Placement and Fixed Cost Allocation of ESS
Submitted By: Agam Goel (2011EE20505)
A report of EED 422 – B.Tech. Major Project Part 2 (EP) submitted in partial fulfilment of the requirements of the degree of Bachelor of Technology
Department of Electrical Engineering (Power) Indian Institute of Technology Delhi
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Placement and Fixed Cost Allocation of ESS
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CERTIFICATE I certify that this report explains the work carried out by me in the EED 422 – Major Project Part 2 (EP) under the overall supervision of Dr. B.K. Panigrahi. The contents of the report including text, figures, tables etc. have not been reproduced from other sources such as books, journals, reports, manuals or websites. Wherever reproduction from another source had been made, the source had been duly acknowledged at that point and also listed in the references.
Date:
Agam Goel 2011EE20505 Department of Electrical Engineering Indian Institute of Technology, Delhi
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CERTIFICATE This is to certify that the report submitted by Agam Goel (2011EE20505) describes the work carried out by him in the course EED 422 – Major Project Part 2 (EP) under my overall supervision.
Date:
Dr. B.K. Panigrahi Associate Professor Department of Electrical Engineering Indian Institute of Technology, Delhi
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ACKNOWLEDGEMENT
I am extremely grateful to Dr. B.K. Panigrahi for the guidance, encouragement and cooperation received throughout the project work. I owe the timely completion of this project work to his valuable advice, support and suggestions. I am also grateful to Deep Kiran, a research scholar working with Dr. B.K. Panigrahi. His constant efforts and guidance enhanced my understanding of the project and were critical to the completion of the project.
May, 2015 Agam Goel (2011EE20505)
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ABSTRACT The study presents a framework for placement of energy storage in a power system with three types of demand response - load curtailment, loads shifting and energy storage. The study also proposes a mechanism to allocate the fixed costs of ES among various beneficiary load buses. The studies are done on a modified IEEE 6 bus system. The optimisation problem solved by system operator is a Mixed Integer Non Linear Programming problem (MINLP) The study compares the unit commitment results across various models - without DR and with various DR and their combinations. The study shows that operators choose to curtail load/discharge battery during peak hours and shift load/charge battery to off-peak hours. The study also shows that LC/LS are preferred as compared to ES due to the latter being more expensive. The placement of ES is done considering both system cost and ES utilisation factor. The sharing of operational costs is automatically done during unit commitment and fixed cost sharing is done using the concept of nucleolus.
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CONTENTS ABSTRACT ............................................................................................................................... 6 1.
INTRODUCTION ............................................................................................................ 11 1.1
Motivation ................................................................................................................. 11
1.2
Objectives .................................................................................................................. 11
2. LITERATURE REVIEW .................................................................................................... 12 3. THEORY ............................................................................................................................. 13 3.1 Unit Commitment........................................................................................................... 13 3.2 Demand Response Methods ........................................................................................... 13
5.
6.
3.2.1
Load Curtailment (LC) .......................................................................................... 14
3.2.2
Load Shifting (LS) ................................................................................................. 14
3.2.3
Energy Storage (ES) .............................................................................................. 15
3.3
Nucleolus ................................................................................................................... 16
3.4
Placement and Cost Allocation ................................................................................. 17
MATHEMATICAL MODELLING ................................................................................. 19 5.1
Notations ................................................................................................................... 19
5.2
Standard Unit Commitment ...................................................................................... 21
5.3
Unit Commitment with Load Curtailment ................................................................ 21
5.4
Unit Commitment with Load Shifting ...................................................................... 22
5.5
Unit Commitment with Energy Storage .................................................................... 23
5.6
Unit Commitment with LC/LS/ES ............................................................................ 23
5.7
Unit Commitment with LC/LS/ES (considering utilisation factor) .......................... 24
NUMERICAL STUDIES ................................................................................................. 25 6.1
Standard Unit Commitment ...................................................................................... 26
6.2
Unit Commitment (with LC) ..................................................................................... 27
6.3
Unit Commitment (with LS) ..................................................................................... 28
6.4
Unit Commitment (with LC and LS) ........................................................................ 29
6.5
Unit Commitment (with ES) ..................................................................................... 30
6.6
Unit Commitment (with LC, LS and ES) .................................................................. 31
6.7
Unit Commitment considering utilisation factor (with LC, LS and ES) ................... 32
6.8
Placement and Cost Allocation Problem ................................................................... 33 7|Page
7.
SUMMARY AND CONCLUSION ................................................................................. 37
8.
REFERENCES ................................................................................................................. 38
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LIST OF TABLES Table 6.1 Generator Data Table 6.2 Transmission Lines Data Table 6.3 Load Data Table 6.2.1 Load Curtailment Data Table 6.3.1 Load Shifting Data Table 6.5.1 Energy Storage Data Table 6.8.1 Nucleolus Data
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LIST OF FIGURES
Fig 6.1 One-Line Diagram of the 6 Bus Systems Fig 6.1.1 Generator Status Fig 6.2.1 Generator Status Fig 6.2.2 Load Curves (Normal vs LC) Fig 6.3.1 Generator Status Fig 6.3.2 Load Curves (Normal vs LS) Fig 6.4.1 Generator Status Fig 6.4.2 Load Curves (Normal vs LC, LS) Fig 6.5.1 Generator Status Fig 6.5.2 Load Curves (Normal vs ES) Fig 6.6.1 Generator Status Fig 6.6.2 Load Curves (Normal vs LC, LS, ES) Fig 6.7.1 Generator Status Fig 6.7.2 Load Curves considering UF (Normal vs LC, LS, ES) Fig 6.8.1 Load Curves considering UF (Normal vs LC, LS, ES at 3) Fig 6.8.2 Load Curves considering UF (Normal vs LC, LS, ES at 4) Fig 6.8.3 Load Curves considering UF (Normal vs LC, LS, ES at 5)
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1. INTRODUCTION 1.1 Motivation The emergence of various smart grid technologies and distributed energy resources has impacted power systems operations. Demand side management continues to play a significant role in day-ahead clearing of electricity markets. Customers these days participate in demand response (DR) programs (such as load curtailment and load shifting) and own small energy resources as well. Customers can adjust their load on basis of real-time time varying electricity prices. Also, incentive based demand response programmes give financial incentives to participants for adjusting their loads at specific times as requested by operator. Apart from financial benefits to market participants (customers and operators), DR methods can also contribute to system reliability, reducing outages. They also mitigate the ability of electricity supplier to increase prices by taking advantage of market power. DR methods such as load curtailment and load shifting are highly dependent on customer and change in load pattern is not guaranteed. Energy storage, on the other hand, is an effective method to reduce demand at peak timings and shift it to off-peak timings. With various ES methods available, the operator has to not only decide the type of ES but also determine its size and placement. These are extremely critical from an economic and operational standpoint. Finally, allocation of various costs of ES has to be done in a fair manner according to the benefits each customer receives.
1.2 Objectives The study has the following objectives 1. Study a 6 bus system with demand response (Load Curtailment (LC), Load Shifting (LS) and Energy Storage (ES)) at load buses and devise an algorithm for placement of Energy Storage so as to minimise LC, LS and maximise ES 2. Give a mechanism to allocate the fixed costs of ES among various beneficiary load buses
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2. LITERATURE REVIEW The problem of unit commitment has garnered large amount of interest of researchers since the last 40 years. However, it still hasn’t been solved using for all practical sizes and operating environment, as it is a Mixed Integer Non Linear Programming problem (MINLP). Approximated MILP solutions have been presented by Frangioni and Gentile in [15] and Carrrion and Arroyo in [16]. Several other techniques such as heuristics [17][18], Lagrangian relaxation [19][20] and evolution inspired approaches have also been proposed. In the last few years, with impetus towards demand side management, various demand response techniques have emerged as outlined in [3]. They have various financial, market performance and system stability benefits as given in [1], [2], [3]. Load Curtailment, Load Shifting and Energy Storage have garnered high research interest. Optimal placement of energy storage has been of high interests to researchers across the globe. This problem has often been dealt with the questions of choosing the type and size of energy storage, as the three problems are interdependent to an extent. Kraning et al. dealt with the problem in [12], where they look at configuring the portfolio of storage devices i.e. choosing single portfolio from a set of candidate portfolio. They also look at real time operation of a portfolio of storage devices. Denholm and Sioshansi analyse the advantages of collocating energy and wind storage to reduce transmission costs and increase transmission utilisation in [13]. Sjodin et. al propose a risk mitigating optimal power flow (OPF) framework to study the dispatch and placement of energy storage units in a power system with wind generators that are supplemented by fast-ramping conventional back-up generators in [14] Nucleolus has been used significantly in the past in the area of power systems. Jia and Yokoyama used it to allocate profit of independent power producers in [21]. Zolezzi and Rudnick used it to allocate costs of transmission system in [22]. Stamtsis and Erlich used the concepts of Shapley and Nucleolus to allocate fixed costs in [23]
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3. THEORY 3.1 Unit Commitment Unit Commitment problem is one of the critical problems to be solved by power system operators. It can be defined as determining the least cost power generation schedule from a set of online generating units to meet the total power demand at any given point of time. Unit commitment is often done for a time horizon of a day to a week. [9] There can be a wide variety of generating units such as 1. Thermal (using coal, gas, biomass) 2. Renewable (using hydro, wind, solar etc.) 3. Nuclear Unit commitment problem has to consider a number of transmission and operational constraints such as 1. Power balance constraint: The power supplied by generating units must meet load demand after accounting for transmission losses 2. Generating capacity constraints: The real and reactive power supplied by generating units must lie within minimum and maximum capacity of the units 3. Generator ramp rate limits: A generating unit’s real and reactive power output is constrained by the amount by which it can ramp up from one time unit to the next time unit. 4. Minimum generator uptime/downtime: Generating units have specific minimum uptime/downtime for feasible operation. 5. Prohibited operating zone constraints: To avoid system collapse due to resonance, some frequencies of operations are usually prohibited 6. Bus voltage constraints: The bus voltage magnitude and angle usually lie within an upper and lower limit for system stability 7. Transmission line constraint: Power flow from one bus to another is limited by the maximum capacity of transmission line.
3.2 Demand Response Methods According to the Federal Energy Regulatory Commission, a United States federal agency, demand response (DR) is defined as: “Changes in electricity usage by end-use customers from their normal consumption patterns in response to changes in the price of electricity over time, or to incentive payments designed to induce lower electricity use at times of high wholesale market prices or when system reliability is jeopardized.” 13 | P a g e
There are primarily two types of demand response methods, as categorised by US Department of Energy 1. Price Based Demand Response: These include critical peak pricing, real time pricing and time-of-use tariffs that allow customers to take advantage of time varying electricity rates by adjusting their usage based on prices. [3] 2. Incentive Based Demand Response Programmes: Such programmes give financial incentives to participants for adjusting their loads at specific times as requested by operator. Such requests are normally a result of high electricity prices or grid reliability problems. [3] The benefits of demand response can be categorised into three broad groups 1. Financial Benefits: Direct participants benefit financially due to incentive based payments by operators and reduced electricity bill costs either in response to time varying electricity rates or incentive based programmes. The market benefits as a whole due to efficient utilisation of infrastructure, such as reduction in demand from costly generating units. [1][3] 2. Reliability benefits: Demand Response methods can also contribute to system reliability by increasing the resources operator has to maintain system reliability, thus reducing forced outages and their consequences. [2] 3. Market Performance benefits: Ability of electricity supplier to increase prices by taking advantage of its market power is mitigated [3] For the purpose of this study, we will delve deeper into three specific types of demand response methods – Load Curtailment, Load Shifting and Energy Storage Systems
3.2.1 Load Curtailment (LC) In Load Curtailment, participants reduce their hourly electricity usage without shifting it to other hours. A typical LC offer includes LC quantity at offering hours, LC price that specifies how much the participant is willing to be compensated for curtailing load, LC initiation costs that cover the participants fixed costs. Participant constraints often include minimum and maximum hourly duration for LCs. [4]
3.2.2 Load Shifting (LS) In Load Shifting, participants reduce their electricity usage at peak-hours and shift it to offpeak hours. A typical LS offer includes LS quantity at offering hours, periods of the day curtailed load will be shifted to, LS price that specifies how much the participant is willing to be compensated for shifting load, LS initiation costs that cover the participants fixed costs. Participant constraints often include minimum and maximum hourly duration for LSs. [4] 14 | P a g e
3.2.3 Energy Storage (ES) In AC system, electrical energy can’t be stored directly but has to be converted from AC electrically and stored as kinetic/potential energy or electromagnetically/electromechanically. All types of energy storage can be modelled as a conversion unit to convert the energy from one form to another [5] Energy Storage Systems have to be charged initially and act as additional local load on the system before they can be used to be supply power to customer and lead to customer load reduction. A typical ES offer includes ES power rating and energy capacity, ES price, charge and discharge efficiency of ES, charge and discharge ramp of ES and the energy retention time of storage system. [4][6] Various kinds of energy storage options are: 1. Pumped Hydro Pumped Hydro pumps water from a reservoir at low elevation to a reservoir at high elevation using electricity in off peak hours. When electrical energy is needed, water is released via a hydroelectric turbine. Pumped Hydro has the highest capacity out of all the energy storage systems. Its capacity is constrained by the size of the available upper and lower reservoirs. [7] 2. Compressed Air Energy Storage Compressed Air Energy Storage compress and stores air in an underground cavern/aboveground pipes/vessels using electricity in off peak hours. When electrical energy is required, this air is heated, expanded, and sent to a turbine or an expander. [7]
3. Fly Wheel Energy Storage Flywheels store energy in the angular momentum of a rotor having a large inertia. The work done to spin the rotor is stored as kinetic energy. When electrical energy is needed, a flywheel energy storage system converts this kinetic energy through the use of power conversion systems and controls. [7]
4. Battery Energy Storage Batteries are charged during off peak hours and discharged during peak hours to reduce customer load. Various kinds of battery energy storage used are Sodium-Nickel-Chloride Battery, Sodium Sulphur Battery, Vanadium Redox Battery, Iron Chromium Battery, Zinc Bromine Battery and Lead Acid Battery
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3.3 Nucleolus In Game Theory, a cooperative game is a game where a group of players (henceforth referred as ‘coalitions’) may enforce cooperative behaviour, hence the game, instead of being played by individual players is played by coalitions. This is because according to principle of superadditivity, if players form a coalition of size , the amount received by players, is as large as the total amount received by any disjoint set of coalitions they could form. [8] Before delving deeper, we will consider a few definitions: Imputations: A payoff vector of proposed amounts to be received by the players, with the understanding that player is to receive , is sometimes called an imputation. An imputation is a payoff vector that is group rational and individually rational. [8]The set of imputations may be written {
{}
∑
Excess: It is a measure of the inequity of an imputation
for a coalition
}
and is defined as
∑
This measures the amount (the size of the inequity) by which coalition falls short of its potential in the allocation . Since the core is defined as the set of imputations such that ∑ for all coalitions , we immediately have that an imputation x is in the core if and only if all its excesses are negative or zero. Let be the vector of excesses arranged in non-increasing (lexicographic) order. The nucleolus is defined as an efficient allocation that minimises in the lexicographic ordering. [8] Nucleolus: Let { ∑ } be the set of efficient allocations. We say that a vector is a nucleolus if for every we have
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The nucleolus of a game in coalitional form exists and is unique. The nucleolus is group rational, individually rational, and satisfies the symmetry axiom and the dummy axiom. If the core is not empty, the nucleolus is in the core. [8]
3.4 Placement and Cost Allocation As discussed earlier, energy storage is one of the important demand response methods considered by power system operators. System operators typically face the following important questions with regards to energy storage systems [10]: 1. Type of storage: There are various types of ES such as pumped hydro, compresses air energy storage, fly wheel, battery. What type of energy storage system is feasible economically and operationally? 2. Sizing: What should be the size of energy storage? Should we consider a large single site installation or smaller distributed resources? Type of storage and space availability influence the sizing of ES 3. Placement: On which bus should the ES be installed? Space availability and economics of the power system influence placement of ES 4. Cost Allocation: How should ES costs involved be shared among various stakeholders? What costs should be borne by system operator? What costs should be borne by customers? Which should be the ratio in which costs are borne by different customers? Clearly, type of storage, sizing, placement and cost allocation of ES are inter-dependent problems. However, in this study, we tackle the problems of placement and cost allocation of ES. Placement of ES involved determining the bus at which a specified size of ES should be installed. Assuming that space availability is not an issue at any of the load buses, economics of the system will play a critical role in determining the solution. One of the approaches is to simulate unit commitment and find out the system cost by placing ES at each of the load buses one by one. The bus at which the least system cost occurs should be chooses for ES placement. However, as shown later using data backed analysis, such an approach is not recommended as the utilisation factor of ES comes out to be very low and usage of LC and LS is high. To avoid the undesirable situation of wasted capacity, it is recommended to also consider utilisation factor of ES while determining the final solution. There are two types of costs involved in ES [7] 1. Fixed Costs: These are one-time costs. They include : a. Equipment costs 17 | P a g e
b. c. d. e.
Installation costs Enclosures costs Owner Interconnection costs Miscellaneous costs (such as Engineering Fees, Project Contingency Application costs, Process Contingency Application costs)
The fixed costs are borne by system operators initially and are passed onto the beneficiary customers over the lifetime of ES. In some cases, part of the costs may be subsidised by government schemes to promote usage of ES 2. Operational Costs: These costs occur over the lifetime of ES based on its usage. They include a. Fixed operational and maintenance costs: Occur every year and depend on capacity of ES b. Variable operational and maintenance costs: Depend on charging and discharging of ES c. Periodic major maintenance costs: Occur 2-5 times in the lifetime of ES and depend on capacity of ES The operational costs are borne by beneficiary customers. They are automatically charged by the system operator during the unit commitment process via increased LMPs In this study, we propose that fixed costs of ES should be allocated by operator to various beneficiary customers using Nucleolus, a game theory concept as mentioned above.
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5. MATHEMATICAL MODELLING 5.1 Notations
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5.2 Standard Unit Commitment As discussed earlier, unit commitment has a number of equality and inequality constraints which need to be considered while optimising the system cost. These constraints have been modelled below: 1. Power balance constraint: ∑∑ 2. Generating capacity constraints: [
]
3. Generator ramp rate limits: [
]
4. Minimum generator uptime/downtime: [
] [
]
5. Transmission line constraint: [
]
|
|
The objective function is modelled as: ∑∑
5.3 Unit Commitment with Load Curtailment Apart from the constraints in standard unit commitment, a few constraints due to LC are also introduced as outlined below: 21 | P a g e
1. Maximum Load Curtailment Constraint
2. Minimum/Maximum Load Curtailment Duration
[
]
The objective function is also changed to include load curtailment costs borne by system operator: ∑∑
∑ ∑
5.4 Unit Commitment with Load Shifting Apart from the constraints in standard unit commitment, a few constraints due to LS are also introduced as outlined below: 1. Maximum Load Shifting Constraint
2. Load Shifting Balance Equation ∑
∑
3. Minimum/Maximum Load Curtailment Duration
[
]
The objective function is also changed to include load shifting costs borne by system operator: 22 | P a g e
∑∑
∑ ∑
5.5 Unit Commitment with Energy Storage Apart from the constraints in standard unit commitment, a few constraints due to ES are also introduced as outlined below: 1. Charging/Discharging Ramp Constraint
2. Energy Capacity Constraint
3. Energy Equation (for charging)
4. Energy Equation (for discharging)
The objective function is also changed to include energy storage costs borne by system operator: ∑∑
∑∑
5.6 Unit Commitment with LC/LS/ES Apart from the constraints in standard unit commitment, constraints due to LC, LS and ES are also introduced as outlined in the above sections. The objective function is also changed to include LC/LS/ES costs borne by system operator: ∑ ∑
∑
∑
∑ +∑
∑
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∑
5.7 Unit Commitment with LC/LS/ES (considering utilisation factor) UF for energy storage is computed as: ∑
/(
The cost remains the same as outlined in the above section: ∑ ∑
∑
∑
∑ +∑
∑
The objective function is changed to now include a factor for UF as well:
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∑
6. NUMERICAL STUDIES We consider a modified IEEE 6 bus system as shown in the figure below.
Fig 6.1 One-Line Diagram of the 6 Bus System [4]
The 6 bus system has generators at bus 1, 2 and 6. Bus 3, 4, 5 are load buses with facilities for considering demand response methods (LC, LS, ES). The data pertaining to generating units is given in Table 6.1 below: Table 6.1: Generator Data
Unit
G1 G2 G3
a ($) 177 130 137
Cost Coefficients Startup Cost b c 2 ($) ($/MW) ($/MW ) 13.5 0.00045 100 40 0.001 200 17.7 0.005 0
Shutdown Pmin Cost (MW) ($) 50 100 100 10 0 10
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Pmax (MW) 220 100 40
Min On (h) 4 3 1
Min Off (h) 4 2 1
Ramp (MW/h) 55 50 20
The transmission line reactance and flow limit is given in Table 6.2 below: Table 6.2: Transmission Lines Data
Line No. 1 2 3 4 5 6 7
From Bus 1 2 1 2 4 5 3
To Bus 2 3 4 4 5 6 6
X(pu) 0.170 0.037 0.258 0.197 0.037 0.140 0.018
Flow Limit (MW) 200 100 100 100 100 100 100
The load distribution across 24 hours is given in Table 6.3 below: Table 6.3: Load Data
Hour Load (MW) Hour Load (MW)
1 2 166.4 156
3 4 5 6 7 8 9 10 150.8 145.6 145.6 150.8 166.4 197.6 226.2 247
13 14 257.4 260
15 260
11 12 257.4 260
16 17 18 19 20 21 22 23 24 252.2 249.6 249.6 241.8 239.2 239.2 241.8 226.2 187.2
The load is distributed across bus 3, 4, 5 in the ratio 2:4:4 The optimisation problem is a Mixed Integer Non Linear Programming problem and is solved using CVX solver by M Grant.
6.1 Standard Unit Commitment In Case 1, we perform traditional unit commitment. The overall system cost comes out to be $ 84683.1. The status of generating units is given in Fig 6.1.1 4 3.5 G1, G2, G3 3 2.5 G1, G3
G1, G3
2 1.5 G1
G1
1 0.5 0
2
4
6
8
10
12 Hours (h)
14
16
Fig 6.1.1 Generator Status
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18
20
22
24
6.2 Unit Commitment (with LC) In Case 2, we perform unit commitment after allowing for load curtailment at load buses 3, 4 and 5. The LC quantity offered by load buses for hours 10-16 is mentioned in Table along with the LC price, LC initiation cost and min/max LC Duration. Table 6.2.1: Load Curtailment Data
Bus
LC quantity at offering hours (MW) 11 12 13 14 15
10 3 4 5
0.494 0.515 0.52 0.515 0.52 0.99 1.03 1.04 1.03 1.04 0.99 1.03 1.04 1.03 1.04
0.52 1.04 1.04
LC LC Min LC Max LC Price Initiation Duration Duration ($/MW) Cost ($) (h) (h) 0.504 10 20 3 6 1.00 10 20 3 6 1.00 10 20 3 6 16
After the optimisation process, the overall system cost comes out to be $79837.7. The status of generating units is given in Fig 6.2.1. It can be observed that in Case1, G2 is switched for 10 hours and in Case 2, G2 is switched only for 4 hours. 4 3.5 G1, G2, G3 3 2.5 G1, G3
G1, G3
2 1.5 G1 G1
1 0.5 0
2
4
6
8
10
12 Hours (h)
14
16
18
20
22
24
Fig 6.2.1 Generator Status
Fig 6.2.2 shows a comparison between original load curve and the new load curve clearly showing that the ISO chooses to schedule load curtailment at peak hours to reduce system cost.
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260 Normal Load Load (after LC) 240
Load (MW)
220
200
180
160
140
2
4
6
8
10
12 Hours (h)
14
16
18
20
22
24
Fig 6.2.2Load Curves (Normal vs LC)
6.3 Unit Commitment (with LS) In Case 3, we perform unit commitment after allowing for load shifting at load buses 3, 4 and 5. The LS quantity offered by load buses for hours 10-18 is mentioned in Table along with the LC price, LC initiation cost and min/max LC Duration. The curtailed load can be shifted to hours 2-10 Table 6.3.1: Load Shifting Data Bus
3 4 5
10
11
0.49 0.99 0.99
0.515 1.03 1.03
LS quantity at offering hours (MW) 12 13 14 15 16
0.52 1.04 1.04
0.515 1.03 1.03
0.52 1.04 1.04
0.52 1.04 1.04
0.504 1.00 1.00
17
18
LS Price ($/MW)
LS Initiation Cost ($)
0.499 1.00 1.00
0.499 1.00 1.00
10 10 10
20 20 20
Min LS time (h) 3 3 3
Max LS time (h) 6 6 6
T
2-10 2-10 2-10
After the optimisation process, the overall system cost comes out to be $84264.7. The status of generating units is given in Fig 6.3.1. It can be observed that in Case1, G2 is switched for 10 hours and in Case 3, G2 is switched only for 4 hours.
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4
3.5 G1, G2, G3 3
Load (MW)
2.5 G1, G3
G1, G3 2
1.5 G1 G1
1
0.5
0
2
4
6
8
10
12 Hours (h)
14
16
18
20
22
24
Fig 6.3.1 Generator Status
Fig 6.3.2 shows a comparison between original load curve and the new load curve clearly showing that the ISO chooses to curtail load primarily at peak hours of 10-16 and shift it to off-peak hours of 3-6. 260 Normal Load Load (after LS) 240
Load (MW)
220
200
180
160
140
2
4
6
8
10
12 Hours (h)
14
16
18
20
22
24
Fig 6.3.2Load Curves (Normal vs LS)
6.4 Unit Commitment (with LC and LS) In Case 4, we perform unit commitment after allowing for both load curtailment and load shifting at load buses 3, 4 and 5. The LC and LS specifications remain the same as in Case 2 and Case 3 After the optimisation process, the overall system cost comes out to be $78336.5. The status of generating units is given in Fig 6.4.1. Interestingly, ISO utilises LC and LS offers in such a way so as to prevent the switching on of Generator 2, leading to savings in start-up and shutdown costs.
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4 3.5 3 2.5 G1, G3
G1, G3 2 1.5 G1
G1
G1
1 0.5
0
2
4
6
8
10
12 Hours (h)
14
16
18
20
22
24
Fig 6.4.1 Generator Status
Fig 6.4.2 shows a comparison between original load curve and the new load curve clearly showing that the ISO chooses to curtail load primarily at peak hours of 9-19 and shift it to off-peak hours of 2-7 260 Normal Load Load (after LC,LS) 240
Load (MW)
220
200
180
160
140
2
4
6
8
10
12 Hours (h)
14
16
18
20
22
24
Fig 6.4.2Load Curves (Normal vs LC, LS)
6.5 Unit Commitment (with ES) In Case 5, we perform unit commitment after allowing for energy storage at bus 5. The Energy storage system capacity, efficiency and other constraints are mentioned in Table 6.5.1 Table 6.5.1: Energy Storage Data
Bus
3 4 5
ES Power Rating (MW) 0.520 1.04 1.04
Energy Capacity (MWh)
ES Price ($/MW)
Initial Energy (MWh)
Charge/Discharge Charge/Discharge Energy Efficiency Ramp (MW/h) Retention Time (h)
3.12 6.24 6.24
10 10 10
0 0 0
0.9 0.9 0.9
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20 20 20
18 18 18
After the optimisation process, the overall system cost comes out to be $84113.8. The status of generating units is given in Fig 6.5.1 4 3.5 G1, G2, G3 3
2.5 G1, G3
G1, G3 2
1.5 G1 1
G1
0.5
0
2
4
6
8
10
12 Hours (h)
14
16
18
20
22
24
Fig 6.5.1 Generator Status
Fig 6.5.2 shows a comparison between original load curve and the new load curve clearly showing that the ISO chooses to charge the battery during off peak hours and uses the stored energy to curtail customer load during on-peak. 260 Normal Load Load (after ES) 240
Load (MW)
220
200
180
160
140
2
4
6
8
10
12 Hours (h)
14
16
18
20
22
24
Fig 6.5.2Load Curves (Normal vs ES)
6.6 Unit Commitment (with LC, LS and ES) In Case 6, we perform unit commitment after allowing for both load curtailment and load shifting at load buses 3, 4 and 5. The LC, LS and ES specifications remain the same as in Case 2, Case 3 and Case 5 After the optimisation process, the overall system cost comes out to be $78334.6. The status of generating units is given in Fig 6.6.1. As observed in Case 4, here also LC, LS and ES offers are scheduled by ISO in such a way so as to prevent the switching on of Generator 2, leading to savings in start-up and shutdown costs.
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4
3.5
3
2.5 G1, G3
G1, G3
2
1.5 G1
G1 G1
1
0.5
0
2
4
6
8
10
12 Hours (h)
14
16
18
20
22
24
Fig 6.6.1 Generator Status
Fig 6.6.2 shows a comparison between original load curve and the new load curve clearly showing that the ISO chooses to curtail load primarily during peak hours of 10-18 and shift it partially to hours 2-8. Here, ISO has minimised the usage of Energy Storage Systems as it is expensive compared to LC and LS offers. 260 Normal Load Net Load Load after LC Load after LS Load after ESS
240
Load (MW)
220
200
180
160
140
2
4
6
8
10
12 Hours (h)
14
16
18
20
22
24
Fig 6.6.2Load Curves (Normal vs LC, LS, ES)
6.7 Unit Commitment considering utilisation factor (with LC, LS and ES) In Case 7, we perform unit commitment after allowing for both load curtailment and load shifting at load buses 3, 4 and 5. The LC, LS and ES specifications remain the same as in Case 2, Case 3 and Case 5. Here, both system cost and utilisation factor of energy storage are considered in the optimisation process. Also, the weights taken are and
After the optimisation process, the overall system cost comes out to be $79475. The utilisation factor comes out to be 0.5704. The status of generating units is given in Fig 6.7.1. As observed in Case 4, here also LC, LS and ES offers are scheduled by ISO in such a way so 32 | P a g e
as to prevent the switching on of Generator 2, leading to savings in start-up and shutdown costs. 4
3.5
3
2.5 G1, G3
G1, G3
2
1.5 G1
G1
G1
1
0.5
0
2
4
6
8
10
12 Hours (h)
14
16
18
20
22
24
Fig 6.7.1 Generator Status
Fig 6.7.2 shows a comparison between original load curve and the new load curve. Also, here LC, LS and ESS offers used have been explicitly shown. As can be seen after accounting for utilisation factor, we observe two cycles of charging and discharging. Also, LC and LS offers used have reduced as compared Case 6. 300 Total Load Net Load LC offers used LS offers used ESS offers used Energy Ess
250
Load (MW)
200
150
100
50 X= 22 Y= 0
0
-50
2
4
6
8
10
12 Hours (h)
14
16
18
20
22
24
Fig 6.7.2Load Curves consid ering UF (Normal vs LC, LS, ES)
6.8 Placement and Cost Allocation Problem As mentioned earlier, the placement of energy storage is done after accounting for overall system costs and utilisation factor of energy storage systems. Firstly, we consider the results of unit commitment when energy storage is placed at Bus 3, 4, 5 1. Bus 3 The overall system cost is $79443 and the utilisation factor of energy storage system is 0.4838. 33 | P a g e
300 Total Load Net Load LC offers used LS offers used ESS offers used Energy ESS
250
Load (MW)
200
150
100
50 X= 24 Y= 0.043167
0
-50
2
4
6
8
10
12 Hours (h)
14
16
18
20
22
24
Fig 6.8.1Load Curves considering UF (Normal vs LC, LS, ES at 3)
2. Bus 4 The overall system cost is $79461 and the utilisation factor of energy storage system is 0.5703. 300 Total Load Net Load LC offers used LS offers used ESS offers used Energy ESS
250
Load (MW)
200
150
100
50
0
-50
2
4
6
8
10
12 Hours (h)
14
16
18
20
22
24
Fig 6.8.2Load Curve s considering UF (Normal vs LC, LS, ES at 4)
3. Bus 5 The overall system cost is $79475 and the utilisation factor of energy storage system is 0.5704.
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300 Total Load Net Load LC offers used LS offers used ESS offers used Energy Ess
250
Load (MW)
200
150
100
50 X= 22 Y= 0
0
-50
2
4
6
8
10
12 Hours (h)
14
16
18
20
22
24
Fig 6.8.3Load Curves considering UF (Normal vs LC, LS, ES at 5)
Here, we observe that the overall system cost is minimised when ES placement is done at bus 3. However, then the UF is 0.4838 which is much less as compared to UF when ES placement is done at bus 4 and bus 5. Since, system cost is lesser when ES placement is done at bus 4 as compared to when placement is done at bus 5; the final placement is done at bus 4. The operating costs of ES are allocated automatically by system operator when solving for unit commitment via increased LMPs. However, the fixed costs have to be allocated among various beneficiary load buses by the operator. As discussed above, this will be done using Nucleolus, a game theory concept. Here, the coalitions characterisation function
considered is:
are
{
}.
The
Here, is the system cost when unit commitment is performed without any DR options. This cost is $84684.3. The system costs and characterisation function value considering various coalitions have been computed and are mentioned in Table 6.8.1 Table 6.8.1: Nucleolus Data
S 3 4 5 3,4 3,5 4,5 3,4,5
System Cost ($) 84488.6 84034.1 84113.3 83988.7 84030.5 83834.6 83828.1
v (S) 195.7 650.2 571 695.6 653.8 849.7 856.2
The nucleolus imputation is calculated according to the standard Nucleolus algorithm as mentioned earlier and the imputation comes out to be (64.1; 426.3; 365.8). 35 | P a g e
Hence, the fixed costs of ES will be allotted among buses 3, 4 and 5 in the ratio 64.1: 426.3: 365.8. This allocation is according to the benefits each customer receives from ES installation.
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7. SUMMARY AND CONCLUSION The study has proposed a framework for placement of energy storage in a power system with three types of demand response - load curtailment, load shifting and energy storage. The framework seeks to minimise the usage of LC and LS and maximise the usage of ES. The study also proposes a mechanism to allocate the fixed costs of ES among various beneficiary load buses. The studies are done on a modified IEEE 6 bus system. The optimisation problem is a Mixed Integer Non Linear Programming problem and is solved using CVX solver by M Grant. The study compares the unit commitment results across various models - without DR and with various DR and their combinations. It is observed that the ISO curtails load during peak hours and shifts them to off-peak hours. Also, the system cost is lesser when LC and LS are deployed as compared to the base case. It is also observed that ISO charges energy storage during off peak hours and discharges it during peak hours. Only one cycle of charging-discharging is observed when ES is deployed alone. When ES is deployed along with LC and LS, system operator accepts LC and LS offers and minimises ES as it is expensive compared to LC and LS. The utilisation factor of ES is low in this case. To increase the utilisation factor of ES, a weighted optimisation is done giving due weights to system cost and utilisation factor of ES. Such an optimisation results in a decrease in LC/LS usage and increase in ES usage. Also, two cycles of charging and discharging are observed in this case. Finally, placement of ES is done by analysing the system cost and utilisation factor when ES is placed at bus 3, 4 and 5 each. Even though the cost was least in case of bus 3, the final placement is done at bus 4 as it had a higher utilisation factor and the cost was also slightly higher. The sharing of operational costs is automatically done during unit commitment and fixed cost sharing is done using the concept of nucleolus.
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8. REFERENCES 1. Albadi, Mohamed H., and E. F. El-Saadany. "A summary of demand response in electricity markets." Electric Power Systems Research 78.11 (2008): 1989-1996. 2. Goel, L., Qiuwei Wu, and Peng Wang. "Reliability enhancement of a deregulated power system considering demand response." Power Engineering Society General Meeting, 2006. IEEE. IEEE. 3. QDR, Q. "Benefits of demand response in electricity markets and recommendations for achieving them." (2006). 4. Parvania, Masood, Mahmud Fotuhi-Firuzabad, and Mohammad Shahidehpour. "ISO's Optimal Strategies for Scheduling the Hourly Demand Response in Day-Ahead Markets." (2014): 1-10. 5. Gupta, Ravi, N. Nigam, and A. Gupta. "Application of energy storage devices in power systems." International Journal of Engineering, Science and Technology 3.1 (2011). 6. Eyer, Jim, and Garth Corey. "Energy storage for the electricity grid: Benefits and market potential assessment guide." Sandia National Laboratories (2010): 69-73. 7. Akhil, Abbas A., et al. "DOE/EPRI 2013 electricity storage handbook in collaboration with NRECA." ed: Albuquerque, NM: Sandia National Laboratories (2013) 8. Game Theory by Thomas S Ferguson 9. Lelic, A. "I." Unit Commitment and Dispatch." Introduction to Wholesale Electricity Markets (WEM 101), Northampton, MA, November 5-9, 2012." 10. A review of unit commitment by Brittany Wright 11. Bose, Subhonmesh, et al. "Optimal placement of energy storage in the grid." CDC. 2012. 12. Kraning, Matt, et al. "Operation and configuration of a storage portfolio via convex optimization." Proceedings of the 18th IFAC World Congress. 2011. 13. Denholm, Paul, and Ramteen Sioshansi. "The value of compressed air energy storage with wind in transmission-constrained electric power systems." Energy Policy 37.8 (2009): 3149-3158. 14. Sjodin, Emma, Dennice F. Gayme, and Ufuk Topcu. "Risk-mitigated optimal power flow for wind powered grids." American Control Conference (ACC), 2012. IEEE, 2012. 15. Frangioni, Antonio, and Claudio Gentile. "Perspective cuts for a class of convex 0–1 mixed integer programs." Mathematical Programming 106.2 (2006): 225-236. 16. Carrión, Miguel, and José M. Arroyo. "A computationally efficient mixed-integer linear formulation for the thermal unit commitment problem." Power Systems, IEEE Transactions on 21.3 (2006): 1371-1378. 17. Lee, Fred N. "Short-term thermal unit commitment-a new method." Power Systems, IEEE Transactions on 3.2 (1988): 421-428. 18. Li, Chao-An, Raymond B. Johnson, and Alva J. Svoboda. "A new unit commitment method." Power Systems, IEEE Transactions on 12.1 (1997): 113-119. 19. Merlin, André, and Patrick Sandrin. "A new method for unit commitment at Electricité de France." IEEE Trans. Power Appar. Syst.;(United States) 102.5 (1983).
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20. Zhuang, Fulin, and Frank D. Galiana. "Towards a more rigorous and practical unit commitment by Lagrangian relaxation." Power Systems, IEEE Transactions on 3.2 (1988): 763-773. 21. Jia, N. X., and R. Yokoyama. "Profit allocation of independent power producers based on cooperative Game theory." International journal of electrical power & energy systems 25.8 (2003): 633-641. 22. Zolezzi, Juan M., and Hugh Rudnick. "Transmission cost allocation by cooperative games and coalition formation." Power Systems, IEEE Transactions on 17.4 (2002): 1008-1015. 23. Stamtsis, Georgios C., and István Erlich. "Use of cooperative game theory in power system fixed-cost allocation." IEE Proceedings-Generation, Transmission and Distribution 151.3 (2004): 401-406.
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