Long-term Reliability Evaluation of Small Hydro-Power Generators Based on Flow Runoff Theory

Long-term reliability evaluation for small hydro-power generations based on fl ow runoff theory

Lili Chen

¹

, Yi Ding

²

, Haitao Li

¹

, Guiyang Jin

¹

1

College of Electrical Engineering, Zhejiang University of Water Resources and Electric Power, Hangzhou, People

’

s Republic of China

2

College of Electrical Engineering, Zhejiang University, Hangzhou, People

’

s Republic of China E-mail: chenye415@163.com

Published inThe Journal of Engineering; Received on 10th October 2017; Accepted on 3rd November 2017

Abstract:Electric power output from a small hydro-power (SHP) generator is usually determined by the waterflow, whichfluctuates slowly in short term. However, for long term, the waterflow varies greatly with the seasonal changes. This uncertainty will take great impacts on system reliability, especially for systems with high hydro-power penetration. This study presents a methodology to evaluate the reliability of SHP generators. The mechanism of producing and conflux offlow runoff is studied and modelled utilising universal generating function (UGF) methods. The power generation reliability and availability of a single SHP generator and several SHP generators clustered together in groups are represented as the corresponding UGFs. The expected generated energy and the generation availability are used to evaluate the reliability of SHP generators. The modified IEEE case of six SHP generators in Brazilian rivers is evaluated by the proposed method.

1 Introduction

Small hydro-power (SHP) is internationally recognised as a renew- able green energy. Due to its mature technology, low cost and en- vironmental harmlessness, SHP has been developed throughout the world. In China, areas of rich hydro power resources are usually mountainous areas that have small electricity loads.

Therefore, a SHP plant often can generate more electricity power than the nearby load needs and numbers of small hydro-power clus- tered together in groups to transmit the electrical power remotely.

Electric power output from a SHP generatorfluctuates with the water flow [1] which varies with the seasonal changes and is greatly affected by rainfall. For power systems with high hydro- power penetration, this uncertainty will take great impacts on system reliability. In [2], water flow is cluster as ten states and the corresponding reliability of electric power generated by a single SHP plant is calculated. However if the system has several SHP plants, the relationship of water inflow for those plants has not been studied yet.

This paper will learn the relationship of waterflow of different location basing on the waterflow runoff theory and the relationship between rainfall and waterflow will also been learned utilising uni- versal generating function (UGF) methods. Then the reliability and availability model of electric power generated by a single SHP plant or SHP groups will be given in UGF.

The SHP generator considered here is a run-of-the-river system that does not have a water reservoir or only has a very small water reservoir. The mutual influence by other SHP plants is ignored in this paper.

2 Riverflow model

This paper only considers the rainfall runoff, which means the snow melt runoff is beyond the scope of this paper. Also the weather is assumed not to appear both rainy and sunny at the same place at the same time.

2.1 River runoff models during a storm

A diagram of rainfall runoff given in Fig.1shows that the process of runoff mainly contains three parts which are surface run-off, inter-flow runoff and shallow groundwater runoff [3].

Though the runoff model of different watersheds with different climate, topography, soil and vegetation are different in detail, they still have some general characters and are conclude as the natural storage runoff model and the infiltration excess runoff model [4].

In a natural storage runoff model, the amount of rainfall (A) and the initial watershed storage (W0) has a positive impact on water- shed runoff yield (R), while the amount of evaporation (E) has a negative impact. The total runoff can be formed in a general formula as follows [5]:

R=f_storage(A,E,W₀) (1)

While in the infiltration excess runoff model, it is also affected by rainfall intensity (i) and the general formula of total runoff is shown as

R=f_execess(A,E,W₀,i) (2)

The two models may exit at the same time as shown in Fig.2by Sherman and Musgrave in [6]. The process could be divided into three stages: Thefirst stage happened in thefirst 20 min since the rainfall started, and it was the infiltration excess runoff process that the rainfall mainly supplied for infiltration. The second stage began from then till the rainfall stopped and it was a natural storage runoff process that the runofffluctuated with the rainfall.

The third stage began from the rain stopped, and the runoff dropped rapidly to the basicflow. However in a huge watershed, the runoff at the third stage may not drop so quickly it may drop slowly as shown in Fig.1.

The 6th International Conference on Renewable Power Generation (RPG) 19–20 October 2017

2.2 Regularity of runoff between two storms

According to the runoff curve, the interval between two storms is divided into two main parts, the rainy period and the non-rainy period, as shown in Fig.3.

The rainy period is also divided into two parts, the initial period (marked as Stage 1) and the continuous period (marked as Stage 2).

During the Stage 1, the runoff rate of a river will climb straightly.

While during the Stage 2, the runoff rate will keep almost stable.

The non-rainy period is also divided into two parts. The first period (marked as Stage 3) is about 1 or 2 hours just after the rain, and the second period (marked as Stage 4) is from then on until the next storm comes. During the Stage 3, the runoff will drop rapidly to basic flow during the Stage 3 and keep almost stable during Stage 4. The runoff between two storms is concluded in Table1.

It is also found that the intensity of solar radiation is not strong enough to make photovoltaic power (PV) generation at Stage 1 and Stage 2 while PV generation fluctuates randomly at Stage 3 and Stage 4 depending on the clear air index [7]. So in a small- hydro solar hybrid system, the electric power is mainly generated by SHP generators at Stage 2 and by PV at Stage 4. The electric power output may vary little at the beginning of Stage 1 and may reach its maximum at Stage 3. The research on complementarity of SHP and PV will be considered in the future and it is not the scope of this paper.

2.3 Multi-state model of riverflow

According to the above analysis, the riverflow can be simply mod- elled as a multi-state problem of discrete random variables with a finite number of possible values. Suppose there are Nf possible states for rainfall days andN_ustates for non-rainfall days. The prob- abilistic distribution of runoff rate at locationifor rainfall days can be represented by the vectorQ^A_i = {q^A_{i, 1}, q^A_{i, 2}, · · ·, q^A_i,N

A with the probabilityp^A_i,j=P_r(Q^A_i =q^A_i,j)at statejThe value of total probabil- ity is to be 1. Similarly, the probabilistic distribution of runoff rate at locationi for non-rainfall days can be represented by the vector Q^U_i = {q^U_i,1, q^U_i,2, · · ·, q^U_i,N

u} with the probability

p^U_i,j=P_r(Q^U_i =q^U_i,j)at statej. The value of total probability is to be 1.

The UGF technique takes a discrete random probability problem as a polynomial function, and it is much easy to get the expected value of the variable or the expected value of its nth power by nth derivative of the function at z= 1, where z represents the z-transform. Therefore it is widely used to solve multi-state pro- blems. The corresponding UGF to represent the riverflow at loca- tionican be defined as follows:

u^A_Qi( ) =z ^NA

j=1

p^A_i,j· z^qAi,j (3)

u^U_Qi( ) =z ^Nu

j=1

p^u_i,j· z^qUi,j (4)

whereu^A_Qi( )z andu^U_Qi( )z represent thez-transform of runoff rate at the locationifor rainfall days and non-rainfall days, respectively.

The UGF of the riverflow at locationiin a whole year can be formed as follows:

u_Qi(z)=p_Au^A_Qi(z)+p_Uu^U_Qi(z)

=^NA

j=1

p^A_i,j·p_A·z^qAi,j+^Nu

j=1

p^U_i,j·p_U·z^qUi,j

=^NA

j=1

p^′_i,j^A·z^qri,jri +^NU

j=1

p^′_i,j^U ·z^qUi,j

=^NS

j=1

p^S_i,j·z^qi,j

(5)

wherep_Aandp_Uare the probability of rainfall and non-rainfall, re- spectively.p_Acan be calculated byp_A=(h_A/8760)×100%, where hA is the total raining hours in a year, and Fig. 2 Relationship of Horton overlandflow to infiltration for constant rain-

fall intensity

Fig. 1 Diagram of rainfall runoff

Fig. 3 Runoffflow between two storms

Table 1 Regularity of runoff of the stages between two storms

Stage Stage l Stage 2 Stage 3 Stage 4

runoff characteristic low to high keep high high to low keep low

p_A+p

U =1, p^′_i.j^A=p^A_i.j·p_A, p^′_i.j^U =p^U_i.j·p_A,q_i,j is the water flow including both the rainfall and non-rainfall conditions andp^s_i,j is its probability, andN_s=N_A+N_U.

3 Reliability model for SHP generators 3.1 Reliability model for a SHP plant

Electric power output from SHP plant (SHPP)iis considered as a whole in this paper and the units schedule [8] in a single plant is out of the scope of this paper. Then the power output of SHPPi is determined by the steamflow rate, the height of water fall and the efficiencies of the generator and turbine [9], and is given by

hp_i=h_T

i·h_G

i·g·Q_i·H_i (6)

whereh_T

iandh_G

iare the efficiency of the turbine and generator of SHPPi, respectively,γis the specific weight of water (9810 N/m³), Hiis the water fall height (m) of SHPPi.

The efficiency of a hydraulic turbine varies with waterflow as shown in Fig.4, and for most types of hydraulic turbines, the effi- ciency is very close to the peak for a wide range offlows [10]. The head loss in a through a pipe is propositional to the square of water inflow and can be calculated byΔH=kQ², wherekis a constant.

The efficiency of generator usually varies in a very narrow range like from 80 to 90% or more narrow than that like from 96.6 to 98.6% [11]. Therefore the power output from SHPPiis a function of water inflow

hp_i=f Q_i (7)

Considering the multistate waterflow, and combining (5) and (7), the multistate power outputs of a SHPPiwill be

u_hp

i(z)=^NS

j=1

p^s_i,j·z^hpi,j (8)

wherehpi,jis the power output of SHPPiat the water inflow statej.

The power output of a SHPP also depends on its reliability and the two-state reliability model [12] is used to represent the reliabil- ity of a SHPP. The UGF of SHPPiconsidering random failures of unit is defined as

u^′_hp

i(z)=^N

j_i=1

p^S_i,j·p_riz^hpi,ji+p_uiz⁰

(9)

wherepriandpuiare the availability and unavailability probabilities of SHPPi, respectively.

3.2 Reliability model for SHP plants in a watershed

It can be simply supposed that the rainfall in a watershed area is very similar and the rivers have the same numbers of total states, and they reach the same state or the near state at the same time that means

0≤p^s_j

k|j_l

( ) ≤1, j_k−j_l≤1 p^s_j

k|jl

( ) =0, j_k−j_l.1

(10)

wherep^s_j

k|j_l

( )is the probability of the riverkinflow at the statej_k while the riverlat the statejl..

In a perfectly correlated model, formulation (10) will be p^s_j

k|jl

( ) =1, j_k=j_l p^s_j

k|j_l

( ) =0, else

(11)

Therefore while ignoring the reliability factor of SHPP itself, the UGF of the total power outputs by SHP plants will be

u_HP(z)=^Ns

j₁=1. . .^NS

j_K=1

p^s_j

l|j_l

( ) · · · · ·p^s_j

k|j_l

( ) ·p^S_jl

·z

K i=1

hp_i.

ji

=^NS′

j_s=1

p^′_js^S·z^HPjs

(12)

whereKis the total number of SHP plants. Also the total number of states will beN^′_s=N_s·(2^K−1)−2^K+2.

While considering the reliability of SHPP, a parallel operatorΩφP

[13] is used to represent the UGF of SHP plants at rainfall statej_s u_HP^js(z)=V_fpp_r1·z^hp1.js+p_u1z⁰, . . .,p_rK·z^hpK.js+p_uKz⁰

=^K

i=1

p_ri·z

K i=l

hp_ij_s

+^K

l=1

^K

i=1,i=l

p_ri·p_ul·z

K i=l,i=l

hp_ij_s

⎛

⎜⎝

⎞

⎟⎠

+ · · · +^K

i=1

p_ui·z⁰=^Nr

j_r=1

p^r_jr·z^HPjr,js

(13) where p^R_jr and HPjr, js are the probability and the total power outputs, respectively, of all the SHPPs at the reliability state jr

and the rainfall statejs·Nris the total states of reliability, and if the number of SHPPs isK, thenN_r=S^K_i=0Cⁱ_K=2^K.

Considering all the rainfall states, the UGF of SHP plants will be

u^′_HP(z)=^N′s

j_s=1

^Nr

j_r=1

p^′_js^s ·p^r_j

r·z^HPjr,js (14)

3.3 Energy reliability indices

The energy reliability indices are always calculated on annual basis [14]. The expected available energy (EAE), the expected generated energy (EGE), the capacity factor (FC) and the generation availabil- ity (GAF) are used to indicate the reliability of a power system.

Fig. 4 Typical efficient curve for a hydraulic turbine varies withflow plotted

For multi-state power outputs from SHP plants described by (10), EAE can be calculated as

EAE=8760^N′s

j_s=1

p^′_js^s ·HP_js

(15)

The EGE considers the failure of generators and the power outputs states described in (12) can be calculated as

EGE=8760^N′s

js=1

^Nr

jr=1

p^′_js^s ·p^r_j

r·HP_jr,j

s

(16)

If the installed capacity of total SHP generators is installed power (IP), then FC and GAF can be calculated as (17) and (18), respect- ively

FC= EAE

8760IP (17)

GAF= EGE

8760IP (18)

4 Case study

The IEEE case of Brazilian rivers in [8] is modified to illustrate the proposed methods. The river inflow of two rivers is clustered in ten states as shown below:

The rated inflows of river 1 and river 2 are 91 and 124 m³/s, re- spectively. The correlation of the river inflow is

p( ) =1 1| 1; p( ) =8 8| 0.28;

p( ) =1 2| 0.06; p( ) =3 4| 0.13; p( ) =5 6| 0.77; p( ) =7 8| 0.72;

p( ) =2 2| 0.94; p( ) =4 4| 0.8; p( ) =6 6| 0.23; p( ) =8 9| 0.34;

p( ) =2 3| 0.25; p( ) =5 4| 0.07; p( ) =6 7| 0.85; p( ) =9 9| 0.66;

p( ) =3 3| 0.75; p( ) =5 5| 1; p( ) =7 7| 0.15; p(10 10| ) =1;

where, for example,p( ) =1 2| 0.06 means when river 1 is at state 2, the probability of river 2 at state 2 is 0.06.

There are four SHP plants (marked as SHPP 1, SHPP 2, SHPP 3 and SHPP 4) at river 1 at different locations. The water heights of these SHP plants are 40 m, 50 m (it is the raw data in [8]), 60 m, 70 m, respectively. The efficiency of generator is 80%, and the turbine efficiency is shown in Table2. The IP of these SHP genera- tors are 25, 30, 35 and 40 MW, respectively. The generators are considered to have a forced outage rate (FOR) of 2%.

There are two SHP plants (marked as SHPP 5 and SHPP 6) at river 2. The water height of these SHPP is 35 m (it is the raw data in [8]) and 70 m. The efficiency of generator is 90%, and the turbine efficiency is shown in Table 3. The IP of these SHP

generators are 30, 60 MW, respectively. The SHP plants that have bigger capacity will affect more to generators are considered to have a FOR system reliability of 9.79%.

The generation power of SHPPs is shown in Fig.5and the state of each SHPP is the same as the water inflow states. The situation is the same for river 2.

The energy reliability indices of SHPPs in two rivers are shown in Table4.

Fig. 5 Power of SHPP 1 to 4 in ten states and its probability

Table 4 Energy reliability indices of SHPPs in two rivers Indices River l (four

SHPPs)

River 2 (two SHPPs)

Total (six SHPPs)

EAE 629,210 MWh 505,899 MWh 1,135,054 MWh

EGE 616,626 MWh 456,371 MWh 1,072,997 MWh

FC 0.5321 0.6417 0.5759

GAF 0.5214 0.5789 0.5444

Table 2 Multistate inflow of river 1 and the corresponding turbine efficiency of the SHP plants

State no. Inflow, %Qn Probability, % Turbine efficiency, %

1 28.62 8.00 79

2 39.69 14.87 87

3 46.13 20.72 88.5

4 51.54 16.55 89

5 55.35 7.65 89

6 57.88 7.43 89

7 61.22 6.87 89

8 66.63 10.13 88.5

9 80.68 5.97 83

10 100 1.81 78

Table 3 Multistate inflow of river 2 and the corresponding turbine efficiency of the SHPP

State no. Inflow, %Qn Probability, % Turbine efficiency, %

1 44.95 8.90 80

2 50.53 19.14 81

3 54.95 17.79 82

4 59.34 13.18 83

5 64.29 14.52 83

6 69.14 7.55 83.5

7 74.75 8.34 83

8 81.41 4.84 82

9 87.80 3.95 81

10 100 1.81 76

Fig. 6 Duration curve of the generation power by SHPPs without consider- ing the failure of generation

According to the law of conservation of energy, the total EAE or the EGE of SHP plants in two rivers is the sum of every single one as shown in Table4. However the power–probability curve will be different and are more likely to be as similar as the one that has the biggest installed capacity as shown in Fig.6. The indices of FC and GAF will also follow the law.

5 Conclusion

This paper studied the impact of waterflow on the generation of SHP plants in a watershed for long term. The model of available and reliability of the generation from SHP plants are given. The IEEE case of Brazilian rivers is modified to illustrate the proposed method. Case studies show that the SHP plants which have bigger capacity will affect more to system reliability.

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