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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
Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera
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.
Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera
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
Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera
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
Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera
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
Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera
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:
Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera
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.
Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera
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
Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera
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.
Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera
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
Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera
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
Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera
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.
𝑀𝑒𝑎𝑛 𝐶𝑦𝑐𝑙𝑒 𝑡𝑖𝑚𝑒: 𝑀𝐶𝑇 =1
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
Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera
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
𝑀𝑒𝑎𝑛 𝐶𝑦𝑐𝑙𝑒 𝑡𝑖𝑚𝑒: 𝑀𝐶𝑇 =1
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
Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera
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
𝑀𝑒𝑎𝑛 𝐶𝑦𝑐𝑙𝑒 𝑡𝑖𝑚𝑒: 𝑀𝐶𝑇 =1
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
Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera
Power Electronics
&
Alternative Energy
Source
S t
Equivalent
Power
System
Parameter Alternative energy system
𝝀 0.302𝑑𝑎𝑦
𝝁 43.48𝑑𝑎𝑦
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
Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera
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
𝑀𝑒𝑎𝑛 𝐶𝑦𝑐𝑙𝑒 𝑡𝑖𝑚𝑒: 𝑀𝐶𝑇 =1
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
Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera
Parameter Equivalent Proposed system
𝝀 0.00227𝑑𝑎𝑦
𝝁 45.48𝑑𝑎𝑦
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
Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera
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
𝑀𝑒𝑎𝑛 𝐶𝑦𝑐𝑙𝑒 𝑡𝑖𝑚𝑒: 𝑀𝐶𝑇 =1
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
Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera
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.
Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera
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.
Engineering Reliability Project Samer Sulaeman Jorge G. Cintrón-Rivera
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.
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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