**4. Case study 2: investments in energy infrastructure**

and data acquisition (SCADA) system is the infrastructure with the highest score because it affects three very important nodes such as electricity transmission, electricity plant, and

phone/Internet infrastructure.

102 System of System Failures

**Table 2.** Summary results of network analysis of urban infrastructure systems.

**Figure 5.** Infrastructure-actor network in the context of Florida urban systems.

Uncertainties abound in making investment decisions in energy infrastructure such as electricity power plant. There are some major uncertainties they have to deal with in liberalized energy markets ([11]). It is difficult to predict the future electricity demand price as well as the price of input fuels. In addition, there are several structural uncertainties. These include regulation on price mechanisms (e.g., price cap) and environment (e.g., cooling water, emissions, and waste), the developments in the natural gas industry (e.g., the extraction of gas through fracking), and the unbundling of the energy industry into separate electricity generation, transmission, and distribution function.

#### **4.1. SoS model of investment in energy infrastructure**

An SoS model for electricity power plant investment is given in **Figure 6**. It consists of two engineered (power plant and house building technologies) and three actor systems (utility companies, household consumers, and public utilities commission).

**Figure 6.** SoS model for electricity power plant investment.

Some of the main elements of system-of-systems model are described as follows:

• Policies (P): At the beta level, policy variables for utility companies involved: the size of the plant, the timing of plant construction, and maintenance policies. These are the actions that would become external forces to the power plant technologies at the alpha level. For the household consumers, their decisions are mainly associated with energy consumption and investments in energy saving measures, which in turn affect house building technologies (at alpha level).

grow between −20 and 20% per 10 year. Lastly, the volatility of natural gas price is modeled using a binomial method [13]. The gas price change follows a 'random walk' pattern with

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To assess the success of investment decisions, three decision criteria are used: net present value (NPV), regret, and robustness criterion. A regret value represents the difference between the NPV of a decision compared to the NPV of the *best alternative* in a particular scenario. Based on the NPV and regret criteria, an investment is considered to be successful if it has a positive NPV and has 'no' (NPV difference: 0—\$0.09 million) or 'mild' (0.1—\$14.9 million) regret. On the other hand, an investment is considered to fail, if it has 'a lot' (15—\$99.9 million) and 'overwhelming' (greater than \$100 million) regret even though the NPV is positive. Failure

A robustness score represents the ratio of the number of successful scenarios with the total number of scenarios. Four categories of robustness can be specified. The robustness falls into Category I if the score is between 1 and 0.75 and Category II for the score between 0.5 and 0.74. A decision is considered robust if it has Category I and II score. Decision makers should then compare the robustness of decision alternatives and choose a decision with maximum

Computational experiments were performed across the uncertainty space. The resulting regret category and robustness score of *Investment1* and *Investment2* is given and compared in **Figure 7**. For Investment1, a mapping of regret category is illustrated for a scenario at Period1 (i.e., year 1–10), in which electricity demand grows by 5%, the gas price moves upward, and electricity price increases by 20%. Compared to *Investment2*, at the end of Period2 (i.e., year 20), *Investment1* ends up largely successful. This is indicated by 44 scenarios (out of 50) with 'no' and 'mild' regret. This performance is aggregated into a single robustness score of 0.88 (i.e., 44 divided by 50), which falls into robustness Category I. The same calculation is repeated for all other

In a multiple period decision problem, the robustness score can be further aggregated by taking score average. In this way, the path dependency of decision performance can be traced back to the time when the decision is made (i.e., Period0). The nested robustness score for *Investment1* and *Investment2* is 0.16 and 0.42, respectively. Based on these results, *Investment2*

should be chosen because it performs better in more scenarios than *Investment1*.

**4.4. Seeking failure modes: future conditions that might turn a robust decision into** 

Decision makers are also interested in knowing other conditions that will make their seemingly promising decision fail. To illustrate sensitivity, analysis was performed on the interest rate, which has been held constant at 5%. **Figure 8** shows that the ranges of interest rate that will make Investment1 fail. For example, when the interest rate reaches 11%, the Investment1 is no longer robust across some of the most favorable conditions in period1 because all the

specific upward (up) and downward (down) movement factor.

also includes all regret outcomes with negative NPV.

robustness.

**4.3. Results and analysis**

scenarios (a total of 2500).

robustness scores fall into Categories III and IV.

**a failure**


#### **4.2. Computational model of electricity power plant investment**

Based on the abovementioned definition of SoS, a simple computational model of electricity infrastructure investment was developed. In response to these uncertainties, utility companies may choose not to invest in capital intensive, long lead-time generating technologies such as large nuclear- or hydropower plants or in technologies with relatively high pollution such as coal plant. Instead, they may opt for cheaper, smaller, and less polluting plants that have shorter lead times to build [12].

The model compares the performance of two alternative investment decisions. *Investment1* builds a power plant with a production capacity of 563 MW, whereas *Investment2* constructs a smaller plant of 264 MW. Both power plants use natural gas fueled combined cycle plant technology. The complete model is described in [6].

The uncertainty space for the investment decisions spans a period of 20 years and is discretized into an interval of 10 years. Major uncertainties of future conditions over the time span include several factors. First is electricity demand of which an annual growth rate range between −5 and 5% was taken. Second is the change in electricity price that was assumed to grow between −20 and 20% per 10 year. Lastly, the volatility of natural gas price is modeled using a binomial method [13]. The gas price change follows a 'random walk' pattern with specific upward (up) and downward (down) movement factor.

To assess the success of investment decisions, three decision criteria are used: net present value (NPV), regret, and robustness criterion. A regret value represents the difference between the NPV of a decision compared to the NPV of the *best alternative* in a particular scenario. Based on the NPV and regret criteria, an investment is considered to be successful if it has a positive NPV and has 'no' (NPV difference: 0—\$0.09 million) or 'mild' (0.1—\$14.9 million) regret. On the other hand, an investment is considered to fail, if it has 'a lot' (15—\$99.9 million) and 'overwhelming' (greater than \$100 million) regret even though the NPV is positive. Failure also includes all regret outcomes with negative NPV.

A robustness score represents the ratio of the number of successful scenarios with the total number of scenarios. Four categories of robustness can be specified. The robustness falls into Category I if the score is between 1 and 0.75 and Category II for the score between 0.5 and 0.74. A decision is considered robust if it has Category I and II score. Decision makers should then compare the robustness of decision alternatives and choose a decision with maximum robustness.

#### **4.3. Results and analysis**

Some of the main elements of system-of-systems model are described as follows:

(at alpha level).

104 System of System Failures

public interests.

shorter lead times to build [12].

• Policies (P): At the beta level, policy variables for utility companies involved: the size of the plant, the timing of plant construction, and maintenance policies. These are the actions that would become external forces to the power plant technologies at the alpha level. For the household consumers, their decisions are mainly associated with energy consumption and investments in energy saving measures, which in turn affect house building technologies

• External forces (X): At the beta level, the utility companies would be concerned and uncertain factors such as electricity pricing regulations, macroeconomic variables, and technological options. The household consumers would be uncertain about natural gas price, electricity demand, and electricity price. At the gamma level, the public utilities seemingly

• Endogenous factors I: For utility companies, they are the variables that determine the cash flow of the investment: (1) installed and used capacity, (2) costs: construction (sunk cost),

• Outcome of interest (O): Profitability is one key outcome for utility companies, which will be measured in net present value (NPV). For public utilities commissions, one outcome

• The relationships (R): For utility companies, the relationships involved include: (1) revenue functions, (2) cost functions, and (3) functions that translate the costs, revenues, and dis-

• The value system of the decision makers (W): Utility companies are driven to maximize profitability. In contrast, the utilities commissions are mandated to promote and protect

Based on the abovementioned definition of SoS, a simple computational model of electricity infrastructure investment was developed. In response to these uncertainties, utility companies may choose not to invest in capital intensive, long lead-time generating technologies such as large nuclear- or hydropower plants or in technologies with relatively high pollution such as coal plant. Instead, they may opt for cheaper, smaller, and less polluting plants that have

The model compares the performance of two alternative investment decisions. *Investment1* builds a power plant with a production capacity of 563 MW, whereas *Investment2* constructs a smaller plant of 264 MW. Both power plants use natural gas fueled combined cycle plant

The uncertainty space for the investment decisions spans a period of 20 years and is discretized into an interval of 10 years. Major uncertainties of future conditions over the time span include several factors. First is electricity demand of which an annual growth rate range between −5 and 5% was taken. Second is the change in electricity price that was assumed to

would face uncertainties about political climate and dynamics in societal values.

fixed and variable operations costs, and fuel, and (3) revenues.

**4.2. Computational model of electricity power plant investment**

count factors (i.e., interest rate) into NPV.

technology. The complete model is described in [6].

they want to monitor is the level of service reliability and affordability.

Computational experiments were performed across the uncertainty space. The resulting regret category and robustness score of *Investment1* and *Investment2* is given and compared in **Figure 7**. For Investment1, a mapping of regret category is illustrated for a scenario at Period1 (i.e., year 1–10), in which electricity demand grows by 5%, the gas price moves upward, and electricity price increases by 20%. Compared to *Investment2*, at the end of Period2 (i.e., year 20), *Investment1* ends up largely successful. This is indicated by 44 scenarios (out of 50) with 'no' and 'mild' regret. This performance is aggregated into a single robustness score of 0.88 (i.e., 44 divided by 50), which falls into robustness Category I. The same calculation is repeated for all other scenarios (a total of 2500).

In a multiple period decision problem, the robustness score can be further aggregated by taking score average. In this way, the path dependency of decision performance can be traced back to the time when the decision is made (i.e., Period0). The nested robustness score for *Investment1* and *Investment2* is 0.16 and 0.42, respectively. Based on these results, *Investment2* should be chosen because it performs better in more scenarios than *Investment1*.

### **4.4. Seeking failure modes: future conditions that might turn a robust decision into a failure**

Decision makers are also interested in knowing other conditions that will make their seemingly promising decision fail. To illustrate sensitivity, analysis was performed on the interest rate, which has been held constant at 5%. **Figure 8** shows that the ranges of interest rate that will make Investment1 fail. For example, when the interest rate reaches 11%, the Investment1 is no longer robust across some of the most favorable conditions in period1 because all the robustness scores fall into Categories III and IV.

**5. Case study 3: informing economic revival initiatives in the** 

The economy of the Northern Illinois Region, USA with Rockford as its largest city has suffered since the late 1980s as a result of the decline of manufacturing industry. Currently, a

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The case study presents a development of a decision-support tool to inform policymakers and stakeholders to revive the region's economy. To this end, the proposal will implement a holistic system approach. The approach used will be a combined system dynamics and SOS perspective. The issues that will be addressed include the interactions between the city qual-

The combined SOS perspective and system dynamics have a capability to model economic decisions at three different levels such as city, company, and individual. **Figure 9** shows the

System dynamics is an approach to understand the behavior of complex systems over time. It deals with internal feedback loops and time delays that affect the behavior of the entire

multi-level decision making occurring within a macroeconomic context.

diverse initiative has been launched by various agencies to try to reverse the trend.

**northern Illinois region**

ity of life factors and investment decisions.

**5.2. SoS conceptualization**

**5.3. System dynamics approach**

**Figure 9.** SoS for urban systems.

**5.1. Introduction**

**Figure 7.** Investment robustness outcomes (a) Investment1 (563 MW) and (b) Investment2 (264 MW).

**Figure 8.** Sensitivity of favorable scenarios to interest rate.
