid is defined as the desired discharging price of ݇ ௧ EV at time t, ǡ௧ . Mode of ݇ ௧ EV at time t ሺ݁݀ܯǡ௧ ሻ is defined by ܾܸ݀݅ܧ ǡ௧ the following conditions. If ܥௗ ܾܸ݀݅ܧ then it is in ǡ௧ ǡ௧ discharging mode i.e. ݁݀ܯൌ െͳ. If ܥௗ ܾܸ݀݅ܧ , ǡ௧ then the EV is in charging mode i.e. ݁݀ܯൌ ͳ. If ǡ௧ ǡ௧ ܾܸ݀݅ܧ ܥௗ ܾܸ݀݅ܧ then it is in idle and ܹ are the SOC and RBC modeሺ݁݀ܯǡ௧ ൌ Ͳሻ. ܹ (remaining battery capacity) dependent discharging and charging weighing factors of kth EV. It also depends on the remaining time of discharging/charging period and elapsed time of battery life [10]. Expenses of MGCC in the market is given in (3) which includes purchase of power from load curtailment at ܥܥܮ, grid at ܥௗ , generators at ܾ݀݅݊݁ܩand discharging EVs at ǡ௧ . ܾܸ݀݅ܧ ݔܧሺܲሻ ൌ ൣ൛σ ୀଵ ܾ݀݅݊݁ܩ൫ܲ ൯ൟ ܾ݀݅݊݁ܩሺܲ௪ ሻ ܾ݀݅݊݁ܩሺܲ௦ ሻ ൛ܥௗ ൈ ܲௗ ൟ σୀଵ ܥܥܮ൫ܲ ൯
(3)
Where, ܲ is the input power of ݇ ௧ charging EV, ݄݊ܿ is the total number of available charging EVs in the parking lots. Now, profit of MGCC is defined as (5).
Now, the two objectives of the MGCC, operational cost minimization (Objective-1) and overall profit maximization (Objective-2) are given in (6) and (7) respectively.
ܴ݁ݒሺܲሻ ൌ ൣܥௗ ൈ ൛ܲௗ ൫σ ୀଵ ܲ ൯ ሺܲ௪ ሻ ሺܲ௦ ሻ ൫σ ܹ ൈ ܲ ൯ െ ൫σ ሺܹ ൈ ܲ ൯ൟ ൫σ ሺܹ ൈ ܲ ൈ
ǡ௧ ܾܸ݀݅ܧ ሻ൯൧
In objective-1, the exchange of power with the main grid is minimized and thus tries to have a lesser participation in the open market. (7)
ݐ݂݅ݎܲ݁ݖ݅݉݅ݔܽܯሺܲሻ
With objective-2, the microgrid maximizes its value in the external market by increased participation, to earn maximum overall profit. However, it depends on the local generation and the load demand of the microgrid. If there is excess local power, it can be utilized to have earn a high profit by using this objective. III. OPERATIONAL CONSTRAINTS A. Power Balance Equality Constraint σ ୀଵሺܲ ሻ ܲ௪ ܲ௦ σୀଵ ܲ σୀଵ ܲ
(8)
ܲௗ ൌ ܲௗ ܲ௦௦ σ ܲ
Where, ܲௗ is the remaining active power load demand after curtailment, ݈ is the total number of curtailable loads, ܲ௦௦ is the total loss of the microgrid network. B. Generation Constraint: ሺ݉݅݊ሻ ሺ݉ܽݔሻ (9) ܲ ܲ ܲ ݃݅
݃݅
݃݅
C. Voltage Constraint for ith Node: ሺ݉݅݊ሻ
ܸ݅
(4)
(6)
ݔܧ݁ݖ݅݉݅݊݅ܯሺܲሻ
ǡ௧ σ ୀଵ ሺܹ ൈ ܲ ൈ ܾܸ݀݅ܧ ሻ൧
Where, ݊ܿ is the number of conventional energy sources in the microgrid, ݆ is the number of curtailable loads, ܲ is the curtailed power from ݆th curtailable load (kW), ݊ ݄ܿܦis the total number of available discharging EVs, ܲ is the power ௧ output from ݇ discharging EV (kW), ܲ௪ is the active power output (kW) of wind generator, ܲ௦ is the active power output (kW) from solar generation, ܲௗ is the net grid power (purchased kW – sold kW). Similarly, equation (4) gives the MGCC’s revenue from the market. The purchased power from different sources viz. grid, generators and EVs, are sold to needy power sinks to earn revenue. It includes earnings from selling of power to the loads, charging electric vehicles and grid at the market price.
(5)
ܲݐ݂݅ݎሺܲሻ ൌ ܴ݁ݒሺܲሻ െ ݔܧሺܲሻ
(10)
ሺ݉ܽݔሻ
ܸ݅ ܸ ݅
D. Grid Power Constraint: ሺ݉݅݊ሻ
(11)
ሺ݉ܽݔሻ
ܲ݃ ݀݅ݎ ܲ݃ ݀݅ݎ ܲ݃݀݅ݎ E. Load Curtailment Constraint
(12)
ሺ௫ሻ
Ͳ ܲ ܲ F. EV constraints ݇ǡݐ
݇ǡݐെͳ
݇ǡݐ
ܥܱܵܧൌ ܥܱܵܧ ߟ ݇ܥൈ ܲ ݄ܥെ ݇ǡݐ
ͳ
݇ǡݐ
݇ǡݐ
ൈ ܲ ݄ܿܦെ ݅ݎݐܧ ܦ
(13)
ߟ݇
݉ܽݔ ܥܱܵܧ ߔ݉ܽݔ ݇ ൈ ݐݐܽܤܧǡ݇ Ǣ ݐ
(14)
୩ǡ୲ Stored energy at the tth hour ሺୗେ ሻ in the EV battery depends on the charging & discharging power and ୩ǡ୲ିଵ efficienciesሺɄେ୩ ƬɄୈ ), SOC of the previous hour ሺ ሻ and ୩ ୗେ
୩ǡ୲ energy discharged during tripsሺ୲୰୧୮ ሻ. Ȱ୩୫୧୬ and ୫ୟ୶ Ȱ୩ represent the minimum and maximum battery capacity.
Start Initialize np within the limits. Set maximum iteration count = itr_max for PSO-TVAC. Initialize iteration count,
(15)
݇ǡݐ
݉ܽݔ ܥܱܵܧ ߔ݉݅݊ ݇ ൈ ݐݐܽܤܧǡ݇ Ǣ ݐ
EV charger constraints for maximum charging and discharging rate is given by: ǡ௧ (16) ܲ ܲǡ௫ Ǣݐ
Set power flow iteration count K=1 and initial voltages 1+j0 for all nodes ൌͳ
݇ǡݐ
ܲ ݄ܿܦ ݄ܲ݇ܿܦǡ݉ܽ ݔǢ ݐ Where, ܲǡ௫ and ܲǡ௫ are the maximum charging and ݄ݐ discharging powers of ݇ EV. Charging/Discharging rate limits are given in (17). οܱܵ ݔܽ݉݇ܥis the maximum permitted rate for charging/discharging of the ݇ ݄ݐEV. (17) െοܱܵ ݇ܥ οܱܵ݇ܥǡ ݐ οܱܵ݇ܥ ݉ܽݔ
Execute backward sweep to find injected current,
Execute forward sweep to find voltage at jth node connected to ith node,
݉ܽݔ
Duration of parking of EV is given in (18). ݐ and ݐௗ are the time of arrival and departure of kth EV, ܶ is the time span of parking. This allows the MGCC to schedule the discharging and charging of each EV while they are in the parking lot. ݀݇ݐ
݇ǡݐ
σݐൌ ݇ݐȁ ݁݀ܯȁ ൌ ܽݎ
ܶ݇ݎ
and update
and update
(18)
Switching limit for charging and discharging is given in (19). (19) ݇ܦ ܵܰ ݉ܽݔ
Where,ܦ is the number of switching between discharging and charging modes of the ݇ ௧ EV during parked period and ܵܰ௫ is its maximum number. IV.
METHODOLOGY
Here, PSO-TVAC [11] is used for optimizing the objective of the MGCC different cases. The control variables are active power generations associated with MT, FC, DG, CL1, CL2, and EV. The velocity and position of the particles are updated using (20) and (21).
Set initial voltage at nodes as UK and K=1
Calculate line flow,
=
and loss, Update velocity and position of the particle using equations (20) – (21)
Evaluate the fitness function to find Pbest and Gbest
Iteration Termination Criterion
ݒǡௗ
ାଵ
ൌ ߱ ൈ ݒǡௗ ܽଵ ൈ ݀݊ܽݎଵ ൫௦௧ െ ݔǡௗ ൯ ܽଶ ൈ ݀݊ܽݎଶ ሺ݃௦௧ െ ݔǡௗ ሻ
(20)
Output the final cost, real and reactive power injections, line flows, losses and voltage at each node Stop
(a)
(21)
ݔǡௗ ାଵ ൌ ݔǡௗ ݒǡௗ Where, ߱ ൌ ሾ߱௫ െ ሾሼ
ఠೌೣ ିఠ ೌೣ
ೌೣ ି
ܽ ൌ ሾܽ௫ െ ሾሼ
ೌೣ
ሽ ൈ ݅ܿሿ
ሽ ൈ ݅ܿሿǢ ݅ ൌ ͳǡ ʹ
(22) (23)
݀݊ܽݎଵ and ݀݊ܽݎଶ are random numbers generated between 0 and 1, ߱ is the inertia factor in ݅ܿ ௧ iteration,ܽଵ ܽ݊݀ܽଶ are the cognitive and social parameters in ݅ܿ ௧ iteration to control the behavior and efficacy of the method. ݔǡௗ is the ith element of dth particle in ݅ܿ ௧ iteration. ݒǡௗ is the velocity of ith
(b) Figure 1. (a) Flowchart of online OPF (b) Node voltage and line current representations.
element of dth particle in ݅ܿ ௧ iteration. The methodology for online optimization in a microgrid, combining PSO-TVAC and backward-forward sweep is presented in the flowchart of Fig. 1(a). The voltage and current representations are in line with Fig. 1(b).
Figure 2. CIGRE LV Benchmark Microgrid with information from the parking lot
V. SYSTEM STUDIES A. Test System Model CIGRE LV benchmark microgrid [1] shown in Fig. 2 is used as the test system. The corresponding 24hrs load curve is shown in Fig. 3. The models of FC, MT and DG are modelled as 1st order systems derived from their dynamic responses in cold start and running modes. Their incremental cost (ICi) functions [12] are shown in Fig. 4. The values of ci for fuel cell (FC), micro-turbine (MT), diesel generator (DG), wind generator (WG) and solar power source are assumed as 1.06$/hr, 0.376$/hr, 0.3$/hr, 0.068$/h and 0.761$/h respectively. Accordingly, the DER bids are in the following descending order: DG>MT>FC>Solar>Wind. PQ-inverter/PQ node model is used for solar PV source in power flow [6]. Nodal power factor is assumed to be 0.9 and voltage range is 0.95p.u to 1.05p.u. The loads (CL1 AND CL2) at nodes 9 and
Figure 3. Demand for 24 hours
8 are curtailable by a maximum of 50%. ߚ for CL1 is 1.5 (costlier than grid price; critical) and CL2 is 0.8 (cheaper and less critical).
Figure 4. Cost functions of conventional sources
Figure 5. Open Market price for 24 hours
TABLE I. COMPARISON OF POLICIES
Curtailed load (kW)
Conventional gen (kW)
Renewable gen (kW)
EV Discharging Power (kW)
EV Charging Power (kW)
CL1
CL2
Profit(P) ($)
Exp(P)
Rev(P)
($)
($)
Grid Power (kW)
Strategy1
118.86
476.93
595.79
3764.42
1014.42
175.84
229.12
948
22.49
62.49
Strategy2
133.44
469.38
602.82
3862.57
917.31
175.84
288.20
988
23.36
36.05
Policies
For EVs, a power consumption of 3kW/hr is assumed for their trip [10]. A random number between 10% and 70% of the battery capacity (16.5kWh) is considered as the initial SOC. The 24 hrs grid power price is given in Fig. 5 and renewable generation is given in Fig. 6. B. Results and Discussions
Figure 9. Policy 1 - Net EV and grid power
Figure 6. Renewable energy generation
Table 1 shows the comparison of results of cost minimization (Strategy-1) and profit maximization (Strategy-2). Strategy-2 earns a higher profit of 133.44$ compared to 118.86$ earned by strategy-1. This is because of the higher revenue (602.82$) and lower cost (469.38$) obtained in strategy-2. This is in line with the included terms of revenue and cost in (5) for the objective given in (7). Though net grid power is the difference between purchased and sold power, there is no sold power in
Figure 7. Policy 1 – Micro-sources power dispatch
Figure 8. Policy 2 – Micro-sources power dispatch
Figure 10. Policy 2 - Net EV and grid power
the entire time frame of both the strategies (Figures 9 and 10). This implies that there is only cost (no revenue) related to grid trade. Thus, better cost associated for grid is for strategy-1 and hence, purchased power (3764$) is less for the same. Since, renewable energy sources’ dispatch uses measured data, their values are same for both the strategies (Table. 1). In view of generating increased revenue, strategy-2 uses more EVs for discharging (288.2kW in Table) compared to strategy-1 (229.12kW in Table). Regarding load curtailment, CL2 is more curtailed compared to CL1 (Table. 1), in both the cases because of its cheap compensation rate. But total power curtailment is more for strategy-1. This makes the voltage profile of node-8 better in strategy-1 than in strategy-2 (Figures 11 and 12). Similarly, higher usage of MT in strategy-1 (Fig. 7) compared to strategy-2 (Fig. 8) leads to a better voltage profile for node12 (Figures 11 and 12) in strategy-1. The costliest DG is utilized more in strategy-1 than in strategy-2 (Figures 7 and 8). This is because of the higher grid dependency of strategy-2 (Table. 1). EVs are predominantly in the charging mode till it reaches its SOCmax at 5th hr (Figures 9 and 10). From 5th to 8th hour, the grid price is low (Fig. 5) and the EVs are in the idle mode. They are at the residential feeder during this period (till 5th hr) and hence the voltage profile of node 8 is comparatively low in both the strategies (Figures 11 and 12). The EVs are on trip from 8th hr to 9th hr and thus, the net EV power is found to be zero in Figures 9 and 10. However, the grid power price has
spikes at the 13th, 17th and 21st hours, which lead to discharging spikes at these hours (Figures 9 and 10). Most of the EVs are at the 14th node of the commercial feeder (Fig. 2) at these hours. Consequently, a small voltage hike is found at this node during these hours (Figures 11 and 12). As a whole, it can be noticed from Figures 11 and 12 that all the voltages are within the limits. In respect of the online execution time, strategy1(0.5s) is somewhat better than policy-2 (0.8 s). From Figures 7 and 8, the dynamics of DER outputs are smoother for strategy-2 than for strategy-1.
the CIGRE LV benchmark microgrid. It can be inferred that profit maximization performed better in terms of expense, revenue and smoother dynamics of DERs whereas cost minimization outperformed with respect to faster execution time and higher voltage profiles. However, profit maximization could utilize more EVs in the parking lots for settling the market without curtailing much load. In short, the MGCC should switch between the strategies in accordance with the grid price, availability of EVs, measured demand and renewable energy to extract maximum benefits out of the market. REFERENCES
Figure 11. Voltage profiles-Policy 1
Figure 12. Voltage profiles-Policy 2
VI. CONCLUSION Online power management and benefit optimization were simultaneously carried out in a microgrid energy market in the online mode. Economic and technical aspects were considered at the same time by using PSO-TVAC and modified BFS based OPF. Two strategies adopted by the MGCC, were compared in
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