11

2.1 INTRODUCTION

The most distinguishing feature of probabilistic planning is a combination of probabi-listic reliability evaluation and economic analysis into the planning process. In tradi-tional deterministic planning, system reliability is considered through some simple rules such as the N − 1 principle, whereas in probabilistic planning, system reliability is quantitatively assessed and expressed using one or more indices that represent system risks. Two essential tasks of probabilistic planning are (1) establishment of probabilistic planning criteria through reliability indices and (2) combination of quantitative reli-ability evaluation with probabilistic economic analysis to form a basic procedure. It is important to appreciate that the objective of introducing probabilistic planning is to enhance but not to replace traditional planning. The new procedure must be designed in such a way that both deterministic and probabilistic criteria are coordinated in a unifi ed process.

Probabilistic planning also requires other power system analysis and assessment techniques in addition to reliability evaluation and economic analysis. These include probabilistic methods in load forecast and load modeling, power fl ow and probabilistic power fl ow, traditional and probabilistic contingency analyses, and optimal power fl ow

2

BASIC CONCEPTS OF PROBABILISTIC PLANNING

Probabilistic Transmission System Planning, by Wenyuan LiCopyright © 2011 Institute of Electrical and Electronics Engineers

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12 BASIC CONCEPTS OF PROBABILISTIC PLANNING

and probabilistic search - based optimization methods, as well as conventional and proba-bilistic voltage and transient stability assessments. Another important task is preparation and management of various data required by probabilistic planning activities as well as treatment of data uncertainties. All of these will be discussed in Chapters 3 – 8 .

This chapter focuses on the basic concepts of probabilistic transmission planning. The probabilistic criteria are presented in Section 2.2 . The general procedure of proba-bilistic planning is illustrated in Section 2.3 , and other relevant aspects are briefl y outlined in Section 2.4 .

2.2 PROBABILISTIC PLANNING CRITERIA

Although probabilistic planning criteria are not as straightforward as the deterministic N − 1 criterion, different approaches can be developed to establish probabilistic criteria [7 – 9] . Four possible approaches are presented in this section. Which one is used depends on the utility business model and the project to which the criterion is applied. For instance, different approaches can be used for bulk networks and regional systems, or for transmission - line addition and substation enhancement.

2.2.1 Probabilistic Cost Criteria

Reliability is one of multiple factors considered in probabilistic transmission planning. System unreliability can be expressed using unreliability costs so that system reliability and economic effects can be assessed on a unifi ed monetary basis. There are two methods for incorporating the unreliability cost: the total cost method and the benefi t/cost ratio method.

1. Total Cost Method. The basic idea is that the best alternative in system planning should achieve the minimum total cost:

Total cost investment cost operation cost unreliability co= + + sst

The calculation of investment cost is a routine economic analysis activity in transmission planning. The operation cost includes OMA (operation, mainte-nance, and administration) expenditures, network losses, fi nancial charges, and other ongoing costs. The unreliability cost is obtained using the EENS index (expected energy not supplied, in MWh/year) times the unit interruption cost (UIC, $/kWh), which will be discussed in Chapter 5 .

2. Benefi t/Cost Ratio Method. The capital investment of a planning alternative is the cost, whereas the reduction in operation and unreliability costs is the benefi t due to the alternative. The benefi t/cost ratios for all preselected alternatives are calculated and compared. In other words, the alternatives can be ranked using their benefi t/cost ratios. A project may be associated with multistage invest-ments and a planning timeframe (such as 5 – 20 years) is always considered. All three cost components should be estimated on an annual basis to create their

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2.2 PROBABILISTIC PLANNING CRITERIA 13

cash fl ows on the timeframe fi rst, and then a present value method is applied to calculate the benefi t/cost ratios. The BCR method will be discussed in further detail in Chapter 6 .

2.2.2 Specifi ed Reliability Index Target

Many utilities have used reliability indices to measure the system performance and made an investment decision based on the metrics. One or more reliability indices can be specifi ed as a target reliability level. For example, the target of an outage duration index such as the T - SAIDI (system average interruption duration index) or an outage frequency index such as the T - SAIFI (system average interruption frequency index) (where the T prefi x denotes transmission ) can be specifi ed with a tolerant variance range. If the evaluated result exceeds the specifi ed range, an enhancement is required. The defi nitions of transmission system reliability evaluation indices and historical performance - based indices will be discussed in Chapters 5 and 7 , respectively.

The essence of this approach is to use a reliability index as a target. It is well known, for instance, that the LOLE (loss of load expectation) index of one day per 10 years has been used as a target index in generation planning for many years. Unfortunately, it is not easy to set an appropriate index target for transmission system reliability. Historical statistics can help in determination of an index target. On the other hand, caution should be taken regarding the coherent uncertainty and inaccuracy in historical records when this approach is used.

2.2.3 Relative Comparison

In most cases, the purpose of transmission planning is to compare different alternatives (including the doing nothing option). One major index or multiple indices (such as the EENS, probability, frequency, and duration indices) can be used in the comparison.

Performing a relative comparison is often better than using an absolute index target because

• Not only reliability indices but also economic and other aspects can be compared.

• Historical statistics and input data used in probabilistic reliability evaluation are always fraught with uncertainties.

• The historical system performance may not represent the future performance that a planning projects targets.

• There are computational errors in modeling and calculation methods, and errors can be offset in a relative comparison.

2.2.4 Incremental Reliability Index

If it is diffi cult to use unreliability cost in some cases, an incremental reliability index (IRI) can be applied. The IRI is defi ned as the reliability improvement due to per M$ (million dollars) of investment, which can be expressed as follows:

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14 BASIC CONCEPTS OF PROBABILISTIC PLANNING

IRIRI RI

cost=

−B A

The cost is the total cost for investment and operation (in M$) required for a reinforce-ment option. The RI B and RI A respectively are the reliability indices before and after the reinforcement. Conceptually, any appropriate reliability index (such as the EENS, probability, frequency, or duration index) can be used. In most cases, the EENS is sug-gested if it can be quantifi ed since this index is a combination of outage frequency, duration, and severity, and carries more information than does any other single index.

The IRI can be used to rank projects or compare alternatives for a project. The disadvantage of the IRI approach is the fact that the “ doing nothing ” option cannot be included.

2.3 PROCEDURE OF PROBABILISTIC PLANNING

There are different ways to perform probabilistic transmission planning [7 – 9] . Figure 2.1 shows a general process that includes the criteria mentioned above. It also indicates how to combine the deterministic N − 1 principle with the probabilistic criteria.

The basic procedure of probabilistic transmission planning includes the following four major steps:

1. If the single - contingency criterion is a mandate, select the planning alternatives that meet the N − 1 principle. Otherwise, if the N − 1 principle is not considered as the strict criterion, select all feasible alternatives. In either case, system analysis using the traditional assessment techniques (power fl ow, optimal power fl ow, contingency analysis, and stability studies) is needed. These techniques will be summarized in Chapter 4 .

2. Conduct probabilistic reliability evaluation and unreliability cost evaluation for the selected alternatives over a planning timeframe (such as 5 – 20 years) using a reliability assessment tool for transmission systems.

3. Calculate the cash fl ows and present values of investment, operation, and unreli-ability costs for the selected alternatives in the planning time period.

4. Select an appropriate criterion described in Section 2.2 and conduct an overall probabilistic economic analysis.

It can be seen that probabilistic reliability evaluation and economic analysis are two key steps, which are briefl y discussed in Sections 2.3.1 and 2.3.2 and will be detailed in Chapters 5 and 6 .

2.3.1 Probabilistic Reliability Evaluation

There are two fundamental methods for probabilistic reliability evaluation [6,10,11] of transmission systems: Monte Carlo simulation and state enumeration. The difference

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2.3 PROCEDURE OF PROBABILISTIC PLANNING 15

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16 BASIC CONCEPTS OF PROBABILISTIC PLANNING

between the two methods is associated with how to select system states, whereas the system analysis in assessing the consequences of selected outage states is the same. The probabilistic reliability assessment of composite generation – transmission systems using the Monte Carlo method is summarized as follows:

1. A multistep load model is created that eliminates the chronology and aggregates load states using hourly load records during one year. The uncertainty of load at each step can be modeled using a probability distribution if necessary. Annualized indices are calculated fi rst by using only a single load level and are expressed on the one - year basis. All the load - level steps are considered succes-sively, and the resulting indices for each load level that are weighted by the probability for that load level are summed up to obtain annual indices.

2. The system states at a particular load level are selected using Monte Carlo simulation techniques. This includes the following:

a. Generally, generating unit states are modeled using multistate random vari-ables. If generating units do not create different impacts on selected transmis-sion planning alternatives, the generating units can be assumed to be 100% reliable.

b. Transmission component states are modeled using two - state (up and down) random variables. For some special transmission components such as HVDC lines, a multistate random variable can be applied. Weather - related transmission - line forced outage frequencies and repair times can be deter-mined using the method of recognizing regional weather effects. Transmission - line common - cause outages are simulated by separate random numbers.

c. Bus load uncertainty and correlation are modeled using a correlative normal distribution random vector. A correlation sampling technique for the normal distribution vector is used to select bus load states.

3. System analyses are performed for each selected system state. In many cases, this requires power fl ow and contingency analysis studies to identify possible system problems. In some cases, transient and voltage stability studies may also be required.

4. An optimal power fl ow (OPF) model is used to reschedule generations and reactive sources, eliminate limit violations (line overloading and/or bus voltage violations), and avoid any load curtailment if possible or minimize the total load curtailment or interruption cost if unavoidable.

5. The reliability indices are calculated on the basis of the probabilities and con-sequences of all sampled system states.

If the state enumeration method is used, step 2 is carried out differently and all other steps basically remain the same. The reliability evaluation for substation confi gurations follows a simpler procedure since it is essentially a problem of connectivity between sources and load points, and no power - fl ow - based model is required. The probabilistic reliability evaluation will be discussed in more detail in Chapter 5 .

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2.4 OTHER ASPECTS IN PROBABILISTIC PLANNING 17

2.3.2 Probabilistic Economic Analysis

There are three cost components in probabilistic economic analysis [6,10] : investment, operation, and unreliability costs.

Investment analysis is a fundamental part of the economic assessment in a planning process. The cash fl ow of annual investment cost can be created using the capital return factor (CRF) method and actual capital estimates. The parameters associated with economic analysis of capital investment (such as the useful life of a project, discount rate, and capital estimates) are usually given by deterministic numbers. However, a probabilistic method can be applied to capture the uncertainty of the parameters. For instance, a discrete probability distribution of discount rate can be obtained from his-torical statistics and considered in the calculation model. The concepts and methods used in the economic analysis will be illustrated in Chapter 6 .

The cash fl ows of operation and unreliability costs are calculated through year - by - year evaluations. In addition to fi xed cost components, the operation cost in a transmis-sion system is also related to evaluation of network losses, simulation of system production costs, and estimation of energy prices on the power market. This is associ-ated with considerable uncertainty factors, including load forecasts, generation patterns, maintenance schedules, and power market behaviors. In some cases, on the other hand, the planning alternatives selected may involve only limited modifi cations of network confi guration and have basically the same or close operation cost. In such a situation, the operation cost may not have to be included in the total cost for comparison. This is case - dependent.

As mentioned earlier, the unreliability cost equals to the product of EENS and a unit interruption cost. Obviously, this cost component is a random number that depends on various probabilistic factors in a transmission system, particularly on random outage events. The EENS can be calculated by a probabilistic reliability evaluation method, whereas the unit interruption cost (UIC) can be estimated using one of the following four techniques. The fi rst one is based on customer damage functions (CDFs) that can be obtained from customer surveys. A CDF provides the relationship curve between the average unit interruption cost and duration of power outage. The second one is based on a gross domestic product divided by a total electric energy consumption, which gives a dollar value per kilowatt - hour (kWh) refl ecting the average economic damage cost due 1 kWh of energy loss. The third one is based on the relationship between capital investment projects and system EENS indices. The fourth one is based on the lost revenue to the utility due to power outages. This last technique would typi-cally represent the lowest level of UIC. Utilities can select an appropriate technique that best aligns with their business objectives. The details of unreliability cost assess-ment will be given in Chapter 5 .

2.4 OTHER ASPECTS IN PROBABILISTIC PLANNING

Probabilistic planning involves a wide range of study activities, including traditional deterministic analyses and new probabilistic assessments. The traditional analysis

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18 BASIC CONCEPTS OF PROBABILISTIC PLANNING

techniques used in transmission planning, including power fl ow, contingency analysis, optimal power fl ow, transient stability, and voltage stability, will continue to be impor-tant while new probabilistic assessment methods are introduced.

Load forecast and generation conditions are two crucial prerequisites of transmis-sion planning. Load forecast has been performed using probabilistic methods even in the conventional planning practice because of the inherent uncertainty in predicting future loads. However, applications of new methods (such as neural network and fuzzy clustering) provide vehicles to improve accuracy in long - term load forecasting. Load forecast and other load modeling issues will be discussed in Chapter 3 . Generation conditions, including types of generators, locations, capacities and availability in the future, are the outcome of generation planning, which is a complex task by itself. Detailed discussion of generation planning is beyond the scope of the book. An inte-grated planning of generation and transmission may be necessary in some cases.

Obviously, probabilistic methods are not limited to reliability evaluation and eco-nomic analysis. Probabilistic power fl ow and probabilistic contingency analysis are often useful tools in probabilistic transmission planning studies. In the optimization analysis for system planning, probabilistic search optimization techniques can provide solutions to some special problems. Probabilistic transient stability and voltage stability assessments should also be considered when necessary. Essentially, these are extensions of conventional transient and voltage stability analyses in order to incorporate proba-bilistic modeling of various uncertain factors. The basic procedure includes three main aspects: (1) a probabilistic method is used to select random factors for dynamic system states, (2) a stability analysis technique is used to conduct stability simulations of sto-chastically selected system states, and (3) a probabilistic index or its distribution is created to represent system instability risk. Generally, probabilistic stability assess-ments provide a deeper and broader insight into system dynamic behavior and instabil-ity risk. The additional probabilistic techniques will also be presented in Chapters 4 and 5 .

Another crucial aspect is the data preparation for probabilistic transmission plan-ning. This includes not only the regular data for conventional system analyses but also the data for probabilistic assessments. The data required in probabilistic planning will be discussed in detail in Chapter 7 . Reliability data are obtained from historical statisti-cal records, and a computerized database is required to collect, store, and manage outage data. Maintaining a high quality of data is a key for successful probabilistic planning.

There are two types of uncertainty in input data and modeling: randomness and fuzziness. Randomness is characterized by probability, whereas fuzziness is character-ized by fuzzy variables. Dealing with the two uncertainties is an important issue in probabilistic transmission planning. This will be addressed in Chapter 8 .

2.5 CONCLUSIONS

This chapter described the basic concepts of probabilistic transmission planning. The fi rst step toward probabilistic planning is to establish and understand its criteria and procedure. The four probabilistic planning criteria have been discussed. Utilities may

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2.5 CONCLUSIONS 19

select one or more criteria in actual applications to suit their business requirements. A probabilistic planning fl owchart is presented to illustrate the details of planning proce-dure and the coordination between probabilistic and deterministic N − 1 criteria.

The most important tasks in probabilistic planning are quantifi ed probabilistic reli-ability evaluation and probabilistic economic analysis. The basic ideas of the two tasks have been discussed. Besides, probabilistic studies in other aspects are also required depending on the particular cases and problems under study. These include probabilistic load forecast and load modeling, probabilistic power fl ow and contingency analysis, and probabilistic transient and voltage stability assessments. It is essential to recognize that the deterministic N − 1 criteria must be used to select initial alternatives for proba-bilistic planning and the conventional system analysis techniques including power fl ow, contingency analysis, optimal power fl ow, and stability simulations are still important tools in the integrated planning process. Probabilistic planning methods are designed to complement and enhance traditional transmission planning.

This chapter provided only a high - level description of the subject. Detailed discus-sions of each topic will be developed in subsequent chapters.

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