Adequacy assessment of power systems incorporating building cooling, heating and power plants

Energy and Buildings 105 (2015) 236–246

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Adequacy assessment of power systems incorporating building cooling, heating and power plants Seyed Mohsen Miryousefi Aval ∗ , Amir Ahadi ∗ , Hosein Hayati Young Researchers and Elite Club, Ardabil Branch, Islamic Azad University, Ardabil, Iran

a r t i c l e

i n f o

Article history: Received 6 January 2015 Received in revised form 15 April 2015 Accepted 19 May 2015 Available online 18 July 2015 Keywords: Adequacy evaluation Reliability Markov method Building cooling, heating and power (BCHP) system

a b s t r a c t Electric power systems have been changing from the conventional and traditional electric units to the efficient, economical, less-polluting and reliable ones. Building cooling, heating and power (BCHP) systems can yield these goals and save energy as well as improve the reliability of the system. However, for significant integration and the use of large amount of BCHP generation in electric power systems, some approaches should be followed in order to study the reliability of the BCHP systems. In this study, we focused on the reliability aspects of power systems incorporating BCHP systems in the local distribution systems. The Markov method based on the state-space analysis is used to investigate the impacts of implementation of BCHP systems on the power systems’ reliability. The Markov method is well suited to analyze the reliability of systems based on a continuous stochastic process. The Roy Billinton test system and the IEEE reliability test system are used to illustrate the results. Case studies show the effects of BCHP systems on general adequacy of electric power systems. Various case results demonstrate the efficiency and effectiveness of the proposed method. © 2015 Elsevier B.V. All rights reserved.

1. Introduction Over the last few decades, some changes have been made in the field of distributed generation which overcame some major issues of power systems. With the advancement of energy technology, heating and cooling can be supplied simultaneously in the distributed generation systems [1]. Building cooling, heating and power (BCHP) systems are broadly identified as an alternative resource to solve dilemmas such as energy supply security, increasing energy demands and cost, as well as environmental issues [2–4]. Many applications of the BCHP systems have been investigated so far. Some major benefits of the BCHP systems consist of increasing resource energy efficiency, reducing air pollutant emissions, producing combined electricity, heating, and cooling. In recent studies, BCHP systems have been investigated from different aspects such as optimization, model, feasibility analysis, evaluation, and reliability. For instance, a method based on the mixed integer linear programming is used in [5,6] to study the optimization of operation and design of trigeneration systems for building applications. This method is also used in [7] to investigate the optimal design of trigeneration systems in a hospital complex. The performance of a small combined heat and power (CHP) plant for use in a

∗ Corresponding authors. E-mail address: [email protected] (A. Ahadi). http://dx.doi.org/10.1016/j.enbuild.2015.05.059 0378-7788/© 2015 Elsevier B.V. All rights reserved.

conventional house in the Republic of Ireland is evaluated in [8]. The environmental sustainability of a micro-CHP unit fueled by solar energy is discussed in [9] which is useful for the long-term exploitation of the designed system. Ref. [10] investigated the performance of a CHP system installed at the Mississippi State University where both summer and winter conditions are considered. The most interesting approach to this issue has been proposed by [11] which provides the near real-time optimization making use of an aggregation of micro CHP devices in Belgium. Ref. [12] proposed a novel model of the CHP systems based on the three models which are cooling, heating, and power; heating and power; and cooling and power to demonstrate the improvement of the site energy. A new model of the CHP systems based on the two bed silica gel-water adsorption chiller is proposed in [13] in order to achieve an accurate prediction of the chiller performance considering both variable and stable heat source temperature. Ref. [14] proposed a comprehensive input–output matrix approach for modeling trigeneration systems for optimal operation of a composite scheme with electric chillers and absorption. Ref. [15] discussed a new model of the CHP systems to guarantee primary energy savings considering the quality and type of the energy being consumed. In [16], the energy demands for electricity and heat in the CHP systems for residential applications are analyzed to demonstrate that the condensing gas boilers are economically more interesting and also have a modest effect on primary energy consumption. In [17], it has been revealed that the increased flexibility in the structure of

S.M. Miryousefi Aval et al. / Energy and Buildings 105 (2015) 236–246

electricity markets will lead to both negative and positive effects for CHP systems in which these effects should be modeled properly. Ref. [18] developed a new concept of the CHP systems where the catalysts development, design of the stack and its components, design and testing of the natural gas reformer are modeled. The problem of economic feasibility analysis and energy efficiency evaluation of the micro trigeneration systems for CHP systems with an available Stirling engine is investigated in [19]. Ref. [20] studied various integrated configurations of different types of commercially available micro gas turbine cogeneration systems in absorption cooling chillers based on the biogas. Economic viability of several options in the trigeneration systems are analyzed based on the net present value and a simple payback time in [21]. An interesting approach in [22] investigated the optimal design of CHP systems considering fluctuating electricity prices in Denmark. The results obtained in [23] suggested an optimal design of the CHP systems based on several aspects such as economical, energy, and environmental considerations. The feasibility of landfill gas trigeneration in Hong Kong is studied in [24] based on the greenhouse gas emission reduction, primary energy-saving, and economic benefit. Ref. [25] proposed a unified general model to assess the energy performance of different types of poly-generation systems with natural gas as the energy input. Refs. [26,27] studied the reliability considerations of BCHP systems in terms of optimal design and operation. A method based on the Monte Carlo simulation is proposed in [28] to estimate the reliability of two suggested configuration of cogeneration plants. The methods were improved in [29,30] in terms of risk analysis of the BCHP systems in order to achieve the best optimization model of the systems. An analytical approach based on the Markov method is presented in [31] to evaluate the availability as well as the unavailability of the BCHP system based in the failure and repair rate of each BCHP system’s component. Ref. [32] proposed a method based on the fault tree logic modeling in order to assess the reliability and critical failure predictability requirements for fuel cell stacks. The main contribution is investigating the effects of stack reliability and critical components on the system availability and reliability. A power system for the purposes of operation, planning and analysis can be divided into three appropriate subsystems which are generation, transmission and distribution. For this aim, the hierarchical levels (HL) have been developed for adequacy assessment of power systems [33] in order to establish a consistent means of grouping and identifying these subsections. The hierarchical level I (HLI) refers to generation facilities and their abilities to satisfy the system demand. The HLI is also known as “generating capacity reliability evaluation” where distribution and transmission are not included. The hierarchical level II (HLII) refers to the composite generation and transmission (bulk power) system to deliver energy to the bulk supply points. In other words, composite system (HL-II or bulk system) reliability evaluation considers both the transmission and generation system in the analysis. The hierarchical level III (HLIII) refers to the complete assessment of the system including distribution and its ability to satisfy the customer demand. It is worth noting that the complete HLIII studies are mainly impractical because of the scale and complexity of the problem. Therefore, unlike the HLI and HLII studies which are regularly performed, analysis at the HLIII is performed separately using the HLII load point indices as input values. Adequacy assessment in power systems is the basic and most important step which should be involved in either the proposed or existing facilities to satisfy the operational constraints as well as the system load and demand. The methods used for conducting the probabilistic adequacy analysis on power systems fall into three categories, analytical [34], Monte Carlo simulation [35], and combinations [36] of the simulation and analytical techniques. The reliability parameters used in analytical techniques are usually assumed to be constant. The proposed way for the BCHP

237

model to be used in this study is similar to the approach in [37] which is compatible with the system adequacy and can be used for other particular considerations like the system complexity (e.g. the system assessment incorporating transmission lines). Thus, the proposed method can be extended to different types of complex models. The BCHP model used is based on the multi-state capacity outage probability table (COPT) which also provides more accurate results. After review of the literature and to the best of the authors’ knowledge, none of the previous works have investigated the effects of the BCHP systems on the probability distributions of power system reliability indices. Markov method is well suited to evaluate the reliability of systems based on a continuous stochastic process. This paper proposes a novel procedure and method based on the Markov method for estimating the reliability of the power systems at the HLI incorporating BCHP systems. The rest of this paper is organized as follows. Section 2 introduces the structure of BCHP systems with the major focus on the electricity side. An analytical approach based on the Markov method for the reliability assessment of the BCHP systems is proposed in Section 3. Test results and case studies are summarized in Section 4. Section 5 concludes this paper. 2. System construction of the redundant BCHP systems The structure of BCHP systems is given in Fig. 1. It can be seen that in order to produce electricity, the gas turbine powered by natural gas is used. Following this, the exhaust output of the gas turbine is entered to the heat recovery steam generator (HRSG). This process is conducted by dividing the recovered heat between the absorption chiller (i.e. for providing the cooling load) and the heat exchanger (i.e. for providing the heating load). However, if either the cooling or heating cannot completely satisfy the demand, an auxiliary gas-fired boiler would be served to mitigate the shortage. Furthermore, if the electricity generated is not enough for the energy demand, the electricity needed is taken from the outside electric power grid. Finally, in order to improve the thermal efficiency as well as store the extra exhausted heat, the heat storage tank can be added [38,39]. The BCHP system has capability of connecting to the outside power grid. If both the power supply from the BCHP system and the outside grid is not sufficient for the system’s load, the BCHP is considered to be in failure mode. On the other hand, for being in success mode, both the BCHP system and the outside power grid should be in the success mode. If the islanding issue is occurred, the BCHP system is disconnected from the grid. In this case, the electricity demand of the system comes from either the outside grid or the BCHP system. In case of heat production, there is always possibility of some excess electric power generation which is difficult to be disposed, especially if there is no demand in consumer side. However, in case of electricity production, the extra heat can be recovered [31]. 3. The reliability evaluation framework In the reliability evaluation, a system is considered to be either in success mode or failure mode [40]. If a power system has sufficient energy to supply the load, the system is defined as a success mode. The power system is considered to be in failure mode if the system capacity is not enough for the load demand. Hence, each failure and success states have their own probabilities and duration which are also called the reliability indices. In the following subsections, an analytical approach based on the Markov method is proposed to investigate the reliability of the BCHP systems. The Markov method serves as a useful tool to model the BCHP system accurately. This model is invaluable for the operator, since the

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Natural Gas

Compressor

Air

Combustor

Gas Turbine

Electricity

Generator

Transformer

Electric Chiller

Heat Recovery Steam Generator

Natural Gas

Load Cooling

Absorption Chiller Auxiliary Boiler

Heat

Heat Exchanger Fig. 1. The schematic diagram of the BCHP system under study.

UP

µ

where Pup , Pdown , , and  denote the probability of the up state, the probability of the down state, failure rate, and repair rate, respectively.

DOWN

3.2. Equivalent series and parallel state space model

Fig. 2. Two-state model of the BCHP system.

operator will be able to plan for providing future extra demands from the existing electrical grid as well as optimizing reliability and its costs.

The equivalent model of failure and repair rates for two series systems is defined as [45] eq = 1 + 2 eq

3.1. Reliability analysis based on the two-state Markov chain The Markov model serves as an applicable tool to demonstrate system states and behaviors and transition between these states based on two assumptions. The first assumption is that the system does not have any long or short term memory. This means that the future probability of events is only a function of the existing condition of the current system state and does not depend on the prior state of the system. The second assumption is that the system states do not vary with time, which means that transition probabilities between states are constant and the system state is in a permanent state [41]. In this study, we considered the BCHP system as a repairable system which is classified as operational/up state or failure/down state. There are several distribution functions to model the component failure (e.g. Weibull distribution [42], and exponential distribution function [43,44]). In this paper, since the BCHP system’s components have constant failure during their operation, the exponential distribution function is used in the reliability evaluation framework. The two-state model of the Markov method is shown in Fig. 2. The probability of being in the up and down state can be obtained as follows [34]: Pup =

 +

Pdown =

 +

(2)

(4)

The equivalent model of failure and repair rates for parallel systems is expressed as eq =

(1 2 )(1 + 2 ) 1 2 + 1 2 + 2 1

eq = 1 + 2

(5) (6)

where eq , and eq are the system equivalent failure rate, and repair rate, respectively. As shown in Fig. 3, failure of one of the series components in the BCHP system (i.e. compressor, combustor, gas turbine, generator, transformer) can lead to the failure of electrical section of the BCHP system and no electricity generation. An equivalent state space diagram of a BCHP system with N gas turbines and N + 1 states is depicted in Fig. 4. The equivalent model of a system with n-series components are presented below [34,46]: eq =

n 

(7)

i

i=1

Ueq =

n 

Ui =

i=1

(1)

(3)

(1 + 2 )(1 2 ) = . 1 2 + 1 2 + 2 1

Aeq = 1 − Ueq

n i ri req = i=1 n  i=1 i

n 

i ri

(8)

i=1

(9) (10)

S.M. Miryousefi Aval et al. / Energy and Buildings 105 (2015) 236–246

00

239

10

1

µ1

Compressor µ2

µ2

2

Combustor

2

01

1

µ1

11

Gas turbine Fig. 5. Four-state model of rapid start units.

Generator

Transformer

where i , Ui , and ri represent the failure rate, unavailability, and repair time of the component i, respectively. req , Aeq , and Ueq are the equivalent repair time, availability, and unavailability, respectively. The probability of state m with m − 1 gas turbines failed can be obtained as [46]

Fig. 3. Reliability block diagram of the BCHP system with five components in series.

Pm =

N! (N−m+1) (m−1) Ueq . A (m − 1)!(N − m + 1)! eq

(11)

where Pm is the probability of state m and N is the number of gas turbines. Ueq , and Aeq can be obtained from (8) and (9), respectively.

1 N units are up µ eq N eq 2 (N-1) units are up

N 1 unit is up Nµ eq eq

N+1 0 unit is up

3.3. Rapid start units model based on the Markov method In the reliability analysis of the power systems, each component might be modeled with three states which are success, failure, and derated. These states are easily defined and, therefore, the probabilities of each states can be explicitly obtained. As mentioned above, the Markov method can be used for such systems, especially for systems that have a constant failure rate with exponential distribution. Rapid start units (e.g. hydro plants and gas turbines) can be defined as a four-state model [48] as shown in Fig. 5. From Fig. 5, a transition matrix can be created with certain dimensions, depending on the number of components in the system. For a system with n components, the dimension of the transition matrix is n × n. The parameters in the transition matrix are defined by either the failure or repair rate between states. For / j), the instance, in a transition between the state i and j (with i = transition rate is entered into the ith row and jth column of the transition matrix. The diagonal parameters of the matrix must be equal to 1 minus the sum of the other parameters on the row [48]. The transition matrix (T) of Fig. 5 becomes

⎛

1 − (1 + 2 )

1

2

1

1 − (2 + 1 )

0

2

0

1 − (1 + 2 )

0

2

1

⎜ ⎜ ⎜ T=⎜ ⎜ ⎝

⎞

⎟ ⎟ ⎟ 1 ⎟ ⎟ 1 − (1 + 2 ) ⎠ 2

(12)

where T is the transition matrix. Based on the Markov method, the limiting state probability cannot be changed in the further transition procedure. Thus, this statement can be expressed as P×T=P

(13)

or P × (T − I) = 0

Fig. 4. Equivalent model of the BCHP system.

0

(14)

where P represents the limiting state probability vector and I is the identity matrix. Then, based on formula (14), we have the following results

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⎛ [P1 P2 P3 P4 ] ×

−(1 + 2 )

1

2

1

−(2 + 1 )

0

2

0

−(1 + 2 )

0

2

1

⎜ ⎜ ⎜ ⎜ ⎜ ⎝

0

⎞

when the cumulative probability Pi is used, LOLE is given as

⎟ ⎟ ⎟ 1 ⎟ ⎟ −(1 + 2 ) ⎠ 2

N 

LOLE =

N 

EENS =

PLC =

⎛

−(1 + 2 )

1

2

1

−(2 + 1 )

0

2

0

−(1 + 2 )

0

2

1

⎜ ⎜ ⎜ ⎜ ⎜ ⎝

N 

⎞

⎛ P1 ⎞ ⎛ ⎞ 0 ⎟ ⎟ ⎜ P2 ⎟ 0⎟ ⎟ ⎜ ⎟ ⎜ 1 ⎟ × ⎜ P3 ⎟ = ⎝ 0 ⎠ . ⎟ ⎝ ⎠ −(1 + 2 ) ⎠ 0 0

2

P4

(17)

This condition should be able to solve the above equation based on the n − 1 independent equations which there are four state variables involved. Thus, any row within the above equation is

⎛

1

⎜ 1 ⎜ ⎜ 2 ⎜ ⎝0

1

1

1

−(2 + 1 )

0

2

0

−(1 + 2 )

1

2

1

−(1 + 2 )

⎞ ⎛ ⎞ P1 ⎛ ⎞ 1 ⎟ ⎜ P2 ⎟ ⎟ ⎜ ⎟ ⎜0⎟ ⎟ × ⎜ ⎟ = ⎝ ⎠ . (18) 0 ⎟ ⎝ P3 ⎠ ⎠ 0 P4

Finally, based on (18), we get the following results: P1 =

1 2 (1 + 1 )(2 + 2 )

(19)

P2 =

1 2 (1 + 1 )(2 + 2 )

(20)

P3 =

1 2 (1 + 1 )(2 + 2 )

(21)

P4 =

1 2 . (1 + 1 )(2 + 2 )

(22)

3.4. Calculation of the reliability indices in composite system adequacy assessment Calculation of the reliability indices is a significant outcome of quantitative adequacy assessment of a composite system. In this study, the reliability of the system is evaluated by LOLE, EENS, PLC, EDNS, EDC, BPECI, MBECI, and SI [49]. LOLE index is loss of load expectation, EENS is expected energy not supplied, PLC is probability of load curtailment, EDNS is expected demand not supplied, EDC is expected damage cost, BPECI is power/energy curtailment index, MBECI is modified energy curtailment index, and SI is severity index. These indices can be expressed as follows: LOLE =

N  i=1

Pi ti

(h/yr)

(23)

N 

ti Ci Pi

(MWh/yr)

(25)

i=1

Pi

N 

EDNS =

(26)

Ci Pi

(MW)

(27)

i=1 N 

(16)

[P1 + P2 + P3 + P4 ] = 1.

(24)

i=1

EDC =

where P1 , P2 , P3 , and P4 are the probability of states 1, 2, 3, and 4 in Fig. 5, respectively. Also, we can compute the individual probabilities as follows:

Ci Fi Di =

i=1

(15)

= [0 0 0 0]

Pi (ti − ti−1 ) (h/yr)

i=1

Ci Fi Di W

(k$ /yr)

(28)

($ /kWh)

(29)

i=1

IEAR =

NB 

IEARk qk

k=1

BPECI =

EENS L

MBPECI =

(MWh/MW-yr)

EDNS (MW/MW) L

SI = BPECI × 60 (system-min/yr).

(30) (31) (32)

In all equations, N is the set of all system states associated with load curtailments, ti is the duration of loss of power supply in days, Pi is the probability of system state i, Ci is the load curtailment of system state i. Fi , and Di are the frequency, and the duration of system state i, respectively. W is the unit damage cost in $/kWh. NB is the total number of load buses in the system, IEARk is the interrupted energy assessment rate at load bus k, and qk is the fraction of the system load utilized by the customers at load bus k. L is the annual system peak load in MW. The EDC is an important index that can be used to conduct economic analysis in composite system adequacy assessment. In this study, this index is obtained by multiplying the EENS of the overall system by a representative system IEAR (interrupted energy assessment rate). The representative system IEAR of the RBTS and IEEE-RTS can be calculated using the data in [51] and [52] which are 4.42 $/kWh and 4.22 $/kWh, respectively. 4. Case study In this section, two published test systems as the Roy Billinton test system (RBTS) and the IEEE-reliability test system (IEEE-RTS) are investigated. These systems are slightly different from each other and they can serve as a significant test system for a wide range of applications. Both the RTS and the RBTS use the same per-unit load model which are designated as the IEEE-RTS load model [52]. This load model can be used to create 8760 hourly chronological loads on a per unit value. The following sections illustrate the effects of BCHP systems on the overall adequacy in electric power generation. To meet this goal, a few modifications in the RBTS and the IEEE-RTS have been incorporated. These modifications have been made by adding some BCHP systems in the determined capacities. It is worth noting that the reliability investigations are performed at HLI. Moreover, some well-known adequacy indices are considered to analyze the BCHP abilities in mitigating the reliability of the system. In [47], the probability values less than 1 × 10−8 have been ignored which indicate that the IEEE-RTS has 1872 states without table rounding. However, for getting more accurate results, we considered all the probabilities with 3180 states. The results are radical

S.M. Miryousefi Aval et al. / Energy and Buildings 105 (2015) 236–246

Table 2 Outage state enumeration of the BCHP system based on monotonically increasing order.

100

Cap. in (MW)

Daily peak load (%)

241

40 30 20 10 0

60

2×40 MW 1×20 MW 1×10 MW

Individual prob.

Cumulative prob.

0.98872 0.01122 4.776 ×10−5 9.036 ×10−8 6.410 ×10−11

1 0.01127 4.785 ×10−5 9.043 ×10−8 6.410 ×10−11

G

G

L3

Bus 2

Bus 1 0

Time (%)

20 MW

100

L6

L1

L2

Table 1 Components’ failure and repair rates.

Bus 3

Failure rate (occ/yr)

Repair rate (occ/hrs)

Reference

Compressor + combustor + gas turbine Generator Transformer

1.999

0.10590

[31]

L7

L4

Fig. 6. The system load model based on the daily peak load variation curve.

BCHP components

1×40 MW 4×20 MW 2×5 MW

Bus 4

85 MW

L8

L5

40 MW

Bus 5 0.16899 0.0150

0.05677 0.005

[31] [50]

20 MW L9

Bus 6 and the indices can be considered as a reference value for comparing with other methods. The complete COPT with no rounding increment, will have a large number of states. In order to quantify all the states, a MATLAB program is developed for the reliability analysis. The period of study in RBTS and RTS can be considered as an hour, day, week, month or year. In both case studies (i.e. RBTS and RTS), the system load is considered by the daily peak load variation curve which is also modeled as a straight line from 100% to 60% of the peak load in each case studies. Fig. 6 shows the system load model which was assumed to be linear, although such a linear representation is not likely to occur in practice. The study period is assumed to be a year and therefore 100% on the abscissa corresponds to 8760 h.

4.1. Reliability parameters of the BCHP system based on the Markov method In this study, it is assumed that the BCHP system has ten 4 MW generators. Failure and repair rates of the BCHP’s electric side components are listed in Table 1. Based on the proposed method, the COPT of the BCHP system is given in Table 2.

20 MW Fig. 7. Single line diagram of the RBTS.

4.2. Assessment of the RBTS A detailed case study on the RBTS [51] is performed to study the feasibility of the proposed method and the benefits of the presented BCHP system. Fig. 7 illustrates the RBTS which is an educational test system developed by the power system research group at the University of Saskatchewan [51]. This system has six buses, five load buses, nine transmission lines, and 11 generators in buses 1 and 2 which are ranged from 5 MW to 40 MW. The total installed generating capacity is 240 MW while the peak load of the system is 185 MW. The system voltage level is 230 kV. The generating unit ratings and reliability data for the RBTS are given in Table 3. In order to estimate the effects of BCHP systems on the system’s reliability in different conditions, the peak load of the RBTS varies from 160 MW to 235 MW in steps of 10 MW. The results for the following cases are presented: 1. Base case study of the RBTS. 2. The RBTS plus a 40 MW BCHP system (4 × 10MW).

Table 3 Generating unit reliability data for the RBTS. Size (MW)

Type

Number

Force outage rate (FOR)

MTTF (h)

MTTR (h)

Maintenance (week/yr)

5 10 20 20 40 40

Hydro Thermal Hydro Thermal Hydro Thermal

2 1 4 1 1 2

0.010 0.020 0.015 0.025 0.020 0.030

4380 2190 3650 1752 2920 1460

45 45 55 45 60 45

2 2 2 2 2 2

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Table 4 System LOLE (h/yr) of four case studies with different peak loads.

Table 7 Generating unit reliability data for the IEEE-RTS.

Peak load (MW)

Case 1

Case 2

Case 3

Case 4

160 165 170 175 180 185 190 195 200 205 210 215 220 225 230 235

0.68182 2.169 3.572 4.968 6.359 11.125 15.656 20.752 26.360 68.695 109.028 148.221 186.339 257.005 324.758 397.396

0.00578 0.02135 0.03606 0.05307 0.07109 0.18177 0.28736 0.42295 0.57366 1.774 2.920 4.107 5.297 9.249 13.049 17.705

0.00657 0.04393 0.07996 0.15548 0.24582 1.247 2.205 3.594 5.132 17.160 28.649 41.215 53.951 101.981 148.273 209.600

0.03924 0.12841 0.21245 0.29738 0.38303 0.72619 1.052 1.424 1.836 5.093 8.198 11.253 14.260 21.540 28.524 36.229

Table 5 System EENS (MWh/yr) of four case studies with different peak loads. Peak load (MW)

Case 1

Case 2

Case 3

Case 4

160 165 170 175 180 185 190 195 200 205 210 215 220 225 230 235

7.933 14.771 28.532 48.813 75.433 116.677 179.827 265.235 375.090 601.973 1027.861 1640.744 2431.435 3475.415 4840.304 6525.431

0.05526 0.12099 0.25940 0.47227 0.76590 1.372 2.497 4.190 6.551 12.227 23.570 40.422 62.782 97.459 150.584 223.573

0.04630 0.17068 0.47220 1.041 2.005 5.667 14.068 28.067 48.958 103.183 214.232 382.249 609.139 982.439 1581.177 2434.332

0.44685 0.84947 1.667 2.878 4.479 7.105 11.317 17.151 24.784 41.393 73.335 119.782 180.204 264.908 383.141 535.356

Table 6 System EDC (k$/yr) of four case studies with different peak loads. Peak load (MW)

Case 1

Case 2

Case 3

Case 4

160 165 170 175 180 185 190 195 200 205 210 215 220 225 230 235

35.067 65.288 126.111 215.757 333.418 515.713 794.839 1172.341 1657.901 2660.724 4543.147 7252.088 10746.947 15361.336 21394.147 28842.407

0.24426 0.53481 1.146 2.087 3.385 6.066 11.038 18.522 28.955 54.046 104.181 178.668 277.498 430.770 665.584 988.196

0.20465 0.75443 2.087 4.604 8.862 25.048 62.184 124.059 216.394 456.072 946.908 1689.543 2692.396 4342.381 6988.803 10759.750

1.975 3.754 7.369 12.725 19.798 31.406 50.024 75.809 109.546 182.958 324.143 529.439 796.504 1170.896 1693.483 2366.274

3. The RBTS plus an 80 MW BCHP system (8 × 10MW) which replaced two thermal units (with the FOR of 0.030) in the RBTS. 4. The RBTS plus a 40 MW traditional unit with the FOR of 0.05. Three reliability indices which noted in the previous sections are analyzed through the four case studies, which are tabulated in Tables 4–6. Since the demand from existing generation is everincreasing, the system peak load is growing as well. As seen in Tables 4–6, the LOLE, EENS, and EDC indices are increased with the peak load. From case 3 in Tables 4–6, one can draw the conclusion that the added BCHP system improved the reliability parameters of

Size (MW)

Quantity

Force outage rate (FOR)

MTTF (h)

MTTR (h)

Maintenance (week/yr)

12 20 50 76 100 155 197 350 400

5 4 6 4 3 4 3 1 2

0.02 0.10 0.01 0.02 0.04 0.04 0.05 0.08 0.12

2940 450 1980 1960 1200 960 960 1150 1100

60 50 20 40 50 40 50 100 150

2 2 2 3 3 4 4 5 6

Table 8 Base case reliability indices for the IEEE-RTS. Index

RTS (load = 2850 MW)

RTS (load = 2992.5 MW)

RTS (load = 3135 MW)

LOLE (h/yr) EENS (MWh/yr) PLC EDNS (MW) EDC (k$/yr) BPECI (MWh/MW-yr) MBECI (MW/MW) SI (system min/yr)

112.909 16983.906 0.08457 14.693 71672.084 5.959 0.00515 357.555

240.889 40029.245 0.18799 32.916 168923.415 13.376 0.01099 802.591

520.928 90323.065 0.33397 74.571 381163.336 28.811 0.02378 1728.671

the overall system. This improvement is further demonstrated in case 2. Additionally, case 4 reveals that the traditional units cannot be considered as an optimal choice in comparison with the BCHP systems (cases 2 and 3). According to the results, case 3 cannot be an effective choice for the peak loads larger than 200 MW. For instance, LOLE in case 3, is 17.160 h/year for the peak load of 205 MW; however, this index is 1.774 h/year in case 2 for the same peak load. This procedure is similar for the EENS and EDC indices. For example, for the peak load of 220 MW, EENS for case 2 and 3 is 62.782 MWh/yr and 609.139 MWh/yr, respectively. For case 3, the EDC index is 10759.750 k$/yr, while this value is reduced to 988.196 k$/yr in case 2 for the same peak load of 235 MW. On the other hand, for case 4, the increase rate of the LOLE, EENS, and EDC indices is slight and follows a normal increase for each peak load. The results indicate that besides other benefits of the BCHP systems, the reliability impacts of these systems on the power system are reasonable. It was also shown that the reliability improvement of case 2 (i.e. RBTS plus a 40 MW BCHP system) is more than case 3 (i.e. 80 MW of the BCHP system which replaced two thermal units of the RBTS). In order to obtain further results of the proposed implementations, Figs. 8–10 demonstrate the variation of the LOLE, EENS and EDC indices versus FOR of the BCHP system with default peak load of the RBTS (i.e. 185 MW) in case 2. Fig. 8 indicates the changes of the LOLE index versus FOR of the BCHP system. LOLE is increased by increase in FOR. However, the changes are not linear. Improving the FOR of the BCHP system is a very important issue. A BCHP system with an optimal FOR is more reliable and also more expensive. It is necessary to trade-off between cost and reliability. Fig. 8 shows that decreasing the FOR to less than 0.032 will not significantly affect the reliability. As a result, it is not efficient to choose a BCHP system with high investment costs. Additionally, Fig. 9 depicts the EENS index versus the BCHP system FOR where the EENS is increased with the increasing the FOR. Similarly, the EENS index is not dramatically affected for the FOR lower than 0.052. Moreover, from Fig. 10, it can be clearly understood that the improvements of the FOR can affect the EDC index of the system which is a near linear change.

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12

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4 Base case Case 2

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0 0.002

0.012

0.022

0.032

0.042

0.052

0.062

0.072

0.082

0.092

0.102

FOR of the BCHP

Fig. 8. LOLE versus FOR of the BCHP system.

120

EENS (MWh/yr)

100

80

60

40

20

0 0.002

Base case Case 2

0.012

0.022

0.032

0.042

0.052

0.062

0.072

0.082

0.092

0.102

FOR of the BCHP

Fig. 9. EENS versus FOR of the BCHP system.

600

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EDC (k\$/yr)

400

300

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100 Base case Case 2 0 0.002

0.012

0.022

0.032

0.042

0.052

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0.072

0.082

0.092

0.102

FOR of the BCHP

Fig. 10. EDC versus FOR of the BCHP system.

4.3. IEEE-RTS study results Here, the proposed BCHP allocation method is tested on the IEEE reliability test system (IEEE RTS-79) [52] shown in Fig. 11. The IEEE-RTS has 32 generation units, 24 buses, 17 load points, and 38 lines. The overall conventional generation capacity in the IEEE-RTS is 3405 MW and the annual peak load is 2850 MW. Table 7 shows the reliability data of each generator in the IEEE-RTS.

In this study, the most heavily loaded bus (bus 18) is incorporated with the BCHP systems. As noted above, the peak load of the IEEE-RTS is 2850 MW. Considering the fact that the system becomes less reliable when the annual peak load is increased, the peak load of the system is assumed to be 2992.5 MW (2850 × 1.05) and 3135 (2850 × 1.1). Table 8 shows the base studies of the IEEERTS for the three peak loads which are 2850 MW, 2992.5 MW, and 3135 MW. In the case study, four BCHP systems are added to the

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Table 9 Reliability indices of the IEEE-RTS (105% load scale) with the BCHP system. Index

Base case

RTS + 40 MW BCHP

RTS + 80 MW BCHP

RTS + 120 MW BCHP

LOLE (h/yr) EENS (MWh/yr) PLC EDNS (MW) EDC (k$/yr) BPECI (MWh/MW-yr) MBECI (MW/MW) SI (system min/yr)

240.889 40029.245 0.18799 32.916 168923.415 13.376 0.01099 802.591

194.921 31382.730 0.13744 26.634 132435.124 10.487 0.00890 629.227

156.449 24391.066 0.12521 21.377 102930.299 8.150 0.00714 489.043

124.119 18819.374 0.10159 16.960 79417.761 6.288 0.00566 377.330

Table 10 Reliability indices of the IEEE-RTS (105% load scale) with the conventional generating units. Index

Base case

RTS + 40 MW

RTS + 80 MW

RTS + 120 MW

LOLE (h/yr) EENS (MWh/yr) PLC EDNS (MW) EDC (k$/yr) BPECI (MWh/MW-yr) MBECI (MW/MW) SI (system min/yr)

240.889 40029.245 0.18799 32.916 168923.415 13.376 0.01099 802.591

197.106 31793.545 0.13987 26.933 134168.761 10.624 0.00900 637.464

160.115 25059.340 0.12650 21.878 105750.416 8.374 0.00731 502.442

128.767 19623.532 0.10497 17.595 82811.306 6.557 0.00587 393.454

Table 11 Reliability indices of the IEEE-RTS (110% load scale) with the BCHP system. Index

Base case

RTS + 40 MW BCHP

RTS + 80 MW BCHP

RTS + 120 MW BCHP

LOLE (h/yr) EENS (MWh/yr) PLC EDNS (MW) EDC (k$/yr) BPECI (MWh/MW-yr) MBECI (MW/MW) SI (system min/yr)

520.928 90323.065 0.33397 74.571 381163.336 28.811 0.02378 1728.671

430.159 71369.115 0.31704 61.577 301177.668 22.765 0.01964 1365.916

342.813 55960.623 0.29079 49.073 236153.832 17.850 0.01565 1071.016

265.983 43844.980 0.26488 38.075 185025.815 13.985 0.01214 839.138

Table 12 Reliability indices of the IEEE-RTS (110% load scale) with the conventional generating units. Index

Base case

RTS + 40 MW

RTS + 80 MW

RTS + 120 MW

LOLE (h/yr) EENS (MWh/yr) PLC EDNS (MW) EDC (k$/yr) BPECI (MWh/MW-yr) MBECI (MW/MW) SI (system min/yr)

520.928 90323.065 0.33397 74.571 381163.336 28.811 0.02378 1728.671

434.457 72269.375 0.31785 62.192 304976.763 23.052 0.01983 1383.145

351.087 57433.391 0.29296 50.258 242368.913 18.320 0.01603 1099.203

276.974 45595.824 0.26861 39.649 192414.377 14.544 0.01264 872.647

IEEE-RTS. Each BCHP system has an installed capacity of 10 MW. Additionally, the results are compared with the four traditional units with capacity of 40 MW. For different capacities of the BCHP, system adequacy indices are obtained using the proposed methods which are listed in Tables 9–12. All of the reliability indices have been improved after inclusion of the BCHP in the system. Tables 9–12 present the investigation results on several factors that affect the reliability of the system. The comparison results show that adding the BCHP system is very effective on the improvement of the system’s reliability. According to Tables 9–12, the BCHP system with only 40 MW capacity could improve all of the system’s indices. For instance, in Table 9, the improvement of the LOLE index is 19.082% ((240.889− 194.921)/240.889 = 19.082 %). When the traditional units are used, we see a smaller improvement. For example, in Table 10, the system’s EENS is improved by only 20.57% ((40029.245− 31793.545)/40029.245 = 20.57 %). However, from the sensitivity analysis results, it was verified that in the both proposed peak loads, by adding more BCHP systems, the reliability of the system cannot be significantly improved. This is

due to the each BCHP system components’ failure and repair rate which makes the system unreliable. The comparative results show that when the system becomes heavily loaded or even unreliable, the BCHP system could be able to improve the system reliability. As shown in Tables 9–12, different capacities of the BCHP system will affect the system reliability. However, as it is expected, there is no significant improvement in terms of the number of the BCHP systems. In other words, using a large capacity of the BCHP systems cannot satisfy the system’s reliability. This is because of the failure and repair rate of the BCHP system’s component. For example, in Table 11, for a peak load of 3135 MW, the system’s LOLE was decreased from 520.928 h/yr to 430.159 h/yr by employing a 40 MW BCHP system. If a 80 MW and 120 MW BCHP is used, the LOLE index is reduced to 342.813 h/yr and 265.983 h/yr, respectively. It is clear that the improvement in the LOLE index in comparison with base case for the 40 MW, 80 MW and 120 MW is 17.42%, 34.19%, and 48.92%, respectively. Although the improvement by the 120 MW BCHP system is 48.92%, it is worth noting that the implementations of this study are case sensitive and the

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Bus 22

Bus 21

Bus 18

Bus 17

G

G

G

Bus 23

G

G Bus 19

Bus 16

Bus 20 Bus 14

230 kV

EDNS, EDC, BPECI, MBECI, and SI, show significant improvement that are reasonable for each selected capacity of the BCHP systems. For example, in Table 11, the EDC decreases from 381163.336 k$/yr to 185025.815 k$/yr, which is about a 51.45% improvement at a peak load of 3135 MW when using a 120 MW BCHP system. Also, this reduction is 192414.377 k$/yr (49.51% improvement) for the 120 MW traditional unit (see Table 12). However, in terms of the PLC index, the improvement is less in all case studies. For instance, in Table 12 for the peak load of 3135 MW, the system’s PLC for the base case is 0.33397 where this value is 0.26861 after adding 120 MW BCHP system (only 19.57% improvement).

G

Bus 15

Bus 13

Synch. Cond.

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5. Summary and conclusions G Bus 24

Bus 12

Bus 11

Bus 6

Bus 9

Bus 3

Bus 10 Bus 4 Bus 8

138 kV Bus 5

Bus 7

Bus 2

Bus 1 G

G

G

Fig. 11. Single line diagram of the IEEE-RTS.

optimal decisions can be concluded when the economical issues are considered. As a result, in order to make the final decision, the economic terms must be determined and evaluated based on the reliability/cost analysis. In addition to the study results shown in Tables 9–12, most of the reliability indices such as LOLE, EENS,

This paper has presented the reliability evaluation of the BCHP systems for the adequacy assessment of the power systems. The state-space model based on the Markov method has been developed to identify the effects of the BCHP systems as well as quantify the BCHP system reliability impact on the power system. The BCHP systems’ capacity additions were analyzed and were compared against the traditional and conventional generating units. Fig. 12 presents the improvement percentage of LOLE with two types of generation and three different capacities in two load scales of default RBTS system. One can deduce that the bigger added capacity and lesser load peak leads to the greater improvement. The results revealed that adding the traditional units to the power system mitigate the system’s reliability. This is, however, not equal to the BCHP systems’ additions where several adequacy assessment are conducted. In the presented case studies, the application of the proposed method has been explained and carried out on the RBTS and the IEEE-RTS. It revealed that, besides other benefits from the BCHP systems such as the economic efficiency and having less greenhouse gas emissions, there is a huge need to move from the traditional units to the BCHP systems, especially where the system peak load increases. Using the state-space technique, the model is applied to the test systems to assess the variance of the LOLE, EENS, PLC, EDNS, EDC, BPECI, MBECI, and SI. The reliability framework in this study can be useful for conducting several important factors in system adequacy studies, and also defining a particular model approach. Since the BCHP systems have the potential to be used in large scale capacities, the reliability studies can

50 45

LOLE improvement (%)

40 35 30 25 20 15 10 5 0

105%

110%

Load scale based on default peak load of 2850 MW Fig. 12. Impact of adding different types of generations and capacities in different load scales.

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