Exhibit 10.2

CENTERPOINT ENERGY, INC.

2009 LONG TERM INCENTIVE PLAN

RESTRICTED STOCK UNIT AWARD AGREEMENT

(With Performance Goal)

Pursuant to this Restricted Stock Unit Award Agreement (“Award Agreement”), CenterPoint Energy, Inc. (the “Company”) hereby grants to the Participant, an employee of the Company, on the Award Date, a restricted stock unit award of the number of units of Common Stock of the Company (the “RSU Award”) as specified on this BNY Mellon Shareholder Services web site (“Award Notice”), pursuant to the CenterPoint Energy, Inc. 2009 Long Term Incentive Plan (the “Plan”), which is a qualified Performance Award under the Plan, conditioned upon the Company’s achievement of the Performance Goals established by the Committee over the course of the Vesting Period, and subject to the terms, conditions and restrictions described in the Plan and as follows:

1. Relationship to the Plan; Definitions. This RSU Award is subject to all of the terms, conditions and provisions of the Plan in effect on the date hereof and administrative interpretations thereunder, if any, adopted by the Committee. Except as defined herein, capitalized terms shall have the same meanings ascribed to them under the Plan. To the extent that any provision of this Award Agreement conflicts with the express terms of the Plan, it is hereby acknowledged and agreed that the terms of the Plan shall control and, if necessary, the applicable provisions of this Award Agreement shall be hereby deemed amended so as to carry out the purpose and intent of the Plan. References to the Participant herein also include the heirs or other legal representatives of the Participant. For purposes of this Award Agreement:

“Award Date” means the date this RSU Award is granted to the Participant as specified in the Award Notice.

“Change in Control Closing Date” means the date a Change in Control (as defined in the Plan) is consummated during the Vesting Period.

“Change in Control Payment Date” means the following:

(i) If the Participant is not Retirement Eligible, then the Change in Control Payment Date shall be not later than the 70th day after the Change in Control Closing Date (regardless of whether or not the Participant is a Specified Employee); and

(ii) If the Participant is Retirement Eligible and the Change in Control is a Section 409A Change in Control, then the Change in Control Payment Date shall be not later than the 70th day after the Change in Control Closing Date (regardless of whether or not the Participant is a Specified Employee); and

(iii) If the Participant is Retirement Eligible, the Change in Control is not a Section 409A Change in Control and the Participant is not a Specified Employee, then the Change in Control Payment Date shall be not later than the 70th day after the earlier of:

(iv) If the Participant is Retirement Eligible, the Change in Control is not a Section 409A Change in Control and the Participant is a Specified Employee, then the Change in Control Payment Date shall be as follows:

“Disability” means that the Participant is both eligible for and in receipt of benefits under the Company’s long-term disability plan.

“Employment” means employment with the Company or any of its Subsidiaries.

“Performance Goals” means the standards established by the Committee to determine in whole or in part whether the units of Common Stock under the RSU Award shall vest, which are specified in the performance goals section of the Award Notice and made a part hereof for all purposes.

2

“Retirement” means a Separation from Service (i) on or after attainment of age 55 and (ii) with at least five years of Employment; provided, however, that such Separation from Service is not by the Company for Cause and occurs on or after July 1 of the calendar year in which this RSU Award is granted. For purposes of this Award Agreement, “Cause” means the Participant’s (a) gross negligence in the performance of his or her duties, (b) intentional and continued failure to perform his or her duties, (c) intentional engagement in conduct which is materially injurious to the Company or its Subsidiaries (monetarily or otherwise) or (d) conviction of a felony or a misdemeanor involving moral turpitude. For this purpose, an act or failure to act on the part of the Participant will be deemed “intentional” only if done or omitted to be done by the Participant not in good faith and without reasonable belief that his or her action or omission was in the best interest of the Company, and no act or failure to act on the part of the Participant will be deemed “intentional” if it was due primarily to an error in judgment or negligence.

“Retirement Eligible” means the Participant (i) is or will be age 55 or older and (ii) has or will have at least five years of Employment, on or after July 1 of the calendar year in which this RSU Award is granted but prior to the calendar year in which the Vesting Date occurs.

“Section 409A” means Code Section 409A and the Treasury regulations and guidance issued thereunder.

“Section 409A Change in Control” means a Change in Control that satisfies the requirements of a change in control for purposes of Code Section 409A(a)(2)(A)(v) and the Treasury regulations and guidance issued thereunder.

“Separation from Service” means a separation from service with the Company or any of its Subsidiaries within the meaning of Treasury Regulation § 1.409A-1(h) (or any successor regulation).

“Specified Employee” has the meaning of that term under Code Section 409A(a)(2)(B)(i) and the Treasury regulations and guidance issued thereunder.

“Termination Date” means the date of the Participant’s Separation from Service.

“Vesting Date” means the vesting date specified in the Award Notice.

“Vesting Period” means the period commencing on the Award Date and ending on the Vesting Date.

2. Establishment of RSU Award Account. The grant of units of Common Stock of the Company pursuant to this Award Agreement shall be implemented by a credit to a bookkeeping account maintained by the Company evidencing the accrual in favor of the Participant of the unfunded and unsecured right to receive such units of Common Stock, which right shall be subject to the terms, conditions and restrictions set forth in the Plan and to the further terms, conditions and restrictions set forth in this Award Agreement. Except as otherwise provided in Section 10 of this Award Agreement, the units of Common Stock credited to the Participant’s bookkeeping account may not be sold, assigned, transferred, pledged or otherwise encumbered until the Participant has been registered as the holder of shares of Common Stock on the records of the Company, as provided in Sections 4, 5 or 6 of this Award Agreement.

3

3. Vesting of RSU Award. Unless earlier (a) vested or forfeited pursuant to this Section 3 or Section 4(a) below or (b) vested upon the occurrence of a Change in Control pursuant to Section 5 below, the Participant’s right to receive shares of Common Stock (if any) under this Award Agreement shall vest on the Vesting Date. No later than 60 days after the Vesting Date, the Committee shall determine the extent to which the Performance Goal has been achieved. Upon completing its determination of the level at which the Performance Goal has been achieved, the Committee shall notify the Participant, in the form and manner as determined by the Committee, of the number of shares of Common Stock (if any) under this Award Agreement that will be issued to the Participant pursuant to Section 6. Except as provided in Sections 4 and 5 below, the Participant must be in continuous Employment during the Vesting Period in order for the RSU Award to vest; otherwise, all such units shall be forfeited as of the Participant’s Termination Date.

4. Effect of Separation from Service; Timing of Distribution.

(a) Separation from Service Prior to the Vesting Date or Change in Control. Notwithstanding Section 3 above, if prior to (i) the Vesting Date or (ii) the occurrence of a Change in Control, the Participant’s Separation from Service occurs due to Retirement, death or Disability, then:

(1) Retirement. In the event of Retirement, the Participant shall vest in the right to receive a number, if any, of the shares of Common Stock (rounded up to the nearest whole share) determined by multiplying (x) the total number of units of Common Stock subject to this Award Agreement based upon the Committee’s determination of the achievement of the Performance Goal after the end of the Vesting Period, as provided in Section 3, by (y) a fraction, the numerator of which is the number of days that have elapsed from the Award Date to the Participant’s Termination Date, and the denominator of which is the total number of days in the Vesting Period; or

(2) Death or Disability. In the event of the Participant’s death or Separation from Service due to Disability, without regard to the Performance Goals, the Participant shall vest in the right to receive a number of the shares of Common Stock (rounded up to the nearest whole share) determined by multiplying (x) the total number of units of Common Stock granted subject to this Award Agreement by (y) a fraction, the numerator of which is the number of days that have elapsed from the Award Date to the Participant’s Termination Date, and the denominator of which is the total number of days in the Vesting Period.

(b) Timing of Distribution.

(1) Retirement. If the Participant is entitled to a benefit pursuant to Section 4(a)(1) hereof, a number of shares of Common Stock equal to the number of vested shares of Common Stock subject to this Award Agreement (as determined by the Committee in accordance with Section 3 and Section 4(a)(1), if any) shall be registered in the name of the Participant and delivered to the Participant not later than the 70th day after the Vesting Date.

4

(2) Death. If the Participant is entitled to a benefit pursuant to Section 4(a)(2) hereof due to the Participant’s death, the number of shares of Common Stock determined in accordance with Section 4(a)(2) shall be registered in the name of the Participant’s estate and delivered to the Participant’s estate as soon as practicable but not later than the 70th day after the date of the Participant’s death.

(3) Disability.

(A) Specified Employee and Retirement Eligible. If the Participant (i) is entitled to a benefit pursuant to Section 4(a)(2) hereof due to the Participant’s Separation from Service due to Disability, (ii) is a Specified Employee, and (iii) is Retirement Eligible, the number of shares of Common Stock determined in accordance with Section 4(a)(2) shall be registered in the name of the Participant and delivered to the Participant on the date that is the earlier of (x) the second business day following the end of the six-month period commencing on the Participant’s Termination Date or (y) the Participant’s date of death, if death occurs during such six-month period.

(B) All Other Participants. Except as provided in Section 4(b)(3)(A), if the Participant is entitled to a benefit pursuant to Section 4(a)(2) hereof due to the Participant’s Separation from Service due to Disability, the number of shares of Common Stock determined in accordance with Section 4(a)(2) shall be registered in the name of the Participant and delivered to the Participant as soon as practicable but not later than the 70th day after the date of the Participant’s Termination Date.

(c) Dividend Equivalents. Upon the date of delivery of shares of Common Stock under this Section 4, the Participant shall also be entitled to receive Dividend Equivalents for the period from the Award Date to the date such vested shares of Common Stock are distributed to the Participant (in accordance with the requirements of Section 409A, to the extent applicable).

5. Distribution Upon a Change in Control. Notwithstanding any provision of this Award Agreement to the contrary, if during the Participant’s Employment and prior to the end of the Vesting Period or an accelerated vesting event under Section 4 above there is a Change in Control of the Company, then, upon the Change in Control Closing Date and without regard to the Performance Goal, the Participant’s right to receive the unvested units of Common Stock subject to this Award Agreement shall be vested and settled by a distribution, on the Change in Control Payment Date, to the Participant of:

5

(a) The number of units of Common Stock subject to this Award Agreement not previously vested or forfeited pursuant to Sections 3 or 4 above, plus

(b) Dividend Equivalents in the form of shares of Common Stock (rounded up to the nearest whole share) for the period commencing on the Award Date and ending on the date immediately preceding the Change in Control Payment Date;

with such shares of Common Stock registered in the name of the Participant and delivered to the Participant. In lieu of the foregoing distribution in shares, the Committee, in its sole discretion, may direct that such distribution be made to the Participant in a lump sum cash payment equal to:

(x) The product of (i) the Fair Market Value per share of Common Stock on the date immediately preceding the Change in Control Closing Date and (ii) the number of units of Common Stock subject to this Award Agreement not previously vested or forfeited pursuant to Sections 3 or 4 above, plus

(y) Dividend Equivalents for the period commencing on the Award Date and ending on the date immediately preceding the Change in Control Payment Date;

with such cash payment to be made on the Change in Control Payment Date. Such distribution under this Section 5, whether in the form of shares of Common Stock or, if directed by the Committee, in cash, shall satisfy the rights of the Participant and the obligations of the Company under this Award Agreement in full.

6. Payment of RSU Award Under Section 3. Upon the vesting of the Participant’s right to receive the shares of Common Stock pursuant to Section 3 under this Award Agreement, a number of shares of Common Stock equal to the number of vested shares of Common Stock subject to this Award Agreement (as determined by the Committee in accordance with Section 3, if any) shall be registered in the name of the Participant and delivered to the Participant not later than the 70th day after the Vesting Date. Moreover, upon the date of delivery of shares of Common Stock, the Participant shall also be entitled to receive Dividend Equivalents for the period commencing on the Award Date and ending on the date such vested shares of Common Stock are distributed to the Participant (in accordance with the requirements of Section 409A, to the extent applicable).

7. Confidentiality. The Participant agrees that the terms of this Award Agreement are confidential and that any disclosure to anyone for any purpose whatsoever (save and except disclosure to financial institutions as part of a financial statement, financial, tax and legal advisors, or as required by law) by the Participant or his or her agents, representatives, heirs, children, spouse, employees or spokespersons shall be a breach of this Award Agreement and the Company may elect to revoke the grant made hereunder, seek damages, plus interest and reasonable attorneys’ fees, and take any other lawful actions to enforce this Award Agreement.

8. Notices. For purposes of this Award Agreement, notices to the Company shall be deemed to have been duly given upon receipt of written notice by the Corporate Secretary of CenterPoint Energy, Inc., 1111 Louisiana, Houston, Texas 77002, or to such other address as the Company may furnish to the Participant.

6

Notices to the Participant shall be deemed effectively delivered or given upon personal, electronic, or postal delivery of written notice to the Participant, the place of Employment of the Participant, the address on record for the Participant at the human resources department of the Company, or such other address as the Participant hereafter designates by written notice to the Company.

9. Shareholder Rights. The Participant shall have no rights of a shareholder with respect to the units of Common Stock subject to this Award Agreement, unless and until the Participant is registered as the holder of such shares of Common Stock.

10. Successors and Assigns. This Award Agreement shall bind and inure to the benefit of and be enforceable by the Participant, the Company and their respective permitted successors and assigns except as expressly prohibited herein and in the Plan. Notwithstanding anything herein or in the Plan to the contrary, the units of Common Stock are transferable by the Participant to Immediate Family Members, Immediate Family Member trusts, and Immediate Family Member partnerships pursuant to Section 13 of the Plan.

11. No Employment Guaranteed. Nothing in this Award Agreement shall give the Participant any rights to (or impose any obligations for) continued Employment by the Company or any Subsidiary, or any successor thereto, nor shall it give such entities any rights (or impose any obligations) with respect to continued performance of duties by the Participant.

12. Waiver. Failure of either party to demand strict compliance with any of the terms or conditions hereof shall not be deemed a waiver of such term or condition, nor shall any waiver by either party of any right hereunder at any one time or more times be deemed a waiver of such right at any other time or times. No term or condition hereof shall be deemed to have been waived except by written instrument.

13. Compliance with Section 409A. It is the intent of the Company and the Participant that the provisions of the Plan and this Award Agreement comply with Section 409A and will be interpreted and administered consistent therewith. Accordingly, (i) no adjustment to the RSU Award pursuant to Section 14 of the Plan and (ii) no substitutions of the benefits under this Award Agreement, in each case, shall be made in a manner that results in noncompliance with the requirements of Section 409A, to the extent applicable. The foregoing notwithstanding, if the Participant is not Retirement Eligible, then at all times prior to the payment date, the benefit payable under this Award Agreement is subject to a substantial risk of forfeiture within the meaning of Treasury Regulation § 1.409A-1(d) (or any successor regulation) and, accordingly, with respect to such Participant, this RSU Award is not subject to Section 409A under the short term deferral exclusion, and this Award Agreement shall be interpreted and administered consistent therewith.

7

14. Withholding. The Company shall have the right to withhold applicable taxes from any distribution of the Common Stock (including, but not limited to, Dividend Equivalents) or from other cash compensation payable to the Participant at the time of such vesting and delivery pursuant to Section 11 of the Plan (but subject to compliance with the requirements of Section 409A, if applicable).

15. Compliance with Recoupment Policy. Any amounts payable, paid, or distributed under this Award Agreement are subject to the recoupment policy of the Company as in effect from time to time.

16. Modification of Award Agreement. Any modification of this Award Agreement is subject to Section 13 hereof and shall be binding only if evidenced in writing and signed by an authorized representative of the Company.

8