Hierarchical Risk Assessment of Transmission Network Considering the Influence of Micro-grid Zhe Liu, Bingdong Wang Hongjie Jia, Yuan Zeng, Tao Xu School of Electrical Engineering & Automation Tianjin University Tianjin China
[email protected] Abstract — Transmission network risk is calculated by multiplying occurrence probability and consequence of contingencies. Since power flow in the traditional distribution system is unidirectional, its loads are usually aggregated into an equal load and connected to the transmission network through a substation in the traditional risk assessment. And, all loads are simply treated as constant-power type. Details of distribution network and loads are usually ignored. However, today a growing number of distributed generators (DGs) based on renewable resources being connected to modern power systems. How to properly evaluate their influence on risk assessment of transmission network should be considered. Micro-grid has been regarded as a good way to integrate various renewable resources into distribution network. It can increase DG’s penetration and reduce its negative impact. However, micro-grid can be considered as a controllable load or a small virtual power plant, so it can significantly change characteristics of distribution loads and operational modes of distribution network. In this paper, microgrid is used as a tool to reduce load curtailment under some critical contingencies. And its influence on risk assessment of transmission network is then analyzed and discussed. In the study, a linear optimization method is used to determine the load curtailment. Discrete probability model of DGs in micro-grid and detailed model of distribution system are taken into account in the optimal process, such as island, tie switches, links, etc. Risk calculation of whole power system is executed though iterations between transmission network and distribution system. Load curtailment expectation instead of absolute load curtailment is used to risk calculation. The correctness and effectiveness of the proposed method is finally validated by RTS and RBTS test system. Index terms — risk analysis; distributed generation (DG); micro-grid; virtual power plant;
Supported by the National Basic Research Program(2009CB219701), NSFC (51277128), 863 Program(2011AA05A114, 2011AA05A115) of China and the Independent Program of CSPG on Power Grid Dispatching & Operation Risk Assessment Model and Applied System Construction. Zhe Liu, Bingdong Wang, Hongjie Jia, Yuan Zeng and Tao Xu are all with Key Laboratory of Smart Grid of Ministry of Education, Tianjin University,China.
978-1-4799-1303-9/13/$31.00 ©2013 IEEE
Jianing Liu, Dong Chen, Yuefeng Lu Dispatching and Control Center Guangdong Power Grid Guangdong China
I INTRODUCTION Considering the fluctuations, intermittences and uncertainties of renewable energy resources, risk assessment is widely used to analyze the security of power system with integrating renewable resources in planning and operation stages. There are numbers of literatures analyzing the effect of renewable energy on the risk assessment of transmission network, where renewable energy resources are normally connected to bulk power system directly and centrally. For instance, [1] studied the impacts on bus voltage and power system stability while different capacities of wind farms were connected to the power grid at the same point and at different points respectively. Well-Being Analysis (WBA) method was used to assess power system risk in [2]-[4], in which some aspects, such as the risk evaluation of renewable energy, short-term operation benefits calculation, et al. were involved. On the customer side, numbers of renewable based DGs are connecting to distribution network through microgrid mode nowadays. Micro-grid can effectively integrate various DGs to power system and make them as a good citizen. So it has been recognized as a good way to integrate various renewable resources, to increase DG’s penetration in power system and reduce its negative impact. However, micro-grid can be considered as a controllable load or a small virtual power plant. It can significantly change characteristics of distribution loads and operational modes of distribution network, while its influence on transmission network turns more and more important. There are several previous studies in this field. e.g. influence of DG integration in distribution networks at different access points was illustrated by using reliability worth analysis (RWA) method in [5]. Transient stability of micro-grid with multiple DGs was analyzed and its impact to bulk power system was simply discussed in [6]-[7]. Influence of renewable based DGs on risk analysis of distribution system was illustrated in [8]-[9], which gave a probability model of DG and some practical risk assessment methods for distribution system with DG integration. In this paper, a novel method to evaluate the influence
of micro-grid on transmission system risk analysis is given. Traditional linear optimization method and discrete probability model of DGs are used. Risk calculation of whole system is executed though iterations between transmission network and distribution system. To balance the efficiency and accuracy of the algorithm, contingency enumeration method is used in transmission network level and Monte-Carlo method is applied in distribution system level. Load curtailment expectation instead of absolute load curtailment is utilized in risk calculation. Some aspects, such as island, tie switches and links are also considered in the simulation. II BASIC CONCEPT OF RISK ASSESSMENT This paper focuses on how to calculate the influence of micro-grid on risk analysis of transmission network. In this section, a brief introduction to the concept of risk assessment is first given. Probability model of components is shown in Fig.1[10]-[12]. l normal
failure m Figure 1. Probability model of components
where l is the failure rate of components, μ is the repair rate of components. Contingency enumeration method is used to select transmission network status. Probability of transmission system status pT(s) can be expressed as follows,
= pT ( s )
Nf
Nt − N f
∏U ∏ (1 − U )
i =i 1 =j 1
λi Ui = λµ i + i
j
(1) (2)
where Ui and Uj are average unavailability of component i and component j; Nf and Nt are the numbers of failure and total components. Monte-Carlo simulation method is used to select distribution system status. And, probability of distribution system status pD(s) can be expressed as follows, m pD ( s ) = (3) M where M is number of Monte-Carlo simulation; m is number of system status s selected in all the simulation. Another important aspect of risk analysis is contingency consequence. For simplicity, method given by [13]-[14] is adopted in this paper. Power system risk can be expressed as follows,
= R
Ns
∑ p (s)× I (s)
only the formula of EENS is illustrated as follows,
RE =
Ns
∑ p ⋅C i =1
i
0, i
⋅ Di
(5)
where, pi is the probability of system status i; C0,i is load curtailment of system status i; Di is duration of system status i. III DISCRETE PROBABILITY MODEL OF DISTRIBUTED GENERATION Power outputs of DGs, such as wind, PV are fluctuant and intermittent depending on the local weather conditions. To precisely describe their complex dynamics is very difficult and time consuming. So, in our presented method, a discrete probability weather model is adopted to determine the power output of DGs[17]. Probability density function f(w) of weather condition can be obtained by fitting historical data. An example is illustrated in Fig. 2, where w represents wind speed or light intensity, and wmin, wmax means lower and upper limits of w. Interval [wmin, wmax] can be divided into several subintervals. Calculation accuracy and density are decided by the number of subintervals. i.e. more accurate means more number of subintervals. f(w)
f(wk-1) f(w3)
f(wk)
f(w2) f(w1)
f(wn-1) ……
f(wn)
……
0
wn-1 wn wmax w wmin w1 w2 w3 wk-1 wk Figure 2. Probability density function of weather condition
If the parameter of weather condition w locates in the kth subinterval [wk-1, wk], its probability can be expressed as follows,
pk =
w = wk
∫
f ( w)dw
(6)
w = wk −1
Relationship between parameter w and power output g(w) can be gained as shown in Fig. 3, which is dependent on the design and characteristic of DGs. g(w)
g(wk) g(wk-1）
(4) ……
s =1
where, R is the system risk index; p(s) is the probability of system status s; I(s) is the consequences of system status s; and Ns is the total number of system statuses. Load curtailment is used to weigh the severity of system statuses in this paper. Some traditional risk indices such as EENS,PLC, EFLC and SI are adopted[15]-[16],
0
……
wk-1 wk
w
Figure 3. Relationship between weather condition and power output
When parameter w locates in the kth subinterval [wk-1, wk], the average power output of DGs can be calculated as follows,
wk
Pk =
∫
g ( w ) f ( w ) dw
wk −1
(7)
wk
∫ f ( w) dw
wk −1
IV HIERARCHICAL RISK ASSESSMENT METHOD A. Frame of Hierarchical Risk Assessment Active distribution system (with DGs integration) is a typical characteristic of smart grid. Load curtailment caused by system outages can be reduced by optimally dispatching power output of DGs in this occasion. Power supply reliability of transmission network is also affected accordingly. In order to properly consider such condition, we provide a hierarchical risk assessment as shown in Fig.4. This method consists of two parts. One part is traditional transmission network risk assessment, and the other part is calculation of expected load curtailment for distribution system considering integration of DGs. So in (5) load curtailment of system status C0,i is replaced by the expected load curtailment E(C0,i), which will be introduced and discussed in the following subsection C.
Transmission Network
Absolute Load Curtailment
Expected Load Curtailment
Data interface
Distribution System
Expected Load Curtailment
Absolute Load Curtailment
Figure 4. Frame of hierarchical risk assessment
This method is an interactive process between transmission network and distribution system. Absolute load curtailment is calculated in the transmission network level so as to guarantee the system stability. The result is then delivered to the distribution system analysis as an initial state. And, expected load curtailment is calculated in distribution system level and the result is fed back to transmission network for risk assessment. To balance the algorithm’s efficiency and accuracy, contingency enumeration method is used in transmission network analysis and Monte-Carlo simulation method is applied in distribution system analysis.
Figure 5. Depth-first algorithm for island search
B. Island Analysis Distribution system is operated with radial structure even there are several DGs connecting to the system. When an outage occurs, distribution system can be decomposed into several islands instantly. If the loads located on an island can’t be supplied by sufficient energy, some of them should be curtailed for power balance. When there are some micro-grids in the distribution system, loads within them can be survived during the failure. So island analysis is essential to get the expected load curtailment. A depth-first algorithm is adopted in this paper and its search path is illustrated in Fig. 5. Suppose that line B3- B8 is out of work, system will be decomposed into two islands. In the algorithm, two stacks are utilized to save the searched nodes. Main busbar, say B1, is firstly chosen as a root node. Then, B1 is then saved into the stack and the searching process starts. Step 1: Using depth-first algorithm to determine the busbars connecting with current root node, which are added to the stack buffer. Step 2: Busbars saved in stack should be popped out one by one in descending order. If the busbar popped from the stack has other branches which haven’t been reached, the popped bus can be treated as root node and go back to step 1. Otherwise, continue the popping process until there is no busbar in the stack. All reached buses linking with current root node will form an island. Step 3: If all busbars in the system are reached, algorithm terminates automatically. Otherwise, select one unreached bus randomly as root node and add it to the stack. Then go back to step1. A simple example is given in Fig.5 to illustrate the whole process before starting, B1 is firstly selected as the root node and is added to the stack. 1) In step1, B2, B6 and B7 are found to connect with B1. They are added into the stack. At bus B7, there is no descendent node, step1 terminates. 2) In step2, Node B7 is firstly popped out. It is found that there is no more bus connecting with B7 except B6 which exists in the stack. Then, B6 is popped out and it is same as B7. Then, B2 is popped out. It is found that B3 is connecting to B2. Then B2, B3 are added into the stack and jump back to step1. 3) Since there are no more buses connecting to B3. Step1 terminates again with stack including B1, B2 and B3. Step2 is started again. Busbar B3, B2 and B1 are popped out continuously. But they do not have extra connecting buses. So Step2 terminates. And, the first island is composed by bus B1, B2, B3, B6 and B7. 4) In step3, B4 is randomly selected as root node and added into the stack. Searching process then goes back to step1. The subsequent steps are similar to the above one just as shown in Fig.5. And, the second island is found to include bus B4, B5, B8, B9, B10 and B11. C. Calculation of Expected Load Curtailment
In this paper, expected load curtailment is used to take place of absolute load curtailment that can be obtained using the method proposed by [13]-[14]. DGs in distribution system can be used to reduce load curtailment caused by outages in transmission network, since they can supply some energy to local in the island operation mode. So the values determined by absolute load curtailment used in traditional risk assessment are larger than its actual values since the contribution of DGs are ignored in this method. That is the reason why this algorithm is abandoned in the study. Monte Carol method is used to select a status of distribution system and determine power output of DGs. Suppose that C0 is absolute load curtailment calculated by transmission network analysis and M0 is total power output of DGs in this system status. Then the islands are found using the method mentioned in subsection B, results of the islands analysis is shown in Fig. 6. Whole system can be decomposed into several parts, including remaining distribution system and some isolated islands.
Remaining distribution system
Island 1 C1 M1 L1
Cm Mm
Distribution system C0 M0
Island 2 C2 M2 L2 Island n Cn M n L n
Nm
E ( C0 ) =
∑ C (i ) i =1
e
where Nm is sampling times in Monte Carol simulation, Ce(i) is actual load curtailment of system status i. Then (5) can be modified as follows, Ns
RE = ∑ pi ⋅ E ( C0,i ) ⋅ Di
It should be noted that the isolated islands integrating some DGs are considered as micro-grids or a virtual power plants in this paper, and their critical loads can be supplied by DGs during the contingencies. In the study, only the power balance of the system is considered. Some other facts, such as voltage, frequency and power flow of the system is not considered, which would be studied in subsequent work. V CASE STUDY A modified IEEE RTS test system is used to validate the proposed method above. Its load buses are expanded to distribution systems. Distribution system for RBTS bus 6 shown in Fig.7 is used as an example. All parameters of RTS system, such as load level, generation capacity, component outage probability can be referred to [18]-[19]. 33kV
35 L18
……
36 L19
Figure 6. Description of decomposed distribution system
If
n
∑C i =1
n
i =1
i =1
And, expected load curtailment is given as follows,
2
31
5
4
33
46
55 56
48
7
L3 6
9
8
11
10
L5 L6 12
L33
16
19
18
L8 L9 L10 21
20
23
22
25
24
L11 L12 L13 26
L26
L32
14
17
L4
L25
54
L7
15
L2
47 L27
57
49
58
50
59
51
60
L34 L35
L1
L1
L36
52
62
L37 61 L38
63
L39 L40
(9)
n if C0 -∑ Ci ≤ M m 0 i =1 Cm = (10) n n ∆L - C -M if C C > M i m 0 ∑ i m 0 ∑ i =1 i =1 Finally, the actual load curtailment Ce is given as follows,
Ce = ∑ Ci +Cm
3
45
L31
L1
29
34
44 53
13
1
64
Otherwise, loads in remaining distribution system should be curtailed as follows,
n
L15 30
L16 L23 32 41 L17 42
L24 43
(8)
calculated as,
Ce = ∑ Ci
27 L14 L21 28
40
L1
≥ C0 , the actual load curtailment Ce can be
i
39
L22
If there are n islands, Li, Ci and Mi are total load, total load curtailment and power output of DGs in island i. Cm and Mm are total load curtailment and power output of DGs in remaining distribution system. Power balance of islands should be firstly checked and Ci can be determined as follows,
11kV
37 38
if Li ≤ M i if Li >M i
(13)
i =1
L20
0 Ci = Li -M i
(12)
Nm
(11)
Figure 7. Single line diagram of distribution system for RBTS bus 6
A. Influence of Micro-grid on System Risk In case A, as shown in Fig.7 three types of DGs are connecting to the system. i.e. wind generator, PV and micro-turbine. They are installed at feeder 9, 13 and 24, respectively. Total generation capacity of DGs accounts for 30% of total load on corresponding bus. Their output proportions are 30%:30%:40%. In other words generation capacity of wind generator, PV and micro-turbine are 9%, 9% and 12% of total bus load. TABLE I. COMPARISON RESULTS OF SYSTEM RISK WITH OR WITHOUT MICRO-GRID Risk indices
EENS (MWh/a)
PLC
EFLC (Times/a)
SI (Min)
Without DGs
2724.4
0.0051
2.244
57.4
With DGs
1649.2
0.0041
1.305
34.7
Comparison results of risk indices with or without DGs are shown in Tab. I. When DGs exist in the system, it can supply some critical loads near feeder 9, 13 and 26. So the curtailed load is reduced comparing with the scenario without DGs. For example, EENS, EFLC and SI are reduced to 60% of their original values (without DGs) and PLC to 80%. B. Influence of DGs’ Capacity on System Risk
2000
5
1500
-3
4.5
4
1000
500
x 10
0
2.5
0.8 0.6 0.4 0.2 Generation capacity of Micro-grid (a)
3.5
1
0
0.8 0.6 0.4 0.2 Generation capacity of Micro-grid (b)
1
50 45 40 SI(Min)
EFLC(Times/a)
2
1.5
35 30 25
1
20 0.5
0
0.2
0.6
0.4
0.8
Generation capacity of Micro-grid (c)
1
15
0
0.2
0.4
0.6
0.8
Generation capacity of Micro-grid (d)
1
Figure 8. Curves of system risk versus generation capacity of DGs
With increment of DG’s generation capacity, EENS and SI decrease smoothly. The slope reaches maximum at the point that generation capacity is 50% of total load. PLC and EFLC decreases discretely. When DG’s capacity is larger than 50%, PLC and EFLC will keep constant. So, 50% may be a more advisable installation capacity to the test system.
It can be found that risk of scenario 2 and 3 is lower than scenario 1. EENS and SI in three scenarios are very similar, but PLC and EFLC are different, which is caused by different dispersion of DGs in three scenarios. If the distribution of DGs is more scattered, when outages happen in distribution system, DGs are more possible to be located in islands to supply power. In other words scattered distribution of DGs can reduce the probability of islands occurrence caused by outages without power sources. D. Influence of DGs’ Location and Outage Probability on System Risk In case D, three DGs are connected to distribution system, whose generation proportion is same as case A. Their total generation capacity is 40% of total load. And they are installed at the same feeder. Four scenarios are studied and illustrated in Tab. III. Outage probability increases with twenty times of original value. The calculation results are shown in Fig. 10. TABLE III. FOUR SCENARIOS FOR RISK ANALYSIS Feeder with Branch with outage Scenarios DGs installation probability increasing * Scenario 1 Feeder 36 F35-F44 Scenario 2 Feeder 40 F35-F44 Scenario 3 Feeder 62 F59-F64 Scenario 4 Feeder 64 F59-F64 *: F35-F44 represents all the branches between Feeder 35 and Feeder 44. -3
1500
C. Influence of DGs’ Dispersion on System Risk
TABLE II. DETAILED CONFIGURATIONS OF THREE SCENARIOS Wind Micro-turbine Scenarios PV generator generator Scenario 1 Feeder 9 Feeder 13 Feeder 24 Scenario 2 Feeder 9, 10, 11 Feeder 13, 14, 15 Feeder 24, 25, 26 Feeder 13, 14, 15, Feeder 22, 23, 24, Feeder 3, 4, 5, Scenario 3 16, 17, 18, 19, 20, 25, 26, 61, 62, 63, 6, 7, 8, 9, 10, 11 21 64
EENS(MWh/a)
1480 1460
5
1440
4.6 4.4
1400
4.2
1380
1
20 40 60 Occurrence probability of outages (a)
x 10
4.8
1420
4
80
1
20 40 60 Occurrence probability of outages (b)
80
1
20 40 60 Occurrence probability of outages (d)
80
31.5
2.6 2.4
EFLC(Times/a)
In case C, 27 DGs containing 9 wind generators, 9 PVs and 9 micro-turbine generators are connected to distribution system, whose total generation capacity and proportion of DGs are the same as case A. Three scenarios are created to illustrate influence of DGs’ dispersion on system risk. In the first scenario, all DGs are connected to 3 feeders; in the second, all DGs are connected to 9 feeders; and in the last one, they are connected to 27 feeders and the detailed configuration is shown in Tab. II. Three results are shown and compared in Fig. 9, in which risk indices are normalized by the original system ones.
5.2 Scenario 1 Scenario 2 Scenario 3 Scenario 4
PLC
5.5
Fig. 9 Comparison results of system risk for three scenarios
31
2.2 2
SI(Min)
2500
PLC
EENS(MWh/a)
In case B, DG’s location and generation proportion of are the same as case A. Their total generation capacity varies from 10% to 90% of total load. Curves of system risk versus generation capacity of DGs are shown in Fig. 8.
1.8
30.5 30
1.6 29.5
1.4 1
20 40 60 Occurrence probability of outages (c)
80
29
Figure 10. Curve of system risk with increment of outage probability
From Fig. 10, it can be found the risk indices increase with the increment of outage probability, so outage
probability has significant influence on system risk. Comparing scenario 1 with scenario 2, it can be easily found that the risk of scenario 1 is higher than scenario 2. Similarly, scenario 4 has a higher risk than scenario 3. It can be concluded that DGs connecting to feeders near to the middle of radical structure of distribution system can reduce system risk, and this effect is enlarged with increment of feeder outage probability. Scenario 1 and scenario 2 are used to analyze the reason for the above phenomenon in details. When outage probability of branches between feeder 35 and feeder 44 increases, these feeders are easier to be out of work to eliminate outages, so the island forms more frequently which contain lots of load. Then DGs installed on feeder 40 have larger possibility to be included in islands to supply power than on feeder 36, so the load curtailment can be reduced. VI CONCLUSION DGs can be considered as a virtual power plant system while they are connected to distribution system by a micro-grid. On the other hand, DGs can supply power energy to local loads when outages occur. Therefore, DG or micro-grid integration has brought significant influence on load characteristics and operational modes of distribution system. Furthermore, the latter has close relationship with power system risk assessment. In this paper, a hierarchical risk assessment method is introduced to properly consider the impacts of DGs and micro-grids on risk analysis of transmission system. One important point in this method is that expectation of load curtailment is used to replace the absolute value of load curtailment for risk calculation. From the simulation results conducted, installation of DGs in distribution system can reduce the probability of load curtailment, thus the risk of transmission network is also reduced. At the same time sensitivity analysis is used to study the influence of DGs’ capacity, dispersion and location on system risk, and the best generation capacity of DGs can be determined by this method. However, some issues such as power flow constraints of distribution system would be further taken into account in the future research. VII REFERENCES [1] Yang Q, Zhang J, Wu Z, et al. "Analysis on stability of integration of wind farms into power systems", in Proc. 2009 Power and Energy Engineering Conference, pp. 1-4. [2] Billinton R and Karki B, "Well-being analysis of wind integrated power system", IEEE Trans. on Power Systems, vol. 26, Issue. 4, pp. 2101-2108, 2011. [3] Fotuhi-Firuzabad M and Billiton R, "Impact of load management on composite system reliability evaluation short-term operating benefits", IEEE Trans. on Power Systems, vol. 15, Issue. 2, pp. 858-864, 2000. [4] Dange H and Billinton R, "Effects of wind power on bulk system adequacy evaluation using the well-being analysis framework", IEEE Trans. on Power Systems, vol. 24, Issue. 3, pp. 1232-1240, 2009. [5] Vallée F, Lobry J and Deblecker O, "System reliability assessment method for wind power integration", IEEE Trans. on Power Systems, vol. 23, Issue. 3, pp. 1288-1297, 2008.
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