Optimal Distributed Generation Allocation and Load Shedding for

Optimal Distributed Generation Allocation and Load Shedding for Improving Distribution System Reliability A. S. A. Awad1, T. H. M. EL-Fouly2, and M. M. A. Salama1 1

Electrical and Computer Engineering Department, University of Waterloo, Ontario, Canada 2

CanmetENERGY, Natural Resources Canada, Varennes, Québec, Canada

Abstract—Recent deployment of distributed generation has led to a revolution in distribution systems and the emergence of “smart grid” concepts. Smart grid mainly intends to facilitate integration of renewable energy sources and to achieve higher system reliability and efficiency. Different distributed generation types found in modern distribution systems can be classified into two main categories: intermittent- and dispatchable-based distributed generation; the latter has a unique capability of enabling successful islanding operation, thus improving system reliability. This paper proposes a methodology for allocating dispatchable distributed generation units in distribution systems to economically improve system reliability. Distributed generation installation and operation costs are to be optimized against the reliability value expressed as customers’ “willingness to pay” to avoid power interruptions. Therefore, the main goal of this research work is to determine the optimal combination between distributed generation units to be installed and loads to be shed during all possible contingencies. Probabilistic load model is adopted to determine the optimal size of allocated distributed generation units. Index Terms—distributed generation; smart grid; islanding; load shedding; willingness to pay

1. Introduction Power systems are now evolving from the conventional regulated system, with centralized generation connected to the transmission networks, to the de-regulated structure that allows for small generators to be connected directly to the distribution networks. Such networks thus become active and are usually referred to as “active distribution networks,” in which new technologies should facilitate adaptation to such active environments and enable the use of “smart grid” concepts [1]. “Smart grid” may be defined from different perspectives; it can be defined as the two-way flow of electricity and information between supply and demand. Another definition is the application of intelligent devices and communication technologies in power systems [2]. 1

Generally, smart grids intend to facilitate integration of renewable energy sources and to satisfy the needs of higher system reliability and efficiency. According to [3], distributed energy resources (DERs) can provide power to the system loads during planned or unplanned network outages. Allowing for successful islanding operation is actually one of the benefits of distributed generation (DG) that improves system reliability by avoiding loss of load or minimizing loss of energy supplied to non-affected customers during network disturbances. However, distribution utilities cannot only rely on intermittent based DG units, e.g., wind turbines and photovoltaic (PV) arrays, to improve system reliability due to their uncontrollable power generation. Therefore, distribution companies may utilize dispatchable DG units as standby sources to cover network disturbances. High capital and running costs associated with DG, on the other hand, represent the main challenge for introducing this concept of “nonvolatile” distribution systems. As a result, distribution utilities need to calculate the optimal size of DG units to be installed in order to minimize their installation costs and maximize their reliability benefit as well. A lot of research work has tackled the problem of DG allocation in distribution networks in which several objectives have been considered. Total energy system losses have been minimized in [4] in which the authors developed a probabilistic approach that considers the variations in wind speeds and load demand in allocating wind turbine based DG units in distribution systems. Furthermore, the power losses at the peak load have been minimized in [5-8], while the authors in [9] have considered minimizing the active power losses evaluated at multi-load levels. Other objectives include minimizing voltage deviations and total harmonic distortion [10]. The authors in [11, 12] have presented multi-objective DG allocation models that consist of several performance indices such as voltage deviation, active and reactive power loss, line loading, and short circuit indices. Similar work has also been developed in [13]. In [14], the fixed and variable 2

costs of DG, costs of energy losses, and investment costs of distribution lines have been minimized in order to determine the optimal size and location of DG units. Moreover, a few studies have addressed the problem of optimal DG allocation to improve system reliability such as the work in [15], in which DG units and circuit reclosers are allocated to minimize a composite reliability index. The results proved that the more reclosers and the higher DG sizes used, the less reliability index the system achieve. However, the authors did not consider the cost effectiveness of the solution. This is very important factor since adding more reclosers and/or DG units might be more expensive compared to the higher reliability level achieved. This drawback has been considered in [16] in which the authors optimally allocated DG units and remote controllable switches while they considered their costs in the objective function. Furthermore, the authors in [17] applied a multi-objective optimization approach that minimizes DG investment and operation costs while maximizing DG benefits, i.e., reliability improvement and power loss reduction. The reliability benefit has been evaluated through interruption costs due to faults during the study period. Reliability evaluation of distribution systems has been conventionally conducted using segmentation concept [15, 18]. In this concept, the distribution system is divided into a limited number of segments according to the number and positions of protection devices. A failure of any component in one segment leads to isolating the whole segment from the entire system; however, self-healing capability requires the system to detect and isolate the fault quickly, and to restore the service in the healthy sections of the system, hence improving service reliability. The literature includes numerous accounts of the use of time series models for modeling the stochastic nature of a variety of components, such as renewable-based DG and load demand [19, 20]. Such work usually adopts one-year estimation for all loads and generation units. The estimated profiles are then used for optimizing the size of equipment required. Despite the 3

difficulties associated with forecasting highly stochastic components, such as wind speed and solar irradiance, the application of time series models in planning studies provides an optimal solution that is valid only for the time series pattern that is applied. Consequently, the solution obtained is not guaranteed to be the global optimal for other possible patterns. A preferable solution would therefore be to derive probabilistic models that take into account all possible system states, as proposed in this paper. Instead of the usual time series models, available historical data are used in order to generate probability distribution functions (PDFs), which are then applied in a probabilistic approach, as discussed in section 3. From the above survey, it can be concluded that little work has addressed the problem of siting and sizing DG units to improve system reliability. However, according to the best knowledge of the authors, previous work in this area did not consider load shedding as a means to achieve a trade-off between the reliability enhancement and the size of DG to be installed. As well, the concept of self-healing capability has not been fully applied in terms of considering all possible islanding scenarios for allocating the DG units. Therefore, the ultimate goal of the work presented in this paper is to develop a value-based reliability approach for allocating DG units in distribution systems taking into account selfhealing capability. In order to achieve this capability, the system is assumed to be equipped with two automatic switches at the sending and the receiving ends of each line. Consequently, the failure across any line will result in isolating that line and island formation downstream of the isolated line. In this approach, as opposed to the segmentation concept, every distribution system has a number of possible island formations that equals to the number of system branches. All of these possible island formations will be considered in this work to allocate DG units that best fit all possible network configurations. Load shedding decision variables are further determined by the proposed approach to economically optimize the size of the allocated DG units against 4

interruption costs of served customers. The main contributions of this paper can be summarized as follows:  The paper presents a probabilistic approach for determining the most cost-effective siting and sizing of DG units in distribution networks.  Self-healing capability is considered in this work in order to determine the optimal DG allocation that best fit all possible islanding scenarios.  The approach proposed includes identifying the load points to be shed, during contingencies, in order to minimize the total interruption cost via increasing the probability of successful islanding operation. The rest of this paper is organized in five sections. Section 2 describes the problem under study. The methodology and the mathematical formulation are further discussed in Section 3. Section 4 introduces a sample case study. The results and conclusions are finally provided in Sections 5 and 6, respectively.

2. Problem description A value-based reliability approach is utilized in this research work to economically improve distribution systems reliability. In practice, distribution utilities set some arbitrary targets, not obligatory standards, as objectives for their reliability indices [21]. Those targets usually depend on utilities’ perception of customer tolerance levels for interruptions. However, due to expensive investments adopted in planning stage, planning decisions should not rely on such “rule of thumb” criterion in reducing customer interruption costs. In other words, achieving those arbitrary targets may cost the distribution utilities much more than what customers would actually pay as interruption costs. In this case, the reliability target is overestimated and thus resulting in unnecessary extra costs. Moreover, in most cases, there is no reward/penalty system 5

that forces distribution utilities to target certain reliability levels; however, some customers are willing to pay more for receiving higher reliability levels. Willingness to pay (WTP) represents the reliability value that utilities might lose if they did not achieve the desired reliability level for those customers. As a result, it is crucial to apply economic optimization approaches to determine the optimal investment plan as well as the optimal reliability level. From the aforementioned discussion, it can be concluded that the rationale behind this research work is based on optimizing the DG investment costs against the reliability value expressed as interruption costs/WTP of served customers. Therefore, the goal of this work is to determine the optimum combination between DG units to be installed and loads to be shed to economically improve distribution system reliability. In other words, the proposed problem includes some planning decisions, i.e., sizes and locations of DG units to be installed, and contingency planning decisions, i.e., load points to be shed during contingencies. It is worth mentioning that the size of allocated DG units is calculated taking into consideration the load shedding decision variables. Therefore, the corresponding load points should be disconnected whenever islands are formed with one or more DG units to avoid overloading the allocated DG units.

3. Methodology In this section, the mathematical formulation for integrating DG to improve system reliability is discussed. This problem is formulated as optimal power flow model which has an objective function of minimizing the total annual cost comprising the annualized DG capital and operation costs, and the annual interruption costs considering the failure of every single line (feeder) in the system under study, as in (1). In this formulation, a probabilistic approach takes into account the stochastic nature of all load demands and any existing intermittent DG sources. 6

Available historical data are utilized so that each component is represented by a specific PDF. Continuous PDFs are further divided into several states with associated probabilities, thus creating a probabilistic model for every component. The number of states for each component should be carefully selected so that the simplicity and accuracy of the analysis are not compromised: a large number of states increases accuracy but at the expense of also adding to the complexity, and a small number of states has the opposite effect. A combined load-DG model can then be generated by convolving all of the individual probabilistic models [4]. Such a model combines all possible operating states for the available DG units and the different load levels. The total number of states is therefore equal to the product of the number of states for each component.

DG capital costs + DG operation and maintenance costs +  Minimize   interruption costs 

(1)

Where: N

DG capital costs =  CP  S DGi

(2)

i 1

N

DG operation and maintenance costs =   CE  CM   PDGi ,k ,l  k  rk  l i 1

k

(3)

l

N

Interruption costs =  CS  PSHi ,k  PDi  k  rk  l i 1

k

(4)

l

where CP , CE , and CM are the DG annualized capital cost, annual operation (fuel) cost, and annual maintenance cost, respectively; CS is the service interruption cost; i and j are the system bus indices; N is the total number of system buses; load state index; PDG

and QDG

k

is the faulty line (contingency) index; l is the

are the DG output active and reactive power variables; S DG is the DG

output apparent power variable; PD and QD are the demand active and reactive powers; k and rk are the average failure frequency and the average duration of contingency k; l is the probability of 7

state l; PSH is the binary load shedding decision variable that is equal to 1 if load is shed, and 0 otherwise.

In this work, genetic algorithm (GA) is adopted for minimizing the above objective function. The main step of GA is chromosome encoding; each solution (chromosome) consists of some binary variables, representing DG installation and load shedding decision variables at every bus. For every population generated by GA, load flow equations (5-11) are solved for each island to determine the power requirements from the allocated DG units at all possible states, taking into account the load shedding decision variables. It is worth mentioning that load shedding variables are set to zero for grid connected buses, and set to one for islands without any DG allocated. Furthermore, the states’ probabilities are adopted to calculate the expected size of each DG as in (12). In the load flow analysis, all system buses are modeled as P-Q nodes, except the nodes which are connected to DG units. In every island, only one DG should act as a slack (reference) bus to all other nodes in that island, and any other DG units (if exist) should be treated as voltagefrequency controlled buses, as discussed in Appendix A. Other system constraints, i.e., nodal voltages and lines’ power flow limits, and DG size constraints are given in (13-16). Afterwards, all solutions (chromosomes) of one population are evaluated by means of the fitness (objective) function. Finally, a new population is generated and the aforementioned process is repeated until a stopping criterion is met. The flowchart, shown in Figure 1, summarizes the proposed approach for allocating DG units to improve system reliability.

8

A. Load flow equations: - No DG installed at bus i during contingency k and state l:



 V

PG i ,l  PD i ,l 1  PSH i 





N

i , k ,l

j 1

V j ,k ,l  Yij ,k  cos ij ,k   j ,k ,l   i ,k ,l 

QG i ,l  QD i ,l 1  PSH i  Vi ,k ,l V j ,k ,l  Yij ,k  sin ij ,k   j ,k ,l   i ,k ,l  N

i, k , l

(5)

i, k , l

(6)

j 1

- DG installed at bus i during contingency k and state l:

Vi ,k ,l  1

i  min 

k

:

k

 M k , and k , l

(7)

Vi ,k ,l  1

i  min 

k

:

k

 M k , and k , l

(8)

Qi ,k ,l  Q j ,k ,l

 i, j 

k

, i  j, and k , l

(9)

N  PDG i ,k ,l   Vi ,k ,l  V j ,k ,l  Yij ,k  cos ij ,k   j ,k ,l   i ,k ,l     PG i ,l  PD i ,l 1  PSH i     j 1 

i, k , l

(10)

 N  QDG i ,k ,l   Vi ,k ,l  V j ,k ,l  Yij ,k  sin ij ,k   j ,k ,l   i ,k ,l    QG i ,l  QD i ,l 1  PSH i     j 1 

i, k , l

(11)







  2 2 S DGi  max  l  PDG  Q  DG i ,k ,l i ,k ,l k  l 

i



(12)

B. Voltage limits:

Vmin  Vi ,k ,l Vmax

i , k , l

(13)

V1,k ,l  1

k , l

(14)

i  j, k , l

(15)

C. Line flow limits:

0  Iij ,k ,l  Iij max D. DG size constraints:

SDGi  SDG max where

i

PG and QG

are the generated active and reactive powers;

equipped with DG units for contingency k; angle;

Y and 

(16)

V and 

k

is the set of system buses

are the voltage magnitude and the phase

are the bus admittance matrix element magnitude and angle; I is the line flow

current. 9

Start

GA generates an initial population Generate new population k=1

Isolate faulty line (k) and identify set of formed islands End Analyze island #M Display results

l=1 M=M+1 Any DGs are allocated ?

Yes

Success state  Calculate

PDS i ,k ,l and QDS i ,k ,l

Yes

No

No

Failure state  Disconnect all loads in that island

Stopping criteria ?

Evaluate the population generated by GA Yes

No

l=l+1

No

l=number of load states?

All islands analyzed ?

Yes

k=k+1

Figure 1 Proposed methodology flowchart

10

Yes

k = number of scenarios ?

No

4. Case study The system under study is a 33-bus radial distribution system, as shown in Figure 2. Load point rated active and reactive powers and feeder data are given in [22]. Load demands are further assumed to follow the IEEE-RTS discrete load model in Table 1 [4]. The reliability parameters of the substation and the system feeders are presented in [18]. Moreover, interruption costs are assumed to be 20 $/kWh [23]. A total of 33 islanding configuration scenarios are tested in this case study. The proposed GA based model has been solved on a personal computer in almost 4 hours, which are acceptable since the proposed algorithm is applied in the planning stage. The setting parameters of GA are further given in Table 2. 23 24 25

1

2

3

4

5

6

26

7

8

27

9

28 29 30 31 32 33

10 11 12 13 14 15 16 17 18

Substation 19 20

21 22

Figure 2 System under study Table 1 Probabilistic load model

Load state no.

Load magnitude (% of peak load)

Probability

1

0.351

0.033

2

0.406

0.0473

3

0.451

0.0912

4

0.51

0.163

5

0.585

0.163

6

0.65

0.1654

7

0.713

0.1654

8

0.774

0.1057

9

0.853

0.056

10

1

0.01

11

Table 2 GA parameters Population size

50

Selection criteria

Roulette wheel

Crossover algorithm and probability

Scattered – 0.6

Mutation algorithm

Gaussian

Mutation scale and shrink values

1 and 0.01

As discussed earlier, dispatchable DG types are only considered in this study, and four candidate technologies are selected as follows: biomass, diesel, natural gas, and micro-turbine (MT). Their sizes are assumed to be discrete in steps of 100 kVA. Table 3 presents the annual capital, operation, and maintenance costs for the four candidate technologies assuming 20 years life cycle. Based on land availability and/or utility regulations, the candidate buses for DG installation are assumed to be included in the set B: {16, 17, 18, ..., 33}. In this work, the economic parameters are assumed as follows: 5% interest rate and 1% inflation rate. Fixed capital costs are annualized by dividing them by the present value function (PVF) which is expressed in terms of interest rate (IR), inflation rate (F), and lifetime of the equipment (n), as calculated in (17) and (18) [24]

1  IR    1 PV F (IR , n )  n IR  1  IR   n

IR  

(17)

IR  F 1 F

(18)

12

Table 3 Annual capital, operation, and maintenance costs for the different DG technologies

Biomass [25]

Diesel [26, 27]

Natural gas [28]

MT [29]

1500

5000

5000

250

Capital power cost ($/kVA)

2293

900

500

1333

Annual operation (fuel) cost ($/kWh)

0.63

0.46

0.042

0.045

Annual maintenance cost ($/kWh)

0.012

0.02

-

0.005

168.13

65.99

36.66

97.74

Rated output power (kVA) Capital, operation, and maintenance costs

Annualized capital costs Annual capital power cost ($/kVA)

5. Results This section summarizes the outcomes of this research work. The optimal locations and sizes of DG units as well as the load points to be shed are presented in Table 4 for each generation technology under consideration. It can be concluded that the more expensive the generation technology is, the less the number and/or the size of allocated DG units is and there are more loads to be shed. This is clear in the case of biomass based DG, which has the highest capital and operation costs; no DG units are allocated and all isolated nodes have to be shed whenever islanded. Table 4 Optimal DG allocation and loads to be shed Biomass

Diesel

16

---

700

Natural gas

MT

700

200

17

---

---

---

200

Optimal DG sizes

25

---

---

900

---

at every bus (kVA)

30

---

---

---

250

32

---

---

---

250

33

---

700

700

---

Optimal load points to be

---

2 to 5, 7, and 19 to 25

2, 4, 5, 7, and 19 to 22

2 to 13, 19 to 26, 29, and 33

shed

13

Moreover, Figure 3 compares the total annual costs for the different technologies with respect to the base case (i.e., without DG integration). In the base case, the annual cost comprises only interruption costs during all contingencies. It is revealed from Figure 3 that natural gas based DG provide the cheapest solution in which interruption costs were decreased from $ 0.22 million (base case) to $ 0.03 million. Furthermore, Figure 4 depicts the reliability level measured in expected energy not supplied (EENS) for each DG technology compared to the base case. As an example, Figure 5 shows a graphical representation for natural gas based DG allocation during a failure at the line 2-3 as an example. The three DG units allocated at buses #16, #25, and #33 are utilized to supply the formed island. Further, load points #4, #5, and #7 should be disconnected by the utility as quick as possible to avoid overloading the allocated DG units and to guarantee continuity of supply in the isolated system during the expected contingency duration. Moreover, the graphical representation of GA convergence is presented in Figure 6, which shows the superior performance of GA in terms of the number of iterations before stopping.

Total annual cost ($ million) Interruption cost

DG capital and operation costs

0.25 0.2 0.15 0.1 0.05 0 Base case

Biomass

Diesel

Natural gas

MT

Figure 3 Total annual costs for the base case and the different DG technologies

14

EENS (MWhr) 12 10 8 6 4 2 0 Base case

Biomass

Diesel

Natural gas

MT

Figure 4 EENS for the base case and the different DG technologies

Formed island 23 24 25

26 27

DG_2

1

2

3

4

28 29 30 31 32 33

DG_3

5

6

7

8

9

10 11 12 13 14 15 16 17 18

Substation DG_1

19 20

21 22

Figure 5 Graphical representation of DG allocation and load shedding during contingency at line 2-3

Figure 6 Graphical representation of GA convergence

15

6. Conclusions In this paper, a probabilistic approach is proposed for allocating dispatchable DG units in distribution systems. A value-based reliability approach is adopted in this work that considers customers’ WTP as the reliability value that distribution utilities gain from improving system reliability. The total annual costs comprising the costs of installation and operation of DG units as well as the interruption costs are minimized to determine the optimal combination between DG units to be installed and loads to be shed during all possible contingencies. A sample case study is presented and four generation technologies are compared with respect to the base case. The results show that integrating dispatchable DG with distribution systems reduces utilities’ annual costs due to their capability of enabling successful islanding operation and minimizing interruption costs.

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Appendix A According to conventional load flow analysis, the buses equipped with DG units during islanding operation cannot be classified to any of the typical three types, i.e., slack, P-Q, or P-V buses. Therefore, another modified load flow algorithm is needed to analyze the formed islands. Power flow calculation method for islanded network is introduced in [30], in which the droop characteristics are used to solve the load flow of voltage-frequency controlled buses in the islanded system. These characteristics add two equations for each voltage-frequency controlled bus, as in (A.1 and A.2)

f s  fo i  K f i PG i

(A.1)

Vt i  Vo i  KV i QG i

(A.2)

Where:

PG i and QG i : generated active and reactive power at bus i, respectively,

f o i and f s : open circuit frequency of generator i and system frequency, respectively, Vo i and Vt i : open circuit voltage of generator i and its terminal voltage, respectively, K f i and KV i : frequency–active power and voltage–reactive power droop constants, respectively.

Therefore, when islands are formed, only one DG is considered as a slack bus, and any other DG units are modeled as voltage-frequency controlled bus. For sake of simplicity, it is assumed that all droop controllers’ parameters are identical and the terminal voltage of each DG is set to one per unit. Applying these assumptions results in equating the net reactive power generated from each DG bus, and hence for M number of DG units installed, (M-1) equations can be obtained. These equations are added to the basic two load flow equations at every bus, thus 17

summing up to 3 × (M-1) equations. This number of equations is required to calculate the three unknowns at every DG bus, and hence the load flow can be calculated for islanded networks equipped with DG units.

Acknowledgment The authors would like to thank the Government of Canada for financially supporting this research through the Program on Energy Research and Development.

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