Exhibit 3.1

EXECUTION VERSION

SECOND AMENDED AND RESTATED

AGREEMENT OF LIMITED PARTNERSHIP

OF

WILLIAMS PARTNERS L.P.

This Second Amended and Restated Agreement of Limited Partnership (as it may be amended, supplemented or restated from time to time, the “Agreement”) of Williams Partners L.P. (the “Partnership”) dated as of February 2, 2015 and effective as of the Effective Time (as defined below), is entered into by and between VHMS GP LLC, a Delaware limited liability company, as the general partner (the “General Partner”), and Access Midstream Partners, L.P., a Delaware limited partnership, as the sole limited partner (the “Limited Partner”).

WHEREAS, on February 23, 2005, Williams Partners GP LLC, a Delaware limited liability company (“WPGP”), formed the Partnership pursuant to and in accordance with the Delaware Revised United Limited Partnership Act, as amended from time to time (the “Act”).

WHEREAS, on August 23, 2005, WPGP, as the general partner, and each of Williams Energy Services, LLC, a Delaware limited liability company (“WP ES”), Williams Energy, L.L.C., a Delaware limited liability company (“WP Energy”), Williams Discovery Pipeline, LLC, a Delaware limited liability company (“WP Discovery”), and Williams Partners Holdings, a Delaware limited liability company (“WP Holdings”), as limited partners, amended and restated the original Agreement of Limited Partnership of the Partnership (as amended and restated, the “Amended and Restated Agreement of Limited Partnership”).

WHEREAS, on August 7, 2006, WPGP amended the Amended and Restated Agreement of Limited Partnership of the Partnership (“Amendment No. 1”), pursuant to authority granted to WPGP in Article 13 of the Amended and Restated Agreement of Limited Partnership.

WHEREAS, on August 23, 2006, WPGP amended the Amended and Restated Agreement of Limited Partnership of the Partnership (“Amendment No. 2”), pursuant to authority granted to WPGP in Article 13 of the Amended and Restated Agreement of Limited Partnership.

WHEREAS, on December 13, 2006, WPGP amended the Amended and Restated Agreement of Limited Partnership of the Partnership (“Amendment No. 3”), pursuant to authority granted to WPGP in Article 13 of the Amended and Restated Agreement of Limited Partnership.

WHEREAS, on August 15, 2008, WPGP amended the Amended and Restated Agreement of Limited Partnership of the Partnership (“Amendment No. 4”), pursuant to authority granted to WPGP in Article 13 of the Amended and Restated Agreement of Limited Partnership.

WHEREAS, on April 16, 2009, WPGP amended the Amended and Restated Agreement of Limited Partnership of the Partnership (“Amendment No. 5”), pursuant to authority granted to WPGP in Article 13 of the Amended and Restated Agreement of Limited Partnership.

WHEREAS, on February 17, 2010, WPGP amended the Amended and Restated Agreement of Limited Partnership of the Partnership (“Amendment No. 6”), pursuant to authority granted to WPGP in Article 13 of the Amended and Restated Agreement of Limited Partnership.

WHEREAS, on November 17, 2010, WPGP amended the Amended and Restated Agreement of Limited Partnership of the Partnership (“Amendment No. 7”), pursuant to authority granted to WPGP in Article 13 of the Amended and Restated Agreement of Limited Partnership.

WHEREAS, on April 27, 2012, WPGP amended the Amended and Restated Agreement of Limited Partnership of the Partnership (“Amendment No. 8”), pursuant to authority granted to WPGP in Article 13 of the Amended and Restated Agreement of Limited Partnership.

WHEREAS, on November 5, 2012, WPGP amended the Amended and Restated Agreement of Limited Partnership of the Partnership (“Amendment No. 9”), pursuant to authority granted to WPGP in Article 13 of the Amended and Restated Agreement of Limited Partnership.

WHEREAS, on October 25, 2013, WPGP amended the Amended and Restated Agreement of Limited Partnership of the Partnership (“Amendment No. 10”), pursuant to authority granted to WPGP in Article 13 of the Amended and Restated Agreement of Limited Partnership.

WHEREAS, on February 28, 2014, WPGP amended the Amended and Restated Agreement of Limited Partnership of the Partnership (“Amendment No. 11”), pursuant to authority granted to WPGP in Article 13 of the Amended and Restated Agreement of Limited Partnership.

WHEREAS, the Partnership, WPGP, the Limited Partner, VHMS LLC, a Delaware limited liability company (“Merger Sub”), and Access Midstream Partners GP, L.L.C., a Delaware limited liability company (“ACMP GP”), entered into an Agreement and Plan of Merger (the “Merger Agreement”) dated as of October 24, 2014, providing for, among other things, the merger of Merger Sub with and into the Partnership, the merger of WPGP into ACMP GP, the admission of the Limited Partner as a limited partner of the Partnership, all other limited partners of the Partnership simultaneously ceasing to be limited partners of the Partnership and the amendment and restatement of the Amended and Restated Agreement of Limited Partnership.

NOW, THEREFORE, pursuant to the Merger Agreement and the Amended and Restated Agreement of Limited Partnership, the General Partner and the Limited Partner do hereby amend and restate the Amended and Restated Agreement of Limited Partnership (as amended by Amendment No. 1, Amendment No. 2, Amendment No. 3, Amendment No. 4, Amendment No. 5, Amendment No. 6, Amendment No. 7, Amendment No. 8, Amendment No. 9, Amendment No. 10 and Amendment No. 11) as follows, to be effective as of the Effective Time (as such term is defined in the Merger Agreement):

1. Name. The name of the limited partnership formed by the Partnership’s Certificate of Limited Partnership shall continue to be “Williams Partners L.P.”.

2. Purpose. The Partnership is formed for the object and purpose of, and the nature of the business to be conducted and promoted by the Partnership is, engaging in any lawful act or activity for which limited partnerships may be formed under the Act and engaging in any and all activities necessary or incidental to the foregoing.

3. Registered Office. The registered office of the Partnership in the State of Delaware is The Corporation Trust Company, 1209 N. Orange Street, Wilmington, New Castle County, Delaware 19801.

4. Registered Agent. The name and address of the registered agent of the Partnership for service of process on the Partnership in the State of Delaware is The Corporation Trust Company, 1209 N. Orange Street, Wilmington, New Castle County, Delaware 19801.

5. Partners. Effective as of the Effective Time, WPGP shall cease to be a general partner of the Partnership, the General Partner shall be and is hereby admitted as the sole general partner of the Partnership and the Partnership is hereby continued without dissolution. The names and the business, residence or mailing addresses of the General Partner and the Limited Partner (which is hereby and pursuant to the Merger Agreement admitted as the sole limited partner of the Partnership) are as follows:

6. Powers. The Partnership shall be managed by the General Partner, and the powers of the General Partner include all powers, statutory and otherwise, possessed by general partners under the laws of the State of Delaware. Notwithstanding any other provisions of this Agreement, the General Partner is authorized to execute and deliver any document on behalf of the Partnership without any vote or consent of any other partner, including, but not limited to, any and all mergers, acquisitions or dissolution.

7. Dissolution. The Partnership shall dissolve, and its affairs shall be wound up if (a) all of the partners of the Partnership approve in writing, (b) an event of withdrawal of a general partner has occurred under the Act unless there is a remaining general partner who is hereby authorized to, and does, carry on the business of the Partnership without dissolution or the business of the Partnership is continued without dissolution in accordance with the Act, (c) there are no limited partners of the Partnership unless the business of the Partnership is continued without dissolution in accordance with the Act, (d) an entry of a decree of judicial dissolution has occurred under § 17-802 of the Act or (e) the General Partner approves.

8. Partnership Interests. As of the date of this Agreement, the General Partner has a non-economic general partner interest in the Partnership, such interest granting the General Partner the exclusive right to manage and operate the Partnership in its capacity as General Partner. The Limited Partner has a limited partner interest in the Partnership which constitutes 100% of the aggregate partnership interest (as defined in the Act) of all partners in the Partnership.

9. Distributions. Distributions shall be made to the partners of the Partnership at the times and in the aggregate amounts determined by the General Partner. Such distributions shall be allocated among the partners of the Partnership in accordance with their percentage of partnership interests in the Partnership. Notwithstanding any other provision of this Agreement, neither the Partnership, nor the General Partner on behalf of the Partnership, shall be required to make a distribution to a partner of the Partnership on account of its interest in the Partnership if such distribution would violate the Act or other applicable law.

10. Taxes. The General Partner shall prepare and timely file (on behalf of the Partnership) all state and local tax returns, if any, required to be filed by the Partnership. The Partnership and the partners acknowledge that for federal income tax purposes, the Partnership is intended to be disregarded as an entity separate from the partners of the Partnership.

11. Assignments.

(a) The Limited Partner may assign all or any part of its partnership interest in the Partnership and may withdraw from the Partnership only if the Partnership will have a limited partner after such withdrawal. Upon the withdrawal of the Limited Partner, the Limited Partner shall receive any amount the Limited Partner contributed to the Partnership.

(b) The General Partner may assign all or any part of its partnership interest in the Partnership and may withdraw from the Partnership without the consent of the Limited Partner.

12. Withdrawal. Except to the extent set forth in Section 11, no right is given to any partner of the Partnership to withdraw from the Partnership.

13. Admission of Additional or Substitute Partners.

(a) One or more additional or substitute limited partners of the Partnership may be admitted to the Partnership with only the consent of the General Partner.

(b) One or more additional or substitute general partners of the Partnership may be admitted to the Partnership with only the consent of the General Partner.

14. Indemnification.

(a) As used in Sections 14, 15 and 16, the following terms shall have the following meanings respectively:

“Indemnitee” means (a) any Person (together with such Person’s heirs, executors and administrators) who is or was an officer or director of any WPZ Group Entity (as defined in the Merger Agreement) and (b) any Person (together with such Person’s heirs, executors and administrators) who is or was serving at the request of the Partnership as an officer, director, employee, member, partner, agent, fiduciary or trustee of another Person; provided that a Person shall not be an Indemnitee by reason of providing, on a fee-for-services basis, trustee, fiduciary or custodial services.

“Person” means an individual or a corporation, firm, limited liability company, partnership, joint venture, trust, unincorporated organization, association, governmental agency or political subdivision thereof or other entity.

(b) To the fullest extent permitted by law but subject to the limitations expressly provided in this Agreement, all Indemnitees shall be indemnified and held harmless by the Partnership from and against any and all losses, claims, damages, liabilities, joint or several, expenses (including legal fees and expenses), judgments, fines, penalties, interest, settlements or other amounts arising from any and all claims, demands, actions, suits or proceedings, whether civil, criminal, administrative or investigative, in which any Indemnitee may be involved, or is threatened to be involved, as a party or otherwise, by reason of its status as an Indemnitee, for acts or omissions occurring at or prior to the Effective Time; provided that the Indemnitee shall not be indemnified and held harmless if there has been a final and non-appealable judgment entered by a court of competent jurisdiction determining that, in respect of the matter for which the Indemnitee is seeking indemnification pursuant to this Section 14, the Indemnitee acted in bad faith or engaged in fraud, willful misconduct or, in the case of a criminal matter, acted with knowledge that the Indemnitee’s conduct was unlawful. Any indemnification pursuant to this Section 14 shall be made only out of the assets of the Partnership, it being agreed that the General Partner shall not be personally liable for such indemnification and shall have no obligation to contribute or loan any monies or property to the Partnership to enable it to effectuate such indemnification.

(c) To the fullest extent permitted by law, expenses (including legal fees and expenses) incurred by an Indemnitee who is indemnified pursuant to Section 14(b) in defending any claim, demand, action, suit or proceeding shall, from time to time, be advanced by the Partnership prior to a determination that the Indemnitee is not entitled to be indemnified upon receipt by the Partnership of any undertaking by or on behalf of the Indemnitee to repay such amount if it shall be determined that the Indemnitee is not entitled to be indemnified as authorized in this Section 14.

(d) The indemnification provided by this Section 14 shall be in addition to any other rights to which an Indemnitee may be entitled under any agreement, as a matter of law or otherwise, both as to actions in the Indemnitee’s capacity as an Indemnitee and as to actions in any other capacity, and shall continue as to an Indemnitee who has ceased to serve in such capacity and shall inure to the benefit of the heirs, successors, assigns and administrators of the Indemnitee.

(e) The Partnership may purchase and maintain (or reimburse the General Partner or its affiliates for the cost of) insurance, on behalf of the General Partner, its affiliates

and such other Persons as the General Partner shall determine, against any liability that may be asserted against, or expense that may be incurred by, such Person in connection with the Partnership’s activities or such Person’s activities on behalf of the Partnership, regardless of whether the Partnership would have the power to indemnify such Person against such liability under the provisions of this Agreement.

(f) For purposes of this Section 14, the Partnership shall be deemed to have requested an Indemnitee to serve as fiduciary of an employee benefit plan whenever the performance by it of its duties to the Partnership also imposes duties on, or otherwise involves services by, it to the plan or participants or beneficiaries of the plan; excise taxes assessed on an Indemnitee with respect to an employee benefit plan pursuant to applicable law shall constitute “fines” within the meaning of Section 14(b); and action taken or omitted by it with respect to any employee benefit plan in the performance of its duties for a purpose reasonably believed by it to be in the best interest of the participants and beneficiaries of the plan shall be deemed to be for a purpose that is in the best interests of the Partnership.

(g) In no event may an Indemnitee subject the Limited Partner to personal liability by reason of the indemnification provisions set forth in this Agreement.

(h) An Indemnitee shall not be denied indemnification in whole or in part under this Section 14 because the Indemnitee had an interest in the transaction with respect to which the indemnification applies if the transaction was otherwise permitted by the terms of this Agreement or the Amended and Restated Agreement of Limited Partnership.

(i) The provisions of this Section 14 are for the benefit of the Indemnitees, their heirs, successors, assigns and administrators and shall not be deemed to create any rights for the benefit of any other Persons.

(j) No amendment, modification or repeal of this Section 14 or any provision hereof shall in any manner terminate, reduce or impair the right of any past, present or future Indemnitee to be indemnified by the Partnership, nor the obligations of the Partnership to indemnify any such Indemnitee under and in accordance with the provisions of this Section 14 as in effect immediately prior to such amendment, modification or repeal with respect to claims arising from or relating to matters occurring, in whole or in part, prior to such amendment, modification or repeal, regardless of when such claims may arise or be asserted.

15. Liability of Indemnitees.

(a) Notwithstanding anything to the contrary set forth in this Agreement, no Indemnitee shall be liable for monetary damages to the Partnership, the Limited Partner or a permitted assignee thereof that is admitted as a limited partner or any other Persons who have acquired equity interests in the Partnership or are otherwise bound by this Agreement, for losses sustained or liabilities incurred as a result of any act or omission of an Indemnitee unless there has been a final and non-appealable judgment entered by a court of competent jurisdiction determining that, in respect of the matter in question, the Indemnitee acted in bad faith or engaged in fraud, willful misconduct or, in the case of a criminal matter, acted with knowledge that the Indemnitee’s conduct was criminal.

(b) To the extent that, at law, in equity or otherwise, an Indemnitee has duties (including fiduciary duties) and liabilities relating thereto to the Partnership or to the partners, and any other Indemnitee acting in connection with the Partnership’s business or affairs shall not be liable to the Partnership, any partner or any of their permitted assignees that are admitted as partners or any other Person bound by this Agreement for its good faith reliance on the provisions of this Agreement.

(c) Any amendment, modification or repeal of this Section 15 or any provision hereof shall be prospective only and shall not in any way affect the limitations on the liability of the Indemnitees under this Section 15 as in effect immediately prior to such amendment, modification or repeal with respect to claims arising from or relating to matters occurring, in whole or in part, prior to such amendment, modification or repeal, regardless of when such claims may arise or be asserted.

16. Third-Party Beneficiaries. Each partner agrees that any Indemnitee shall be entitled to assert rights and remedies hereunder as a third-party beneficiary hereto with respect to those provisions of this Agreement affording a right, benefit or privilege to such Indemnitee.

17. Governing Law. This Agreement shall be governed by, and construed under, the laws of the State of Delaware, all rights and remedies being governed by said laws.

18. Severability. If any provision of this Agreement is or becomes invalid, illegal or unenforceable in any respect, the validity, legality and enforceability of the remaining provisions contained herein shall not be affected thereby.

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IN WITNESS WHEREOF, the parties hereto have executed this Agreement as of the date first written above.

[Signature Page to Second A&R Agreement of Limited Partnership of Williams Partners L.P. (6.11)]