By Samer Sulaeman Jorge G. Cintrón-Riveramitraj/teaching/projects/cintron-rivera_and_sulae… · Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera 1.3 project

Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera

Michigan State University Department of Electrical and Computer engineering

East Lansing, Michigan

Alternative Energy Proposal to Increase the MSU Power Grid Reliability

By

Samer Sulaeman &

Jorge G. Cintrón-Rivera

Dr. J. Mitra ECE 802, Engineering Reliability final project

Final Project


1.1 Summary

In this project more attention is given to implement reliability evaluation for a small power

system, providing renewable energy source to feed Michigan State university campus as a proposal for

future reliability analysis. Reliability evaluation for the existing system has been evaluated and

compared to the reliability evaluation of the proposed system for a different configurations, the system

reliability of the existing power supply increased. The evaluation carried out through three stages, first

stage evaluating the existing power supply, in the second stage the evaluation carried out by adding

renewable energy source to the existing system. Finally, reliability evaluation for the utility grid and

renewable energy source configuration has bas been evaluated and compared to existing power system.

It’s been proved in this project that providing a renewable energy source will increase system

reliability and will help to reduce pollution and harmful emissions, even tough; the renewable energy

can only meet a partial of the load capacity and demand. Future research can help to investigate the

possibility of applying renewable energy sources in terms of cost, power capacity and availability, which

can be carried out by implementing reliability evaluation.

1.2 Introduction

The term of reliability can be applied to any functional system, the definition of system

reliability is the probability of the system to carry out its planned function for a particular time interval

under stated conditions [1]. For this project, applying reliability evaluation methods will be limited to the

available data for the system components. The Michigan State university power generator and utility

grid will be presented as main system components for reliability evaluation. In this report the existing

Michigan State power system is evaluated and compared to a new system configuration. The proposed

system is based on the addition of alternative energy to the current power system. It is shown by means

of calculations that the proposed method increases the system reliability. Furthermore, there are

additional benefits of using alternative energy, such as lower emissions that contribute to

environmental issues.

Recently more attention has been given to the renewable energy resources as alternative clean

source of energy to reduce the impact of co2, co and other emissions that contribute to the global

warming and climate changes. The majority of the US electric power comes from burning fossil fuels,

i.e., coal, oil, natural gas and from nuclear power. According to the government data released by

Environment Michigan, Michigan’s power plants rank 13th nationwide for most carbon dioxide (CO2)

pollution. [2].

Michigan state University power plant consumes 250,000 tons of coal and 340 million cubic feet

of natural gas this produce around 175.55 tons of CO yearly to produce 250 MW of electricity and to

operate other facilities.[3]. Obtaining a greener power source of energy will help to reduce the emission,

which is the goal of Michigan State, as stated in their lemma, be green.


1.3 project limitation

In this project there are many limitations the may affect on the evaluation results, therefore, the

analysis are carried out based on available information. Some of these limitations are:

1. Availability of data

2. Accuracy of available Data

3. Time limit for this project

2.1 Research Aim

The aim of this project is to evaluate the current Michigan State University Power network configuration, shown on figure 2. Then, proposing incorporation of renewable energy to the existing

network and compare both systems reliabilities and benefits. In this report we are proposing to add an alternative energy source, such as solar power generation or wind energy turbine to the existing power network. It is expected that the system reliability will be much higher, in addition to other benefits will be highly considered.

2.2 Modeling and methodology

The proposed system reliability block diagram is shown on figure 1. And transient state diagram is

shown in figure 2.The proposed power network is composed of three separated power sources, two of

them burn fossil fuels and the clean and green renewable energy source. It is expected that the new

system will:

Be more Reliable

Possibility and capability of Reducing emissions

Have long term benefits, the extra power from the renewable sources translate to less fossil fuel burning and less maintenance cost

MSU Power

Plant

Power

Grid

Renewable

Energy

Source

S t

Figure 1: Proposed Power Network reliability block diagram


The transition state diagram for this system is representing by the following figure, Where the

state so representing the only failure state.

Figure 2: Transition state diagram

Gm Gg

G T L

µRE µ Gm

µ Gg

λ Gg

Gm

µ Gm µ RE

Gg RE λ RE

λ RE

λ Gm

λGm

µGg λGg

µ Gg

𝑮𝒈 RE

Gm

µ RE µ Gm

λ Gg

Gm Gg

µ RE λ RE

λ Gm

µ Gm

λ Gg

µ Gg

Failure

state

λ Gm

λ RE

Gg


In the transition diagram is shown how the system fails if an only if the three components fail.

The existing power network at Michigan State University is composed by its Power Generation

plant and assisted by the power grid, as shown on figure 1.

MSU Power Plant

Power GridLoad

Fig 2: Existing Power System

The Reliability Block Diagram for the existing power network is basically a two block parallel

system, where failure occurs only when both power sources fail.

MSU Power

Plant

Power

Grid

StBlock 1

Block 2

Fig 2b: Reliability Block Diagram for the

existing MSU Power System


The reliability information is given in the following table:

Parameter Power Grid MSU Power Plant

𝝀 0.087𝑑𝑎𝑦 0.099

𝑑𝑎𝑦

MDT 1 𝑑𝑎𝑦𝑠 1 𝑑𝑎𝑦𝑠

𝝁 1𝑑𝑎𝑦 1

𝑑𝑎𝑦

𝑷 𝑃 =𝜇

𝜇 + 𝜆= 0.92 𝑃 =

𝜇

𝜇 + 𝜆= 0.91

𝑸 𝑄 = 1 − 𝑃 = 0.08 𝑄 = 1 − 𝑃 = 0.09

Table 1: MSU and Power Grid reliability information. [1]

Reliability and system indices are calculated using the reliability bock diagrams technique. The

block diagram shown figure 2b, we will be used to apply parallel reduction blocks.

3.1 Reliability Evaluation

For parallel systems, the system is unavailable only when all the components are down,

then the equivalent unavailability of the system is given by:

𝑈𝑛𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦: 𝑈𝑃𝑠𝑦𝑠 = 𝑈𝑖 = 𝑈𝑀𝑆𝑈 ∙ 𝑈𝑃𝐺

2

𝑖=1

= 0.09 ∗ 0.08 = 𝟎. 𝟎𝟎𝟕𝟐

Then the probability of been UP or Availability is given by:

𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦: 𝐴𝑃𝑠𝑦𝑠 = 1 − 𝑈𝑠𝑦𝑠 = 𝟎. 𝟗𝟗𝟐𝟖

In parallel systems the repair rates of each component is added, this way the equivalent system

repair rate is obtained. The reason is because the system fails completely only when each

component fails, hence the repair rates must be added as shown next.

𝑅𝑒𝑝𝑎𝑖𝑟 𝑅𝑎𝑡𝑒: 𝜇𝑃𝑠𝑦𝑠 = 𝜇𝑀𝑆𝑈 + 𝜇𝑃𝐺 = 2𝑑𝑎𝑦

A system period is composed of transitions from the working state to the fail state. This can be

seen as a periodic function with a frequency given by:


𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦: 𝐹𝑃𝑠𝑦𝑠 = 𝑈𝑃𝑠𝑦𝑠 ∗ 𝜇𝑃𝑠𝑦𝑠 = 𝑈𝑠𝑦𝑠 ∙ 𝜇𝑠𝑦𝑠 = 𝟎. 𝟎𝟏𝟒𝟒𝒅𝒂𝒚

As mentioned before this working and fails states are similar to a time function, hence the

Mean cycle time can be calculated as a period, 𝑇 = 1𝑓 .

𝑀𝑒𝑎𝑛 𝐶𝑦𝑐𝑙𝑒 𝑡𝑖𝑚𝑒: 𝑀𝐶𝑇 =1

𝐹𝑃𝑠𝑦𝑠=

1

𝟎. 𝟎𝟏𝟒𝟒= 𝟔𝟗. 𝟒𝟒 𝒅𝒂𝒚𝒔

During this mean cycle time, the fraction for which the system is UP can be found by using the

availability probability time the mean cycle time.

𝑀𝑒𝑎𝑛 𝑈𝑃 𝑡𝑖𝑚𝑒: 𝑀𝑈𝑇 = 𝑀𝐶𝑇 ∙ 𝐴𝑃𝑠𝑦𝑠 = 𝟔𝟖.𝟗𝟒 𝒅𝒂𝒚𝒔

One cycle is composed by the UP and Downtime of the system. The mean cycle time can be

expressed as 𝑀𝐶𝑇 = 𝑀𝑈𝑇 + 𝑀𝐷𝑇. This relationship can be used to obtain the mean downtime

of the system.

𝑀𝑒𝑎𝑛 𝐷𝑜𝑤𝑛𝑡𝑖𝑚𝑒: 𝑀𝐷𝑇 = 𝑀𝐶𝑇 − 𝑀𝑈𝑇 = 𝟎. 𝟓𝟎 𝒅𝒂𝒚𝒔

Now that we have the mean downtime of the system, then the failure rate can be obtained by:

𝐹𝑎𝑖𝑙𝑢𝑟𝑒 𝑅𝑎𝑡𝑒: 𝜆𝑃𝑠𝑦𝑠 =1

𝑀𝑈𝑇= 𝟎. 𝟎𝟏𝟒𝟓

𝒅𝒂𝒚

Summary:

This information can be used to reduce the two parallel systems to a single equivalent

system, as shown on figure 3.

Remarks:

Equivalent system Availability is substantially higher than each of the previous systems

availability. This was expected since parallel systems system reliability or availability

always increases.


S tEquivalent

Power

System

Equivalent system:

Figure 3: Equivalent existing power network.

Parameter Equivalent Power system

𝝀 0.0145𝑑𝑎𝑦

𝝁 2𝑑𝑎𝑦

𝑷 0.9928

𝑸 0.0072

Table 2: Equivalent Power System reliability information

3.2 Reliability evaluation for the proposed system.

The proposed system is shown on figure 4, where an alternative energy system is added

to the existing power network. It is important to mention, that when dealing with renewable

energy, a power electronics interface is required.

S t

Renewable

Energy Source

Power

Electronics

Interface

Fig 4: Reliability Block Diagram for the

Proposed MSU Power System

Equivalent

Power

System


Before further analysis is made, the power electronics interface system, the battery and the

alternative energy source must be analyzed.

The system circuitry selected for this project is shown in figure 5. This system is composed of:

1. Alternative energy source to provide extra power

2. Full-Bridge DC to DC converter: Used to perform Maximum Power Point tracking

(MPPT), to optimize the source.

3. The step up transformer: This is a DC to DC high frequency transformer, used to step up

the DC pulses from the Full-Bridge. Since this is a high frequency transformer, its size is

not that big.

4. The battery: Is used as an energy storage device and it also helps to do the MPPT.

5. High voltage doublers capacitors: These are used to stabilize the DC link voltage and

double the transformer output voltage.

6. The inverter: Use to inverter the DC voltage to AC controlled voltage.

Remark:

All components are assumed to be in the steady state and be only in up and down states for this analysis.

Sw

AC

LoadRenewable

DC inputC1

C2

Full bridge

Switches

Step up

Transformer

Inverter

SwitchesBattery

Fig 5: Power Electronics System Circuit

The circuit in figure 5 can be transformed its reliability block diagram as shown in figure 6.


Full-Bridge

DC-DC

Switches

Transformer

Capacitors

Inverter

DC to AC

Switches

Renewable

Energy Source

Battery

Storage

tS

Fig 6: Power Electronics System Circuit, reliability block diagram

For the system on figure 6, it is clear that if the inverter and its capacitor fail, the whole system

will fail. However, if the rest fails, this does not imply that the system will fails. For example, if

the renewable energy source or the full-bridge or the transformer fails, then the battery can

supply the power for a certain time period until the repair is achieved. The following

parameters, as shown in Table (2) are used for steady sate reliability evaluation.

Reliability information about this system:

Parameter Battery Full-Bridge Inverter Capacitor Transformer

𝝀 8.04 ∙ 10−3

𝑑𝑎𝑦 0.2𝑑𝑎𝑦 0.290

𝑑𝑎𝑦 12.01 ∙ 10−3

𝑑𝑎𝑦 12.01 ∙ 10−3

𝑑𝑎𝑦

𝝁 4.008𝑑𝑎𝑦 10

𝑑𝑎𝑦 48𝑑𝑎𝑦 12

𝑑𝑎𝑦 12𝑑𝑎𝑦

𝑷 0.998 0.996 0.994 0.999 0.999

𝑸 0.002 0.004 0.006 0.001 0.001

Table 2: Power Electronics reliability information. [5,6,7,8,9]

Parameter Alternative Energy Source

𝝀 0.00802𝑑𝑎𝑦

𝝁 4𝑑𝑎𝑦

𝑷 0.998 𝑸 0.002

Table 3: Power Electronics reliability information


As shown in the reliability block diagram on figure (6) the system can be split into 3 parts.

Part #1: A series system composed of the renewable energy source, the full-bridge and

the transformer.

Part #2: The Battery, which is in parallel with the equivalent system mentioned on 1.

Part #3: The Inverter and its capacitors,

In order to analyze the power electronics system we need to work it out in parts. The system is analyzed

in three steps, as follow.

Step #1: Develop the Equivalent system for the part #1.

Step #2: Combine the Equivalent system on step #1 with the parallel battery system, (part

#2).

Step #3: Finally, combine the equivalent system of step#2 with the part #3.

Step #1: Series combination for part #1:

Full-Bridge

DC-DC

Switches

TransformerRenewable

Energy Source

Fig 7: Reliability Block Diagram of part #1

For Series systems the Availability of the system depends directly on the availability of each

component. So saying this, then equivalent system Availability is given by:

𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦: 𝐴#1 = 𝑃𝑖 = 𝑃𝑅𝐸2𝑖=1 ∙ 𝑃𝐹𝐵 ∙ 𝑃𝑋𝑚𝑒𝑟 = 0.998 ∗ 0.996 ∗ 0.999 = 𝟎. 𝟗𝟗𝟑

𝑈𝑛𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦: 𝑈#1 = 1 − 𝐴#1 = 𝟎. 𝟎𝟎𝟕


Step #1ts

Since there is a system fail if any of the parts of the system fail, the failure rate of the system is

given as the summation of all the individual system failure rates.

𝐹𝑎𝑖𝑙𝑢𝑟𝑒 𝑅𝑎𝑡𝑒: 𝜆#1 = 𝜆𝑖

3

𝑖=1

= 0.00802 + 0.2 + 12.01 ∙ 10−3 = 0.220𝑑𝑎𝑦

Similar to the parallel case done in previously to find the system frequency, the frequency

balance equation can be used. 𝐹 = 𝑈 ∗ 𝜇 = 𝐴 ∗ 𝜆

𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦: 𝐹#1 = 𝐴#1 ∗ 𝜆#1 = 𝟎. 𝟐𝟏𝟖𝟓𝒅𝒂𝒚

The mean cycle time can be found using the same relationship used previously for the parallel case.


𝐹#1=

1

0.2185= 𝟒. 𝟓𝟖 𝒅𝒂𝒚𝒔

The Mean Down time in parallel systems is found by multiplying the mean cycle time by the

probability of been down. In the other hand, in series system, we get the mean up time instead

of the mean down time.

𝑀𝑒𝑎𝑛 𝐷𝑜𝑤𝑛 𝑡𝑖𝑚𝑒: 𝑀𝐷𝑇 = 𝑀𝐶𝑇 ∙ 𝑈#1 = 𝟎. 𝟎𝟑𝟐 𝒅𝒂𝒚𝒔

The mean up time can be easily found using:

𝑀𝑒𝑎𝑛 𝑈𝑃 𝑡𝑖𝑚𝑒: 𝑀𝑈𝑇 = 𝑀𝐶𝑇 − 𝑀𝐷𝑇 = 𝟒. 𝟓𝟒𝒅𝒂𝒚𝒔

Finally we can use the simple equation to get the repair rate of the equivalent system:

𝑅𝑒𝑝𝑎𝑖𝑟 𝑅𝑎𝑡𝑒: 𝜇#1 =1

𝑀𝐷𝑇= 𝟑𝟏. 𝟐𝟓

𝒅𝒂𝒚

Summary of Step #1:

Fig 8: Equivalent Reliability Block Diagram for step #3


Parameter Step #1 Equivalent

𝝀 0.301𝑑𝑎𝑦

𝝁 43.48𝑑𝑎𝑦

𝑷 0.9930

𝑸 0.007

Table 4: Step #1 Equivalent reliability information

Step #2: Parallel combination, of equivalent system on step#1 and part #2

Step #1t

Battery

Storage

s

Fig 8: System for step #2

Parallel system, the analyses is performed in the same way as before.

𝑈𝑛𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦: 𝑈#2 = 𝑄𝑖 = 𝑈𝑠𝑡𝑒𝑝 #1 ∙ 𝑈𝑏𝑎𝑡𝑡𝑒𝑟𝑦

2

𝑖=1

= 0.007 ∗ 0.002 = 𝟎. 𝟎𝟎𝟎𝟎𝟏𝟒

𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦: 𝐴#2 = 1 − 𝑈#2 = 𝟎. 𝟗𝟗𝟗𝟗𝟖𝟔

𝑅𝑒𝑝𝑎𝑖𝑟 𝑅𝑎𝑡𝑒: 𝜇#2 = 𝜇𝑠𝑡𝑒𝑝 #1 + 𝜇𝑏𝑎𝑡𝑡𝑒𝑟𝑦 = 31.25 + 4.008 = 35.25𝑑𝑎𝑦

𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦: 𝐹#2 = 𝑈#2 ∗ 𝜇#2 = 𝟎. 𝟎𝟎𝟎𝟒𝟗𝒅𝒂𝒚


𝐹#2=

1

𝟎. 𝟎𝟎𝟓𝟔= 𝟐𝟎𝟒𝟎. 𝟖𝟐 𝒅𝒂𝒚𝒔

𝑀𝑒𝑎𝑛 𝑈𝑃 𝑡𝑖𝑚𝑒: 𝑀𝑈𝑇 = 𝑀𝐶𝑇 ∙ 𝐴#2 = 𝟐𝟎𝟒𝟎.𝟕𝟖 𝒅𝒂𝒚𝒔

𝑀𝑒𝑎𝑛 𝐷𝑜𝑤𝑛 𝑡𝑖𝑚𝑒: 𝑀𝐷𝑇 = 𝑀𝐶𝑇 − 𝑀𝑈𝑇 = 𝟎. 𝟎𝟐𝟖𝒅𝒂𝒚𝒔

𝐹𝑎𝑖𝑙𝑢𝑟𝑒 𝑅𝑎𝑡𝑒: 𝜆#2 =1

𝑀𝑈𝑇= 𝟎. 𝟎𝟎𝟎𝟒𝟗

𝒅𝒂𝒚


Power Electronics

&

Alternative Energy

Source

S t

Equivalent System up to this step:

Step #1 &

Step #2

SCapacitors

Inverter

DC to AC

Switches

t

Fig 9: Reliability Block Diagram to be analyzed on step #3

No let’s reduce the output series part as the previous series system:

Step #3: Series Combination

𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦: 𝐴𝑠𝑦𝑠 = 𝑃𝑖 = 𝑃𝑠𝑡𝑒𝑝𝑠 1&2

2

𝑖=1

∙ 𝑃𝐶 ∙ 𝑃𝐼𝑁𝑉 = 0.999986 ∗ 0.999 ∗ 0.994 = 0.9930

𝑈𝑛𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦: 𝑈𝑠𝑦𝑠 = 1 − 𝐴𝑠𝑦𝑠 = 𝟎. 𝟎𝟎𝟕

𝐹𝑎𝑖𝑙𝑢𝑟𝑒 𝑅𝑎𝑡𝑒: 𝜆𝑠𝑦𝑠 = 𝜆𝑖

3

𝑖=1

= 0.00049 + 12.01 ∙ 10−3 + 0.290 = 𝟎. 𝟑𝟎𝟐𝒅𝒂𝒚

𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦: 𝐹𝑠𝑦𝑠 = 𝐴𝑠𝑦𝑠 ∗ 𝜆𝑠𝑦𝑠 = 𝟎. 𝟑𝒅𝒂𝒚


𝐹𝑠𝑦𝑠=

1

0.3= 𝟑. 𝟑𝟑𝟑 𝒅𝒂𝒚𝒔

𝑀𝑒𝑎𝑛 𝐷𝑜𝑤𝑛 𝑡𝑖𝑚𝑒: 𝑀𝐷𝑇 = 𝑀𝐶𝑇 ∙ 𝑈𝑠𝑦𝑠 = 𝟎. 𝟎𝟐𝟑 𝒅𝒂𝒚𝒔

𝑀𝑒𝑎𝑛 𝑈𝑃 𝑡𝑖𝑚𝑒: 𝑀𝑈𝑇 = 𝑀𝐶𝑇 − 𝑀𝐷𝑇 = 𝟑. 𝟑𝟏 𝒅𝒂𝒚𝒔

𝐹𝑎𝑖𝑙𝑢𝑟𝑒 𝑅𝑎𝑡𝑒: 𝜇𝑠𝑦𝑠 =1

𝑀𝐷𝑇= 𝟒𝟑. 𝟒𝟖

𝒅𝒂𝒚

Equivalent System:

Fig 9: Reliability Block Diagram for the Equivalent Power Electronics system


Power Electronics

&

Alternative Energy

Source

S t

Equivalent

Power

System

Parameter Alternative energy system

𝝀 0.302𝑑𝑎𝑦


𝑷 0.9930

𝑸 0.007

Table 5: Equivalent Power Electronics Reliability Information

Remarks for the equivalent Power Electronics System:

The power electronics system for alternative energy generation is a very reliable system.

o Very high repair rate: the system can be repaired very fast in the case of failure.

o Low failure rate: The system fairly fails

o Low Mean Down time: In one cycle time, the system spends most of its time in the Up

state. This means that 𝑀𝑈𝑇 ≈ 𝑀𝐶𝑇, this characteristic is very important, since is a

measurement of how reliable is the system.

Now this existing system is compared with our proposed system. Our proposal is the addition

of an alternative energy system to the existing Michigan State Power network shown on figure 2. The

proposed system is shown on figure 10. It expected that the overall system reliability will increase,

because of the parallel connection. There are other advantages when alternative energy, such as solar

energy or wind energy. Some of these advantages are:

1. Pollutants emissions reduction.

2. Less fossil fuel usage

3. Operational cost may be lower

4. Maintenance and repair cost is lower for long run operation.

Fig 10: Proposed Power Network


Equivalent

SystemS t

Parameter Equivalent Power System

Equivalent Power Electronics System

𝝀 0.0145𝑑𝑎𝑦 0.302

𝑑𝑎𝑦

𝝁 2𝑑𝑎𝑦 43.48

𝑑𝑎𝑦

𝑷 0.9928 0.9930

𝑸 0.0072 0.007

Table 6: MSU and Power Grid reliability information

To analyze the proposed system reliability parallel reliability block diagrams techniques are used.

The parallel block reduction technique is the same used previously.

𝑈𝑛𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦: 𝑈𝑒𝑞𝑢 = 𝑈𝑖 = 𝑈𝑃𝐸 𝑠𝑦𝑠 ∙ 𝑈𝑃𝑠𝑦𝑠

2

𝑖=1

= 0.007 ∗ 0.0072 = 𝟎. 𝟎𝟎𝟎𝟎𝟓

𝐴𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦: 𝐴𝑒𝑞𝑢 = 1 − 𝑈#2 = 𝟎. 𝟗𝟗𝟗𝟗𝟓

𝑅𝑒𝑝𝑎𝑖𝑟 𝑅𝑎𝑡𝑒: 𝜇𝑒𝑞𝑢 = 𝜇𝑃𝐸 𝑠𝑦𝑠 + 𝜇𝑃𝑠𝑦𝑠 = 2 + 43.48 = 45.48𝑑𝑎𝑦

𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦: 𝐹𝑒𝑞𝑢 = 𝑈𝑒𝑞𝑢 ∗ 𝜇𝑒𝑞𝑢 = 𝟎. 𝟎𝟎𝟐𝟐𝟕𝒅𝒂𝒚


𝐹𝑒𝑞𝑢=

1

𝟎. 𝟎𝟎𝟐𝟐𝟕= 𝟒𝟒𝟎.𝟓𝟑 𝒅𝒂𝒚𝒔

𝑀𝑒𝑎𝑛 𝑈𝑃 𝑡𝑖𝑚𝑒: 𝑀𝑈𝑇 = 𝑀𝐶𝑇 ∙ 𝐴𝑒𝑞𝑢 = 𝟒𝟒𝟎. 𝟓𝟎 𝒅𝒂𝒚𝒔

𝑀𝑒𝑎𝑛 𝐷𝑜𝑤𝑛 𝑡𝑖𝑚𝑒: 𝑀𝐷𝑇 = 𝑀𝐶𝑇 − 𝑀𝑈𝑇 = 𝟎. 𝟎𝟑𝒅𝒂𝒚𝒔

𝐹𝑎𝑖𝑙𝑢𝑟𝑒 𝑅𝑎𝑡𝑒: 𝜆𝑒𝑞𝑢 =1

𝑀𝑈𝑇= 𝟎. 𝟎𝟎𝟐𝟐𝟕

𝒅𝒂𝒚

Proposed Equivalent system:

Fig 10: Proposed equivalent System


Parameter Equivalent Proposed system

𝝀 0.00227𝑑𝑎𝑦


𝑷 0.99995

𝑸 0.005

Table 7: Proposed Equivalent Power System

Parameter Existing Power System

Proposed Power System

𝝀 0.0145𝑑𝑎𝑦 0.00227

𝑑𝑎𝑦

𝝁 2𝑑𝑎𝑦 45.48

𝑑𝑎𝑦

𝑷 𝟎. 𝟗𝟗𝟐𝟖 𝟎. 𝟗𝟗𝟗𝟗𝟓

𝑸 0.0072 0.005

𝑴𝑪𝑻 𝟔𝟗. 𝟒𝟒 𝒅𝒂𝒚𝒔 𝟒𝟒𝟎.𝟓𝟑 𝒅𝒂𝒚𝒔

𝑴𝑫𝑻 𝟎. 𝟓𝟎 𝒅𝒂𝒚𝒔 𝟎. 𝟎𝟑𝒅𝒂𝒚𝒔

𝑴𝑼𝑻 𝟔𝟖. 𝟗𝟒 𝒅𝒂𝒚𝒔 𝟒𝟒𝟎.𝟓𝟎 𝒅𝒂𝒚𝒔

𝑭 𝟎. 𝟎𝟏𝟒𝟒𝒅𝒂𝒚 𝟎. 𝟎𝟎𝟐𝟐𝟕

𝒅𝒂𝒚

Table 8: Comparison between the existing and proposed power network

3.3 Evaluation and Comparison:

After the evaluation of the existing system configuration has been carried out, an

examination of the reliability of proposed renewable source with only the power provided by

grid utility as shown in figure 11 is performed.

Fig.11 Reliability block diagram for the proposed configuration

Grid utility supply

Renewable energy

source

S t


Reliability evaluation for the gird utility supply connected with renewable energy source

configuration will be carried out using the data from table 1 and table 6.

𝑈𝑛𝑎𝑣𝑎𝑖𝑙𝑎𝑏𝑖𝑙𝑖𝑡𝑦: 𝑈𝑒𝑞𝑢 = 𝑈𝑖 = 𝑈 𝑔𝑟𝑖𝑑 ∗ 𝑈𝑃𝐸 𝑠𝑦𝑠

2

𝑖=1

= 0.08 ∗ 0.007 = 𝟎. 𝟎𝟎𝟎𝟓𝟔

Availability: 𝐴𝑒𝑞𝑢 = 1 − 𝑈#2 = 𝟎. 𝟗𝟗𝟗𝟒𝟒

𝑅𝑒𝑝𝑎𝑖𝑟 𝑅𝑎𝑡𝑒: 𝜇𝑒𝑞𝑢 = 𝜇𝑔𝑟𝑖𝑑𝑠𝑦𝑠 + 𝜇𝑃𝑠𝑦𝑠 = 1 + 43.48 = 45.48𝑑𝑎𝑦

𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦: 𝐹𝑒𝑞𝑢 = 45.48 ∗ 0.00056 = 𝟎. 𝟎𝟐𝟓𝟒𝟔𝟖𝟖𝒅𝒂𝒚


𝐹𝑒𝑞𝑢=

1

𝟎. 𝟎𝟎𝟐𝟖𝟔𝟓𝟐𝟒= 𝟑𝟗. 𝟐𝟔𝟑𝟕𝟐𝟔𝟔 𝒅𝒂𝒚𝒔

𝑀𝑒𝑎𝑛 𝑈𝑃 𝑡𝑖𝑚𝑒: 𝑀𝑈𝑇 = 𝑀𝐶𝑇 ∙ 𝐴𝑒𝑞𝑢 = 𝟑𝟗.𝟐𝟒𝟏𝟕𝟑𝟖𝟗𝟏 𝒅𝒂𝒚𝒔

𝑚𝑒𝑎𝑛 𝐷𝑜𝑤𝑛𝑡𝑖𝑚𝑒: 𝑀𝐷𝑇 = 𝑀𝐶𝑇 − 𝑀𝑈𝑇 = 𝟎. 𝟎𝟐𝟐𝒅𝒂𝒚𝒔

𝐹𝑎𝑖𝑙𝑢𝑟𝑒 𝑅𝑎𝑡𝑒: 𝜆𝑒𝑞𝑢 =1

𝑀𝑈𝑇= 𝟎. 𝟎𝟐𝟓𝟒

𝒅𝒂𝒚

Parameter Power Grid Power Grid and Alternative energy

𝝀 0.087𝑑𝑎𝑦 0.0254

𝑑𝑎𝑦

𝝁 1𝑑𝑎𝑦 45.48

𝑑𝑎𝑦

𝑷 0.92 0.99944

𝑸 0.08 0.00056

Table 9: Second Proposed Equivalent Power System


It’s clear that the reliability of the system increased from 𝟎. 𝟗𝟐 to .99944 which is

almost perfect. If you compare this with three system configuration or to the existing power

system, the reliability of the system still improved from 𝟎. 𝟗𝟗𝟐𝟖 to 0.99944.

Therefore the benefits of using renewable energy source increased it terms of system reliability

and surly in terms of environmental benefits.

Remarks:

The Proposed system has considerably higher Reliability (𝑃).

The Steady State Mean Cycle Time on the proposed power system is considerably higher.

o This means that the system has longer periods and hence the system spends more time

in the working state. In other words, one cycle time contains working time period and a

fail period, as shown in table 8, the proposed system expend 440.5 days in the Working

State out of 440.53 days, Instead of 68.94 working days out of 69.44 days in the existing

power system.

The Proposed System has lower failure rate and significantly higher repair rates, which make the

system more reliable.

Monte Carlos Simulation Results:

A non-sequential Monte Carlos simulation was created to corroborate the calculations results. The

Results for the Monte Carlos simulation are:

Probability Existing System Proposed System

P 0.992808 0.9999525

By means of a simple Monte Carlos simulation, we have confirmed our block diagram calculations

results.


4.1. Conclusion:

In the project we have proven how to increase the system reliability of the existing

power system. The reliability of the existing power supply of Michigan State University has been

evaluated and then evaluated with a combined proposed renewable energy source. This

proposed method will help the campus to become even greener. The emission produced by

actual coal power plant can be decreased. The decrease will be given by the renewable energy

capacity. The following relationships show the amount of Tons of gas per GWh.

𝑇𝑜𝑛𝑠𝐶𝑂2 = 411 𝑇𝐺𝑊𝑕 , 𝐶𝑂 = 0.005 𝑇

𝐺𝑊𝑕 , 𝑁𝑂𝑥 = 0.039 𝑇𝐺𝑊𝑕

Theses formulas tell us know that every watt that comes from a renewable energy source is

translated to less pollutants emissions.

Finally, there is a huge reliability improvement in the proposed overall power system. The increase is

from 99.28% availability to 99.995%, which is almost perfect. The proposed system showed increase in

availability, where the proposed system spends 440.5 days in the Working State out of 440.53 days,

Instead of 68.94 working days out of 69.44 days in the existing power system. Furthermore, reliability

evaluation for renewable energy with utility grid showed that the reliability of the system increased

from 𝟎. 𝟗𝟐 to .99944 which is almost perfect. If you compare this with three system

configuration or to the existing power system, the reliability of the system improved

from 𝟎. 𝟗𝟗𝟐𝟖 to 0.99944. There is no question that the proposed system increases the reliability of

the system and by obtaining such system will also help to decrease the emissions that impact harmfully

to the environment.

4.2. Recommendation:

This small project of implementing reliability evaluation for the existing power supply for Michigan

State University combined with proposed renewable energy showed improvement of system reliability.

Recommendation for Further and detailed researches can be lead to more accurate data, therefore, the

following should be considered:

1. Obtaining an accurate data for the existing power system capacity and power load demand.

2. Implementing real time analysis to carryout reliability evaluation.

3. Considering environmental issues as motivation to use renewable energy source.


4. Getting the benefits of available renewable energy sources that can be used to provide a clean

energy source to Michigan state university, such as wind energy.

5. Providing a renewable energy source can help to reduce the emissions, even tough, the

renewable resource can only meet a partial of the desired load capacity, it’s valuable to be

considered.

References 1. R.Ramakumar ,”Engineering reliability: fundamental and application”, Prentice hall, 1993 .

2. Environment Michigan Challenges DTE on Carbon Dioxide Emissions,11/25/0, http://blogpublic.lib.msu.edu/index.php/2009/11/25/environment-michigan-challenges-dte-on-c?blog=33

3. Michigan Air Emissions Reporting System,Annual Pollutant Totals Query Results

http://www.deq.state.mi.us/maers/emissions_query_results.asp?SRN=k3249&Facility_Name=m

ichigan+state+university&EI_Year=&City=&County=&AQD_District=&cmdSubmit=Submit+Query

4. Natural Gas Combined Natural Gas Combined- -cycle Gas Turbine Power Plants cycle Gas

Turbine Power Plants , August 8, 2002, Northwest Power Planning Council

5. Multilayer ceramic capacitors, Reliability, EPCOS AG 2006.

6. Reliability of non-hermetic pressure contact IGBT modules,R. Schlegel, E. Herr, F. Richter

ABB Semiconductors AG, Fabrikstrasse 3, CH 5600 Lenzburg, Switzerland

7. Reliability Evaluation of solar photovoltaic arrays, Nalink Gautaman, D. Kaushika, 15 August

2001

8. The Statistical treatment of Battery Failures, Jim McDowall, Business Development Manager.

9. Design for reliability of power electronics modules, Hua Lu,Chris Bailey ,Chunyan Yin

http://blogpublic.lib.msu.edu/index.php/2009/11/25/environment-michigan-challenges-dte-on-c?blog=33

http://blogpublic.lib.msu.edu/index.php/2009/11/25/environment-michigan-challenges-dte-on-c?blog=33

http://www.deq.state.mi.us/maers/emissions_query_results.asp?SRN=k3249&Facility_Name=michigan+state+university&EI_Year=&City=&County=&AQD_District=&cmdSubmit=Submit+Query

http://www.deq.state.mi.us/maers/emissions_query_results.asp?SRN=k3249&Facility_Name=michigan+state+university&EI_Year=&City=&County=&AQD_District=&cmdSubmit=Submit+Query

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By Samer Sulaeman Jorge G. Cintrón-Riveramitraj/teaching/projects/cintron-rivera_and_sulae… · Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera 1.3 project