Coordination method of electricity supply and recipient market day-ahead spot clearing considering hydropower absorption

1 . A coordination method of electricity supply and recipient market day-ahead spot clearing considering hydropower absorption is characterized by the following steps:

(1) construct a day-ahead spot clearing model for electricity supply and recipient market with a goal of minimizing the total power purchase cost, as shown in Eq. (1); a constraint set of spillage is introduced to furthest solve a problem caused by spillage of a high-proportion hydropower system in a supply market, as shown in Eq. (2);

min

⁢

∑

t

∈

T

∑

i

∈

I

(

c

i

,

t

p

+

c

i

,

t

u

)

+

∑

t

∈

T

∑

s

∈

S

M

⁢

(

S

⁢

D

s

,

t

+

+

SD

s

,

t

-

)

(

1

)

{

P

i

,

t

i

⁢

n

≤

N

i

,

t

spill

,

(

S

i

,

t

1

=

true

)

E

i

≥

∑

t

∈

T

⁢

(

Q

i

-

1

,

t

out

+

Q

i

,

t

l

⁢

o

⁢

c

⁢

a

⁢

l

)

-

Δ

⁢

V

i

W

i

,

(

S

1

=

true

)

P

i

,

t

≤

N

i

,

t

u

⁢

p

,

(

S

i

,

t

2

=

true

)

(

2

)

where

c

i

,

t

p

is an operating cost or a power station i at period t;

c

i

,

t

u

is a start-up cost of the power station i at period t; T is a set of time periods; I is a set of power stations participating in a provincial market; M denotes a penalization factor; S is a set of transmission channels;

S

⁢

D

s

,

t

+

is a surplus capacity of a channel s at period t;

SD

s

,

t

-

is an insufficient capacity of the channel s at period t;

S

i

,

t

1

⁢

and

⁢

S

i

,

t

2

respectively represent indicators of spillage status in a first stage and the second stage, where true represents a generation of spillage of the power station i at period t, and false represents no spillage; S 1 represents a status of whether a spillage adjustment strategy has been implemented, where true means that the strategy has been carried out, and false is a default status at an initial stage;

N

i

,

t

spill

is an upper limit of a bided generation of the power station i at period t calculated by a spilled outflow; E i is a daily electricity generated by the power station i;

Q

i

-

1

,

t

out

is the spilled outflow from an upstream power station i−1 at period t;

Q

i

,

t

local

is a natural streamflow of the power station i at period t; ΔV i is a maximum available storage capacity of the power station i; W i is an average daily water consumption rate for the power station i;

N

i

.

t

u

⁢

p

is an upper limit of generation for the power station i positioned upstream at period t;

P

i

,

t

i

⁢

n

is the bided generation in a province of the power station i at period t; P i,t is a total bided generation of the power station i at period t;

(2) based on clearing results of the recipient market and combining technical parameters of the hydropower, a scheduling boundary updating strategy is constructed to update a boundary of a spot trading of the outgoing hydropower; specific steps are as follows:

step 1. prepare the bided generation and start-up and shut-down sequence conditions for outgoing the hydropower in the recipient market;

step 2. determine the start-up and shut-down schedules of the hydropower in each trading session during the day, and update optimization boundaries of the start-up and shut-down schedules of the outgoing hydropower in the recipient market according to Eq. (3):

v

i

,

t

i

⁢

n

=

{

1

,

(

v

i

,

t

out

=

1

,

∀

t

∈

T

)

x

,

(

v

i

,

t

out

=

0

,

∀

t

∈

T

)

(

3

)

where

v

i

,

t

out

is a start-off state of the power station i at period t in the recipient market, and x represents an unknown start-off state of the power station i at period t;

step 3. combining an outgoing hydropower start-off schedule and generation profile, generating and ramping capability boundaries of the outgoing hydropower for corresponding periods are updated according to Eq. (4) and Eq. (5);

{

P

_

i

,

t

i

⁢

n

=

N

i

,

t

m

⁢

ax

-

P

i

,

t

o

⁢

u

⁢

t

,

(

P

_

i

,

t

i

⁢

n

≤

N

¯

i

)

P

_

i

,

t

w

=

λ

i

,

t

min

-

P

i

,

t

o

⁢

u

⁢

t

,

(

P

¯

i

,

t

i

⁢

n

≥

0

)

(

4

)

{

RU

i

,

t

′

=

RU

i

-

P

i

,

t

o

⁢

u

⁢

t

+

P

i

,

t

-

1

o

⁢

u

⁢

t

RD

i

,

t

′

=

RD

i

-

P

i

,

t

out

+

P

i

,

t

-

1

o

⁢

u

⁢

t

(

5

)

where

P

_

i

,

t

i

⁢

n

⁢

and

⁢

P

_

i

,

t

i

⁢

n

are maximum and minimum generation boundaries of the power station i in the province at period t, respectively;

N

i

,

t

max

⁢

and

⁢

N

i

,

t

min

are maximum and minimum technical generation of the power station i at the period t, respectively;

P

i

,

t

o

⁢

u

⁢

t

is an outgoing generation of the power station i at period t; N i is an installed capacity of the power station i; RU′ i,t and RD′ i,t are maximum upward and downward ramping rate boundaries for the power station i at period t, respectively; RU i and RD i are original maximum upward and downward ramping capacities of the power station i, respectively;

step 4. based on the generation profile of a cross-provincial hydropower, a daily power boundary of the outgoing hydropower is updated by Eq. (6) to ensure a precise matching of the electricity and water volume of each power station;

{

E

i

i

⁢

n

≤

E

i

self

,

max

-

λ

⁢

∑

t

∈

T

P

i

,

t

o

⁢

u

⁢

t

,

i

∈

ξ

E

i

i

⁢

n

≤

K

×

E

i

-

1

+

E

i

self

,

max

-

λ

⁢

∑

t

∈

T

P

i

,

t

o

⁢

u

⁢

t

(

6

)

where

E

i

in

is a bided electricity of the power station i in the province,

E

i

self

,

max

is a maximum daily electricity of the power station i; K is a conversion factor for upstream and downstream daily electricity; ξ is a set of serial numbers for a first stage of cascaded hydropower stations; λ is a conversion factor that converts a 15-min average generation to hourly electricity;

step 5. update the boundaries related to the outgoing hydropower in the day-ahead spot-clearing model for the supply market and organize clearing;

(3) to achieve coordinated clearing of the supply and recipient market as well as dynamic adjustment of the outgoing hydropower, an update strategy for the DC transmission plan is constructed taking the spillage adjustment strategy and cross-section power adjustment in supply market as input;

step 1. enter an outgoing plan and the results of the clearing of the supply market; Then check the process of the outgoing hydropower;

Step 2. update the boundaries of the outgoing hydropower for power stations that fail to reach a target generation based on Eq. (7), to solve a problem that an outgoing plan cannot be completed as promised owing to insufficient hydropower generating capability;

E

¯

i

out

=

E

i

out

-

E

i

s

⁢

hort

(

7

)

where

E

_

i

out

is a maximum outgoing electricity of the power station i;

E

i

out

is a planned outgoing electricity of the power station i;

E

i

short

is a short electricity compared to the plan of the power station i;

Step 3. update boundaries of the upstream power station's outgoing plan based on Eq (8) to deal with a reduction in outgoing electricity of the upstream power station due to the spillage adjustment;

P

_

i

,

t

out

=

P

i

,

t

o

⁢

u

⁢

t

-

N

i

,

t

spill

,

(

∀

t

∈

T

)

(

8

)

where

P

¯

i

,

t

o

⁢

u

⁢

t

is an upper limit of the outgoing power of the power station i at period t;

P

i

,

t

out

is a planned generation of the power station i at period t;

N

i

,

t

spill

is a reduction in outgoing power of the power station i at period t due to the spillage adjustment strategy;

step 4. update the boundaries of the outgoing plan based on results of the insufficient capacity in supply market, as shown in Eq (9):

P

_

s

,

t

out

=

P

s

,

t

o

⁢

u

⁢

t

-

S

⁢

D

s

,

t

+

+

SD

s

,

t

-

(

9

)

where

P

_

s

,

t

out

is an upper limit of the outgoing power of the channel s at period t;

P

s

,

t

o

⁢

u

⁢

t

is a planning generation of the channel s at period t;

step 5. update the outgoing boundaries of the recipient market in the day-ahead spot clearing model and reorganize the clearing process, then return to step 2.