# US 11,111,897 B2 · Method for controlling a wave power system by means of a control obtained by minimizing an objective function weighted and discretized by the trapezoidal rule

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- Number: US 11,111,897 B2
- Document ID: US11111897B2
- Status: Granted
- Kind: B2
- Application number: 16/348,215
- Filed: 2017-10-26
- Published: 2019-09-12
- Granted: 2021-09-07
- Earliest claimed: 2016-11-09
- Assignees: Ifp Energies Nouvelles
- Applicants: IFP Energies nouvelles
- Inventors: Paolino Tona; Hoai-Nam Nguyen
- Web page: https://patentgrep.com/patent/US11111897B2

## CPC

- F03B 13/187: {and the wom directly actuates the piston of a pump}
- F03B 13/16: using the relative movement between a wave-operated member, {i.e. a "wom"} and another member, {i.e. a reaction member or "rem"}
- F03B 15/00: Controlling (controlling in general G05 {; regulation of plants characterised by the use of siphons F03B13/086})
- F03B 15/02: by varying liquid flow
- F05B 2240/40: Use of a multiplicity of similar components
- F05B 2260/821: Parameter estimation or prediction
- F05B 2260/84: Modelling or simulation
- F05B 2270/1033: Power (if explicitly mentioned)
- F05B 2270/20: to optimise the performance of a machine
- F05B 2270/30: Control parameters, e.g. input parameters
- Y02E 10/30: Energy from the sea, e.g. using wave energy or salinity gradient
- F03B: MACHINES OR ENGINES FOR LIQUIDS (positive-displacement engines for liquid F03C; machines for liquids and gases F01; positive-displacement machines for liquids F04, rotary fluid gearing of the hydrokinetic type F16H41/00)
- F05B: INDEXING SCHEME RELATING TO WIND, SPRING, WEIGHT, INERTIA OR LIKE MOTORS, TO MACHINES OR ENGINES FOR LIQUIDS COVERED BY SUBCLASSES F03B, F03D AND F03G
- Y02E: REDUCTION OF GREENHOUSE GAS [GHG] EMISSIONS, RELATED TO ENERGY GENERATION, TRANSMISSION OR DISTRIBUTION

## Abstract

The present invention provides improvement of the operation of a wave energy system by use of a method for predictive control (COM) of the converter machine that maximizes the energy generated by considering the energy conversion efficiency (MOD ENE) and a wave prediction (PRED). Furthermore, the method according to the invention determines the optimal control by minimizing an objective function weighted and discretized by the trapezoidal rule.

## Claims

### Claim 1

A method of controlling a wave energy system that converts energy of waves into electrical or hydraulic energy, the wave energy system comprising at least one mobile device that cooperates with at least one energy converter machine, and the at least one mobile device oscillates in motion with respect to the at least one energy converter machine, comprising:
a) constructing a dynamic model of the wave energy system relating velocity of the at least one mobile device to a force exerted by the waves on the at least one mobile device and to the force exerted by the at least one energy converter machine on the at least one mobile device;
b) constructing an energy model of the wave energy system relating average power generated by the at least one energy converter machine to force exerted by the at least one energy converter machine on the at least one mobile device to the velocity of the at least one mobile device and to the efficiency of the wave energy system;
c) predicting the force exerted by the waves on the at least one mobile device for a predetermined time period;
d) determining a control value of the force exerted by the at least one energy converter machine on the at least one mobile device which maximizes average power generated by the at least one energy converter machine by:
i) determining an objective function representative of the power generated by the at least one energy converter machine by use of the prediction of the force exerted by the waves on the at least one mobile device, of the dynamic model and of the energy model;
ii) discretizing the objective function by a trapezoidal rule; and
iii) weighting, in the discretized objective function, future values of control by predetermined weighting coefficients;
iv) determining the control value from the force exerted by the at least one energy converter machine on the at least one mobile device by minimizing the discretized and weighted objective function; and
e) controlling the at least one energy converter machine by use of the control value.

### Claim 2 (depends on 1)

A method as claimed in claim 1, wherein the discretized and weighted objective function J is expressed by a relationship: J=Σj=0Np−2qjua(k+j|k)(v(k+j|k)+v(k+j+1|k)), with qj being the weighting coefficients, ua being the force exerted by the at least one energy converter machine on the at least one mobile device, v being the velocity of the at least one mobile device and Np being a number of time steps contained in a prediction horizon and k and j being time steps.

### Claim 3 (depends on 2)

A method as claimed in claim 2, wherein the discretized and weighted objective function J is written in matrix form as:
J
=
u
e
T
⁢
Hu
e
+
2
⁢
u
e
T
⁢
f
⁡
[
x
⁡
(
k
|
k
)
w
e
]
,
with ue being a vector of the force exerted by the at least one energy converter machine on the at least one mobile device, x being the state vector of a model of the wave energy system with the at least one energy converter machine, we being the vector of the wave force predictions, H being a weighting matrix on vector ue, f being a weighting matrix n on the current state x of a global dynamic model of the wave energy system and the vector of the wave force predictions we and T is duration.

### Claim 4 (depends on 3)

A method as claimed in claim 3, wherein negative or zero eigenvalues of the weighting matrix H are replaced by positive eigenvalues.

### Claim 5 (depends on 1)

A method as claimed in claim 1, wherein force exerted by the waves on the at least one mobile device is predicted by at least one of measurement or estimation of the force exerted by the waves on the at least one mobile device, by using pressure detectors adjacent the at least one mobile device or force sensors between the at least one mobile device and the at least one energy converter machine.

### Claim 6 (depends on 2)

A method as claimed in claim 2, wherein force exerted by the waves on the at least one mobile device is predicted by at least one of measurement or estimation of the force exerted by the waves on the at least one mobile device, by using pressure detectors adjacent the at least one mobile device or force sensors between the at least one mobile device and the at least one energy converter machine.

### Claim 7 (depends on 3)

A method as claimed in claim 3, wherein force exerted by the waves on the at least one mobile device is predicted by at least one of measurement or estimation of the force exerted by the waves on the at least one mobile device, by using pressure detectors adjacent the at least one mobile device or force sensors between the at least one mobile device and the at least one energy converter machine.

### Claim 8 (depends on 4)

A method as claimed in claim 4, wherein force exerted by the waves on the at least one mobile device is predicted by at least one of measurement or estimation of the force exerted by the waves on the at least one mobile device, by using pressure detectors adjacent the at least one mobile device or force sensors between the at least one mobile device and the at least one energy converter machine.

### Claim 9 (depends on 1)

A method as claimed in claim 1, wherein the dynamic model of the wave energy system is written as:
{
x
.
⁡
(
t
)
=
A
c
⁢
x
⁡
(
t
)
+
B
cu
⁢
u
⁡
(
t
)
+
B
cw
⁢
w
⁡
(
t
)
y
⁡
(
t
)
=
C
c
⁢
x
⁡
(
t
)
,
with x and y being the state vectors of the wave energy system with the at least one energy converter machine, u being the control value of the force exerted by the at least one energy converter machine on the at least one mobile device, w being the excitation force of incident waves on the at least one mobile device, Ac, Bcu, Bcw, and Cc being matrices for multiplying the state and inputs of the dynamic model allowing calculation of a dynamic variation of the state and the outputs of the dynamic model.

### Claim 10 (depends on 2)

A method as claimed in claim 2, wherein the dynamic model of the wave energy system is written as:
{
x
.
⁡
(
t
)
=
A
c
⁢
x
⁡
(
t
)
+
B
cu
⁢
u
⁡
(
t
)
+
B
cw
⁢
w
⁡
(
t
)
y
⁡
(
t
)
=
C
c
⁢
x
⁡
(
t
)
,
with x and y being the state vectors of the wave energy system with the at least one energy converter machine, u being the control value of the force exerted by the at least one energy converter machine on the at least one mobile device, w being the excitation force of incident waves on the at least one mobile device, Ac, Bcu, Bcw, and Cc being matrices for multiplying the state and inputs of the dynamic model of the wave energy system allowing calculation of a dynamic variation of the state and the outputs of the dynamic model of the wave energy system.

### Claim 11 (depends on 3)

A method as claimed in claim 3, wherein the dynamic model of the wave energy system is written as:
{
x
.
⁡
(
t
)
=
A
c
⁢
x
⁡
(
t
)
+
B
cu
⁢
u
⁡
(
t
)
+
B
cw
⁢
w
⁡
(
t
)
y
⁡
(
t
)
=
C
c
⁢
x
⁡
(
t
)
,
with x and y being the state vectors of the wave energy system with the at least one energy converter machine, u being the control value of the force exerted by the at least one energy converter machine on the at least one mobile device, w being the excitation force of incident waves on the at least one mobile device, Ac, Bcu, Bcw, and Cc being matrices for multiplying the state and inputs of the dynamic model of the wave energy system allowing calculation of a dynamic variation of the state and the outputs of the dynamic model of the wave energy system.

### Claim 12 (depends on 4)

A method as claimed in claim 4, wherein the dynamic model of the wave energy system is written as:
{
x
.
⁡
(
t
)
=
A
c
⁢
x
⁡
(
t
)
+
B
cu
⁢
u
⁡
(
t
)
+
B
cw
⁢
w
⁡
(
t
)
y
⁡
(
t
)
=
C
c
⁢
x
⁡
(
t
)
,
with x and y being the state vectors of the wave energy system with the at least one energy converter machine, u being the control value of the force exerted by the at least one energy converter machine on the at least one mobile device, w being the excitation force of incident waves on the at least one mobile device, Ac, Bcu, Bcw, and Cc being matrices for multiplying the state and inputs of the dynamic model of the wave energy system allowing calculation of a dynamic variation of the state and the outputs of the dynamic model of the wave energy system.

### Claim 13 (depends on 5)

A method as claimed in claim 5, wherein the dynamic model of the wave energy system is written as:
{
x
.
⁡
(
t
)
=
A
c
⁢
x
⁡
(
t
)
+
B
cu
⁢
u
⁡
(
t
)
+
B
cw
⁢
w
⁡
(
t
)
y
⁡
(
t
)
=
C
c
⁢
x
⁡
(
t
)
,
with x and y being the state vectors of the wave energy system with the at least one energy converter machine, u being the control value of the force exerted by the at least one energy converter machine on the at least one mobile device, w being the excitation force of incident waves on the at least one mobile device, Ac, Bcu, Bcw, and Cc being matrices for multiplying the state and inputs of the dynamic model of the wave energy system allowing calculation of a dynamic variation of the state and the outputs of the dynamic model of the wave energy system.

### Claim 14 (depends on 6)

A method as claimed in claim 6, wherein the dynamic model of the wave energy system is written as:
{
x
.
⁡
(
t
)
=
A
c
⁢
x
⁡
(
t
)
+
B
cu
⁢
u
⁡
(
t
)
+
B
cw
⁢
w
⁡
(
t
)
y
⁡
(
t
)
=
C
c
⁢
x
⁡
(
t
)
,
with x and y being the state vectors of the wave energy system with the at least one energy converter machine, u being the control value of the force exerted by the at least one energy converter machine on the at least one mobile device, w being the excitation force of incident waves on the at least one mobile device, Ac, Bcu, Bcw, and Cc being matrices for multiplying the state and inputs of the dynamic model of the wave energy system allowing calculation of a dynamic variation of the state and the outputs of the dynamic model of the wave energy system.

### Claim 15 (depends on 7)

A method as claimed in claim 7, wherein the dynamic model of the wave energy system is written as:
{
x
.
⁡
(
t
)
=
A
c
⁢
x
⁡
(
t
)
+
B
cu
⁢
u
⁡
(
t
)
+
B
cw
⁢
w
⁡
(
t
)
y
⁡
(
t
)
=
C
c
⁢
x
⁡
(
t
)
,
with x and y being the state vectors of the wave energy system with the at least one energy converter machine, u being the control value of the force exerted by the at least one energy converter machine on the at least one mobile device, w being the excitation force of incident waves on the at least one mobile device, Ac, Bcu, Bcw, and Cc being matrices for multiplying the state and inputs of the dynamic model of the wave energy system allowing calculation of a dynamic variation of the state and the outputs of the dynamic model of the wave energy system.

### Claim 16 (depends on 8)

A method as claimed in claim 8, wherein the dynamic model of the wave energy system is written as:
{
x
.
⁡
(
t
)
=
A
c
⁢
x
⁡
(
t
)
+
B
cu
⁢
u
⁡
(
t
)
+
B
cw
⁢
w
⁡
(
t
)
y
⁡
(
t
)
=
C
c
⁢
x
⁡
(
t
)
,
with x and y being the state vectors of the wave energy system with the at least one energy converter machine, u being the control value of the force exerted by the at least one energy converter machine on the at least one mobile device, w being the excitation force of incident waves on the at least one mobile device, Ac, Bcu, Bcw, and Cc being matrices for multiplying the state and inputs of the dynamic model of the wave energy system allowing calculation of a dynamic variation of the state and the outputs of the dynamic model of the wave energy system.

### Claim 17 (depends on 1)

A method as claimed in claim 1, wherein the dynamic model of the wave energy system incorporates dynamics of the at least one energy converter machine which consider quasi-instantaneous control of the at least one energy converter machine in relation to dynamics of the wave energy system.

### Claim 18 (depends on 1)

A method as claimed in claim 1, wherein the energy model is expressed by a relationship:
P
a
=
-
1
T
⁢
∫
t
=
0
T
⁢
η
⁢
⁢
u
a
⁢
vdt
,
with Pa being the average power generated, t being time, T being a predetermined duration, η being energy conversion efficiency, ua being force exerted by the at least one energy converter machine on the at least one mobile device and v being velocity of the at least one mobile device in relation to the at least one energy converter machine.

### Claim 19 (depends on 18)

A method as claimed in claim 18, wherein the efficiency η is a function of force ua exerted by the at least one energy converter machine on the at least one mobile device and of velocity v of the at least one mobile device in relation to the at least one energy converter machine.

### Claim 20 (depends on 19)

A method as claimed in claim 19, wherein efficiency η is calculated with a formula:
η
⁡
(
u
a
⁢
v
)
=
{
η
p
⁢
⁢
if
⁢
⁢
u
a
⁢
⁢
v
≥
0
η
n
⁢
⁢
if
⁢
⁢
u
a
⁢
v
<
0
,
with ηp being motor efficiency of the at least one energy converter machine, ηn being the generator efficiency of the at least one energy converter machine, with 0<ηp≤1 and ηn≥1.

### Claim 21 (depends on 1)

A method as claimed in claim 1, wherein the method comprises a prior step of optimizing the weighting coefficients using an algorithm, particle swarm optimization, variable neighborhood search, or the Nelder-Mead method.

### Claim 22 (depends on 1)

A method as claimed in claim 1, wherein steps c), d) and e) are repeated to provide a predictive control with a moving horizon.

### Claim 23 (depends on 1)

A method as claimed in claim 1, wherein the energy converter machine is an electrical or hydraulic machine.