Risk Index in Economic Generation Operation in Power Systems with

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Risk Index in Economic Generation Operation in Power Systems with Renewable Sources P. Mazidi, M.A.S. Bobi, E. Shayesteh, and P. Hilber ο€  Abstractβ€” In this paper, we present an index called reliability risk index to help system operator in making decisions and operation based on several parameters considering health, aging, reliability, maintenance, availability and risk of generators including renewable power sources. This approach not only improves reliability and decreases the risk of the failure of the grid, but also bases the decision on economical aspect which in turn results in the least operational costs for the system considering the minimum required risk level. Another feature of our approach is the assistance in proposing preventive maintenance schedules for each of the players in the system. The idea of this technique originates from the transition from conventional electric power system to smart grid. This transition utilizes new level of monitoring which has been the starting point and integration among different components. The approach is demonstrated through IEEE-RTS test system and the results show that this approach can have great impacts on all agents by increasing not only the availability, but also reducing the risk and costs. The model has been programmed in GAMS software and solved with CPLEX solver. Index Termsβ€”Reliability, Risk, Monitoring, System Operator, Maintenance, Renewable Sources

I. NOMENCLATURE πœ†β„Ž,𝑔

π‘žβ„Ž,𝑖,𝑔

total net power dispatched by generator g at hour h at bus i as a variable

π‘’π‘’β„Ž,𝑔

binary variable to indicate whether generator g is producing any power at hour h or not

π‘žπ‘”π‘šπ‘–π‘›

minimum gross power capacity of generator g that must be produced

π‘žπ‘”π‘šπ‘Žπ‘₯

maximum gross power capacity of generator g that can be produced

β€² π‘žβ„Ž,𝑖,𝑔

net power dispatched by generator g at bus i at hour h above minimum stable load as a variable

π‘Ÿπ‘ π‘”

upward ramp rate of generator g

π‘Ÿπ‘π‘”

downward ramp rate of generator g

π‘β„Ž

Number of hours

𝑁𝑔

Number of generators

𝑒𝑔

initial status of generator g

π‘¦β„Ž,𝑔

startup decision for generator g at hour h as a binary variable

Failure rate of generator g at hour h

πœ†β„Ž,π‘π‘œπ‘œπ‘™π‘–π‘›π‘”

Failure rate of cooling of generator at hour h

πœ†β„Ž,𝑀𝑖𝑛𝑑𝑖𝑛𝑔

Failure rate of winding of generator at hour h

π‘§β„Ž,𝑔

shutdown decision of generator g at hour h as a variable

πœ†β„Ž,π‘–π‘›π‘ π‘’π‘™π‘Žπ‘‘π‘–π‘œπ‘›

Failure rate of insulation of generator at hour h

𝛼𝑔

variable fuel consumption coefficient for generator g

π‘žπ‘›π‘’π‘‘

net output power of generator

𝛽𝑔

fixed fuel consumption coefficient for generator g

π‘˜π‘”

gross to net power coefficient for generator g π‘œπ‘π‘”

fixed O&M cost for generator g

π‘žπ‘”π‘Ÿπ‘œπ‘ π‘ 

gross output power of generator π‘œπ‘”

variable cost of O&M of generator g

P. Mazidi is with the Institute for Research in Technology (IIT), ICAI, School of Engineering, Comillas Pontifical University, Santa Cruz de Marcenado26, 28015Madrid, Spain (email: [email protected]).

5th International Conference on Energy, Sustainability and Climate Change (ESCC), Mykonos, Greece, June 4-6, 2018

2 𝑓𝑔

price of fuel used by generator g

𝛾𝑔

fuel consumption of generator g at startup

πœŽπ‘”

fuel consumption coefficient of generator g at shutdown

𝑆𝑖𝑗

Real power between bus i and bus j

𝑃𝑖𝑗

Active power between bus i and bus j

𝑄𝑖𝑗

Reactive power between bus i and bus j

𝑅𝑖𝑗

Resistance of transmission line between bus i and bus j

𝑋𝑖𝑗

Inductance of transmission line between bus i and bus j

𝑉𝑖

Voltage at bus i

πœƒπ‘–

Voltage angle at bus i

𝑆𝐡

Base power

π‘π‘β„Ž,𝑖,𝑗

active power flow at hour h from bus i to bus j as a variable

π‘‘β„Ž,𝑖

demand at but i at hour h

𝑁𝑗

Number of transmission lines

𝑁𝑖

Number of buses

π‘Ÿπ‘–β„Ž,𝑔

Risk index of generator g at hour h

II. INTRODUCTION

S

YSTEM operator (SO) is the entity responsible for reliable operation of electric power grid. As conventional electric power sources age, increase in restrictions and environmental taxes pushes old plants into difficult situations, complexity and uncertainty of maintenance scheduling remains a dilemma and renewable sources with their intermittent nature receive more participation, SO is facing an intertwined planning problem with some degree of uncertainty. Letting aside the planning for such an interconnected system, the move towards smart grid (SG), which is built through addition of new generation of monitoring, intelligent system monitoring, to the conventional electric power system (CEPS), is making this transition more complicated. However, researchers should address this complexity since SG promises an ideal system as a goal. In this regard, the idea is built upon on benefiting from the very large amount of available data and putting them into practice such that this process can be simple and in the direction of automation in future.

One part that our work is connected with is monitoring. condition monitoring (CM) has become possible by installing intelligent electronic devices (IEDs) in the main components in the electric power system (EPS) to monitor and analyze the behavior of these components and has opened a new window to the path to SG. CM has the potential to reduce operating costs, enhance reliability of operation, improve power supply and improve service to customers. [1], [2], [3], [4], [5], [6] apply techniques used for behavior analysis and monitoring of different sizes and types of generators. Reference [7] presents a literature review on concepts and functions of CM and popular monitoring methods and research status on transformers, generators and induction motors. Failure prediction, defection identification and life estimation can bring several advantages like: reducing maintenance cost, extending equipment’s life, enhance safety of operators, minimizing accidents or destruction severity and improving power quality to utility companies. [8] provides an overview on current standards for SG regarding monitoring, protection and control applications and highlights the challenges like integration, implementation, flexibility, compatibility etc. that these are facing. Some other works have also worked on communication aspects of monitoring (cyber network) and the issues related by focusing on the types of interconnections [9], [10]. Since our approach integrates this data as its input, we will not focus on trustworthiness of the data. [11] gives a critical overview on intelligent system monitoring. We have provided a novel approach to connect the knowledge inferred through these monitoring systems in EPS generation level and improve behavior of the system by helping in system operation and maintenance planning level. Another part that our work is connected with is maintenance. There are many studies on the maintenance topic [12], addressing impact of preventive maintenance (PreM) [13], [14], corrective maintenance (CorM) and maintenance degrees on the component and system to different types, e.g. as-good-as-new (AGAS), as-bad-as-old (ABAO) [15], imperfect maintenance (IM) [16] and smart maintenance (SM) [17]. The maintenance optimization is also very common in finding the optimum maintenance time [18], [19]. Some works have also linked reliability and maintenance [20], [21], [22]. Reference [23] proposed severity risk index to show severity of an event and measured the change in reliability of the system. Industry experts set the coefficients in this index. Reference [24] proposed an updated index without taking into account the impact of distribution resources on load. The main contribution of this paper is the introduction of a risk index based on the condition, health, age or failure rate of the generating agents in generation system operation taking into account variability in the generation level by having renewable energy sources. III. RISK INDEX Generally, whenever there is a talk about failure rate of a component, a mean and only one number is assigned to the component, no matter how many parts that component has. It

5th International Conference on Energy, Sustainability and Climate Change (ESCC), Mykonos, Greece, June 4-6, 2018

3

𝑛

Health

0.75 0.50 0.25

0.00

Time

Figure 2

Stair-wise transformation of health and risk Cumulative Distribution Function of Generators

1

0.9

CDF197 = CDF155

(1)

12MW 20MW 50MW 76MW 80MW 100MW 155MW 197MW 350MW 400MW

CDF400 = CDF350 = CDF100

0.8

0.7

= βˆ‘ πœ†β„Ž,𝑖

CDF76 = CDF50 0.6

From a different angle, failure rate behavior can be easily substituted by health, age, life, stability or any other index with reference to the component. For instance, if we are monitoring health of a component in real time and observe that the health is degrading, this degradation can be entered into the model and in the next analysis of the system, the model takes this change and correspondingly its risk into account in the operation. When this ability is made possible, the impact of maintenance based on the change in risk can be evaluated. The notion of the risk index implemented is based on Figure 1. In a simple representation, Figure 1 shows the linear relation between health and risk of a system considering the impact of maintenance.

Health with Maintenance

Risk with Maintenance

CDF

𝑖=1

Health/Risk

Risk

1.00

Health/Risk

can be noticed that though this unique number may present the failure life of a component in total, it cannot be helpful for maintenance of each (or main) parts of the component. Because each part can have a different failure behavior and thus, the maintenance scheme applied to it should be different as well. In this paper, a feature is implemented that change in failure behavior of each generating component is based on the current failure level of their different parts. This makes possible separate study of each component and their impact on the system, therefore, different maintenance schedules can be defined for one component, instead of one general maintenance plan for the component. (1) shows this feature for thermal generators: πœ†β„Ž,𝑔 = πœ†β„Ž,π‘π‘œπ‘œπ‘™π‘–π‘›π‘” + πœ†β„Ž,𝑀𝑖𝑛𝑑𝑖𝑛𝑔 + πœ†β„Ž,π‘–π‘›π‘ π‘’π‘™π‘Žπ‘‘π‘–π‘œπ‘›

0.5

MTBF12=3000

0.4

MTBF20=500

0.3

MTBF76=2000

0.2

MTBF100=MTBF350=MTBF400=1250

0.1

MTBF155=MTBF197=1000

0

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

Time - Hour

Figure 3

Cumulative Distribution Function of Generators

Another feature introduced in this paper is converting this parameter into a piecewise function that the pieces are not intervals but rather points, thus, the characteristic of the function itself is not lost. For this purpose, cumulative distribution function (CDF) of failure rates of generators are considered and illustrated in Figure 3. Moreover, since generators consider to be following a Weibull distribution function for failure behavior, the impact of PreM can be taken into account. Otherwise, it is believed that if failure rates follow an exponential distribution, PreM does not have any impact on component failure behavior, health or risk [25], [26], [27]. IV. MODEL DESCRIPTION

Time

Figure 1

Health and Risk of system considering maintenance

Indeed, it should be mentioned that in reality, this relation is not linear, however, for simplifying the problem, most of researchers consider converting this relation to a stair-wise relation. Figure 2 displays stair-wise transformed of the health and risk. As a result, the impact of maintenance defined in this model can take only fixed values for quantified periods and whenever the maintenance is performed, the health or the risk, based on Figure 2, go back in time and are assigned the new values of health or risk.

Study presented in this paper includes an optimization model for an hourly network constrained economic dispatch (HNCED) integrating a risk index (RI). The RI is considered to give assistance to SO as it introduces the inherent risk of power generating agents in the system. Therefore, the unit commitment is performed by not only considering network constraints, but also the unavailability risk of each of the generators. The general concepts of the model is based on [28]. Output power of the each power plant is defined as: (2) π‘žπ‘›π‘’π‘‘ = π‘˜ Γ— π‘žπ‘”π‘Ÿπ‘œπ‘ π‘  The generators’ minimum and maximum net capacities are: (3) π‘žβ„Ž,𝑖,𝑔 β‰₯ π‘’π‘’β„Ž,𝑔 Γ— π‘˜π‘” Γ— π‘žπ‘”π‘šπ‘–π‘› (4) π‘žβ„Ž,𝑖,𝑔 ≀ π‘’π‘’β„Ž,𝑔 Γ— π‘˜π‘” Γ— π‘žπ‘”π‘šπ‘Žπ‘₯ It can be noted here that implementation of maintenance can be done at this point. For instance, if it is planned that generator

5th International Conference on Energy, Sustainability and Climate Change (ESCC), Mykonos, Greece, June 4-6, 2018

4 number 10 for the period of βˆ†h is under maintenance, this can be implemented into the model by setting uuh,10 = 0 for that period. Ramping constraints of generators are also considered:

Figure 5

Transmission line and nodes including parameters

π‘β„Ž 𝑁𝑔 β€² β€² βˆ‘ βˆ‘(π‘žβ„Ž,𝑖,𝑔 βˆ’ π‘žβ„Žβˆ’1,𝑖,𝑔 ) ≀ π‘Ÿπ‘ π‘”

(5)

β„Ž=1 𝑔=1 π‘β„Ž 𝑁𝑔 β€² β€² βˆ‘ βˆ‘(π‘žβ„Žβˆ’1,𝑖,𝑔 βˆ’ π‘žβ„Ž,𝑖,𝑔 ) ≀ π‘Ÿπ‘π‘”

(6)

β„Ž=1 𝑔=1

It should be noted that in these two constraints, variable qβ€²h,i,g (connected net power in excess of the minimum stable load) has been used and not qh,i,g (total connected net power). The relation between qh,i,g and qβ€²h,i,g is shows in (7). Representing qβ€²h,i,g gives the ability of having ramp-ups and ramp-downs regardless of start-up and shut-down processes, and more, in the cost formulation, extra produced power can be translated into linearized cost function. β€² (7) π‘žβ„Ž,𝑖,𝑔 = π‘’π‘’β„Ž,𝑔 Γ— π‘˜π‘” Γ— π‘žπ‘”π‘šπ‘–π‘› + π‘žβ„Ž,𝑖,𝑔 Start-up and shut-down of generators are also implemented: π‘’π‘’β„Ž,𝑔 = π‘’π‘’β„Žβˆ’1,𝑔 (β„Ž > 1) + 𝑒𝑔 (β„Ž = 1) + π‘¦β„Ž,𝑔 βˆ’ π‘§β„Ž,𝑔 (8) Fuel cost of generators is generally expressed as in (9): π‘žπ‘” π‘žπ‘” 2 (9) 𝐢𝑔 = 𝛽𝑔 + 𝛼𝑔 Γ— + 𝛿𝑔 π‘˜π‘” π‘˜π‘” For simplicity, equation (9) is considered to be linear as shown in Figure 4. O&M costs presented in (10): π‘žβ„Ž,𝑖,𝑔 𝑂&𝑀𝑐 = π‘œπ‘π‘” + π‘œπ‘” Γ— (10) π‘˜π‘”

Fuel Cost

Real I/O curve Simplified I/O curve

1

The formulation for the connection between power and voltage angle of the bus are presented through (12): (12) 𝑆𝑖𝑗 = 𝑃𝑖𝑗 + 𝑗𝑄𝑖𝑗 and the active part of this formulation is shows in (13): 1 𝑃𝑖𝑗 = 2 𝑋 𝑉 𝑉 sin(πœƒπ‘– βˆ’ πœƒπ‘— ) 𝑅𝑖𝑗 + 𝑋𝑖𝑗2 𝑖𝑗 𝑖 𝑗 (13) 2 2 +𝑅𝑖𝑗 𝑉𝑖 βˆ’ 𝑉𝑖 𝑉𝑗 cos(πœƒπ‘– βˆ’ πœƒπ‘— ) As it can be seen, solving this OPF produces nonlinear terms. Here we can assume that the voltage angles have very small differences and the resistive part is greatly smaller than the inductive part. Hence, (12) is converted to (14): πœƒπ‘– βˆ’ πœƒπ‘— 𝑃𝑖𝑗 = 𝑆𝐡 (14) 𝑋𝑖𝑗 The demand balance must also be obtained at each hour and each node in the system: 𝑁𝑔

𝑁𝑗

𝑁𝑗

βˆ‘ π‘žβ„Ž,𝑖,𝑔 βˆ’ βˆ‘ π‘π‘β„Ž,𝑖,𝑗 + βˆ‘ π‘π‘β„Ž,𝑗,𝑖 = π‘‘β„Ž,𝑖 𝑔=1

𝑗=1

(15)

𝑗=1

The HNCED presented here is then supplemented with a new term as RI. This degree of risk is modeled as multiplication of the risk level by the gross power produced by each generator over the period that the system operating in that condition and then represented with MW unit. The objective function is formulated as follow: π‘žβ„Ž,𝑖,𝑔 𝑓𝑔 Γ— 𝛼𝑔 Γ— + 𝑓𝑔 Γ— π‘’π‘’β„Ž,𝑔 Γ— 𝛽𝑔 π‘β„Ž 𝑁𝑖 𝑁𝑔 π‘˜π‘” (16) βˆ‘ βˆ‘ βˆ‘ +𝑓𝑔 Γ— 𝛾𝑔 Γ— π‘¦β„Ž,𝑔 + 𝑓𝑔 Γ— πœŽπ‘” Γ— π‘§β„Ž,𝑔 π‘ž π‘ž β„Ž,𝑖,𝑔 β„Ž,𝑖,𝑔 β„Ž=1 𝑖=1 𝑔=1 +π‘œπ‘π‘” + π‘œπ‘” Γ— + π‘Ÿπ‘–β„Ž,𝑔 Γ— π‘˜π‘” π‘˜π‘” ] [ The model is then coded in general algebraic modeling system (GAMS) high-level modeling system [29] and solved using the mixed-integer linear programming (MILP) solver CPLEX [30] on a PC with 3.4 GHz processor and 16 GB of RAM. V. TEST SYSTEM

Gross Power Figure 4

Fuel cost function

The total operation cost becomes: π‘žβ„Ž,𝑖,𝑔 𝑓𝑔 Γ— 𝛼𝑔 Γ— + 𝑓𝑔 Γ— π‘’π‘’β„Ž,𝑔 Γ— 𝛽𝑔 + 𝑓𝑔 Γ— 𝛾𝑔 Γ— π‘¦β„Ž,𝑔 π‘˜π‘” (11) π‘žβ„Ž,𝑖,𝑔 +𝑓𝑔 Γ— πœŽπ‘” Γ— π‘§β„Ž,𝑔 + π‘œπ‘π‘” + π‘œπ‘” Γ— π‘˜π‘” Another simplification is in solving the optimal power flow problem which determines the voltage at each bus and the active power of the generators as shown in Figure 5.

The model was applied to IEEE-RTS test system [31], [32]. This test system has 24 buses and 38 transmission lines. Two new wind farms (at bus9 and bus19) each with the capacity of 80MW are added to the test system. Hydro generators are supposed that in spring and winter have the maximum capacity of 50MW, 45MW in summer and 40 MW in autumn. The optimization period considered for the studies is 1 year or 8736 hours with hourly load profile. A short summary of the generation units are provided in Table 1. VI. SCENARIOS Several scenarios are defined to analyze the model. The scenarios consider different maintenance degrees and strategies, initial conditions and formulation simplifications.

5th International Conference on Energy, Sustainability and Climate Change (ESCC), Mykonos, Greece, June 4-6, 2018

5 Table 1

Generator1 Generator2 Generator3 Generator4 Generator5 Generator6 Generator7 Generator8 Generator9 Generator10 Generator11 Generator12 Generator13 Generator14 Generator15 Generator16 Generator17 Generator18 Generator19 Generator20 Generator21 Generator22 Generator23 Generator24 Generator25 Generator26 Generator27 Generator28 Generator29 Generator30 Generator31 Generator32 Generator33 Generator34

Summary of generation units information

Type

Fuel

Fossil Steam Fossil Steam Fossil Steam Fossil Steam Fossil Steam Combus. Turbine Combus. Turbine Combus. Turbine Combus. Turbine Fossil Steam Fossil Steam Fossil Steam Fossil Steam Fossil Steam Fossil Steam Fossil Steam Fossil Steam Fossil Steam Fossil Steam Fossil Steam Fossil Steam Fossil Steam Fossil Steam Fossil Steam Nuclear Steam Nuclear Steam Wind Wind Hydro Hydro Hydro Hydro Hydro Hydro

#6 Oil #6 Oil #6 Oil #6 Oil #6 Oil #2 Oil #2 Oil #2 Oil #2 Oil Coal Coal Coal Coal #6 Oil #6 Oil #6 Oil Coal Coal Coal Coal #6 Oil #6 Oil #6 Oil Coal LWR LWR Wind Wind Hydro Hydro Hydro Hydro Hydro Hydro

Fuel Fuel Gross to Cost of Incremental Fixed term of Maximum Minimum Fixed Variable Initial consumption consumption Upward Downwar net power fuel term of fuel fuel gross gross O&M O&M connectio of generator of generator ramp of d ramp of conversion consumed consumption consumption power of power of Cost Cost n state during start- during shut- generator generator factor for by of generator of generator generator generator up down generator generator [Mbtu/MWh] [Mbtu/hr] [Mbtu] [Mbtu] [MW/hr] [MW/hr] [MW] [MW] [p.u.] [$/MBtu] [$/MW/yr] [$/MWh] [on/off] 10.20 69 53 5.3 10 10 12 0 0.94 2.3 10000 0.9 1 10.20 69 53 5.3 10 10 12 0 0.94 2.3 10000 0.9 1 10.20 69 53 5.3 10 10 12 0 0.94 2.3 10000 0.9 1 10.20 69 53 5.3 10 10 12 0 0.94 2.3 10000 0.9 1 10.20 69 53 5.3 10 10 12 0 0.94 2.3 10000 0.9 1 12.67 40 5 0.5 15 15 20 0 0.94 3 300 5 1 12.67 40 5 0.5 15 15 20 0 0.94 3 300 5 1 12.67 40 5 0.5 15 15 20 0 0.94 3 300 5 1 12.67 40 5 0.5 15 15 20 0 0.94 3 300 5 1 10.08 85 596 59.6 60 60 76 0 0.94 1.2 10000 0.9 1 10.08 85 596 59.6 60 60 76 0 0.94 1.2 10000 0.9 1 10.08 85 596 59.6 60 60 76 0 0.94 1.2 10000 0.9 1 10.08 85 596 59.6 60 60 76 0 0.94 1.2 10000 0.9 1 7.77 125 408 40.8 70 70 100 0 0.94 2.3 850 0.8 1 7.77 125 408 40.8 70 70 100 0 0.94 2.3 850 0.8 1 7.77 125 408 40.8 70 70 100 0 0.94 2.3 850 0.8 1 7.62 179 607 60.7 100 100 155 0 0.94 1.2 700 0.8 1 7.62 179 607 60.7 100 100 155 0 0.94 1.2 700 0.8 1 7.62 179 607 60.7 100 100 155 0 0.94 1.2 700 0.8 1 7.62 179 607 60.7 100 100 155 0 0.94 1.2 700 0.8 1 8.67 133 609 60.9 150 150 197 0 0.94 2.3 500 0.7 1 8.67 133 609 60.9 150 150 197 0 0.94 2.3 500 0.7 1 8.67 133 609 60.9 150 150 197 0 0.94 2.3 500 0.7 1 7.32 335 3192 319.2 250 250 350 0 0.94 1.2 450 0.7 1 8.92 360 3500 350 300 300 400 0 0.95 0.6 500 0.3 1 8.92 360 3500 350 300 300 400 0 0.95 0.6 500 0.3 1 0.00 0 0 0 80 80 80 0 1 0 100 0 1 0.00 0 0 0 80 80 80 0 1 0 100 0 1 0.00 0 0 0 50 50 50 0 1 0 100 0 1 0.00 0 0 0 50 50 50 0 1 0 100 0 1 0.00 0 0 0 50 50 50 0 1 0 100 0 1 0.00 0 0 0 50 50 50 0 1 0 100 0 1 0.00 0 0 0 50 50 50 0 1 0 100 0 1 0.00 0 0 0 50 50 50 0 1 0 100 0 1

These scenarios are divided into two main groups from the RI point of view. First group that includes Scenarios1-3 utilizes stair-wise RI presented in Figure 2 whereas Scenarios4-8 apply Weibull RI that is shown in Figure 3. A. Scenario1 In this scenario, all generators are assumed to start at the same age of zero. The maintenance strategy applied to them is PreM with the degree of AGAN. This means that when the generators reached the cumulative failure rate of 1, the life of the generator and hence, the failure rate is set again back to zero. The RI follows stair-wise function defined in Figure 2. B. Scenario2 This scenario considers that some of the generators start their work at different age or health, hence, with a different failure rate. Generators 6-16, 21-23 and 27 are assumed to start their work at their 50% cumulative failure level. These generators with the total capacity of 1355MW, stand for 37% of total installed generation capacity. The maintenance strategy in this scenario is PreM with the degree of AGAN. The RI follows stair-wise function as in Scenario1. C. Scenario3 Similar to Scenario2, in this scenario also not all generators start their work at the same age. Generators 1, 22-26 are considered to start their work at their 50% of cumulative failure distribution. The capacity of these generators in total consists of 37% of the total installed capacity as well. The maintenance consists of PreM strategy with AGAN degree and stair-wise cumulative failure distribution is used in this scenario for the RI.

MTBF

[hr] 3000 3000 3000 3000 3000 500 500 500 500 2000 2000 2000 2000 1250 1250 1250 1000 1000 1000 1000 1000 1000 1000 1250 1250 1250 3600 3600 2000 2000 2000 2000 2000 2000

D. Scenario4 For this scenario all generators start at the same age of zero, meaning with the same cumulative failure distribution level. Furthermore, no maintenance strategy is also considered for this scenario. This indicates that when any of the generators reaches 100% of failure CDF, they continue their work enduring a high level of risk, as a failure could happen at any time. The RI is based on the Weibull function illustrated in Figure 3. E. Scenario5 Scenario5 assumes that all generators start their work with the same condition and the maintenance benefits from AGAN strategy that sets the generator condition back to the beginning whenever its cumulative failure reaches 95%. The Weibull function is used for the RI. F. Scenario6 This scenario considers a condition that all generators start from the same zero failure level condition and the maintenance strategy is imperfect maintenance which means when the generator arrives at its 95% of failure CDF, the maintenance is applied and the CDF failure level goes back to 10%, and not AGAN condition. The RI associated in this scenario is also based on Weibull plotted in Figure 3. G. Scenario7 Same starting conditions for generators mentioned in Scenario2 is applied to the generators in this scenario. However, the maintenance strategy uses imperfect maintenance of from 95% to 10% and RI follows the Weibull function.

5th International Conference on Energy, Sustainability and Climate Change (ESCC), Mykonos, Greece, June 4-6, 2018

6

Scenario1

Scenario5

Figure 6

Comparison between Scenario1 and Scenario5

H. Scenario8 In this final scenario, similarly to Scenario3, generators follow the same starting condition, while the imperfect maintenance with the degree of 95%-10% is applied and RI is as Weibull shown in Figure 3. VII. RESULTS Eight different scenarios were defined to verify and test the model on a test system. The analysis is generally based on the risk and the risk level that each action in each scenario imposes on the system. A summary of the results from maintenance point of view is presented in Table 2. Table 2

Comparison of scenarios from maintenance view

Average Risk Minimum Risk Maximum Risk Maintenance Scenario (MW) (MW) (MW) Effectiveness S1 874 0 2522 100% S2 871 17 2285 100% S3 871 16 2166 100% S4 1549 0 2996 No maintenance S5 1118 0 2194 95% S6 1164 0 2179 85% S7 1174 20 2214 85% S8 1237 187 2325 85%

A look at Scenario2 at Table 2 shows the importance of maintenance in this system and the average MW power at risk in the 1-year period if no maintenance strategy is utilized. Comparing Scenario1 and Scenario5 that have almost the

same characteristics, except that RI applied is through stairwise and Weibull respectively and the maintenance effectiveness is only 5% different, shows that simplifications in terms of using stair-wise functions can hide about 400 MW risk at maximum load demand. Moreover, 10% change in maintenance effectiveness from 95% in Scenario5 to 85% in Scenario6 causes the average risk level to increase 46MW, even though the maximum risk is reduced by 15MW. One big different between Scenario2-Scenario7 and Scenario3-Scenario8 is that although the installed capacity of generators considered in these two groups is the same and they have the same share of the installed capacity, they do not have the same level of participation. For instance, generators considered in one group in Scenario8 hold 59.2% of the share of the production, whereas the other group in Scenario8 have 6.7%. Certainly, these two different participation levels do not have the same level of risk, however, as it can be seen in Table 2, using the simplified RI CDF can result in inaccurate results. As for Scenario3, these participation numbers are: 58.5% and 6.7%. As supposed, in scenarios that the system generators start working with different risk levels, the minimum risk also starts from a level other than zero. This risk difference depends firstly on the number of generators and their installed capacity, secondly on their participation level. By comparing Scenario6 and Scenario7 that both have the same level of maintenance effectiveness, it can be seen that because the participation level of the group of generators which start the work with higher risk level is very low, 6.7%, the average and maximum risk increase

5th International Conference on Energy, Sustainability and Climate Change (ESCC), Mykonos, Greece, June 4-6, 2018

7 are not very big, 10MW and 35MW increase respectively. In more detailed comparison, Figure 6 shows the impact of simplification in failure CDF though the comparison between Scenario1 and Scenario5 over 1-year (8736-hour) horizon. Small fluctuations in Figure 6 are due to the change in load and the big changes are the impact of maintenance. For instance in Scenario1, at hour around 6250, the effect of maintenance of all the generators coincide in a way that they send the risk level about 0MW.

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VIII. CONCLUSION The model presented in this paper is an hourly network constrained economic dispatch where it integrates a risk index based on the failure probability. As it was mentioned during the paper, this failure probability can be substituted with age, health or condition of the system, therefore, any change in the current status of the system automatically is included in the next planning time step. This feature is a great help for the system operator as they make the decisions on the operating phase of the system. To verify the model, it was tested on IEEE-RTS test system and the results showed accuracy of the model as well as the model’s capability in the automation section of smart grid. Another potential of the model is the ability of integration and implementation of the health condition of each component and therefore possibility of detecting anomalies. Study of maintenance scheduling is also one of the features that this model brings about. Furthermore, addition of storage system and solar generation can prepare the model to quickly be adopted in smart grid.

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5th International Conference on Energy, Sustainability and Climate Change (ESCC), Mykonos, Greece, June 4-6, 2018

8 [21] V. Jayalaban and D. Chaudhuri, "Cost Optimization of Maintenance Scheduling for a System with Assured Reliability," IEEE Transactions on Reliability, vol. 41, no. 1, pp. 21-25, March 1992. [22] P. Mazidi, Y. Tohidi, A. Ramos and M. A. Sanz-Bobi, "Profit maximization generation maintenance scheduling through bi-level programming," European Journal of Operational Research, vol. 264, no. 3, pp. 1045 - 1057, 2018. [23] Reliability Metrics Working Group (RMWG), "Integrated Bulk Power System Risk Assessment Concepts," North American Electric Reliability Corporation (NERC), 2010. [24] Performance Analysis Subcommittee, "SRI Enhancement," North American Reliability Corporation (NERC), 2014. [25] R. Billinton, Reliability Evaluation of Engineering Systems, New York: Plenum Press, 1996. [26] R. Billinton and R. N. Allan, Reliability Evaluation of Engineering Systems, Concepts and Techniques, 2nd Edition, New York: Plenum Press, 1992. [27] W. Li, Risk Assessment Of Power Systems: Models, Methods, and Applications 2nd Edition, Wiley-IEEE Press, 2014. [28] J. GarcΓ­a GonzΓ‘lez, "Decision Support Models in Electric Power Systems," Pontifical University of Comillas, Madrid, Spain, 2012. [29] R. E. Rosenthal, GAMS β€” A User’s Guide, Washington, DC, USA: GAMS Development Corporation, 2014. [30] IBM Corp., User's Manual for CPLEX. [31] Reliability Test System Task Force Subcommittee , "IEEE Reliability Test System," IEEE Transactions on Power Apparatus and Systems, Vols. PAS-98, no. 6, pp. 2047 - 2054, Nov. 1979. [32] R. T. S. T. F. Subcommittee, "The IEEE Reliability Test System-1996," IEEE Transactions on Power Systems, vol. 14, no. 3, pp. 1010 - 1020, Aug. 1999.

5th International Conference on Energy, Sustainability and Climate Change (ESCC), Mykonos, Greece, June 4-6, 2018