
<PAGE>   1

                                                                   EXHIBIT 3.1.1

                              AMENDED AND RESTATED
                          CERTIFICATE OF INCORPORATION
                                       OF
                               CALPINE CORPORATION

                             A Delaware corporation
                        (Pursuant to Sections 242 and 245
                    of the Delaware General Corporation Law)

     Calpine Corporation, a corporation organized and existing under and by
virtue of the General Corporation Law of the State of Delaware, hereby certifies
as follows:

     FIRST: That the name of the corporation is Calpine Corporation, and that
the corporation was originally incorporated on June 21, 1982 under the name
Electrowatt Services Inc., pursuant to the General Corporation Law.

     SECOND: The Certificate of Incorporation of this corporation shall be
amended and restated to read in full as is set forth on Exhibit A attached
hereto.

     THIRD: That said amendment and restatement was duly adopted in accordance
with the provisions of Section 242 and Section 245 of the General Corporation
Law by obtaining a majority vote of the Common Stock in favor of said amendment
and restatement in the manner set forth in Section 222 of the General
Corporation Law.

     IN WITNESS WHEREOF, Calpine Corporation has caused its corporate seal to be
hereunto affixed and this Amended and Restated Certificate of Incorporation to
be signed by its President and attested to by its Secretary this 13th day of
September, 1996.

                                        CALPINE CORPORATION

                                        /s/ PETER CARTWRIGHT
                                        ----------------------------------------
                                        Name:  Peter Cartwright
                                        Title: President


ATTEST:

/s/ ANN B. CURTIS
---------------------------------------
Name:  Ann B. Curtis
Title: Secretary


                                       1.

<PAGE>   2

                                                                       EXHIBIT A

                              AMENDED AND RESTATED
                          CERTIFICATE OF INCORPORATION
                                       OF
                               CALPINE CORPORATION

     FIRST. The name of the corporation is Calpine Corporation (the
"Corporation").

     SECOND. The address of its registered office in the State of Delaware is
1209 Orange Street, in the City of Wilmington, County of New Castle. The name of
its registered agent at such address is The Corporation Trust Company.

     THIRD. The purpose of the Corporation is to engage in any lawful act or
activity for which corporations may be organized under the General Corporation
Law of Delaware.

     FOURTH.   (a)  The Corporation is authorized to issue 110,000,000 shares of
capital stock, $.001 par value. The shares shall be divided into two classes,
designated as follows:

<TABLE>
<CAPTION>
          Designation of Class                Number of Shares
          --------------------                ----------------
<S>                                              <C>
          Common Stock                           100,000,000
          Preferred Stock                         10,000,000
                                                 -----------
               Total                             110,000,000
</TABLE>


               (b)  The Preferred Stock may be issued from time to time in one
or more series. The Board of Directors is expressly authorized, in the
resolution or resolutions providing for the issuance of any wholly unissued
series of Preferred Stock, to fix, state and express the powers, rights,
designations, preferences, qualifications, limitations and restrictions thereof,
including without limitation: the rate of dividends upon which and the times at
which dividends on shares of such series shall be payable and the preference, if
any, which such dividends shall have relative to dividends on shares of any
other class or classes or any other series of stock of the Corporation; whether
such dividends shall be cumulative or noncumulative, and if cumulative, the date
or dates from which dividends on shares of such series shall be cumulative; the
voting rights, if any, to be provided for shares of such series; the rights, if
any, which the holders of shares of such series shall have in the event of any
voluntary or involuntary liquidation, dissolution or winding up of the affairs
of the Corporation; the rights, if any, which the holders of shares of such
series shall have to convert such shares into or exchange such shares for shares
of stock of the Corporation, and the terms and conditions, including price and
rate of exchange of such conversion or exchange; the redemption rights
(including sinking fund provisions), if any, for shares of such series; and such
other powers, rights, designations, preferences, qualifications, limitations and
restrictions as the Board of Directors may desire to so fix. The Board of
Directors is also expressly authorized to fix the number of shares constituting
such series and to increase or decrease the number of shares of any series prior
to the issuance of shares of that series and to increase or decrease the number
of shares of any series subsequent to the issuance of shares of that series, but
not to decrease such number below the number of shares of such series then
outstanding. In case the number of shares


                                       2.

<PAGE>   3

of any series shall be so decreased, the shares constituting such decrease shall
resume the status which they had prior to the adoption of the resolution
originally fixing the number of shares of such series.

     FIFTH. In furtherance and not in limitation of the powers conferred by
statute, the Board of Directors is authorized to make, alter or repeal any or
all of the Bylaws of the Corporation; provided, however, that any Bylaw
amendment adopted by the Board of Directors increasing or reducing the
authorized number of Directors shall require the affirmative vote of a majority
of the total number of Directors which the Corporation would have if there were
no vacancies. In addition, new Bylaws may be adopted or the Bylaws may be
amended or repealed by the affirmative vote of at least 66-2/3% of the combined
voting power of all shares of the Corporation entitled to vote generally in the
election of directors, voting together as a single class. Notwithstanding
anything contained in this Certificate of Incorporation to the contrary, the
affirmative vote of the holders of at least 66-2/3% of the combined voting power
of all shares of the Corporation entitled to vote generally in the election of
directors, voting together as a single class, shall be required to alter,
change, amend, repeal or adopt any provision inconsistent with, this Article
FIFTH.

     SIXTH.    (a)  Any action required or permitted to be taken by the
stockholders of the Corporation must be effected at an annual or special meeting
of stockholders of the Corporation and may not be effected by any consent in
writing of such stockholders.

               (b)  Special meetings of stockholders of the Corporation may be
called only (i) by the Chairman of the Board of Directors, or (ii) by the
Chairman or the Secretary at the written request of a majority of the total
number of Directors which the Corporation would have if there were no vacancies
upon not fewer than 10 nor more than 60 days' written notice. Any request for a
special meeting of stockholders shall be sent to the Chairman and the Secretary
and shall state the purposes of the proposed meeting. Special meetings of
holders of the outstanding Preferred Stock may be called in the manner and for
the purposes provided in the resolutions of the Board of Directors providing for
the issue of such stock. Business transacted at special meetings shall be
confined to the purpose or purposes stated in the notice of meeting.

               (c)  Notwithstanding anything contained in this Certificate of
Incorporation to the contrary, the affirmative vote of the holders of at least
66-2/3% of the combined voting power of all shares of the Corporation entitled
to vote generally in the election of directors, voting together as a single
class, shall be required to alter, change, amend, repeal or adopt any provision
inconsistent with, this Article SIXTH.

     SEVENTH.  (a)  The number of Directors which shall constitute the whole
Board of Directors of this corporation shall be as specified in the Bylaws of
this corporation, subject to this Article SEVENTH.

               (b)  The Directors shall be classified with respect to the time
for which they severally hold office into three classes designated Class I,
Class II and Class III, as nearly


                                       3.

<PAGE>   4

equal in number as possible, as shall be provided in the manner specified in the
Bylaws of the Corporation. Each Director shall serve for a term ending on the
date of the third annual meeting of stockholders following the annual meeting at
which the Director was elected; provided, however, that each initial Director in
Class I shall hold office until the annual meeting of stockholders in 1997, each
initial Director in Class II shall hold office until the annual meeting of
stockholders in 1998 and each initial Director in Class III shall hold office
until the annual meeting of stockholders in 1999. Notwithstanding the foregoing
provisions of this Article SEVENTH, each Director shall serve until his
successor is duly elected and qualified or until such Director's death,
resignation or removal.

               (c)  In the event of any increase or decrease in the authorized
number of Directors, (i) each Director then serving as such shall nevertheless
continue as a Director of the class of which such Director is a member until the
expiration of his current term, or his early resignation, removal from office or
death and (ii) the newly created or eliminated directorship resulting from such
increase or decrease shall be apportioned by the Board of Directors among the
three classes of Directors so as to maintain such classes as nearly equally as
possible.

               (d)  Any Director or the entire Board of Directors may be removed
by the affirmative vote of the holders of at least 66-2/3% of the combined
voting power of all shares of the Corporation entitled to vote generally in the
election of directors, voting together as a single class.

               (e)  Notwithstanding anything contained in this Certificate of
Incorporation to the contrary, the affirmative vote of the holders of at least
66-2/3% of the combined voting power of all shares of the Corporation entitled
to vote generally in the election of directors, voting together as a single
class, shall be required to alter, change, amend, repeal or adopt any provision
inconsistent with, this Article SEVENTH.

     EIGHTH.   (a)  1.   In addition to any affirmative vote required by law,
any Business Combination (as hereinafter defined) shall require the affirmative
vote of at least 66-2/3% of the combined voting power of all shares of the
Corporation entitled to vote generally in the election of directors, voting
together as a single class (for purposes of this Article EIGHTH, the "Voting
Shares"). Such affirmative vote shall be required notwithstanding the fact that
no vote may be required, or that some lesser percentage may be specified by law
or in any agreement with any national securities exchange or otherwise.

                    2.   The term "Business Combination" as used in this Article
EIGHTH shall mean any transaction which is referred to in any one or more of the
following clauses (A) through (E):

                         (A)  any merger or consolidation of the Corporation or
any Subsidiary (as hereinafter defined) with or into (i) any Interested
Stockholder (as hereinafter defined) or (ii) any other corporation (whether or
not itself an Interested Stockholder) which is, or after such merger or
consolidation would be, an Affiliate (as hereinafter defined) or Associate (as


                                       4.

<PAGE>   5

hereinafter defined) of an Interested Stockholder; or

                         (B)  any sale, lease, exchange, mortgage, pledge,
transfer or other disposition (in one transaction or a series of related
transactions) to or with, or proposed by or on behalf of, any Interested
Stockholder or any Affiliate or Associate of any Interested Stockholder, of any
assets of the Corporation or any Subsidiary constituting not less than five
percent of the total assets of the Corporation, as reported in the consolidated
balance sheet of the Corporation as of the end of the most recent quarter with
respect to which such balance sheet has been prepared; or

                         (C)  the issuance or transfer by the Corporation or any
Subsidiary (in one transaction or a series of related transactions) of any
securities of the Corporation or any Subsidiary to, or proposed by or on behalf
of, any Interested Stockholder or any Affiliate or Associate of any Interested
Stockholder in exchange for cash, securities or other property (or a combination
thereof) constituting not less than five percent of the total assets of the
Corporation, as reported in the consolidated balance sheet of the Corporation as
of the end of the most recent quarter with respect to which such balance sheet
has been prepared; or

                         (D)  the adoption of any plan or proposal for the
liquidation or dissolution of the Corporation, or any spin-off or split-up of
any kind of the Corporation or any Subsidiary, proposed by or on behalf of an
Interested Stockholder or any Affiliate or Associate of any Interested
Stockholder; or

                         (E)  any reclassification of securities (including any
reverse stock split), or recapitalization of the Corporation, or any merger or
consolidation of the Corporation with any of its Subsidiaries or any similar
transaction (whether or not with or into or otherwise involving an Interested
Stockholder) which has the effect, directly or indirectly, of increasing the
percentage of the outstanding shares of (i) any class of equity securities of
the Corporation or any Subsidiary or (ii) any class of securities of the
Corporation or any Subsidiary convertible into equity securities of the
Corporation or any Subsidiary, represented by securities of such class which are
directly or indirectly owned by any Interested Stockholder or any Affiliate or
Associate of any Interested Stockholder.

               (b)  The provisions of section (a) of this Article EIGHTH shall
not be applicable to any particular Business Combination, and such Business
Combination shall require only such affirmative vote as is required by law and
any other provision of this Certificate of Incorporation, if such Business
Combination has been approved by two-thirds of the whole Board of Directors.

               (c)  For the purposes of this Article EIGHTH:

                    1.   A "person" shall mean any individual, firm, corporation
or other entity.


                                       5.

<PAGE>   6

                    2.   "Interested Stockholder" shall mean, in respect of any
Business Combination, any person (other than the Corporation or any Subsidiary)
who or which, as of the record date for the determination of stockholders
entitled to notice of and to vote on such Business Combination, or immediately
prior to the consummation of any such transaction

                         (A)  is or was, at any time within two years prior
thereto, the beneficial owner, directly or indirectly, of 15% or more of the
then outstanding Voting Shares, or

                         (B)  is an Affiliate or Associate of the Corporation
and at any time within two years prior thereto was the beneficial owner,
directly or indirectly, of 15% or more of the then outstanding Voting Shares, or

                         (C)  is an assignee of or has otherwise succeeded to
any shares of capital stock of the Corporation which were at any time within two
years prior thereto beneficially owned by any Interested Stockholder, if such
assignment or succession shall have occurred in the course of a transaction, or
series of transactions, not involving a public offering within the meaning of
the Securities Act of 1933, as amended.

                    3.   A "person" shall be the "beneficial owner" of any
Voting Shares

                         (A)  which such person or any of its Affiliates and
Associates (as hereinafter defined) beneficially own, directly or indirectly, or

                         (B)  which such person or any of its Affiliates or
Associates has (i) the right to acquire (whether such right is exercisable
immediately or only after the passage of time), pursuant to any agreement,
arrangement or understanding or upon the exercise of conversion rights, exchange
rights, warrants or options, or otherwise, or (ii) the right to vote pursuant to
any agreement, arrangement or understanding, or

                         (C)  which are beneficially owned, directly or
indirectly, by any other person with which such first mentioned person or any of
its Affiliates or Associates has any agreement, arrangement or understanding for
the purposes of acquiring, holding, voting or disposing of any shares of capital
stock of the Corporation.

                    4.   The outstanding Voting Shares shall include shares
deemed owned through application of paragraph 3 above but shall not include any
other Voting Shares which may be issuable pursuant to any agreement, or upon
exercise of conversion rights, warrants or options, or otherwise.

                    5.   "Affiliate" and "Associate" shall have the respective
meanings given those terms in Rule 12b-2 of the General Rules and Regulations
under the Securities Exchange Act of 1934, as in effect on the date of adoption
of this Certificate


                                       6.

<PAGE>   7

of Incorporation (the "Exchange Act").

                    6.   "Subsidiary" shall mean any corporation of which a
majority of any class of equity security (as defined in Rule 3a11-1 of the
General Rules and Regulations under the Exchange Act) is owned, directly or
indirectly, by the Corporation; provided, however, that for the purposes of the
definition of Interested Stockholder set forth in paragraph 2 of this section
(c) the term "Subsidiary" shall mean only a corporation of which a majority of
each class of equity security is owned, directly or indirectly, by the
Corporation.

               (d)  A majority of the directors shall have the power and duty to
determine for the purposes of this Article EIGHTH on the basis of information
known to them, (1) whether a person is an Interested Stockholder, (2) the number
of Voting Shares beneficially owned by any person, (3) whether a person is an
Affiliate or Associate of another, (4) whether a person has an agreement,
arrangement or understanding with another as to the matters referred to in
paragraph 3 of section (c) or (5) whether the assets subject to any Business
Combination or the consideration received for the issuance or transfer of
securities by the Corporation or any Subsidiary constitutes not less than five
percent of the total assets of the Corporation.

               (e)  Nothing contained in this Article EIGHTH shall be construed
to relieve any Interested Stockholder from any fiduciary obligation imposed by
law.

               (f)  Notwithstanding anything contained in this Certificate of
Incorporation to the contrary, the affirmative vote of the holders of at least
66-2/3% of the combined voting power of all shares of the Corporation entitled
to vote generally in the election of directors, voting together as a single
class, shall be required to alter, change, amend, repeal or adopt any provision
inconsistent with, this Article EIGHTH.

     NINTH. This Corporation reserves the right to amend, alter, change or
repeal any provision contained in this Certificate of Incorporation, in the
manner now or hereafter prescribed by statute, and all rights conferred on
stockholders herein are granted subject to this reservation.

     TENTH. A Director of the Corporation shall not be personally liable to the
Corporation or its stockholders for monetary damages for breach of fiduciary
duty as a Director, except for liability (i) for any breach of the Director's
duty of loyalty to the Corporation or its stockholders, (ii) for acts or
omissions not in good faith or which involve intentional misconduct or a knowing
violation of law, (iii) under Section 174 of the General Corporation Law of
Delaware or (iv) for any transaction from which the Director derived any
improper personal benefit. If the General Corporation Law of Delaware is
hereafter amended to authorize, with the approval of a corporation's
stockholders, further reductions in the liability of a corporation's directors
for breach of fiduciary duty, then a Director of the Corporation shall not be
liable for any such breach to the fullest extent permitted by the General
Corporation Law of Delaware as so amended. Any repeal or modification of the
foregoing provisions of this Article NINTH by the stockholders of the
Corporation shall not adversely affect any right or protection of a Director of
the Corporation existing at the time of such repeal or modification. This
corporation is authorized to indemnify the directors and officers of the
corporation to the fullest extent permissible under Delaware law.


                                       7.
